TR29124 Mathematical Special Functions in C++

This repository contains work toward [IS 29124 - Extensions to the C++ Library to Support Mathematical Special Functions] (http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2010/n3060.pdf) hence the awkward name.

This library also contains work towards follow-up published proposals for new special functions: [A proposal to add special mathematical functions according to the ISO/IEC 80000-2:2009 standard, Vincent Reverdy] (http://open-std.org/JTC1/SC22/WG21/docs/papers/2013/n3494.pdf)

[A Proposal to add Mathematical Functions for Statistics to the C++ Standard Library, Paul A Bristow] (http://open-std.org/JTC1/SC22/WG21/docs/papers/2004/n1668.pdf)

[A proposal to add sincos to the standard library, Paul Dreik] (http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/p0081r0.pdf)

This work began as a project to add math extensions to libstdc++. At this point I am abandoning that idea in favor of a general math library. Those still wishing to look at the libstdc++ support should check out the last_libstdc++_support tag. I may create a branch later.

This library has abandoned the 'f' and 'l' suffixed functioned of C++17. These were for C 'compatibility' which never came. They were a source of noise and bitrot. I briefly thought about retaining them for functions of integer argument that can't figure out a floating point type by ADL. But I chose not to do thet either.

This library and sub-libraries are experiencing a lot of churn right now but in the end I expect a set of smaller components that are more independent. It does seem to be in the nature of this work that some interdependencies creep in. In particular, the functions in these libraries are now in namespace emsr and in include/emsr.

The functions in IS 29124 have been accepted into C++17. See Section 2.9.5 Mathematical special functions [sf.cmath] in a recent draft.

In addition to the special functions in C++17, this library adds several extensions:

• Hypergeometric functions
• Carlson elliptic functions
• Jacobi elliptic functions, amplitude, and nome
• Polylogarithm functions
• Airy functions
• Hankel functions
• Statistical distribution functions

Some capabilities have been migrated into separate subprojects:

• Quadrature rules
• Polynomial classes and solvers
• Sequence trasnformations
• Continued fractions
• Chebyshev fitting
• Math constants
• Differentiation

I strive for type genericity. I want C++ numerics to follow the containers + algorithms by having numeric algorithms that will work for any type for which numericlimits, and the basic math functions are available. These functions have been tested with float, dou6ble, long double, and \_float128. Some have been tested with mpreal and efforts are underway to allow full multiprecision usage.

Documentation

Check out the API documentation.

Building

Because there are several submodules, you'll want to clone like this:

• git clone --recurse-submodules https://github.com/emsr/tr29124_test.git
  If you forget, as I often do, and do a normal clone then go into the main project directory and update the submodules:
• git submodule update --init --recursive