Mathematical constants
From cppreference.net
目录 |
常量 (C++20 起)
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定义于头文件
<numbers>
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定义于命名空间
std::numbers
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e_v
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数学常数
e
(变量模板) |
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log2e_v
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log
2
e
(变量模板) |
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log10e_v
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log
10
e
(变量模板) |
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pi_v
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数学常数
π
(变量模板) |
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inv_pi_v
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(变量模板) |
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inv_sqrtpi_v
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(变量模板) |
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ln2_v
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ln 2
(变量模板) |
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ln10_v
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ln 10
(变量模板) |
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sqrt2_v
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√
2
(变量模板) |
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sqrt3_v
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√
3
(变量模板) |
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inv_sqrt3_v
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(变量模板) |
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egamma_v
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欧拉-马斯刻若尼常数 γ
(变量模板) |
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phi_v
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黄金比例 Φ
(
(变量模板) |
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inline constexpr double
e
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e_v
<
double
>
(常量) |
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inline constexpr double
log2e
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log2e_v
<
double
>
(常量) |
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inline constexpr double
log10e
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log10e_v
<
double
>
(常量) |
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inline constexpr double
pi
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pi_v
<
double
>
(常量) |
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inline constexpr double
inv_pi
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inv_pi_v
<
double
>
(常量) |
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inline constexpr double
inv_sqrtpi
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inv_sqrtpi_v
<
double
>
(常量) |
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inline constexpr double
ln2
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ln2_v
<
double
>
(常量) |
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inline constexpr double
ln10
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ln10_v
<
double
>
(常量) |
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inline constexpr double
sqrt2
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sqrt2_v
<
double
>
(常量) |
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inline constexpr double
sqrt3
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sqrt3_v
<
double
>
(常量) |
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inline constexpr double
inv_sqrt3
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inv_sqrt3_v
<
double
>
(常量) |
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inline constexpr double
egamma
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egamma_v
<
double
>
(常量) |
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inline constexpr double
phi
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phi_v
<
double
>
(常量) |
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注释
实例化数学常量变量模板主模板的程序是病式的。
标准库为所有浮点类型(即 float 、 double 、 long double ,以及 固定宽度浮点类型 (C++23 起) )特化了数学常量变量模板。
程序可以部分或显式特化数学常量变量模板,前提是该特化依赖于 程序定义类型 。
| 功能测试 宏 | 值 | 标准 | 功能 |
|---|---|---|---|
__cpp_lib_math_constants
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201907L
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(C++20) | 数学常量 |
示例
运行此代码
#include <cmath> #include <iomanip> #include <iostream> #include <limits> #include <numbers> #include <string_view> auto egamma_aprox(const unsigned iterations) { long double s{}; for (unsigned m{2}; m != iterations; ++m) if (const long double t{std::riemann_zetal(m) / m}; m % 2) s -= t; else s += t; return s; }; int main() { using namespace std::numbers; using namespace std::string_view_literals; const auto x = std::sqrt(inv_pi) / inv_sqrtpi + std::ceil(std::exp2(log2e)) + sqrt3 * inv_sqrt3 + std::exp(0); const auto 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'; constexpr auto 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<long double>::digits10 + 1) << egamma_v<long double> << '\n' << "γ with " << γ.length() - 1 << " digits precision = " << γ << '\n'; }
可能的输出:
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
参见
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(C++11)
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表示精确有理分数
(类模板) |