mrguy123:

Have you tried to use Memoize to cache the results of logfact? If it's repeatedly being called with the same values, you might get a speed boost. You could try to Memoize hypergeom as well--but if there are too many combinations of arguments (i.e., the argument list rarely repeats) it would be a loss.

...roboticus

Update: Just for my own amusement, I added Memoize to the program and found no significant improvements. Apparently the functions are fast enough that there's no big win to be found simply by caching the values. I replaced the single call at the end of the program with a nested loop (to generate enough runtime to be significant). This should call hypergeom 203,401 times:

for my $i (280 .. 320) {
    for my $j (680 .. 720) {
        for my $k (95 .. 105) {
            for my $l (30 .. 40) {
                my $hg = hypergeom($i, $j, $k, $l);
            }
        }
    }
}
[download]

The results are:

39.11s   Without Memoize
35.25s   Memoize logfact only
38.40s   Memoize gammaln only
47.04s   Memoize hypergeom only
[download]

Of course, with the usage pattern given, I may have artificially improved/reduced Memoize's results, so your mileage will vary.