I only just ran across this node, thanks everyone!
For pure speed then you can inline the gammln code, unroll the loop into one big equation, and move the constants into the equation instead of referencing them indirectly in the array. I also got rid of $y for a very small speedup. This code runs about 135% faster than logfact above (i.e. over twice as fast). I renamed the function factln to be consistent with gammaln.
BTW this code appears to originate in Numerical Recipes but no credit was given in Re^4: Challenge: Chasing Knuth's Conjecture, referenced in the parent. All of the function names in that book are 6 characters long, because there's a Fortran (F77) version of the book too. Thus "gammln" instead of "gammaln".
my $x = (shift) + 1;
my $tmp = $x + 5.5;
$tmp -= ($x + .5) * log($tmp);
my $ser = 1.000000000190015
+ 76.18009172947146 / ++$x
- 86.50532032941677 / ++$x
+ 24.01409824083091 / ++$x
- 1.231739572450155 / ++$x
+ 0.12086509738661e-2 / ++$x
- 0.5395239384953e-5 / ++$x;
return log(2.5066282746310005*$ser/($x-6)) - $tmp;
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