jacobi_elliptic

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 sncn 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';
}