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#!/usr/bin/env perl
use warnings;
use strict;
use List::Util qw/min max/;
# From Damgård, Landrock, and Pomerance, 1993. Page 178.
# k = bits in n
my $k = shift;
if (!defined $k || $k < 2) {
die "Usage: $0 <k> [<maxtests>]\n k = the number of bits in n\n";
}
my $maxtests = shift || 30;
foreach my $t (1 .. $maxtests) {
printf("k: %d t:%4d p < %lg\n", $k, $t, min(mr_prob($k, $t)));
#my @p = mr_prob($k, $t); print "k: $k t: $t p: @p\n";
}
sub mr_prob {
my($k, $t) = @_;
die "k must be >= 2" unless $k >= 2;
die "t must be >= 1" unless $t >= 1;
my @probs;
push @probs, 4**-$t;
if ($t == 1) {
push @probs, $k*$k * 4**(2.0-sqrt($k));
}
if (($t == 2 && $k >= 88) || ($t >= 3 && $k >= 21 && $t <= $k/9)) {
push @probs, $k**1.5 * 2**$t * $t**-.5 * 4**(2.0-sqrt($t*$k));
}
if ($t >= $k/9 && $k >= 21) {
push @probs, ( (7.0/20.0) * $k * 2**(-5*$t)
+ (1.0/7.0) * $k**(15.0/4.0) * 2**(-$k/2 - 2*$t)
+ 12 * $k * 2**(-$k/4 - 3*$t) );
}
if ($t >= $k/4 && $k >= 21) {
push @probs, (1.0/7.0) * $k**(15.0/4.0) * 2**(-$k/2 - 2*$t);
}
return @probs;
}
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