gh-117999: fixed small nonnegative integer powers of complex numbers

[skirpichev]

Before, handling of numbers with special values in components (infinities, nans, signed zero) was invalid. Simple example:

    >>> z = complex(1, -0.0)
    >>> z*z
    (1-0j)
    >>> z**2
    (1+0j)

Now:

    >>> z**2
    (1-0j)

---

• Issue: Small integer powers of real±0j are invalid #117999

[skirpichev]

@picnixz, I would appreciate your review on this pr. Or your opinion in the issue thread.

[picnixz]

I'll do it tomorrow! (Monday, Paris time)

[picnixz]

I need to think a bit more on the issue. I'll try to have something by the end of the day or tomorrow. Ideally, I would like to have no inconsistency between the generic algorithm and the non-generic one (namely, the result should be as if we were using the generic algorithm).

[skirpichev]

I would like to have no inconsistency between the generic algorithm and the non-generic one

I'm not sure if it's possible without too much code, that affects performance severely. BTW, I think that numpy code has no such special version for integer exponents. I'll double check.

Edit: Ah, no. numpy mimics CPython here, at least in npy_math_complex.c.src.

Edit2:

JFR, some simple benchmarks.

With specialized code (main):

$ python -m pyperf timeit -q -s 'z=1+1j;e=20' 'pow(z,e)'
Mean +- std dev: 237 ns +- 5 ns
$ python -m pyperf timeit -q -s 'z=1+1j;e=90' 'pow(z,e)'
Mean +- std dev: 259 ns +- 4 ns
$ python -m pyperf timeit -q -s 'z=1+1j;e=110' 'pow(z,e)'
Mean +- std dev: 579 ns +- 5 ns
$ python -m pyperf timeit -q -s 'z=1+1j;e=200' 'pow(z,e)'
Mean +- std dev: 571 ns +- 3 ns

Without:

$ python -m pyperf timeit -q -s 'z=1+1j;e=2' 'pow(z,e)'
Mean +- std dev: 562 ns +- 3 ns
$ python -m pyperf timeit -q -s 'z=1+1j;e=20' 'pow(z,e)'
Mean +- std dev: 576 ns +- 2 ns
$ python -m pyperf timeit -q -s 'z=1+1j;e=90' 'pow(z,e)'
Mean +- std dev: 576 ns +- 3 ns
$ python -m pyperf timeit -q -s 'z=1+1j;e=110' 'pow(z,e)'
Mean +- std dev: 578 ns +- 4 ns
$ python -m pyperf timeit -q -s 'z=1+1j;e=200' 'pow(z,e)'
Mean +- std dev: 573 ns +- 3 ns