jacobi_zeta

eve::jacobi_zeta = functor<jacobi_zeta_t>

inlineconstexpr

Header file

#include <eve/module/elliptic.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto jacobi_zeta(floating_value auto u, floating_value auto x)                  noexcept; // 1
 
   // Lanes masking
   constexpr auto jacobi_zeta[conditional_expr auto c](/*any of the above overloads*/)       noexcept; // 2
   constexpr auto jacobi_zeta[logical_value autolm](/*any of the above overloads*/)          noexcept; // 2
}

Parameters

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

Return value

1. return the jacobi zeta value.
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";
 
   std::cout << "-> jacobi_zeta(wphi, wf)               = " << eve::jacobi_zeta(wphi, wf) << "\n";
   std::cout << "-> jacobi_zeta[ignore_last(2)](wphi,wf)= " << eve::jacobi_zeta[eve::ignore_last(2)](wphi, wf) << "\n";
   std::cout << "-> jacobi_zeta[wf != 1.0](wphi,wf)     = " << eve::jacobi_zeta[wf != -1.0f](wphi, wf) << "\n";
   std::cout << "-> jacobi_zeta(pio_2[lower], wf)       = " << eve::jacobi_zeta(eve::pio_2[eve::lower](eve::as(wphi)), wf) << '\n';
   std::cout << "-> jacobi_zeta(pio_2[upper], wf)       = " << eve::jacobi_zeta(eve::pio_2[eve::upper](eve::as(wphi)), wf) << '\n';
}