ellint_rj

auto eve::ellint_rj = functor<ellint_rj_t>

inlineconstexpr

Header file

#include <eve/module/elliptic.hpp>

Callable Signatures

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

Parameters

• x, y, z: floating real arguments. x, y and z must be non negative and at most one of them equal to 0. In any other case, the result is NaN.
• p: Non-zero floating real arguments. 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 the \(\mathbf{R}_\mathbf{J}\) Carlson elliptic integral: \( \frac32 \int_{0}^{\infty} \scriptstyle(t+p)^{-1}[(t+x)(t+y)(t+z)]^{-1/2}\;\mathrm{d}t\) 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};
eve::wide rf{2.0f, 1.0f, 0.1f, 0.4f};
eve::wide sf{0.19f, 0.5f, 0.87071f, 2.4f};
int main()
{
  std::cout << "<- pf = " << pf << "\n";
  std::cout << "<- qf = " << qf << "\n";
  std::cout << "<- rf = " << rf << "\n";
  std::cout << "<- sf = " << sf << "\n";
 
  std::cout << "-> ellint_rj(pf, qf, rf, sf)                = " << eve::ellint_rj(pf, qf, rf, sf) << "\n";
  std::cout << "-> ellint_rj[ignore_last(2)](pf, qf, rf, sf)= " << eve::ellint_rj[eve::ignore_last(2)](pf, qf, rf, sf) << "\n";
  std::cout << "-> ellint_rj[qf != 4.0f](pf, qf, rf, sf)    = " << eve::ellint_rj[qf != 4.0f](pf, qf, rf, sf) << "\n";
}