jacobi_elliptic

auto eve::jacobi_elliptic = functor<jacobi_elliptic_t>

inlineconstexpr

Header file

#include <eve/module/elliptic.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto jacobi_elliptic(floating_value auto u, floating_value auto x)                  noexcept; // 1
 
   //Semantic modifiers
   constexpr auto jacobi_elliptic[modular](floating_value auto u, floating_value auto alpha)     noexcept; // 1
   constexpr auto jacobi_elliptic[eccentric(floating_value auto u, floating_value auto k)        noexcept; // 1
   constexpr auto jacobi_elliptic[threshold = tol](floating_value auto u, floating_value auto x) noexcept; // 1
 
   // Lanes masking
   constexpr auto jacobi_elliptic[conditional_expr auto c](/*any of the above overloads*/)       noexcept; // 2
   constexpr auto jacobi_elliptic[logical_value autolm](/*any of the above overloads*/)          noexcept; // 2
}

Parameters

• u: argument.
• m: amplitude parameter ( \(0\le m\le 1\)).
• c: Conditional expression masking the operation.
• l: Logical value masking the operation.

Return value

1. return a kumi::tuple containing sn``cn and dn values. Take care that the meaning of the second parameters depends on the option used (see note below).
2. The operation is performed conditionally

External references

• DLMF: Jacobian Elliptic
• Wolfram MathWorld: Jacobi Elliptic Functions
• Wikipedia: Jacobi elliptic functions

Example

// revision 1
#include <eve/module/elliptic.hpp>
#include <iostream>
 
eve::wide wf{1.0, 0.0, 0.75, 0.5};
eve::wide wphi{1.0, 1.0e-30, 0.5, 0.0};
 
int main(){
   std::cout << "<- wf   =                              " << wf << "\n";
   std::cout << "<- wphi =                              " << wphi << "\n";
   auto [sn, cn, dn] = eve::jacobi_elliptic(wphi, wf);
   std::cout << "-> sn =                                " << sn << std::endl;
   std::cout << "-> cn =                                " << cn << std::endl;
   std::cout << "-> dn =                                " << dn << std::endl;
   std::cout << "-> jacobi_elliptic(pio_2[lower], wf) = " << eve::jacobi_elliptic(eve::pio_2[eve::lower](eve::as(wphi)), wf) << '\n';
   std::cout << "-> jacobi_elliptic(pio_2[upper], wf) = " << eve::jacobi_elliptic(eve::pio_2[eve::upper](eve::as(wphi)), wf) << '\n';
}