GCE-Math (Generalized Constant Expression Math) is a templated C++ library enabling compile-time computation of mathematical functions.

  • The library is written in C++11 constexpr format, and is C++11/14/17/20 compatible.

  • Continued fraction and series expansions are implemented using recursive templates.

  • The gcem:: syntax is identical to that of the C++ standard library (std::).

  • Tested and accurate to floating-point precision against the C++ standard library.

  • Released under a permissive, non-GPL license.

Author: Keith O’Hara

License: Apache 2.0


The library is actively maintained, and is still being extended. A list of features includes:

  • basic library functions:
    • abs, max, min, pow, sqrt, inv_sqrt

    • ceil, floor, round, trunc, fmod,

    • exp, expm1, log, log1p, log2, log10 and more

  • trigonometric functions:
    • basic: cos, sin, tan

    • inverse: acos, asin, atan, atan2

  • hyperbolic (area) functions:
    • cosh, sinh, tanh, acosh, asinh, atanh

  • algorithms:
    • gcd, lcm

  • special functions:
    • factorials and the binomial coefficient: factorial, binomial_coef

    • beta, gamma, and multivariate gamma functions: beta, lbeta, lgamma, tgamma, lmgamma

    • the Gaussian error function and inverse error function: erf, erf_inv

    • (regularized) incomplete beta and incomplete gamma functions: incomplete_beta, incomplete_gamma

    • inverse incomplete beta and incomplete gamma functions: incomplete_beta_inv, incomplete_gamma_inv

General Syntax

GCE-Math functions are written as C++ templates with constexpr specifiers. For example, the Gaussian error function (erf) is defined as:

template<typename T>
erf(const T x) noexcept;

A set of internal templated constexpr functions will implement a continued fraction expansion and return a value of type return_t<T>. The output type (’return_t<T>’) is generally determined by the input type, e.g., int, float, double, long double, etc; when T is an intergral type, the output will be upgraded to return_t<T> = double, otherwise return_t<T> = T. For types not covered by std::is_integral, recasts should be used.