cmath.atanh() returns infinity for complex(1.0, 2.0**-511)

Bug report

Bug description:

cmath.atanh() returns an infinite real part for a finite input whose
result should be finite:

>>> import cmath
>>> import math
>>> y = 2.0**-511
>>> cmath.atanh(complex(1.0, y))
(inf+0.7853981633974483j)

The expected result is approximately
(177.445678223346+0.7853981633974483j). The real part is approximately
256 * math.log(2).

The immediately adjacent floating-point inputs both give finite results:

>>> cmath.atanh(complex(1.0, math.nextafter(y, 0.0)))
(177.445678223346+0.7853981633974483j)
>>> cmath.atanh(complex(1.0, math.nextafter(y, math.inf)))
(177.445678223346+0.7853981633974483j)

The same problem occurs for all four sign combinations of the real and
imaginary parts.

In Modules/cmathmodule.c, cmath_atanh_impl() selects the near-pole
formula using ay < CM_SQRT_DBL_MIN. At equality, the general formula
instead forms 4.0 / DBL_MIN, which overflows before the logarithm is
evaluated. Changing the comparison to <= includes the boundary in the
existing near-pole branch.

This also affects cmath.atan(), which uses the same implementation:

>>> cmath.atan(complex(y, 1.0))
(0.7853981633974483+infj)

Here the expected result is approximately
(0.7853981633974483+177.445678223346j).

Reproduced on CPython 3.14.7, 3.14.4, and main. x86-64 Linux (glibc).

CPython versions tested on:

CPython main branch, 3.14

Operating systems tested on:

Linux

Linked PRs

• gh-157860