Add math.cbrt() function: Cube Root

[AjithRamachandran]

BPO	44357
Nosy	@malemburg, @rhettinger, @mdickinson, @vstinner, @serhiy-storchaka, @AjithRamachandran
PRs	bpo-44357:Add math.cbrt() function: Cube Root #26622

^{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 = 'https://github.com/mdickinson'
closed_at = <Date 2021-06-10.16:43:16.244>
created_at = <Date 2021-06-09.07:45:49.555>
labels = ['type-feature', 'library', '3.11']
title = 'Add math.cbrt() function: Cube Root'
updated_at = <Date 2021-06-16.12:21:53.430>
user = 'https://github.com/AjithRamachandran'

bugs.python.org fields:

activity = <Date 2021-06-16.12:21:53.430>
actor = 'mark.dickinson'
assignee = 'mark.dickinson'
closed = True
closed_date = <Date 2021-06-10.16:43:16.244>
closer = 'mark.dickinson'
components = ['Library (Lib)']
creation = <Date 2021-06-09.07:45:49.555>
creator = 'AjithRamachandran'
dependencies = []
files = []
hgrepos = []
issue_num = 44357
keywords = ['patch']
message_count = 13.0
messages = ['395388', '395396', '395399', '395405', '395411', '395415', '395417', '395418', '395420', '395421', '395430', '395553', '395554']
nosy_count = 7.0
nosy_names = ['lemburg', 'rhettinger', 'mark.dickinson', 'vstinner', 'stutzbach', 'serhiy.storchaka', 'AjithRamachandran']
pr_nums = ['26622']
priority = 'normal'
resolution = None
stage = 'resolved'
status = 'closed'
superseder = None
type = 'enhancement'
url = 'https://bugs.python.org/issue44357'
versions = ['Python 3.11']

[serhiy-storchaka]

See also bpo-27353.

[mdickinson]

+1. This is part of C99, so if it's also supported by Visual Studio, then this seems like a no-brainer. If it's _not_ also supported by Visual Studio, or if there are implementations that have serious numerical problems (as was the case with fma) we'll need to write our own fallback implementation, which is less simple.

In principle it should be relatively easy for a math library to provide a correctly-rounded cbrt.

[mdickinson]

BTW, to forestall questions about adding cmath.cbrt: it's not obvious how to extend the real cube root function to a complex cube root, so it might make sense to wait for actual use-cases before doing so.

The issue is that the most natural way to define a complex cube root would use a branch cut along the negative real axis (the same branch cut that cmath.sqrt and cmath.log use). But then the principal branch would *not* be an extension of math.cbrt: it would return non-real values on the negative real axis. (The *real* cube roots of negative numbers would fall on the two non-principal branches.)

See for example https://math.stackexchange.com/questions/71775/extending-the-cube-root-function-to-mathbbc

[AjithRamachandran]

When I needed a function to find cube root, I couldn't find one in the math module. Also found the cbrt() function in C. I didn't account for the complex numbers. I didn't wanted to make it a complex function unnecessarily. So I used the cbrt() function directly and it was working well for my test cases. And it is supported by visual studio.

[serhiy-storchaka]

I am surprised that this was not proposed before. Perhaps because it is so easy to write x**(1/3), and if you want a real root of negative argument, it is -(-x)**(1/3). It can be slightly less accurate that the result of C library function cbrt(), but good enough for any practical applications.

Ajith, was you aware of x**(1/3)?