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, long double , 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(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'; }
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) |
