This subroutine calculates the multiplicative inverse of a number modulo another one. This is similar to the modinv method in Math::BigInt, but that one seems to be only for big numbers. This one works with friendly small numbers too.

Calling is $b = divmod($a, $m) where $a, $m are two relatively prime integers. Then, $b in an integer so that ($a * $b) % $m == 1.

For example, divmod(17, 26) returns 23, as (17 * 23) % 26 == 1.

Update: modified the subroutine so that it works correctly for negative arguments as well. The error was that I assumed int would calculate the floor for negative numbers too. 

use warnings; 
use strict; 
sub divmod { 
        my $m = abs($_[1]); my $a = $_[0] % $m; my($b, $x, $y, $n) = (
+$m, 1, 0);
        while (0 != $a) { $n = int($b / $a); ($a, $b, $x, $y) = ($b - 
+$n * $a, $a, $y - $n * $x, $x); } 
        $y % $m; 
}

[download]
Here's the previous, wrong version of the code: <S> 
# WRONG, DO NOT USE
use warnings; 
use strict; 
sub divmod { 
        my($a, $m) = @_; my($b, $x, $y, $n) = ($m, 1, 0);
        while (0 != $a) { $n = int($b / $a); ($a, $b, $x, $y) = ($b - 
+$n * $a, $a, $y - $n * $x, $x); } 
        $y % $m; 
}

[download]
</s>

In reply to modular inverse by ambrus

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