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bpo-45876: Improve accuracy for stdev() and pstdev() in statistics (GH-29736)

* Inlined code from variance functions

* Added helper functions for the float square root of a fraction

* Call helper functions

* Add blurb

* Fix over-specified test

* Add a test for the _sqrt_frac() helper function

* Increase the tested range

* Add type hints to the internal function.

* Fix test for correct rounding

* Simplify ⌊√(n/m)⌋ calculation

Co-authored-by: Mark Dickinson <dickinsm@gmail.com>

* Add comment and beef-up tests

* Test for zero denominator

* Add algorithmic references

* Add test for the _isqrt_frac_rto() helper function.

* Compute the 109 instead of hard-wiring it

* Stronger test for _isqrt_frac_rto()

* Bigger range

* Bigger range

* Replace float() call with int/int division to be parallel with the other code path.

* Factor out division. Update proof link. Remove internal type declaration

Co-authored-by: Mark Dickinson <dickinsm@gmail.com>
R
Raymond Hettinger committed
af9ee57b96cb872df6574e36027cc753417605f9
Parent: db55f3f
Committed by GitHub <noreply@github.com> on 11/27/2021, 5:54:50 AM