std::comp_ellint_2, std::comp_ellint_2f, std::comp_ellint_2l

Defined in header <cmath>
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 );
(2) (since C++17)
long double comp_ellint_2l( long double k );
(3) (since C++17)
Defined in header <cmath>
template< class Integer >
double      comp_ellint_2 ( Integer k );
(A) (since C++17)
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)
A) Additional overloads are provided for all integer types, which are treated as double.


[edit] Parameters

k - elliptic modulus or eccentricity (a floating-point or integer value)

[edit] 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.

[edit] Error handling

Errors may be reported as specified in math_errhandling.

  • If the argument is NaN, NaN is returned and domain error is not reported.
  • If |k|>1, a domain error may occur.

[edit] 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<double>(num)).

[edit] 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';


E(0) = 1.5708
π/2 = 1.5708
E(1) = 1
E(1, π/2) = 1

[edit] See also

(incomplete) elliptic integral of the second kind
(function) [edit]

[edit] External links

Weisstein, Eric W. "Complete Elliptic Integral of the Second Kind." From MathWorld — A Wolfram Web Resource.