ellint_rd

auto eve::ellint_rd = functor<ellint_rd_t>

inlineconstexpr

Header file

#include <eve/module/elliptic.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto ellint_rd(floating_value auto x, floating_value auto y, floating_value auto z)   noexcept; // 1
 
   // Lanes masking
   constexpr auto ellint_rd[conditional_expr auto c](floating_value auto x, floating_value auto y,
                                                     floating_value auto z)                        noexcept; // 2
   constexpr auto ellint_rd[logical_value auto m](floating_value auto x, floating_value auto y,
                                                  floating_value auto z)                           noexcept; // 2

Parameters

• x, y: floating values. x and y must be strictly positive and y non zero. In any other case, the result is NaN.
• z: strictly positive floating values. In any other case, the result is NaN.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. the value of \( \mathbf{R}_\mathbf{D}(x, y) = \frac32 \int_{0}^{\infty} \scriptstyle[(t+x)(t+y)]^{-1/2} (t+z)^{-3/2}\scriptstyle\;\mathrm{d}t\) is returned.
2. The operation is performed conditionnaly

External references

• DLMF: Elliptic Integrals
• Wolfram MathWorld: Elliptic Integral

Example

// revision 1
#include <eve/module/elliptic.hpp>
#include <iostream>
 
eve::wide pf{1.0f, 0.0f, 1.5f, 3.0f};
eve::wide qf{1.0f, 4.0f, 0.2f, 0.5f};
 
int main()
{
  std::cout << "<- pf = " << pf << "\n";
  std::cout << "<- qf = " << qf << "\n";
 
  std::cout << "-> ellint_rc(pf, qf)                = " << eve::ellint_rc(pf, qf) << "\n";
  std::cout << "-> ellint_rc[ignore_last(2)](pf, qf)= " << eve::ellint_rc[eve::ignore_last(2)](pf, qf) << "\n";
  std::cout << "-> ellint_rc[qf != 4.0f](pf, qf)    = " << eve::ellint_rc[qf != 4.0f](pf, qf) << "\n";
}