Merge m_atan2() and c_atan2() helper functions (or replace libm's atan2)

[skirpichev]

Feature or enhancement

Proposal:

With #29179, many workarounds for buggy libm implementations were removed. Yet, there is m_atan2():

cpython/Modules/mathmodule.c

Lines 546 to 572 in d0b92dd

	static double
	m_atan2(double y, double x)
	{
	if (isnan(x) || isnan(y))
	return Py_NAN;
	if (isinf(y)) {
	if (isinf(x)) {
	if (copysign(1., x) == 1.)
	/* atan2(+-inf, +inf) == +-pi/4 */
	return copysign(0.25*Py_MATH_PI, y);
	else
	/* atan2(+-inf, -inf) == +-pi*3/4 */
	return copysign(0.75*Py_MATH_PI, y);
	}
	/* atan2(+-inf, x) == +-pi/2 for finite x */
	return copysign(0.5*Py_MATH_PI, y);
	}
	if (isinf(x) || y == 0.) {
	if (copysign(1., x) == 1.)
	/* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
	return copysign(0., y);
	else
	/* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
	return copysign(Py_MATH_PI, y);
	}
	return atan2(y, x);
	}

and

cpython/Modules/cmathmodule.c

Lines 329 to 355 in d0b92dd

	static double
	c_atan2(Py_complex z)
	{
	if (isnan(z.real) || isnan(z.imag))
	return Py_NAN;
	if (isinf(z.imag)) {
	if (isinf(z.real)) {
	if (copysign(1., z.real) == 1.)
	/* atan2(+-inf, +inf) == +-pi/4 */
	return copysign(0.25*Py_MATH_PI, z.imag);
	else
	/* atan2(+-inf, -inf) == +-pi*3/4 */
	return copysign(0.75*Py_MATH_PI, z.imag);
	}
	/* atan2(+-inf, x) == +-pi/2 for finite x */
	return copysign(0.5*Py_MATH_PI, z.imag);
	}
	if (isinf(z.real) || z.imag == 0.) {
	if (copysign(1., z.real) == 1.)
	/* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
	return copysign(0., z.imag);
	else
	/* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
	return copysign(Py_MATH_PI, z.imag);
	}
	return atan2(z.imag, z.real);
	}

They are identical, the second one just uses Py_complex to keep arguments.

We should either 1) move first helper to _math.h and reuse it in the cmathmodule.c or 2) just remove these helpers. I'll provide patch for 1) proposal.

But 2) looks also safe for me: it seems that c_atan2() helper was used only for cmath.phase() and cmath.polar(); libm's atan2() used for the rest - and this don't poses any problems in CI or build bots. ("Problem" values are tested, e.g. infinities and nans for acos().)

Has this already been discussed elsewhere?

This is a minor feature, which does not need previous discussion elsewhere

Links to previous discussion of this feature:

No response

Linked PRs

• gh-122681: merge m_atan2() and c_atan2() helper functions #122682
• gh-122681: remove m_atan2()/c_atan2() helpers #122715