Spurious ZeroDivisionError for complex powers when the phase is infinite

[serhiy-storchaka]

>>> complex('inf')**1j
Traceback (most recent call last):
  File "<python-input-0>", line 1, in <module>
    complex('inf')**1j
    ~~~~~~~~~~~~~~^^~~
ZeroDivisionError: zero to a negative or complex power

The base is not zero. The result should be nan+nanj, as in the GNU MPC.

_Py_c_pow() computes an infinite phase here, and cos() and sin() of an infinite argument are domain errors, so libm sets errno to EDOM. complex_pow() translates any EDOM to ZeroDivisionError, as it cannot distinguish it from the EDOM set for a zero base.

Any finite base for which the phase overflows is affected too:

>>> complex(1e300)**complex(0, 1e308)
ZeroDivisionError: zero to a negative or complex power
>>> complex(2)**complex(0, float('inf'))
ZeroDivisionError: zero to a negative or complex power

sin() and cos() set errno only for infinite arguments, so it is enough to discard errno in _Py_c_pow() after computing the result: _Py_ADJUST_ERANGE2() recovers ERANGE from the result itself.

Noticed by @hpkfft in #156694.

Linked PRs

• gh-156886: Fix spurious ZeroDivisionError for complex powers #156887

[serhiy-storchaka]

A similar spurious ZeroDivisionError is raised when x**|n| underflows to zero for a negative integer exponent, e.g. (1e-162+0j)**-2. The cause is different -- _Py_rc_quot() with a zero denominator -- and it is not fixed by discarding errno in _Py_c_pow(). See gh-156695.