gh-108322: Optimize statistics.NormalDist.samples()

[rhettinger]

Timings show a 3.8x speedup:

# Baseline
% ./python.exe -m timeit -s 'from random import random' -s 'from statistics import NormalDist as ND' -s 'Z = ND()' 'Z.samples(1000)'
2000 loops, best of 5: 196 usec per loop

# Patched
% ./python.exe -m timeit -s 'from random import random' -s 'from statistics import NormalDist as ND' -s 'Z = ND()' 'Z.samples(1000)'
5000 loops, best of 5: 51.6 usec per loop

Besides being faster, the PR makes the statistics module more self contained and less vulnerable to concurrency issues (because gauss() is stateful between successive calls).

@stevendaprano
If you have comments or suggestions, feel free to send them to me privately.

• Issue: Speed-up statistics.NormalDist.samples() #108322

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📚 Documentation preview 📚: https://cpython-previews--108324.org.readthedocs.build/

[serhiy-storchaka]

It looks impressive. But I wonder why not use this implementation in Random.normalvariate()?

[gpshead]

Tangentially: This PR would've been improved by code review from an active core dev as it borders on feature territory. Unfortunately stevendaprano has not yet chosen to return and thus may not even have been able to see the request let alone offer visible feedback.

[gpshead]

I see one potential problem with it from an API behavior change point of view in that people do rely on consistent output over time from functions like this when they specify an explicit seed value. We should retain the older slower implementation by default when an explicit seed value is specified.

We're free to use a new faster version that returns different results when no explicit seed is provided given the nature of the function being randomness based.

I'll make a PR.