acosh

kyosu::acosh = eve::functor<acosh_t>

inlineconstexpr

Computes the inverse hyperbolic cosine 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> acosh(Z z) noexcept;
 
  // semantic modifyers
  template<concepts::real Z> constexpr complexify_t<Z> acosh[real_only](Z z) noexcept;
}

Parameters

• z: Value to process.

Return value

• 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, the result will the same as an eve::acosh implying a Nan result if the result is not real.
• For complex input, returns the complex inverse hyperbolic cosine of z, in the range of a strip unbounded along the imaginary axis and in the interval \([0,\pi]\) along the real axis.
  • for every z: acosh(conj(z)) ==conj(acosh(z))
  • If z is \(\pm0\), the result is \(+0+i\pi/2\)
  • If z is \(x+i\infty\) (for any finite x), the result is \(\infty+i\pi/2\)
  • If z is \(x+i \textrm{NaN}\) (for any finite non zero x), the result is \(\textrm{NaN}+i\textrm{NaN}\).
  • If z is \(i \textrm{NaN}\) the result is \(\textrm{NaN}+i\pi/2\).
  • If z is \(-\infty,y\) (for any positive finite y), the result is \(+\infty,\pi\)
  • If z is \(+\infty,y\) (for any positive finite y), the result is \(+\infty+i 0\)
  • If z is \(-\infty+i \infty\), the result is \(+\infty,3\pi/4\)
  • If z is \(\pm\infty+i \textrm{NaN}\), the result is \(+\infty+i \textrm{NaN}\)
  • If z is \(\textrm{NaN},y\) (for any finite y), the result is \(\textrm{NaN}+i \textrm{NaN}\).
  • If z is \(\textrm{NaN}+i \infty\), the result is \(+\infty+i \textrm{NaN}\)
  • If z is \(\textrm{NaN}+i \textrm{NaN}\), the result is \(\textrm{NaN}+i \textrm{NaN}\)
• For general cayley_dickson input, returns \(\log(z+\sqrt{z+1}\sqrt{z-1})\).

External references

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