Mathematical constants
From cppreference.com
Contents |
[edit]Constants (since C++20)
Defined in header <numbers> | |||
Defined in namespace std::numbers | |||
e_v | the mathematical constant e (variable template) | ||
log2e_v | log2e (variable template) | ||
log10e_v | log10e (variable template) | ||
pi_v | the mathematical constant π (variable template) | ||
inv_pi_v |
(variable template) | ||
inv_sqrtpi_v |
(variable template) | ||
ln2_v | ln 2 (variable template) | ||
ln10_v | ln 10 (variable template) | ||
sqrt2_v | √2 (variable template) | ||
sqrt3_v | √3 (variable template) | ||
inv_sqrt3_v |
(variable template) | ||
egamma_v | the Euler–Mascheroni constant γ (variable template) | ||
phi_v | the golden ratio Φ (
(variable template) | ||
inline constexpr double e | e_v<double> (constant) | ||
inline constexpr double log2e | log2e_v<double> (constant) | ||
inline constexpr double log10e | log10e_v<double> (constant) | ||
inline constexpr double pi | pi_v<double> (constant) | ||
inline constexpr double inv_pi | inv_pi_v<double> (constant) | ||
inline constexpr double inv_sqrtpi | inv_sqrtpi_v<double> (constant) | ||
inline constexpr double ln2 | ln2_v<double> (constant) | ||
inline constexpr double ln10 | ln10_v<double> (constant) | ||
inline constexpr double sqrt2 | sqrt2_v<double> (constant) | ||
inline constexpr double sqrt3 | sqrt3_v<double> (constant) | ||
inline constexpr double inv_sqrt3 | inv_sqrt3_v<double> (constant) | ||
inline constexpr double egamma | egamma_v<double> (constant) | ||
inline constexpr double phi | phi_v<double> (constant) | ||
[edit]Notes
A program that instantiates a primary template of a mathematical constant variable template is ill-formed.
The standard library specializes mathematical constant variable templates for all floating-point types (i.e. float, double, longdouble, and fixed width floating-point types(since C++23)).
A program may partially or explicitly specialize a mathematical constant variable template provided that the specialization depends on a program-defined type.
| Feature-test macro | Value | Std | Feature |
|---|---|---|---|
__cpp_lib_math_constants | 201907L | (C++20) | Mathematical constants |
[edit]Example
Run this code
#include <cmath>#include <iomanip>#include <iostream>#include <limits>#include <numbers>#include <string_view> auto egamma_aprox(constunsigned iterations){longdouble s{};for(unsigned m{2}; m != iterations;++m)if(constlongdouble t{std::riemann_zetal(m)/ m}; m %2) s -= t;else s += t;return s;}; int main(){usingnamespace std::numbers;usingnamespace std::string_view_literals; constauto x =std::sqrt(inv_pi)/ inv_sqrtpi +std::ceil(std::exp2(log2e))+ sqrt3 * inv_sqrt3 +std::exp(0);constauto v =(phi * phi - phi)+1/std::log2(sqrt2)+ log10e * ln10 +std::pow(e, ln2)-std::cos(pi);std::cout<<"The answer is "<< x * v <<'\n'; constexprauto γ{"0.577215664901532860606512090082402"sv};std::cout<<"γ as 10⁶ sums of ±ζ(m)/m = "<< egamma_aprox(1'000'000)<<'\n'<<"γ as egamma_v<float> = "<<std::setprecision(std::numeric_limits<float>::digits10+1)<< egamma_v<float><<'\n'<<"γ as egamma_v<double> = "<<std::setprecision(std::numeric_limits<double>::digits10+1)<< egamma_v<double><<'\n'<<"γ as egamma_v<long double> = "<<std::setprecision(std::numeric_limits<longdouble>::digits10+1)<< egamma_v<longdouble><<'\n'<<"γ with "<< γ.length()-1<<" digits precision = "<< γ <<'\n';}
Possible output:
The answer is 42 γ as 10⁶ sums of ±ζ(m)/m = 0.577215 γ as egamma_v<float> = 0.5772157 γ as egamma_v<double> = 0.5772156649015329 γ as egamma_v<long double> = 0.5772156649015328606 γ with 34 digits precision = 0.577215664901532860606512090082402
[edit]See also
(C++11) | represents exact rational fraction (class template) |
