数学常数
来自cppreference.com
常数 (C++20 起)
定义于头文件
<numbers> | |||
定义于命名空间
std::numbers | |||
e_v |
数学常数 e (变量模板) | ||
log2e_v |
log 2e (变量模板) | ||
log10e_v |
log 10e (变量模板) | ||
pi_v |
π (变量模板) | ||
inv_pi_v |
(变量模板) | ||
inv_sqrtpi_v |
(变量模板) | ||
ln2_v |
ln 2 (变量模板) | ||
ln10_v |
ln 10 (变量模板) | ||
sqrt2_v |
√2 (变量模板) | ||
sqrt3_v |
√3 (变量模板) | ||
inv_sqrt3_v |
(变量模板) | ||
egamma_v |
欧拉-马歇罗尼常数 (变量模板) | ||
phi_v |
黄金比 Φ 常数 (
(变量模板) | ||
inline constexpr double e |
e_v<double> (常量) | ||
inline constexpr double log2e |
log2e_v<double> (常量) | ||
inline constexpr double log10e |
log10e_v<double> (常量) | ||
inline constexpr double pi |
pi_v<double> (常量) | ||
inline constexpr double inv_pi |
inv_pi_v<double> (常量) | ||
inline constexpr double inv_sqrtpi |
inv_sqrtpi_v<double> (常量) | ||
inline constexpr double ln2 |
ln2_v<double> (常量) | ||
inline constexpr double ln10 |
ln10_v<double> (常量) | ||
inline constexpr double sqrt2 |
sqrt2_v<double> (常量) | ||
inline constexpr double sqrt3 |
sqrt3_v<double> (常量) | ||
inline constexpr double inv_sqrt3 |
inv_sqrt3_v<double> (常量) | ||
inline constexpr double egamma |
egamma_v<double> (常量) | ||
inline constexpr double phi |
phi_v<double> (常量) |
注解
实例化数学常数变量模板的初等模板的程序为谬构。
标准库对所有浮点类型(即 float 、 double 与 long double )特化数学常数变量模板。
程序可以部分或显式特化数学常数变量模板,只要该特化依赖程序定义的类型。
示例
运行此代码
#include <cmath> #include <iomanip> #include <iostream> #include <limits> #include <numbers> #include <string_view> int main() { using namespace std::numbers; std::cout << std::pow(e, ln2) / 2 << ' ' << std::pow(std::cosh(pi), 2) - std::pow(std::sinh(pi), 2) << ' ' << std::sqrt(pi) * inv_sqrtpi << ' ' << std::pow(sqrt2 * sqrt3, 2) / 6 << ' ' << sqrt3 * inv_sqrt3 << ' ' << log2e * ln2 << ' ' << log10e * ln10 << ' ' << pi * inv_pi << ' ' << phi * phi - phi << '\n'; auto egamma_aprox = [] { long double s = 0, m = 2.0; for (unsigned c = 2; c != 1'000'000; ++c, ++m) { const long double t = std::riemann_zeta(m) / m; (c & 1) == 0 ? s += t : s -= t; } return s; }; std::cout << std::fixed << (egamma_v<long double> - egamma_aprox()) << '\n'; constexpr std::string_view γ {"0.577215664901532860606512090082402"}; std::cout << "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<long double>::digits10 + 1) << egamma_v<long double> << '\n' << "γ with " << γ.length() - 1 << " digits precision = " << γ << '\n'; }
可能的输出:
1 1 1 1 1 1 1 1 1 0.000001 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