nthroot

auto kyosu::nthroot = eve::functor<nthroot_t>

inlineconstexpr

Computes the the kth nth root of the argument.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
  //  regular call
  constexpr auto nthroot(complex_like z, auto n, auto k)             noexcept;
  constexpr auto nthroot(complex_like z, auto n)                     noexcept;
 
  // semantic modifyers
  constexpr auto nthroot[real_only](/*any previous overload*/)       noexcept;
}

Parameters

• z: Value to process. floating or complex.
• n: nth root
• k: kth nth root

Return value

• if the first parameter is floating the call will act as if they were converted to complex before call, unless the option real_only is used in which case the parameter must be a floating_value, the real part of the result will the same as an eve::nthroot and the result will be fnan if no real solution exists.
• the kth nth root of z, is. exp((log(z)+2*k*i*pi)/n). If not present k is taken as 0.

Note

if the first parameter is not real the option real_only has no effect.

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
  using kyosu::complex_t;
  using kyosu::nthroot;
 
  using wi_t = eve::wide<unsigned int, eve::fixed<4>>;
  using wf_t = eve::wide<float, eve::fixed<4>>;
  wi_t wn = eve::iota(eve::as<wi_t>()) + 1;
  wf_t wf{5.0f, 2.3f, 1.2f, 0.0f};
 
  std::cout << "wn                          " << wn << std::endl;
  std::cout << "wf                          " << wf << std::endl;
  std::cout << "kyosu::nthroot(16.0, wn)    " << kyosu::nthroot(16.0, wn) << std::endl;
  std::cout << "kyosu::nthroot(16.0, 4, wn) " << kyosu::nthroot(16.0, 4, wn) << std::endl;
  std::cout << "kyosu::nthroot(16.0, -2)    " << kyosu::nthroot(16.0, -2) << std::endl;
  std::cout << "kyosu::nthroot(wf, wn)      " << kyosu::nthroot(wf, wn) << std::endl;
  std::cout << "kyosu::nthroot(wf, wn, 3)   " << kyosu::nthroot(wf, wn, 3) << std::endl;
 
  return 0;
}