Re^2: Fastest way to calculate hypergeometric distribution probabilities (i.e. BIG factorials)?

Also, the Math::Gsl::Sf has a gamma function, which may speed up calculations (I'm not sure if it would or not, I haven't actually studied the inner workings of the gamma function). The gamma function of any whole number is equal to that number's factorial, ie gamma(300) == 300!, which is why I think this function may be faster than a factorial, since there probably aren't 300 multiplications, I bet it's just some sort of integral, which may have quite a few calculations, but not 300 large multiplications.

-Bryan

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Re^3: Fastest way to calculate hypergeometric distribution probabilities (i.e. BIG factorials)? by Zaxo (Archbishop) on Jun 14, 2005 at 04:51 UTC
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) $ [download] The GSL doesn't handle large numbers. There's also a math error to correct: `gamma($n) == factorial($n - 1)` After Compline, Zaxo	[reply] [d/l] [select]
Re^4: Fastest way to calculate hypergeometric distribution probabilities (i.e. BIG factorials)? by salva (Canon) on Jun 14, 2005 at 08:15 UTC
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))` [download] 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.	[reply] [d/l]
Re^4: Fastest way to calculate hypergeometric distribution probabilities (i.e. BIG factorials)? by mrborisguy (Hermit) on Jun 14, 2005 at 13:05 UTC
Really... all along I thought gamma was equal to the factorial. That's new to me, thanks! -Bryan	[reply]