Re-examine complex pow special case handling

[mdickinson]

BPO	44970
Nosy	@mdickinson, @serhiy-storchaka
Superseder	bpo-15996: pow() for complex numbers is rough around the edges

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

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GitHub fields:

assignee = None
closed_at = <Date 2021-10-22.08:23:37.519>
created_at = <Date 2021-08-21.13:26:43.363>
labels = ['3.11']
title = 'Re-examine complex pow special case handling'
updated_at = <Date 2021-10-22.08:23:37.519>
user = 'https://github.com/mdickinson'

bugs.python.org fields:

activity = <Date 2021-10-22.08:23:37.519>
actor = 'mark.dickinson'
assignee = 'none'
closed = True
closed_date = <Date 2021-10-22.08:23:37.519>
closer = 'mark.dickinson'
components = []
creation = <Date 2021-08-21.13:26:43.363>
creator = 'mark.dickinson'
dependencies = []
files = []
hgrepos = []
issue_num = 44970
keywords = []
message_count = 6.0
messages = ['400025', '400026', '400027', '400037', '404654', '404726']
nosy_count = 2.0
nosy_names = ['mark.dickinson', 'serhiy.storchaka']
pr_nums = []
priority = 'low'
resolution = 'duplicate'
stage = 'resolved'
status = 'closed'
superseder = '15996'
type = None
url = 'https://bugs.python.org/issue44970'
versions = ['Python 3.11']

[mdickinson]

Complex power, both via ** and the built-in pow, and via cmath.pow, is currently a bit of a mess when it comes to special-case handling - particularly handling of signed zeros, infinities, NaNs, and overflow.

At some point it would be nice to rationalise and document the special-case handling, as far as possible, and to make the behaviour of ** and pow consistent with that of cmath.pow. Note that while for all the other cmath functions we have good guidance from the C standards on how special cases should be handled, for pow we're on our own - the C standard refuses to specify anything at all about special case handling.

Note also that there are a *lot* of special cases to consider. We have four real input parameters (the real and imaginary parts of each of the base and the exponent), each of which can be one of the 7 cases nan, -inf, -finite, -0.0, 0.0, finite, inf, for a total of 7**4 = 2401 combinations; moreover, for some cases we might need to distinguish integral from non-integral values, and even integers from odd integers.

This is low priority - in many years of mathematical, scientific and numeric work, I've seen little evidence that anyone actually cares about or uses general complex power. Most users are interested in one or more subcases, like:

• positive real base and complex exponent
• complex base and integral exponent
• complex nth root for positive integers n, especially for small n (square root, cube root, ...)

So a possibly more manageable and more useful subtask would be to ensure that special cases are handled in a sensible manner for these subcases.

[mdickinson]

Here's just one example that doesn't make a whole lot of sense: in this case, z ** 1 should be returning z.

>>> z = complex(3, float("inf"))
>>> z ** 1
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
OverflowError: complex exponentiation

[mdickinson]

Aargh. Brain fail. There is no cmath.pow, of course; this issue applies only to ** and the built-in pow.

[serhiy-storchaka]

The OverflowError should only be raised if finite arguments produce infinite result. Py_ADJUST_ERANGE2 is used improperly.

But after fixing this error I get (nan+infj) for z**1, the same as for z*1.

[serhiy-storchaka]

Is not it a duplicate of bpo-15996?

[mdickinson]

Is not it a duplicate of bpo-15996?

Yes, I think it's close enough. Thanks.