E.V.E  0.1-beta

◆ ellint_rf

eve::ellint_rf = {}
inlineconstexpr

Callable object computing the Carlson's elliptic integral \(\frac12 \int_{0}^{\infty} \scriptstyle[(t+x)(t+y)(t+z)]^{-1/2}\scriptstyle\;\mathrm{d}t\).

Required header: #include <eve/function/ellint_rf.hpp>

Members Functions

Member Effect
operator() the ellint_rf operation
operator[] Construct a conditional version of current function object

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp} */ /** auto operator()( floating_real_value auto x */ /** , floating_real_value auto y) , floating_real_value auto zconst noexcept; ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Parameters

x, y, z: floating values.

This computes the Carlson's elliptic integral

\[ R_F(x, y, z) = \frac12 \int_{0}^{\infty} [(t+x)(t+y)(t+z)]^{-1/2} \mbox{d}t\]

as described in Carlson, Numerische Mathematik, vol 33, 1 (1979)

parameters must be non-negative and at most one zero or the result is nan.

Return value

Returns elementwise the Carlson's integral.

The result type is of the compatibility type of the three parameters.


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp} auto operator[]( conditional_expression auto cond ) const noexcept; ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Higher-order function generating a masked version of eve::ellint_rf

Parameters

cond : conditional expression

Return value

A Callable object so that the expression ellint_rf[cond](x, ...) is equivalent to if_else(cond,ellint_rf(x, ...),x)


Supported decorators

no decorators are supported

Example

See it live on Compiler Explorer

#include <eve/function/ellint_rf.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
wide_ft pf = {1.0f, 0.0f, 1.5f, 3.0f};
wide_ft qf = {1.0f, 4.0f, 0.2f, 0.5f};
wide_ft rf = {2.0f, 1.0f, 0.1f, 0.4f};
std::cout << "---- simd" << '\n'
<< "<- pf = " << pf << '\n'
<< "<- qf = " << qf << '\n'
<< "<- rf = " << rf << '\n'
<< "-> ellint_rf(pf, qf, rf) = " << eve::ellint_rf(pf, qf, rf) << '\n';
float xf = 3.0f;
float yf = 0.5f;
float zf = 1.0f;
std::cout << "---- scalar" << '\n'
<< "<- xf = " << xf << '\n'
<< "<- yf = " << yf << '\n'
<< "<- zf = " << zf << '\n'
<< "-> ellint_rf(xf, yf, zf) = " << eve::ellint_rf(xf, yf, zf) << '\n';
return 0;
}
constexpr callable_ellint_rf_ ellint_rf
Callable object computing the Carlson's elliptic integral .
Definition: ellint_rf.hpp:85
Wrapper for SIMD registers.
Definition: wide.hpp:65