BUG: random: beta can generate nan when the parameters are extremely small. #24266
Description
Describe the issue:
This issue first came up in #24210. I'm creating a new issue to focus on beta.
The beta method of random.Generator can generate nan when both parameters are extremely small. "Extremely small" means subnormal, or normal but only a small multiple the smallest normal float. For example, in the following sample of size 500000000, 413 nan values were generated.
In [1]: rng = np.random.default_rng()
In [2]: tiny = np.finfo(np.float64).tiny
In [3]: x = rng.beta(2*tiny, 1.5*tiny, size=500000000)
In [4]: np.isnan(x).sum()
Out[4]: np.int64(413)
The problem is in the C function random_beta. In this loop
numpy/numpy/random/src/distributions/distributions.c
Lines 413 to 433 in d50fc57
when a and b are sufficiently small, the both variables logX and logY can be -inf. Then the subtraction -inf - (-inf) results in nan.
Reproduce the code example:
See above.Error message:
No response
Runtime information:
In [5]: import sys, numpy; print(numpy.__version__); print(sys.version)
1.25.0rc1+630.gd50fc570a9
3.11.4 (main, Jul 3 2023, 14:49:40) [GCC 11.3.0]
In [6]: print(numpy.show_runtime())
[{'numpy_version': '1.25.0rc1+630.gd50fc570a9',
'python': '3.11.4 (main, Jul 3 2023, 14:49:40) [GCC 11.3.0]',
'uname': uname_result(system='Linux', node='pop-os', release='6.2.6-76060206-generic', version='#202303130630~1689015125~22.04~ab2190e SMP PREEMPT_DYNAMIC Mon J', machine='x86_64')},
{'simd_extensions': {'baseline': [], 'found': [], 'not_found': []}},
{'architecture': 'Zen',
'filepath': '/usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so',
'internal_api': 'openblas',
'num_threads': 24,
'prefix': 'libopenblas',
'threading_layer': 'pthreads',
'user_api': 'blas',
'version': '0.3.20'}]
None
Context for the issue:
No response