On 02/20/2013 06:42 AM, Luke Vilnis wrote:
No problem. They should be faster even for fairly small numbers since
they usually require the evaluation of a polynomial (an approximation of
(log)gamma) versus repeated multiplication/division. From memory the
code should be something like:
(exp (fllog-gamma (+ 1.0 n)) - (fllog-gamma (+ 1.0 r)) - (fllog-gamma (+
1.0 (- n r))))
fllog-gamma should also be faster than bflog-gamma or log-gamma if you
don't need arbitrary precision. You're also right that this won't always
give completely exact results - the Racket manual says that the only
exact values are for log gamma of 1 and 2, but this usually is not a
problem.
PS. It looks like Racket's math collection has a built-in log-factorial
function too, to avoid all the +1's, so you could try that.
There's also `fllog-binomial', which computes the log number of
combinations directly. IIRC, its maximum observed error is 2 ulps.
Neil ⊥
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