[Help-gsl] gsl_sf_beta efficiency question

[Helfer Thomas]

Hi,

I need to use the beta function with the GSL version 1.6. I have tried
to compute it either using gsl_sf_beta or by using the relation
Beta(w,z) = Gamma(w)*Gamma(z)/Gamma(w,z) and calling (gsl_sf_gamma).

I measured the CPU time to compute each solution using the rdtsc
assembly function (my processor is an Intel P4).

The results where quite surprising: using the Gamma function
(gsl_sf_gamma) to compute the Beta function seems to be 2x more
efficient than using directly the Beta function (gsl_sf_beta).

To compare the CPU times, I have made a small loop (10 times) that calls
each solution. Here are the results: 

CPU frequency : 3.19213e+09

Beta CPU    Gamma CPU

Loop 1

150736 11936

Loop 2

8632 4896

Loop 3

8280 4760

Loop 4

8280 4752

Loop 5

8288 4752

Loop 6

8536 4760

Loop 7

8296 4760

Loop 8

8280 4760

Loop 9

8280 4760

Loop 10

8280 4760

I’m also surprise to notice that the first iteration costs much more CPU
time than the following iterations.

I’ve attached my C++ test to my mail.

Regards,

Helfer Thomas

gsl_test_beta.cxx
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