std::comp_ellint_2, std::comp_ellint_2f, std::comp_ellint_2l - cppreference.com (original) (raw)
| Defined in header | ||
|---|---|---|
| (1) | ||
| 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) |
| Additional overloads | ||
| Defined in header | ||
| 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.
Contents
[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 #include #include int main() { constexpr double hpi = std:🔢: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'; }
Output:
E(0) = 1.5708 π/2 = 1.5708 E(1) = 1 E(1, π/2) = 1