Here's a more 'reference' style implementation. Basically, this is the algorithm you'll find in the paper 'Square Roots, From 1; 24, 51, 10 To Dan Shanks' by Ezra Brown, but at the cost of using Math::BigInt. 
#!/usr/bin/perl -w

use Math::BigInt ':constant';
use strict;

sub tonelli {
   my ($s, $e, $n, $x, $b, $g, $r, $m, $t);
   my ($a, $p) = @_;

   die "$a has no square roots (mod $p)" if $a**(($p-1)/2) % $p == -1;

   $s = $p-1;
   $e = 0;
   while ($s % 2 == 0) {
      $s = $s / 2;
      $e++;
   }

   for ($n = 2; $n >= 2; $n++) {
      last if $n**(($p-1)/2) % $p == $p-1;
   }

   $x = $a**(($s+1)/2) % $p;
   $b = $a**$s % $p;
   $g = $n**$s % $p;
   $r = $e;

   $t = $b;
   while (1) {
      for ($m = 0; $m <= $r-1; $m++) {
         last if $t % $p == 1;
         $t = $t**2;
      }

      return $x if $m == 0;

      $x = $x * $g**(2*($r-$m-1)) % $p;
      $b = $b * $g**(2*($r-$m-1)) % $p;
      $g = $g**(2*($r-$m)) % $p;
      $r = $m;
   }
}

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In reply to Re: Re: Re: Re: Factors by gumby
in thread Vampire Numbers by YuckFoo

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