gh-153144: Avoid checking errno for atan2

[hpkfft]

The C23 standard states that for atan2 and atan2pi:

A domain error may occur if both arguments are zero.
A range error occurs if x is positive and nonzero y/x is too close to zero.

Since Python should not raise ValueError in either of these cases (i.e., when both arguments are zero or when the computation underflows), this PR avoids checking errno when calling these trig functions. As a bonus, math.atan2() is about 4% faster.

• Issue: ValueError for math.atan2(0.0, 0.0) and cmath.phase(0.0) using icx #153144

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The statement about range error in the standard should, I think, be interpreted as:

A range error occurs if (x is positive) and (y/x is nonzero) and (y/x is too close to zero).

[bedevere-app]

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[hpkfft]

If this PR is merged, it looks to me like #146402 can (and should) be reverted.

[skirpichev]

No, I doubt that this is a right approach. We must handle error in same way for all libm functions.

Perhaps, m_atan2() (like m_log1p() we have currently) could be restored (see #122681) to workaround broken platform functions.

[hpkfft]

We must handle error in same way for all libm functions.

The mathmodule currently has 3 ways of handling 1-argument libm functions:

• Functions that cannot overflow (e.g., acos, atan) use math_1(arg, func, /*can_overflow=*/0, err_msg)
• Functions that can overflow (e.g., cosh, exp) use math_1(arg, func, /*can_overflow=*/1, err_msg)
• Functions that are known to set errno properly (e.g., erf, gamma) use math_1a(arg, func, err_msg)

Maybe it's not so bad to have math_2ne for 2-argument functions that are known not to need error checking (e.g., atan2) as well as the current math_2 (for the others).

[skirpichev]

Perhaps, we could modify math_2() helper to check that errno!=EDOM, if inputs and output are finite. When domain error occurs - result should be nan.

But I think that a little wrapper for libm's atan2 is better, if we are going to add some workaround for the given issue.

[skirpichev]

Please revert unrelated changes.

[skirpichev]

This is unrelated change.

[skirpichev]

This too, except for the first line.

[hpkfft]

Is better to leave the first line short or better to reflow the entire comment?

[skirpichev]

Leave just change for the first line. Or even revert the whole change. (Technically, comment is still valid for atan2 too, assuming it conforms to Annex F. But not for hypot() ;-))