atanh

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

Parameters

• z: Value to process.

Return value

1. a real input z is treated as if complex(z) was entered.
2. 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 \(NaN+i NaN\)
3. Returns \((\log(1+z)-\log(1-z))/2\).

External references

• C++ standard reference: atanh
• Wolfram MathWorld: Inverse Hyperbolic Tangent
• 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
    << "-> atanh(zc)      = " << kyosu::atanh(zc)<< std::endl
    << "-> atanh(ref2)    = " << kyosu::atanh(ref2) << std::endl;
 
  return 0;
}