Mathematical constants
From cppreference.com
Constants (since C++20)
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Defined in header
<numbers>
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Defined in namespace
std::numbers
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e_v
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the mathematical constant
e
(variable template) |
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log2e_v
|
log
2
e
(variable template) |
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log10e_v
|
log
10
e
(variable template) |
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pi_v
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the mathematical constant
π
(variable template) |
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inv_pi_v
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(variable template) |
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inv_sqrtpi_v
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(variable template) |
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ln2_v
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ln 2
(variable template) |
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ln10_v
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ln 10
(variable template) |
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sqrt2_v
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√
2
(variable template) |
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sqrt3_v
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√
3
(variable template) |
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inv_sqrt3_v
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(variable template) |
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egamma_v
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the Euler–Mascheroni constant γ
(variable template) |
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phi_v
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the golden ratio Φ
(
(variable template) |
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inline constexpr double
e
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e_v
<
double
>
(constant) |
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inline constexpr double
log2e
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log2e_v
<
double
>
(constant) |
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inline constexpr double
log10e
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log10e_v
<
double
>
(constant) |
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inline constexpr double
pi
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pi_v
<
double
>
(constant) |
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inline constexpr double
inv_pi
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inv_pi_v
<
double
>
(constant) |
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inline constexpr double
inv_sqrtpi
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inv_sqrtpi_v
<
double
>
(constant) |
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inline constexpr double
ln2
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ln2_v
<
double
>
(constant) |
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inline constexpr double
ln10
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ln10_v
<
double
>
(constant) |
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inline constexpr double
sqrt2
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sqrt2_v
<
double
>
(constant) |
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inline constexpr double
sqrt3
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sqrt3_v
<
double
>
(constant) |
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inline constexpr double
inv_sqrt3
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inv_sqrt3_v
<
double
>
(constant) |
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inline constexpr double
egamma
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egamma_v
<
double
>
(constant) |
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inline constexpr double
phi
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phi_v
<
double
>
(constant) |
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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 | Feature |
|---|---|---|---|
__cpp_lib_math_constants
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201907L | (c++20) | Mathematical constants |
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 = 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::numbers; 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'; 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
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(C++11)
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represents exact rational fraction
(class template) |