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#!/usr/bin/perl
use strict;
use warnings;
{
package polynomial;
package main;
use Math::GMPz qw/:mpz/;
use Data::Dumper;
if (scalar(@ARGV) != 1) {
print "Usage: aks.pl <number to test>\n";
exit
}
my $n;
print "Math::GMPz version: $Math::GMPz::VERSION\n";
eval {
$n = Math::GMPz->new($ARGV[0]);
1;
} or do {
print "Error converting ", $ARGV[0], "to a number\n";
exit;
};
print "Running AKS with number $n\n";
if(Rmpz_perfect_power_p($n)) {
print "$n is a perfect power.\n";
exit;
}
my $r = Math::GMPz->new(2);
my $logn = Rmpz_sizeinbase($n, 2);
my $limit = Math::GMPz->new($logn * $logn);
Rmpz_mul_ui($limit, $limit, 4);
# Witness search
OUTERLOOP: while (Rmpz_cmp($r, $n) == -1) {
if(Rmpz_divisible_p($n, $r)) {
print "$n is divisible by $r\n";
exit;
}
if(Rmpz_probab_prime_p($n, 5)) {
my $i = Math::GMPz->new(1);
INNERLOOP: for ( ; Rmpz_cmp($n, $limit) <= 0; Rmpz_add_ui($i, $i, 1)) {
my $res = Math::GMPz->new(0);
Rmpz_powm($res, $n, $i, $r);
if (Rmpz_cmp_ui($res, 1) == 0) {
last OUTERLOOP;
}
}
}
Rmpz_add_ui($r, $r, 1);
}
if (Rmpz_cmp($r, $n) == 0) {
print "Found $n is prime while checking for r\n";
exit;
}
# Polynomial check
my $a;
my $sqrtr = Math::GMPz->new(0);
Rmpz_sqrt($sqrtr, $r);
my $polylimit = Math::GMPz->new(0);
Rmpz_add_ui($polylimit, $sqrtr, 1);
Rmpz_mul_ui($polylimit, $polylimit, $logn);
Rmpz_mul_ui($polylimit, $polylimit, 2);
my $intr = Rmpz_get_ui($r);
for($a = 1; Rmpz_cmp_ui($polylimit, $a) <= 0; $a++) {
print "Checking at $a\n";
my $final_size = Math::GMPz->new(0);
Rmpz_mod($final_size, $n, $r);
my $compare = polynomial->new(Rmpz_get_ui($final_size));
$compare->setCoef(1, Rmpz_get_ui($final_size));
$compare->setCoef($a, 0);
my $res = polynomial->new($intr);
my $base = polynomial->new(1);
$base->setCoef($a, 0);
$base->setCoef(1, 1);
mpz_poly_mod_power($res, $base, $n, $n, $intr);
if($res->isEqual($compare)) {
print "Found not prime at $a\n";
exit;
}
}
print "Is prime\n";
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