* 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>
Mark some individual tests to skip when --pgo is used. The tests
marked increase the PGO task time significantly and likely don't
help improve optimization of the final executable.
Responding to suggestions on the tracker and some off-line suggestions.
Davin suggested that english named accessors instead of greek letters would result in more intelligible user code. Steven suggested that the parameters still need to be *mu* and *theta* which are used elsewhere (and I noted those parameter names are used in linked-to resources).
Michael suggested proving-out the API by seeing whether it generalized to *Lognormal*. I did so and found that Lognormal distribution parameters *mu* and *sigma* do not represent the mean and standard deviation of the lognormal distribution (instead, they are for the underlying regular normal distribution).
Putting these ideas together, we have NormalDist parameterized by *mu* and *sigma* but offering English named properties for accessors. That gives lets us match other API that access mu and sigma, it matches the external resources on the topic, gives us clear english names in user code. The API extends nicely to LogNormal where the parameters and the summary statistic accessors are not the same.
https://bugs.python.org/issue36018
Although nth roots of negative numbers are real for odd n, the
statistics module doesn't make use of this. Remove support for
negative roots from the private _nth_root function, which
simplifies the test suite.
Raymond Hettinger
Irit Katriel
Zack Kneupper
Tymoteusz Wołodźko
Hai Shi
Tzanetos Balitsaris
Tim Gates
Min ho Kim
Dong-hee Na
Neil Schemenauer
Xtreak
Serhiy Storchaka
Steven D'Aprano
Victor Stinner
Benjamin Peterson