... is there a reason you aren't using the Chi-square test?

I'm not trying to solve the sample problem. That was just an example I found on the web and used as a test.

I set out to solve the problem of performing the FET using Perl. First I did it with Math::Pari, but which gives a result of 8.070604647867604097576877668E-7030 in 26ms, but I was unsure about the accuracy. It also imposes a binary dependancy.

#! perl -slw
use strict;
use Benchmark::Timer;
use List::Util qw[ sum reduce ];
use Math::Pari qw[ factorial ];

$a=$b;

sub product{ reduce{ $a *= $b } 1, @_ }

sub FishersExactTest {
    my @data = @_;
    return unless @data == 4;
    my @C = ( sum( @data[ 0, 2 ] ), sum( @data[ 1, 3 ] ) );
    my @R = ( sum( @data[ 0, 1 ] ), sum( @data[ 2, 3 ] ) );
    my $N =  sum @C;
    my $dividend = product map{ factorial $_ } grep $_, @R, @C;
    my $divisor  = product map{ factorial $_ } grep $_, $N, @data;
    return $dividend / $divisor;
}

my $T = new Benchmark::Timer;

$T->start( '' );
print FishersExactTest 989, 9400, 43300, 2400;;
$T->stop( '' );

$T->report;

__END__
P:\test>MP-FET.pl
8.070604647867604097576877668E-7030
  1 trial  of _default ( 25.852ms total), 25.852ms/trial
[download]

So, then I coded it using Math::BigFloat

#! perl -slw
use strict;
use Benchmark::Timer;
use List::Util qw[ reduce ];
use Math::BigFloat;

$a=$b;

sub product{ reduce{ $a *= $b } 1, @_ }
sub sum{ reduce{ $a += $b } 0, @_ }

sub FishersExactTest {
    my @data = map{ Math::BigFloat->new( $_ ) } @_;
    return unless @data == 4;
    my @C = ( sum( @data[ 0, 2 ] ), sum( @data[ 1, 3 ] ) );
    my @R = ( sum( @data[ 0, 1 ] ), sum( @data[ 2, 3 ] ) );
    my $N =  sum @C;
    my $dividend = product map{ $_->bfac } grep $_, @R, @C;
    my $divisor  = product map{ $_->bfac } grep $_, $N, @data;
    return $dividend / $divisor;
}

my $T = new Benchmark::Timer;

$T->start( '' );
print FishersExactTest 989, 9400, 43300, 2400;;
$T->stop( '' );

$T->report;
[download]

But that ran for 20 minutes without producing any output before I killed it (I've set it running again now, and my machines fan has been thrashing at full speed for the last 25 minutes).

Whilst I was waiting for the BigFloat version, I coded this version which attempts to reduce the size of the problem by eliminating (exactly common) factors:

sub FishersExactTest2 {
    my @data = @_;
    return unless @data == 4;
    my @C = ( sum( @data[ 0, 2 ] ), sum( @data[ 1, 3 ] ) );
    my @R = ( sum( @data[ 0, 1 ] ), sum( @data[ 2, 3 ] ) );
    my $N =  sum @C;
    my %dividends; $dividends{ $_ }++ for map{ factors $_ } grep $_, @
+R, @C;
    my %divisors;  $divisors { $_ }++ for map{ factors $_ } grep $_, $
+N, @data;
    for my $i ( keys %divisors ) {
        if( exists $dividends{ $i } ) {
            $divisors{ $i }--, $dividends{ $i }-- 
                while $divisors{ $i } and $dividends{ $i };
            delete $divisors { $i } unless $divisors { $i };
            delete $dividends{ $i } unless $dividends{ $i };
        }
    }
    my $dividend = product( map{ ( $_ ) x $dividends{ $_ } } keys %div
+idends );
    my $divisor  = product( map{ ( $_ ) x $divisors { $_ } } keys %div
+isors  );
    return $dividend / $divisor;
}
[download]

This works well for values smallish values, but cannot handle the example I gave above (NV overflow).

It was then I started thinking about how to eliminate more factors from the equation so as to reduce the size of the intermediate terms, and posted my SoPW. I think that hv's solution of expanding all terms to their prime factorizations before performing the cancelling out will be a winner--but I haven't finished coding that yet.