Don't rely on errno values, coming from platform's math functions

Feature or enhancement

Proposal:

In the cmath module most functions don't check errno values. See cosh() example below, which set nonzero errno in some cases, but don't read errno (e.g. to detect overflow in libm's cosh/sinh()). Here we essentially assume, that platform implements Annex F of the C standard:
https://github.com/python/cpython/blob/04242c027feeff726acb15b6463422897b489bcf/Modules/cmathmodule.c#L441-L490

What if we extend this approach to the rest of CPython's floating-point arithmetics? Now this seems natural, as we require that platforms C double has IEEE 754 binary64 format. On practice, that means much more, i.e. that platform supports Annex F (modulo bugs). And we can utilize that, assuming that for invalid input - NaN's produced, for overflows - infinities.

For example, instead of current code of float_pow() that handle finite input
https://github.com/python/cpython/blob/04242c027feeff726acb15b6463422897b489bcf/Objects/floatobject.c#L788-L801
we could use something much more simple:

    ix = pow(iv, iw);
    if (negate_result)
        ix = -ix;
    if (isinf(ix)) {
        PyErr_SetString(PyExc_OverflowError,
                        "float exponentiation result out of range");
        return NULL;
    }

(_Py_ADJUST_ERANGE1 and _Py_ADJUST_ERANGE2 helpers will be removed.)

See recent d.p.o thread for illustration of subtle issues, that can be introduced trying to fix errno, coming from platforms functions. We also have occurring bugreports, when platform libm set errno wrongly, e.g. https://github.com/python/cpython/issues/153144.

Disclaimer: this issue filled, based on my humble understanding of the proposal by @mdickinson. It seems, there are volunteers to work on this (CC @hpkfft), hence issue was opened.

Has this already been discussed elsewhere?

I have already discussed this feature proposal on Discourse

Links to previous discussion of this feature:

https://discuss.python.org/t/108539/

Linked PRs

• gh-156551

Start with the proposal and linked Discourse discussion, then inspect Modules/cmathmodule.c, Objects/floatobject.c, and Include/internal/pycore_pymath.h. Compare the existing errno handling and adjustment helpers with the linked platform-libm bug reports; done requires a decided, consistently testable approach for floating-point error handling across the affected arithmetic.