[Numpy-discussion] Low-level API for Random

[Kevin Sheppard]

There are some users of the NumPy C code in randomkit.  This was never
officially supported.  There has been a long open issue to provide this
officially.

When I wrote randomgen I supplied .pdx files that make it simpler to write
Cython code that uses the components.  The lower-level API has not had much
scrutiny and is in need of a clean-up.   I thought this would also
encourage users to extend the random machinery themselves as part of their
project or code so as to minimize the requests for new (exotic)
distributions to be included in Generator.

Most of the generator functions follow a pattern random_DISTRIBUTION.  Some
have a bit more name mangling which can easily be cleaned up (like
ranomd_gauss_zig, which should become PREFIX_standard_normal).

Ralf Gommers suggested unprefixed names. I tried this in a local branch and
it was a bit ugly since some of the distributions have common math names
(e.g., gamma) and others are very short (e.g., t or f).  I think a prefix
is needed, and after looking through the C API docs npy_random_ seemed like
a reasonable choice (since these live in numpy.random).

Any thoughts on the following questions are welcome (others too):

1. Should there be a prefix on the C functions?
2. If so, what should the prefix be?
3. Should the legacy C functions be part of the API -- these are mostly the
ones that produce or depend on polar transform normals (Box-Muller). I have
a feeling no, but there may be reasons to prefer BM since they do not
depend on rejection sampling.
4. Should low-level API be consumable like any other numpy C API by
including the usual header locations and library locations?  Right now, the
pxd simplifies writing Cython but users have sp specify the location of the
headers and source manually  An alternative would be to provide a function
like np.get_include() -> np.random.get_include() that would specialize in
random.

Kevin
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