atanh

auto kyosu::atanh = eve::functor<atanh_t>

inlineconstexpr

Computes the inverse hyperbolic tangent of the argument.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
  //  regular calls
   constexpr auto atanh(                    z)                 noexcept; // 1
   constexpr auto atanh(cayley_dickson_like z, eve::value k)   noexcept; // 2
 
  // semantic modifyers
  constexpr Z atan[real_only](Real z)                          noexcept; // 1
 
}

Parameters

• z: Value to process.

Return value

1. a real 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 and the result will the same as a call to eve::actanh, In any case returns the complex inverse hyperbolic tangent of z, in the range of a half-strip mathematically unbounded along the real axis and in the interval \(i\times[-\pi/2, \pi/2]\) along the imaginary axis.
   • for every z: atanh(conj(z)) == conj(atanh(z))
   • for every z: atanh(-z) == -atanh(z)
   • If z is \(+0\), the result is \(+0\)
   • If z is \(NaN\), the result is \(NaN\)
   • If z is \(+1\), the result is \(+\infty\)
   • If z is \(x+i \infty\) (for any finite positive x), the result is \(+0,\pi/2\)
   • If z is \(x+i NaN\) (for any finite nonzero x), the result is \(NaN+i NaN\)
   • If z is \(+\infty+i y\) (for any finite positive y), the result is \(i \pi/2\)
   • If z is \(+\infty+i \infty\), the result is \(i \pi/2\)
   • If z is \(+\infty+i NaN\), the result is \(i NaN\)
   • If z is \(NaN+i y\) (for any finite y), the result is \(NaN+i NaN\)
   • If z is \(NaN+i \infty\), the result is \(i \pi/2\) (the sign of the real part is unspecified)
   • If z is \(NaN+i NaN\), the result is \(NaN+i NaN\) Returns \((\log(1+z)-\log(1-z))/2\).
2. Returns the kth branch of atanh. If k is not a flint it is truncated before use.

External references

• C++ standard reference: atanh
• Wolfram MathWorld: Inverse Hyperbolic Tangent
• Wikipedia: Inverse hyperbolic functions
• DLMF: Inverse hyperbolic functions

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
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
            << "<- ref2                   = " << ref2 << std::endl
            << "-> atanh(zc)              = " << kyosu::atanh(zc) << std::endl
            << "-> atanh(ref2)            = " << kyosu::atanh(ref2) << std::endl
            << "-> atanh[real_only](ref2) = " << kyosu::atanh[kyosu::real_only](ref2) << std::endl;
 
  return 0;
}