GCE-Math
GCE-Math (Generalized Constant Expression Math) is a templated C++ library for compile-time computation of mathematical functions.
- The library is written in C++11
constexpr
format, and is C++11/14/17 compatible. - Continued fraction and series expansions are implemented using recursive templates.
- The
gcem::
syntax is identical to the C++ standard library (std::
). - Tested and accurate to machine precision against the C++ standard library.
- Released under a permissive, non-GPL license.
Status
The library is actively maintained, and is still being extended. A list of features includes:
- basic C++ standard library functions:
abs
,exp
,log
,max
,min
,pow
,sqrt
- trigonometric functions:
- basic:
cos
,sin
,tan
- inverse:
acos
,asin
,atan
- hyperbolic (area) functions:
cosh
,sinh
,tanh
,acosh
,asinh
,atanh
- basic:
- special functions:
- factorials and the binomial coefficient:
factorial
,binomial_coef
- beta and gamma functions:
beta
,lbeta
,lgamma
,tgamma
- 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:
Syntax
GCE-Math functions are written as C++ templates with constexpr
specifiers, the format of which might be confusing to users unfamiliar with template-based programming. For example, the Gaussian error function (erf
) is defined as:
template<typename T>
constexpr
return_t<T>
erf(const T x);
where a set of internal templated constexpr
functions will implement a continued fraction expansion to return a value of type return_t<T>
. This 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.
Installation
GCE-Math is a header-only library and does not require any additional libraries (beyond a C++11 compatible compiler). Simply include the gcem header files with your project.
Examples
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:
_main: ## @main
.cfi_startproc
## BB#0:
push rbp
Lcfi0:
.cfi_def_cfa_offset 16
Lcfi1:
.cfi_offset rbp, -16
mov rbp, rsp
Lcfi2:
.cfi_def_cfa_register rbp
xor eax, eax
mov dword ptr [rbp - 4], 0
mov dword ptr [rbp - 8], 10
mov dword ptr [rbp - 12], 3628800
pop rbp
ret
.cfi_endproc
We 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
.section __TEXT,__literal16,16byte_literals
.p2align 4
LCPI0_1:
.quad -622431863250851168 ## x86_fp80 -0.120782237635245167208
.short 49147
.space 6
.section __TEXT,__text,regular,pure_instructions
.globl _main
.p2align 4, 0x90
_main: ## @main
.cfi_startproc
## BB#0:
push rbp
Lcfi0:
.cfi_def_cfa_offset 16
Lcfi1:
.cfi_offset rbp, -16
mov rbp, rsp
Lcfi2:
.cfi_def_cfa_register rbp
xor eax, eax
mov dword ptr [rbp - 4], 0
fld dword ptr [rip + LCPI0_0]
fstp xword ptr [rbp - 32]
fld xword ptr [rip + LCPI0_1]
fstp xword ptr [rbp - 48]
pop rbp
ret
.cfi_endproc
To build the full test suite:
# clone gcem from GitHub
git clone -b master --single-branch https://github.com/kthohr/gcem ./gcem
# compile tests
cd ./gcem/tests
make
./run_tests
Related libraries
For a library built on the GCEM compile-time functionality, see StatsLib.
Author
Keith O'Hara
License
Apache Version 2