Mathematical constants

 

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Mathematical constants

 

Constants (since C++20)

Defined in header <numbers>
Defined in namespace std::numbers
e_v	the mathematical constant e (variable template)
log2e_v	\(\log_{2}e\)log2e (variable template)
log10e_v	\(\log_{10}e\)log10e (variable template)
pi_v	\(\pi\)π (variable template)
inv_pi_v	\(\frac1\pi\) 1 π (variable template)
inv_sqrtpi_v	\(\frac1{\sqrt\pi}\) 1 √π (variable template)
ln2_v	\(\ln{2}\)ln 2 (variable template)
ln10_v	\(\ln{10}\)ln 10 (variable template)
sqrt2_v	\(\sqrt2\)√2 (variable template)
sqrt3_v	\(\sqrt3\)√3 (variable template)
inv_sqrt3_v	\(\frac1{\sqrt3}\) 1 √3 (variable template)
egamma_v	the Euler–Mascheroni constant (variable template)
phi_v	the golden ratio Φ constant (\(\frac{1+\sqrt5}2\) 1 + √5 2 ) (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)

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 and long double).

A program may partially or explicitly specialize a mathematical constant variable template provided that the specialization depends on a program-defined type.

Example

Run this code

#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';
}

Possible output:

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