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Mathematical constants

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< cpp‎ | numeric
 
 
Numerics library
 
Mathematical constants
 

[edit] 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
\(\log_{2}e\)log2e
(variable template)
log10e_v
\(\log_{10}e\)log10e
(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)

[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) [edit]

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