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 2e (variable template) |
| log10e_v | \(\log_{10}e\)log 10e (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) |
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 |
#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
|
(C++11) | represents exact rational fraction (class template) |
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