gsl/randist vs ranlib

[James Theiler <jt at lanl dot gov>]

Hello,

  It has been pointed out to me by my colleague John Pearson that
several of gsl's randist routines are quite slow.  This became
particularly evident in comparing gsl's binomial generator
(gsl_ran_binomial) to the equivalent routine in "ranlib" -- this is a
very old (though very nice) package that is avaliable through CMU's
StatLib.  It is free software, but not GPL; I won't speculate on the
legalities (or moralities!) that might be entailed, but it says it is
"in the public domain" so we should at least be able to use it for
inspiration. See http://lib.stat.cmu.edu/general/Utexas/ranlib.readme
and don't be put off that it says "Fortran routines"; if you read a
little further you see that they have been translated into C
... still, they are very fortran-esque with goto's and such.

(see also http://www.netlib.org/random/, look for ranlib.c.tar.gz)

  We are talking about a factor of 25x slower for n=1000, p=0.33.
It's not clear to me how much of this is due to the choice of the
algorithm for binomial generator -- it scales like O(log n) but O(1)
algorithms exist[*] -- or some other factors, such as its dependence
on the gamma distribution (via the beta distribution) which also seems
much slower for gsl than it does for ranlib, or the different uniform
random generator that is at the base of both algorithms.  (Aside: the
factor drops to a "mere" 15x if p is changed from run to run; this is
because the ranlib version has extra efficiency which exploits the
situation when multiple calls are made with the same argument.)

  This is something we are going to look into a little closer, but in
the meantime, we are soliciting opinions on this topic: maybe others
have already noticed similar behavior, and have some wisdom to impart.
Also, it is to suggest a new item in gsl's TODO list, which is a more
comprehensive examination of the performance of gsl's randist
algorithms, with an eye to the ranlib implementations either as a
benchmark, or as some code to possibly assimilate.

regards,
jt

[*] One of the references in the ranlib documentation, by the way,
makes a good read: Kachitvichyanukul, V. and Schmeiser, B.  W.
Binomial Random Variate Generation.  Communications of the ACM, 31, 2
(February, 1988) 216.

---------------------------------------------
James Theiler                     jt at lanl dot gov
MS-B244, NIS-2, LANL        tel: 505/665-5682
Los Alamos, NM 87545        fax: 505/665-4414
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