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What Are The CMath Mathematical Special Functions in Modern C++?

What Are The CMath Mathematical Special Functions in Modern C++

In C++11 and C++14, we were able to use this math.h library in C++ applications. After the C++17 standard, this library modernized math operations with the cmath library. Functions are declared in <cmath> header. For compatibility reasons the <math.h> is an optional alternative to support older code. In this post, we list most of these mathematical functions declared in the <cmath> header of modern C++.

What is cmath mathematical functions library in C++?

The CMath Mathematical Special Functions Header <cmath> defines mathematical functions and symbols in the std namespace. It includes the previous math functions. It may also define them in the global namespace. You have to add a std namespace using namespace std; or you should use the std:: prefix for each math function.

Some of the mathematical special functions are added to the C++17 cmath library header by the contents of the former international standard ISO/IEC 29124:2010 and math.h functions added too. These are only available in namespace std. If you do not use namespace you should add std:: prefix to use these modern math functions.

In general, they are mostly double functions and can be slower, but they have more accurate results. For example sin() uses double variables, sinf() uses a float variable (same as C++11, faster, less accurate), while sinl() is used with long double variables (same as C++11, also slower, but more accurate).

Here is a simple C++ example using the sin function.

What are the CMath mathematical special functions in modern C++ 17?

There are many new modern mathematical special functions in the C++17 cmath header. Such as functions for associated Laguerre polynomials, elliptic integral of the first kind functions, Cylindrical Bessel functions (of the first kind), Cylindrical Neumann functions, Exponential integral functions, Hermite polynomials functions, Legendre polynomials functions, Laguerre polynomials, Riemann zeta function, and some spherical functions. Here is a list of the CMath special functions.

Descriptiondouble floatlong double
Associated Laguerre polynomialsassoc_laguerreassoc_laguerrefassoc_laguerrel
Associated Legendre polynomialsassoc_legendreassoc_legendrefassoc_legendrel
Beta functionbetabetafbetal
Elliptic integral of the first kind (complete)comp_ellint_1comp_ellint_1fcomp_ellint_1l
Elliptic integral of the second kind (complete)comp_ellint_2comp_ellint_2fcomp_ellint_1l
Elliptic integral of the third kind (complete)comp_ellint_3comp_ellint_3fcomp_ellint_1l
Regular modified cylindrical Bessel functionscyl_bessel_icyl_bessel_ifcyl_bessel_il
Cylindrical Bessel functions (of the first kind)cyl_bessel_jcyl_bessel_jfcyl_bessel_jl
Irregular modified cylindrical Bessel functionscyl_bessel_kcyl_bessel_kfcyl_bessel_kl
Cylindrical Neumann functionscyl_neumanncyl_neumannfcyl_neumannl
Elliptic integral of the first kind (incomplete) ellint_1ellint_1fellint_1l
Elliptic integral of the second kind (incomplete) ellint_2ellint_2fellint_2l
Elliptic integral of the third kind (incomplete) ellint_3ellint_3fellint_3l
Exponential integralexpintexpintexpint
Hermite polynomialshermitehermitefhermitel
Legendre polynomialslegendrelegendreflegendrel
Laguerre polynomialslaguerrelaguerreflaguerrel
Riemann zeta functionriemann_zetariemann_zetafriemann_zetal
spherical associated Legendre functions sph_legendresph_legendrefsph_legendrel
spherical Bessel functions (of the first kind)sph_besselsph_besselfsph_bessell
spherical Neumann functionssph_neumannsph_neumannfsph_neumannl

Note that, by the C++20 standard, only default names of math functions are used. For example, the laguerre() is used for the float, double and long double versions.

For more details about changes in C++17 standard, please see this https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0226r1.pdf

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About author

Dr. Yilmaz Yoru has 35+ years of coding with more than 30+ programming languages, mostly C++ on Windows, Android, Mac-OS, iOS, Linux, and some other operating systems. He graduated and received his MSc and PhD degrees from the Department of Mechanical Engineering of Eskisehir Osmangazi University. He is the founder and CEO of ESENJA LLC Company. His interests are Programming, Thermodynamics, Fluid Mechanics, Artificial Intelligence, 2D & 3D Designs, and high-end innovations.
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