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About the Math Toolkit

This library is divided into several interconnected parts:

Floating Point Utilities

Utility functions for dealing with floating-point arithmetic, includes functions for floating point classification (fpclassify, isnan, isinf etc), sign manipulation, rounding, comparison, and computing the distance between floating point numbers.

Specific Width Floating-Point Types

A set of typedefs similar to those provided by <cstdint> but for floating-point types.

Mathematical Constants

A wide range of high-precision constants ranging from various multiples of π, fractions, through to Euler's constant etc.

These are of course usable from template code, or as non-templates with a simplified interface if that is more appropriate.

Statistical Distributions

Provides a reasonably comprehensive set of statistical distributions, upon which higher level statistical tests can be built.

The initial focus is on the central univariate distributions. Both continuous (like normal & Fisher) and discrete (like binomial & Poisson) distributions are provided.

A comprehensive tutorial is provided, along with a series of worked examples illustrating how the library is used to conduct statistical tests.

Mathematical Special Functions

Provides a small number of high quality special functions, initially these were concentrated on functions used in statistical applications along with those in the Technical Report on C++ Library Extensions.

The function families currently implemented are the gamma, beta & erf functions along with the incomplete gamma and beta functions (four variants of each) and all the possible inverses of these, plus digamma, various factorial functions, Bessel functions, elliptic integrals, sinus cardinals (along with their hyperbolic variants), inverse hyperbolic functions, Legendre/Laguerre/Hermite polynomials and various special power and logarithmic functions.

All the implementations are fully generic and support the use of arbitrary "real-number" types, including Boost.Multiprecision, although they are optimised for use with types with known-about significand (or mantissa) sizes: typically float, double or long double.

These functions also provide the basis of support for the TR1 special functions.

Root Finding and Function Minimisation

A comprehensive set of root finding algorithms over the real-line, both with and without derivative support.

Also function minimisation via Brent's Method.

Polynomials and Rational Functions

Tools for manipulating polynomials and for efficient evaluation of rationals or polynomials.


Function interpolation via Barycentric or cubic B_spline approximations. Smoothing.

Numerical Integration (Quadrature) and Differentiation

A reasonably comprehensive set of routines for integration (trapezoidal, Gauss-Legendre, Gauss-Kronrod and double-exponential) and differentiation. (See also automatic differentiation).

The integration routines are all usable for functions returning complex results - and as a result for contour integrals as well.

Quaternions and Octonions

Quaternions and Octonians as class templates similar to std::complex.

Automatic Differentiation

Autodiff is a header-only C++ library that facilitates the automaticdifferentiation (forward mode) of mathematical functions of single and multiple variables.