std::comp_ellint_1, std::comp_ellint_1f, std::comp_ellint_1l
Header: <cmath>
1-3) Computes the complete elliptic integral of the first kind of k.The library provides overloads of std::comp_ellint_1 for all cv-unqualified floating-point types as the type of the parameter k.(since C++23)
# Declarations
double comp_ellint_1 ( double k );
float comp_ellint_1 ( float k );
long double comp_ellint_1 ( long double k );
(since C++17) (until C++23)
/* floating-point-type */ comp_ellint_1( /* floating-point-type */ k );
(since C++23)
float comp_ellint_1f( float k );
(since C++17)
long double comp_ellint_1l( long double k );
(since C++17)
Additional overloads
template< class Integer >
double comp_ellint_1 ( Integer k );
(since C++17)
# Parameters
k: elliptic modulus or eccentricity (a floating-point or integer value)
# Return value
If no errors occur, value of the complete elliptic integral of the first kind of k, that is std::ellint_1(k, π/2), is returned.
# Notes
Implementations that do not support C++17, but support ISO 29124:2010, provide this function if STDCPP_MATH_SPEC_FUNCS is defined by the implementation to a value at least 201003L and if the user defines STDCPP_WANT_MATH_SPEC_FUNCS before including any standard library headers.
Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header tr1/cmath and namespace std::tr1.
An implementation of this function is also available in boost.math.
The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::comp_ellint_1(num) has the same effect as std::comp_ellint_1(static_cast
# Example
#include <cmath>
#include <iostream>
#include <numbers>
int main()
{
constexpr double π{std::numbers::pi};
std::cout << "K(0) ≈ " << std::comp_ellint_1(0) << '\n'
<< "π/2 ≈ " << π / 2 << '\n'
<< "K(0.5) ≈ " << std::comp_ellint_1(0.5) << '\n'
<< "F(0.5, π/2) ≈ " << std::ellint_1(0.5, π / 2) << '\n'
<< "The period of a pendulum length 1m at 10° initial angle ≈ "
<< 4 * std::sqrt(1 / 9.80665) * std::comp_ellint_1(std::sin(π / 18 / 2))
<< "s,\n" "whereas the linear approximation gives ≈ "
<< 2 * π * std::sqrt(1 / 9.80665) << '\n';
}