Looks good to me overall so far, thanks for pushing this forward @mtsokol.

I think by definiton, function's __module__ attribute should return the name of the module that this function originates from.

To clarify since "originates" could be misunderstood: each function is available in the public API from a single namespace (on rare occasions, some object may be exposed in 2 places still), and we want to ensure that __module__ points to that public namespace, and not to the private namespace/object where the implementation lives.

Ok, I think it's ready for reviews. Some comments:

• I skip all numpy.random module (all functions have __module__ as numpy.random.mtrand there instead of numpy.random) as, it looks like, cython disallows overriding __module__ (need to ask about it in the mailing list).
• I also cleaned up ma a bit to adhere to "each function is exported from one place" rule, as it was required by my test.

I skip all numpy.random module (all functions have __module__ as numpy.random.mtrand there instead of numpy.random) as, it looks like, cython disallows overriding __module__ (need to ask about it in the mailing list).

Ouch, that is bad. In NumPy 1.26 the attribute did contain numpy.random, which is more correct. Worth raising upstream indeed.

When we discussed this at the triage meeting, we recommended an approach to consider the cython-generated code in a separate PR

Thanks @mtsokol. We can adjust this as needed going forward. Hopefully we will find a way to se the cython-generated code in random's __module__.