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
{
  //  regular call
  template<concepts::cayley_dickson_like Z> constexpr complexify_t<Z> acoth(Z z) noexcept;
 
  // semantic modifyers
  template<concepts::real Z> constexpr complexify_t<Z> acoth[real_only](Z z) noexcept;
}

Parameters

• z: Value to process.

Return value

• A real typed input z is treated as if complex(z) was entered, 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::acos implying a Nan result if the result is not real.
• For complex input, 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.
• For general cayley_dickson input, the call is equivalent to atanh(rec(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;
}