Mathematical constants

< cpp‎ | numeric

Constants (since C++20)

Defined in header <numbers>
Defined in namespace std::numbers
e_v
 the mathematical constant e
(variable template)
log2e_v
 log
2e
(variable template)
log10e_v
 log
10e
(variable template)
pi_v
 the mathematical constant π
(variable template)
inv_pi_v
1
π

(variable template)
inv_sqrtpi_v
1
√π

(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
1
√3

(variable template)
egamma_v
 the Euler–Mascheroni constant γ
(variable template)
phi_v
 the golden ratio Φ (
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.

Feature-test macro Value Std Comment
__cpp_lib_math_constants 201907L (c++20) Mathematical constants

Example

#include <cmath>
#include <iomanip>
#include <iostream>
#include <limits>
#include <numbers>
#include <string_view>
 
auto egamma_aprox(const unsigned iterations)
{
    long double s = 0;
    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;
    using namespace std::numbers;
 
    const auto 
        x = sqrt(inv_pi)/inv_sqrtpi + ceil(exp2(log2e)) + sqrt3*inv_sqrt3 + exp(0),
        v = (phi*phi - phi) + 1/log2(sqrt2) + log10e*ln10 + pow(e, ln2) - cos(pi);
 
    std::cout << "The answer is " << x*v << '\n';
 
    using namespace std::string_view_literals;
    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

See also

(C++11)
 represents exact rational fraction
(class template)