Zig: Consider adding 8 math functions to std.math for statistics applications

[dirkschumacher]

Evan Miller (@evanmiller) made a great case that adding just a few more math functions to the standard <math.h> C library would enable a huge range of statistical applications. Or to quote him:

Basic statistical analysis requires special mathematical functions which almost no standard math libraries implement. These functions are not particular to statistics, but they form building blocks for a number of important statistical applications. If standard math libraries were to provide just a few more special functions, including incomplete beta, incomplete gamma, inverse normal, and better Bessel functions, developers would be able to integrate more statistical functions into their applications without having to license specialized libraries, or copy-paste code of dubious origin into their projects. (https://www.evanmiller.org/statistical-shortcomings-in-standard-math-libraries.html)

Since zig provides a rather comprehensive standard library (e.g. all the great stuff in std.crypto) it might be a good idea to add those functions to the standard math library, such that anybody can build great statistical/machine learning work in zig without resorting to third party math libraries.

Just an _idea_. The linked article provides the full rational, but I will list the 8 functions here for completneness:

I realize that implementing all of these specialized numerical functions sounds like a lot of work, but in fact the work is essentially finished: the free Cephes library contains a host of mathematical functions with names and argument orders nearly identical to their counterparts, as well as all of the functions I have mentioned above. So my proposal boils down to “graduating” the following eight double-precision functions, along with their single-precision and extended precision counterparts, from Cephes into the standard C library:

/* Regularized incomplete beta function */
double incbet(double a, double b, double x);

/* Inverse of incomplete beta integral */
double incbi(double a, double b, double y);

/* Regularized incomplete gamma integral */
double igam(double a, double x);

/* Complemented incomplete gamma integral */
double igamc(double a, double x);

/* Inverse of complemented incomplete gamma integral
double igami(double a, double p);

/* Normal distribution function */
double ndtr(double x);

/* Inverse of Normal distribution function */
double ndtri(double y);

/* Bessel function of non-integer order */
double jv(double v, double x);

[rohlem]

In support, though I'd favour more readable names, even if these might be standard in the field, ndtr and jv aren't obvious.
Especially since const xyz = makes it trivial for end users to implement their preferred naming scheme.

[daurnimator]

@dirkschumacher is this something you'd implement?

[marler8997]

In support, though I'd favour more readable names...

You could also have both.

std/math/sciencynames.zig:

pub const incbet = std.math.regularIncompleteBeta;
pub const incbi = std.math.inverseIncompleteBeta;
//...

[dirkschumacher]

I'd favour more readable names

Yes absolutely.

@dirkschumacher is this something you'd implement?

Yeah, but I cannot commit to anything this year. Will try next year. So if anyone wants to go ahead in the meantime, feel free.