add more mathematical functions to the standard library

[vks]

The following special functions are essential for basic statistics. See [1] for an argumentation why they should be included in any standard library. They are implemented in the Cephes library [2]:

/* 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);

We could just link against Cephes, the library is very stable and changes only every few years. The license is not specified in the distribution or on the website, however the author of the library has agreed to distribute Cephes using the BSD license in the past. [3]

(For more special functions that could be implemented see [4], however that might be to extensive.)

[1] http://www.evanmiller.org/statistical-shortcomings-in-standard-math-libraries.html
[2] http://www.moshier.net/#Cephes
[3] https://lists.debian.org/debian-legal/2004/12/msg00295.html
[4] http://open-std.org/jtc1/sc22/wg21/docs/papers/2003/n1422.html

[thestinger]

I don't think the standard library should take on more external dependencies, especially one that's a dead project without clear licensing. It would make sense to expose the full C99 math library but I don't think going beyond that is within the scope of the standard library for the time being. There are still a few functions that are provided by C but not Rust.

[vks]

I don't think it is dead, it seems more like it is done. And it is a tiny dependency, compared to most others.

[ghost]

The author of Cephes allowed the torch-cephes library to distribute Cephes under the BSD license, so it would be acceptable to use that distribution of Cephes instead if there are any licensing concerns with the original Cephes.

See https://github.com/jucor/torch-cephes/blob/master/LICENSE.txt

[huonw]

This is something that can be used as an external library, due to Cargo. Furthermore, Cargo is actively improving with respect to compiling external deps (e.g. rust-lang/rfcs#403) so this will only get easier and easier. It makes sense for external libraries/bindings to be developed, iterated on and improved, and then, in future, we can evaluate the option of pulling in the best one (or best parts of each).

In any case, a good first step in getting this added would be writing that external lib.

[vks]

See https://github.com/vks/special-fun.

[steveklabnik]

I'm pulling a massive triage effort to get us ready for 1.0. As part of this, I'm moving stuff that's wishlist-like to the RFCs repo, as that's where major new things should get discussed/prioritized.

This issue has been moved to the RFCs repo: rust-lang/rfcs#785