Describe the issue:

The documentation suggests that np.random.Generator should be used in favor of np.random.RandomState, except to reproduce exact same random sequences prior to NumPy v1.16. The expectation is that np.random.Generator should have better support for all functions in np.random.RandomState; this is not the case for np.random.Generator.hypergeometric, which allows ngood and nbad up to $10^9$, compared to np.random.RandomState.hypergeometric which allows any ngood and nbad within int64 range. Either np.random.Generator should be updated to support the same cases that np.random.RandomState do, or the docs should be updated to mention that legacy RandomState have to be used for this specific function .

Reproduce the code example:

import numpy as np
np.random.RandomState(1337).hypergeometric(10**15,10**15,10**9) # 499964666
np.random.default_rng(1337).hypergeometric(10**15,10**15,10**9) # ValueError

Error message:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "numpy/random/_generator.pyx", line 3496, in numpy.random._generator.Generator.hypergeometric
ValueError: both ngood and nbad must be less than 1000000000

Python and NumPy Versions:

1.26.4
3.10.14 (main, May 6 2024, 19:42:50) [GCC 11.2.0]

Runtime Environment:

No response

Context for the issue:

The implementation for np.random.Generator.hypergeometric is at

The implementation for np.random.RandomState.hypergeometric is at

I think the math involved in np.random.RandomState.hypergeometric (the "HRUA" algorithm) might be a little bit too complex which made it a little hard to translate it into Python. But the only primitives used in the C implementation are next_double and logfactorial, where logfactorial is implemented in https://github.com/numpy/numpy/blob/main/numpy/random/src/distributions/logfactorial.c. With the help of generative coding assistants it might be easier than ever to translate the code into Python. I don't have experience with NumPy development yet but I hope someone will pick this up.