Hi monks
I am writing a web based bioinformatic program that uses the hypergeometric distribution. I use the code from this perl node 
#!/usr/bin/perl -w
use strict;

sub logfact {
   return gammln(shift(@_) + 1.0);
}

sub hypergeom {
   # There are m "bad" and n "good" balls in an urn.
   # Pick N of them. The probability of i or more successful selection
+s:
   # (m!n!N!(m+n-N)!)/(i!(n-i)!(m+i-N)!(N-i)!(m+n)!)
   my ($n, $m, $N, $i) = @_;

   my $loghyp1 = logfact($m)+logfact($n)+logfact($N)+logfact($m+$n-$N)
+;
   my $loghyp2 = logfact($i)+logfact($n-$i)+logfact($m+$i-$N)+logfact(
+$N-$i)+logfact($m+$n);
   return exp($loghyp1 - $loghyp2);
}

sub gammln {
  my $xx = shift;
  my @cof = (76.18009172947146, -86.50532032941677,
             24.01409824083091, -1.231739572450155,
             0.12086509738661e-2, -0.5395239384953e-5);
  my $y = my $x = $xx;
  my $tmp = $x + 5.5;
  $tmp -= ($x + .5) * log($tmp);
  my $ser = 1.000000000190015;
  for my $j (0..5) {
     $ser += $cof[$j]/++$y;
  }
  -$tmp + log(2.5066282746310005*$ser/$x);
}

print hypergeom(300,700,100,40),"\n";

[download]
For small numbers it works fine. However, for large input it is too slow. For example, I have an input set that needs to call the hypergeom function 137544 times, and it takes about 70 seconds. As this is a web based tool, it is of course too slow.
My question is what other options do I have? I assumed the gammln is very fast but for large numbers it chokes.

Another option is Inline::C which is supposed to be fast but I don't know if calling a C function so often is the best option.
Math::GSL::CDF is also an option, but I'm not sure it is fast enough. Both modules need to be installed, and since I don't have permissions on the University server I would like some advice before asking for installation.

Any other ideas and suggestions would be welcome. This is a part of Perl I'm not very familiar with and would be happy to get input.
Also, I know the thread I mentioned earlier was pretty thorough, but it was also 5 years ago and I think it is worth asking this question again.
Thanks in advance
Guy Naamati

Q:What do Alexander the Great and Kermit the Frog have in common?

A: Their middle name
Update: Solution by BrowserUk brought the time down to 5 seconds. However, the output is different, and I am now trying to figure out why.
Thanks for your help,
Guy
Problem solved. Thanks again!

In reply to Fast hypergeometric calculation in Perl by mrguy123

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