acoth

kyosu::acoth = eve::functor<acoth_t>

inlineconstexpr

Computes the inverse hyperbolic cotangent of the argument.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<eve::floating_ordered_value T>     constexpr auto acoth(T z) noexcept;  //1
   template<kyosu::concepts::complex T>        constexpr auto acoth(T z) noexcept;  //2
   template<kyosu::concepts::cayley_dickson T> constexpr auto acoth(T z) noexcept;  //3
}

Parameters

• z: Value to process.

Return value

1. a real typed input z is treated as if complex(z) was entered.
2. Returns elementwise the complex principal value of the inverse hyperbolic cotangent of the input as the inverse hyperbolic tangent of the inverse of the input.
3. Returns \(I_z \mathrm{acot}(z I_z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).

External references

• Wolfram MathWorld: Inverse Hyperbolic Cotangent
• Wikipedia: Inverse hyperbolic functions
• DLMF: Inverse hyperbolic functions

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
    << "-> acoth(zc)      = " << kyosu::acoth(zc)<< std::endl
    << "-> acoth(ref2)    = " << kyosu::acoth(ref2) << std::endl;
 
  return 0;
}