ellint_rg

eve::ellint_rg = functor<ellint_rg_t>

inlineconstexpr

Header file

#include <eve/module/elliptic.hpp>

Callable Signatures

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

Parameters

• x, y, z: floating real arguments. All arguments must be non-negative or the result is nan.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. the value of the \(\mathbf{R}_\mathbf{G}\) Carlson elliptic integral: \(\frac1{4\pi} \int_{0}^{2\pi}\int_{0}^{\pi} \scriptstyle\sqrt{x\sin^2\theta\cos^2\phi +y\sin^2\theta\sin^2\phi +z\cos^2\theta} \scriptstyle\;\mathrm{d}\theta\;\mathrm{d}\phi\) 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};
 
int main()
{
  std::cout << "<- pf = " << pf << "\n";
  std::cout << "<- qf = " << qf << "\n";
  std::cout << "<- rf = " << rf << "\n";
 
  std::cout << "-> ellint_rg(pf, qf, rf)                = " << eve::ellint_rg(pf, qf, rf) << "\n";
  std::cout << "-> ellint_rg[ignore_last(2)](pf, qf, rf)= " << eve::ellint_rg[eve::ignore_last(2)](pf, qf, rf) << "\n";
  std::cout << "-> ellint_rg[qf != 4.0f](pf, qf, rf)    = " << eve::ellint_rg[qf != 4.0f](pf, qf, rf) << "\n";
}