Add non integral tests for sqrt()

[AjithRamachandran]

BPO	44364
Nosy	@mdickinson, @serhiy-storchaka, @AjithRamachandran
PRs	bpo-44364:Add non integral tests for sqrt() #26625

^{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 2021-06-10.16:29:32.499>
created_at = <Date 2021-06-09.15:14:51.752>
labels = ['type-feature', 'tests', '3.10', '3.11']
title = 'Add non integral tests for `sqrt()`'
updated_at = <Date 2021-06-10.19:41:09.598>
user = 'https://github.com/AjithRamachandran'

bugs.python.org fields:

activity = <Date 2021-06-10.19:41:09.598>
actor = 'mark.dickinson'
assignee = 'none'
closed = True
closed_date = <Date 2021-06-10.16:29:32.499>
closer = 'mark.dickinson'
components = ['Tests']
creation = <Date 2021-06-09.15:14:51.752>
creator = 'AjithRamachandran'
dependencies = []
files = []
hgrepos = []
issue_num = 44364
keywords = ['patch']
message_count = 4.0
messages = ['395549', '395563', '395564', '395566']
nosy_count = 3.0
nosy_names = ['mark.dickinson', 'serhiy.storchaka', 'AjithRamachandran']
pr_nums = ['26625']
priority = 'normal'
resolution = None
stage = 'resolved'
status = 'closed'
superseder = None
type = 'enhancement'
url = 'https://bugs.python.org/issue44364'
versions = ['Python 3.10', 'Python 3.11']

[mdickinson]

New changeset 90cd433 by Ajith Ramachandran in branch 'main':
bpo-44364:Add non integral tests for sqrt() (bpo-26625)
90cd433

[serhiy-storchaka]

>>> math.sqrt(2.5) == 2.5**0.5
True
>>> math.sqrt(25.25) == 25.25**0.5
True

If we test the precision of math.sqrt(), would not be better to test it with data for which naive way of calculating the root returns different result? For example 2921 is the smallest integers for which math.sqrt(x) > x**0.5, and 3541 is the smallest integers for which math.sqrt(x) < x**0.5.

[serhiy-storchaka]

65733 and 262694 are integers in range 1..1000000 with largest relative errors of naive square root (with different signs).

33031 and 524557 are integers in range 1..1000000 with largest relative errors of naive cube root (with different signs).

[mdickinson]

2921 is the smallest integers for which math.sqrt(x) > x**0.5

This is platform-dependent. On my machine, for example, math.sqrt(2921) == 2921**0.5 returns True.

I don't see a lot of value in additional tests here; we're only wrapping the libm sqrt, so we only really need enough testing to catch possible implementation errors in that wrapping. But testing only integers with an exact square root doesn't seem enough.