The documentation for PyNumber_InPlacePower [1] reads:

This is the equivalent of the Python statement o1 **= o2 when o3 is Py_None, or an in-place variant of pow(o1, o2, o3) otherwise. If o3 is to be ignored, pass Py_None in its place (passing NULL for o3 would cause an illegal memory access).

However, if a class A implements __ipow__ then PyNumber_InPlacePower(o1, o2, o3) ALWAYS ignores o3 if o1 is an instance of A.

This happens because if A implements __ipow__ then PyNumber_InPlacePower always calls the nb_inplace_power slot [2] and the slot always drops the third argument [3].

This appears to have always been the case in Python, so likely a small documentation patch is all that is required. If people agree, I will open a documentation pull request.

[1] https://docs.python.org/3/c-api/number.html?highlight=pynumber_inplacepower#c.PyNumber_InPlacePower

[2] https://github.com/python/cpython/blob/master/Objects/abstract.c#L1164

[3] https://github.com/python/cpython/blob/master/Objects/typeobject.c#L6631-L6636

The documentation for __ipow__ [4] suggests that the intention was to support the modulus argument, so perhaps that argues for fixing the behaviour of PyNumber_InPlacePower.

[4] https://docs.python.org/3/reference/datamodel.html#object.__ipow__

Huh, this is weird. I wonder why the data model provides the signature

  object.__ipow__(self, other[, modulo])

if the slot always seems to drop the third argument.

Adding Brett to the nosy who found another issue around the special casing of pow/** recently. See also issue38302

Also of note, there is actually no way to call `PyNumber_InPlacePower` from pure python from what I can tell. Even libraries like numpy don't implement the three-argument version of the nb_inplace_power slot.

Whoops, forgot the numpy link: https://github.com/numpy/numpy/blob/33e1dbee8d9e11a3e96efaae822ff6f3c44e3cef/numpy/core/src/multiarray/number.c#L729-L741