This is a perlified conflation of a nice algorithm stolen from the web.

#!/usr/bin/perl
use strict;
use Math::BigFloat qw(:constant);

$|++;

my $epochs = 100;
my $begin  = time;

print 'PI:', &calc_pi( $epochs ), "\n"
    , '(',   time - $begin,       " sec)\n";

sub calc_pi 
{
    my $iter = shift;
    return 16 * &ataninvint(  5,$iter) 
          - 4 * &ataninvint(239,$iter);
}

sub ataninvint 
{
    my ($x, $iter) = @_;

    my $res  = Math::BigFloat->new(1) / $x;
    my $term = Math::BigFloat->new($res);
    my $x2   = $x * $x;
    my $div  = 1;

   $res += -Math::BigFloat->new($term /= $x2)/($div += 2)
           +Math::BigFloat->new($term /= $x2)/($div += 2)
        for 1..$iter;
       
    return $res;
}
[download]

UPDATE: here are lots of ways to calculate pi