Proposal:

Suggested by @vstinner in #124829 (comment).

I would agree, as these routines could be useful (and it seems, they are used by few projects) to implement mathematical functions just like in the cmath module. No alternatives exist.

It's also suggested to use a different convention for arguments: currently we pass them by value. We could use pointers to Py_complex struct instead. (Though my quick tests shows no measurable difference.)

Also, we should decide on naming. For _Py_c_sum() - PyComplex_Add() was suggested. But this looks misleading, as PyComplex_ is a prefix for functions, operating with PyObject* arguments. Perhaps, rather we could instead use Py_complex_add() and Py_complex_add_real() (in the GNU GSL style). Current semi-private functions should be deprecated.

Edit:
The C-API WG decision: Soft-deprecate the Py_c*() functions and Deprecate PyComplexObject.cval.

Previous discussions:

• _Py_c_sum, _Py_c_diff, etc - were removed from Python.h #112019
• C API: Remove private C API functions (move them to the internal C API) #106320 (comment)

Other:

• Remove public low-level API functions for Py_complex? capi-workgroup/decisions#56
• https://discuss.python.org/t/89919/

Linked PRs

• gh-128813: hide mixed-mode functions for complex arithmetic from C-API #131703
• gh-128813: soft-deprecate _Py_c_*() functions #137261
• gh-128813: deprecate cval field of the PyComplexObject struct #137271
• gh-128813: cleanup C-API docs for PyComplexObject #137579