Re^3: Fastest way to calculate hypergeometric distribution probabilities (i.e. BIG factorials)?

[Zaxo]

Good idea, but no cigar.

$ perl -MMath::Gsl::Sf=:Gamma -e'print gamma(300)'
gsl: gamma.c:1111: ERROR: overflow
Default GSL error handler invoked.
Aborted (core dumped)
$

The GSL doesn't handle large numbers.

There's also a math error to correct: gamma($n) == factorial($n - 1)

[salva]

if your calculations over the factorial numbers are only multiplications and divisions (as I think they are), you can operate over their log values instead, transforming multiplications and divisions to additions and substractions respectively. i.e.:

log ($n! / ($r! * ($n-$r)!)
  = Sum(log(1)..log($n))
    - Sum(log(1)..log($r))
      - Sum(log(1)..log($n-$r))

and as your operations will only involve a small number of integers, you can cache log($n) and log($n!) to speed up the calculations.

[mrborisguy]

Really... all along I thought gamma was equal to the factorial. That's new to me, thanks!

    -Bryan