[Numpy-discussion] Using logfactorial instead of loggamma in random_poisson sampler

[Warren Weckesser]

On 3/6/21, zoj613 <blkzol001 at myuct.ac.za> wrote:
> Hi All,
>
> I noticed that the transformed rejection method for generating Poisson
> random variables used in numpy makes use of the `random_loggam` function
> which directly calculates the log-gamma function. It appears that a
> log-factorial lookup table was added a few years back which could be used
> in
> place of random_loggam since the input is always an integer. Is there a
> reason for not using this table instead? See link below for the line of
> code:
>
> https://github.com/numpy/numpy/blob/6222e283fa0b8fb9ba562dabf6ca9ea7ed65be39/numpy/random/src/distributions/distributions.c#L572
>
> Regards
> Zolisa
>

Hi Zolisa,

In the pull request where the C function logfactorial was added
(https://github.com/numpy/numpy/pull/13761), I originally modified the
Poisson code to use logfactorial as you suggest, but Kevin (@bashtage
on github) pointed out that the change could potentially alter the
random stream for the legacy version. Making the change requires
creating separate C functions, one for the legacy code that remains
unchanged, and one for the newer Generator class that would use
logfactorial.  You can see the comments here (click on "Show
resolved"):

    https://github.com/numpy/numpy/pull/13761#pullrequestreview-249973405

At the time, making that change was not a high priority, so I didn't
pursue it. It does make sense to use the logfactorial function there,
and I'd be happy to see it updated, but be aware that making the
change is more work than changing just the function call.

Warren

>
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