GCE-Math (Generalized Constant Expression Math) is a templated C++ library enabling compile-time computation of mathematical functions.
Features:
- The library is written in C++11
constexprformat, and is C++11/14/17/20 compatible. - Continued fraction expansions 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
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
- basic:
- 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
- factorials and the binomial coefficient:
Full documentation is available online:
A PDF version of the documentation is available here.
GCE-Math is a header-only library and does not require any additional libraries or utilities (beyond a C++11 compatible compiler). Simply add the header files to your project using:
#include "gcem.hpp"
You can install GCE-Math using the Conda package manager.
conda install -c conda-forge gcemYou can also install the library from source using CMake.
# clone gcem from GitHub
git clone https://github.com/kthohr/gcem ./gcem
# make a build directory
cd ./gcem
mkdir build
cd build
# generate Makefiles and install
cmake .. -DCMAKE_INSTALL_PREFIX=/gcem/install/location
make installFor example, /gcem/install/location could be /usr/local/.
There are two ways to build the test suite. On Unix-alike systems, a Makefile is available under tests/.
cd ./gcem/tests
make
./run_testsWith CMake, the option GCEM_BUILD_TESTS=1 generates the necessary Makefiles to build the test suite.
cd ./gcem
mkdir build
cd build
cmake ../ -DGCEM_BUILD_TESTS=1 -DCMAKE_INSTALL_PREFIX=/gcem/install/location
make gcem_tests
cd tests
./exp.testYou can test the library online using an interactive Jupyter notebook:
GCE-Math functions are written as C++ templates with constexpr specifiers, the format of which might appear confusing to users unfamiliar with template-based programming.
For example, the Gaussian error function (erf) is defined as:
template<typename T>
constexpr
retu
8073
rn_t<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 integral 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.
To calculate 10!:
#include "gcem.hpp"
int main()
{
constexpr int x = 10;
constexpr int res = gcem::factorial(x);
return 0;
}Inspecting the assembly code generated by Clang 7.0.0:
push rbp
mov rbp, rsp
xor eax, eax
mov dword ptr [rbp - 4], 0
mov dword ptr [rbp - 8], 10
mov dword ptr [rbp - 12], 3628800
pop rbp
retWe see that a function call has been replaced by a numeric value (10! = 3628800).
Similarly, to compute the log Gamma function at a point:
#include "gcem.hpp"
int main()
{
constexpr long double x = 1.5;
constexpr long double res = gcem::lgamma(x);
return 0;
}Assembly code:
.LCPI0_0:
.long 1069547520 # float 1.5
.LCPI0_1:
.quad -622431863250842976 # x86_fp80 -0.120782237635245222719
.short 49147
.zero 6
main: # @main
push rbp
mov rbp, rsp
xor eax, eax
mov dword ptr [rbp - 4], 0
fld dword ptr [rip + .LCPI0_0]
fstp tbyte ptr [rbp - 32]
fld tbyte ptr [rip + .LCPI0_1]
fstp tbyte ptr [rbp - 48]
pop rbp
ret- StatsLib is built on GCEM's compile-time functionality.