This should easily do large sums of many random variables. The technique to do large convolutions is called http://en.wikipedia.org/wiki/Exponentiation_by_squaring.

BTW P-value has a different meaning. You really just want to call it probability.

Enjoy!

#!/usr/bin/perl -w
use strict;

#Set no. of elements, frequencies and the sum value
my @freq = qw (0.1 0.2 0.7);

my $nElements = 2;
my $targetSum = 4;

#
# If you are only interested in the first few $targetSums
# and @freq is a large array, you can speed up the computation
# and reduce space requirements by setting $maxSum to the
# largest conceivable $targetSum
#
my $maxSum=400;


sub conv
{   my ($p, $q) = @_;
    my ($np, $nq) = (scalar @$p, scalar @$q);
    my @ans = ();
    push @ans, 0 for (1..$np+$nq);
    my $ip = 0;
    for my $vp (@$p)
    {    my $iq = 0;
        for my $vq (@$q)
        {   $ans[$ip+$iq] += $vp*$vq;
            $iq++;
            last if $ip+$iq > $maxSum;
        }
        $ip++;
    }
    return \@ans;
}

# see http://en.wikipedia.org/wiki/Exponentiation_by_squaring
sub convn
{   my ($n, $p) = @_;
    my $ans = [1];
    while ($n)
    {    $ans = conv($ans, $p) if $n & 1;    # if n is odd
        $p = conv($p, $p);
        use integer;
        $n = $n >> 1;
    }
    return $ans;
}

my $ans = convn($nElements, \@freq);

print "Prob(sum of $nElements = $targetSum) = $ans->[$targetSum]\n";

#Prints: Prob(sum of 2 = 4) = 0.49

print convn(200, [0.1, 0.2, 0.3, 0.2, 0.1, 0.1])->[400];
#Prints: 0.000210606620621573
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