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

先閱讀提案和連結的 Discourse 討論，然後檢查 Modules/cmathmodule.c、Objects/floatobject.c 和 Include/internal/pycore_pymath.h。將現有的 errno 處理和調整輔助函式與連結的 platform-libm 錯誤報告進行比較；完成這項工作需要針對所有受影響的算術運算，決定一種一致且可測試的浮點錯誤處理方案。