数学常数

来自cppreference.com
< cpp‎ | numeric

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
2
e

(变量模板)
log10e_v
log
10
e

(变量模板)
pi_v
π
(变量模板)
inv_pi_v
1
π

(变量模板)
inv_sqrtpi_v
1
π

(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
1
3

(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 (
1 + 5
2
)
(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 floatdoublelong 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

#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