bpo-20499: Rounding error in statistics.pvariance

[rhettinger]

Make the _ss() function exact.

Also improve the speed:

$ python -m timeit -r 11 -s 'from statistics import variance' -s 'from random import random, seed' -s 'seed(8564399)' -s 'data = [random() for i in range(1_000)]' 'variance(data)'

100 loops, best of 11: 2.16 msec per loop   # Baseline
200 loops, best of 11: 1.71 msec per loop   # Patched

https://bugs.python.org/issue20499

[miss-islington]

Thanks @rhettinger for the PR 🌮🎉.. I'm working now to backport this PR to: 3.9, 3.10.
🐍🍒⛏🤖

[miss-islington]

Sorry @rhettinger, I had trouble checking out the 3.10 backport branch.
Please backport using cherry_picker on command line.
cherry_picker 4a5cccb02bb2254634c0fbb2cbb14e2e7f45e2d5 3.10

[miss-islington]

Sorry, @rhettinger, I could not cleanly backport this to 3.9 due to a conflict.
Please backport using cherry_picker on command line.
cherry_picker 4a5cccb02bb2254634c0fbb2cbb14e2e7f45e2d5 3.9

[miss-islington]

Thanks @rhettinger for the PR 🌮🎉.. I'm working now to backport this PR to: 3.10.
🐍🍒⛏🤖

[miss-islington]

Sorry @rhettinger, I had trouble checking out the 3.10 backport branch.
Please backport using cherry_picker on command line.
cherry_picker 4a5cccb02bb2254634c0fbb2cbb14e2e7f45e2d5 3.10

[miss-islington]

Thanks @rhettinger for the PR 🌮🎉.. I'm working now to backport this PR to: 3.10.
🐍🍒⛏🤖

[miss-islington]

Sorry, @rhettinger, I could not cleanly backport this to 3.10 due to a conflict.
Please backport using cherry_picker on command line.
cherry_picker 4a5cccb02bb2254634c0fbb2cbb14e2e7f45e2d5 3.10

[bedevere-bot]

GH-28248 is a backport of this pull request to the 3.10 branch.

[bedevere-bot]

⚠️⚠️⚠️ Buildbot failure ⚠️⚠️⚠️

Hi! The buildbot aarch64 RHEL8 3.10 has failed when building commit 3c30805.

What do you need to do:

1. Don't panic.
2. Check the buildbot page in the devguide if you don't know what the buildbots are or how they work.
3. Go to the page of the buildbot that failed (https://buildbot.python.org/all/#builders/612/builds/302) and take a look at the build logs.
4. Check if the failure is related to this commit (3c30805) or if it is a false positive.
5. If the failure is related to this commit, please, reflect that on the issue and make a new Pull Request with a fix.

You can take a look at the buildbot page here:

https://buildbot.python.org/all/#builders/612/builds/302

Failed tests:

• test_readline

Failed subtests:

• test_nonascii - test.test_readline.TestReadline

Summary of the results of the build (if available):

== Tests result: FAILURE then FAILURE ==

413 tests OK.

10 slowest tests:

• test_concurrent_futures: 2 min 54 sec
• test_multiprocessing_spawn: 2 min 13 sec
• test_peg_generator: 1 min 38 sec
• test_asyncio: 1 min 27 sec
• test_multiprocessing_forkserver: 1 min 26 sec
• test_unparse: 1 min 15 sec
• test_multiprocessing_fork: 1 min 13 sec
• test_capi: 1 min 6 sec
• test_gdb: 55.9 sec
• test_tokenize: 53.3 sec

1 test failed:
test_readline

13 tests skipped:
test_devpoll test_ioctl test_kqueue test_msilib test_ossaudiodev
test_startfile test_tix test_tk test_ttk_guionly test_winconsoleio
test_winreg test_winsound test_zipfile64

1 re-run test:
test_readline

Total duration: 3 min 4 sec

Click to see traceback logs

Traceback (most recent call last):
  File "/home/buildbot/buildarea/3.10.cstratak-RHEL8-aarch64/build/Lib/test/test_readline.py", line 258, in test_nonascii
    self.assertIn(b"history " + expected + b"\r\n", output)
AssertionError: b"history '[\\xefnserted]|t\\xebxt[after]'\r\n" not found in bytearray(b"^A^B^B^B^B^B^B^B\t\tx\t\r\n[\xc3\xafnserted]|t\xc3\xab[after]\x08\x08\x08\x08\x08\x08\x08text \'t\\xeb\'\r\nline \'[\\xefnserted]|t\\xeb[after]\'\r\nindexes 11 13\r\n\x07text \'t\\xeb\'\r\nline \'[\\xefnserted]|t\\xeb[after]\'\r\nindexes 11 13\r\nsubstitution \'t\\xeb\'\r\nmatches [\'t\\xebnt\', \'t\\xebxt\']\r\nx[after]\x08\x08\x08\x08\x08\x08\x08t[after]\x08\x08\x08\x08\x08\x08\x08\r\nresult \'[\\xefnserted]|t\\xebxt[after]\'\r\nhistory \'[\\xefnserted]|t\\xebxt[after]\'")