/C++

# Mathematical constants

### Constants (since C++20)

Defined in header <numbers>
Defined in namespace std::numbers
e_v
the mathematical constant $$\small e$$e
(variable template)
log2e_v
$$\log_{2}e$$log
2
e
(variable template)
log10e_v
$$\log_{10}e$$log
10
e
(variable template)
pi_v
the mathematical constant $$\pi$$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 γ
(variable template)
phi_v
the golden ratio Φ ($$\frac{1+\sqrt5}2$$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.

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