std::comp_ellint_2, std::comp_ellint_2f, std::comp_ellint_2l
Header: <cmath>
1-3) Computes the complete elliptic integral of the second kind of k.The library provides overloads of std::comp_ellint_2 for all cv-unqualified floating-point types as the type of the parameter k.(since C++23)
# Declarations
float comp_ellint_2 ( float k );
double comp_ellint_2 ( double k );
long double comp_ellint_2 ( long double k );
(since C++17) (until C++23)
/* floating-point-type */ comp_ellint_2( /* floating-point-type */ k );
(since C++23)
float comp_ellint_2f( float k );
(since C++17)
long double comp_ellint_2l( long double k );
(since C++17)
Additional overloads
template< class Integer >
double comp_ellint_2 ( 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 second kind of k, that is std::ellint_2(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 perimeter of an ellipse with eccentricity k and semimajor axis a equals 4aE(k), where E is std::comp_ellint_2. When eccentricity equals 0, the ellipse degenerates to a circle with radius a and the perimeter equals 2πa, so E(0) = π/2. When eccentricity equals 1, the ellipse degenerates to a line of length 2a, whose perimeter is 4a, so E(1) = 1.
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_2(num) has the same effect as std::comp_ellint_2(static_cast
# Example
#include <cmath>
#include <iostream>
#include <numbers>
int main()
{
constexpr double hpi = std::numbers::pi / 2.0;
std::cout << "E(0) = " << std::comp_ellint_2(0) << '\n'
<< "π/2 = " << hpi << '\n'
<< "E(1) = " << std::comp_ellint_2(1) << '\n'
<< "E(1, π/2) = " << std::ellint_2(1, hpi) << '\n';
}