The easiest way to do this would to to write a pure python implementation
using Python ints of a masked integer sampler. This way you could draw
unsigned integers and then treat this as a bit pool. You would than take
the number of bits needed for your integer, transform these to be a Python
int, and finally apply the mask.
This is how integers are generated in the legacy Random state code.
Kevin
On Sat, Aug 19, 2023, 15:43 Dan Schult <dsch...@colgate.edu> wrote:
> How can we use numpy's random `integers` function to get uniformly
> selected integers from an arbitrarily large `high` limit? This is important
> when dealing with exact probabilities in combinatorially large solution
> spaces.
>
> I propose that we add the capability for `integers` to construct arrays of
> type object_ by having it construct python int's as the objects in the
> returned array. This would allow arbitrarily large integers.
>
> The Python random library's `randrange` constructs values for arbitrary
> upper limits -- and they are exact when using subclasses of `random.Random`
> with a `getrandbits` methods (which includes the default rng for most
> operating systems).
>
> Numpy's random `integers` function rightfully raises on `integers(20**20,
> dtype=int64)` because the upper limit is above what can be held in an
> `int64`. But Python `int` objects store arbitrarily large integers. So I
> would expect `integers(20**20, dtype=object)` to create random integers on
> the desired range. Instead a TypeError is raised `Unsupported dtype
> dtype('O') for integers`. It seems we could provide support for dtype('O')
> by constructing Python `int` values and this would allow arbitrarily large
> ranges of integers.
>
> The core of this functionality would be close to the seven lines used in
> [the code of random.Random._randbelow](
> https://github.com/python/cpython/blob/eb953d6e4484339067837020f77eecac61f8d4f8/Lib/random.py#L242)
> which
> 1) finds the number of bits needed to describe the `high` argument.
> 2) generates that number of random bits.
> 3) converts them to a python int and checks if it is larger than the input
> `high`. If so, repeat from step 2.
>
> I realize that people can just use `random.randrange` to obtain this
> functionality, but that doesn't return an array, and uses a different RNG
> possibly requiring tracking two RNG states.
>
> This text was also used to create [Issue #24458](
> https://github.com/numpy/numpy/issues/24458)
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