faddeeva

kyosu::faddeeva = eve::functor<faddeeva_t>

inlineconstexpr

Callable object computing \(e^{-z^2}\mathrm{erfc}(-iz)\) the scaled complex complementary error function.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<kyosu::concepts::cayley_dickson T> constexpr complexify_t<T> faddeeva(T z) noexcept;
}

Parameters

• z : Value to process.

Return value

Returns the Faddeeva function \( w(z) = e^{-z^2} \left(1+\frac{2i}{\sqrt\pi}\int_0^ze^{t^2}\mbox{d}t \right)\).

External references

• DLMF: Error Functions
• Wikipedia: Faddeeva function

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
 
 using wide_ft = eve::wide <float, eve::fixed<4>>;
  wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
  wide_ft imf1 = { 2.0f , -1.0,  -5.0, 0.0};
  wide_ft ref2 = { 0.0, 1.0, 2.0, 3.0};
  auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
 
  std::cout
    << "---- simd" << std::endl
    << "<- zc                = " << zc << std::endl
    << "-> faddeeva(zc)      = " << kyosu::faddeeva(zc)<< std::endl
    << "-> faddeeva(ref2)    = " << kyosu::faddeeva(ref2) << std::endl;
 
  return 0;
}