Bug description:

Four statements added with the half-turn functions in GH-150555 describe a different function than the one they document.

$ ./python -c 'import math; print(math.atanpi.__doc__); print(math.atanpi(-1), math.atan2pi(-1, -1), math.atanpi(-1 / -1))'
Return the arc tangent (measured in half-turns) of x.

The result is between 0 and 1.
-0.25 -0.75 0.25

• atanpi's docstring in Modules/mathmodule.c says "The result is between 0 and 1". The range is -1/2 to 1/2, as Doc/library/math.rst states.
• The trigonometric summary table in Doc/library/math.rst describes atan2pi(y, x) as "atan(y / x), in half-turns". atan returns radians, and the entry for the function itself says atanpi(y / x).
• The comment above m_atanpi in Modules/mathmodule.c reads "asin(x)/pi". The function computes atan(x)/pi.
• The comment above m_atan2pi in Modules/mathmodule.c reads "asin(x)/pi". The function computes atan2(y, x)/pi.

CPython versions tested on:

CPython main branch

Operating systems tested on:

Linux

Linked PRs

• gh-157135: Fix documentation errors in the half-turn *pi functions #157136