[racket] Math library kudos

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 ⊥