asinh

kyosu::asinh = eve::functor<asinh_t>

inlineconstexpr

Computes the inverse hyperbolic sine of the argument.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

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

Parameters

• z: Value to process.

Return value

1. A real type input z calls eve::asinh(z) and so returns the same type as input.
2. Returns the complex inverse hyperbolic sine of z, with branch cuts outside the interval \(i\times[-\pi/2, \pi/2]\) along the imaginary axis.
   • for every z: asinh(conj(z)) ==conj(asinh(z))
   • for every z: asinh(-z) == -asinh(z)
   • If z is \(+0\), the result is \(+0\)
   • If z is \(x+i \infty\) (for any positive finite x), the result is \(\infty+i \pi/2\)
   • If z is \(x, \textrm{NaN}\) (for any finite x), the result is \( \textrm{NaN}+ i \textrm{NaN}\)
   • If z is \(\infty+ iy\) (for any positive finite y), the result is \(\infty+i 0\)
   • If z is \(\infty+i \infty\), the result is \(\infty+ i\pi/4\)
   • If z is \(\infty+ i \textrm{NaN}\), the result is \(\infty+ i \textrm{NaN}\)
   • If z is \( \textrm{NaN}+i 0\), the result is \( \textrm{NaN}+i 0\)
   • If z is \( \textrm{NaN}+ iy\) (for any finite nonzero y), the result is \( \textrm{NaN}+ i \textrm{NaN}\)
   • If z is \( \textrm{NaN}+i \infty\), the result is \(\pm \infty+ i \textrm{NaN}\) (the sign of the real part is unspecified)
   • If z is \( \textrm{NaN}+ i \textrm{NaN}\), the result is \( \textrm{NaN}+ i \textrm{NaN}\)
3. Returns \(\log(z+\sqrt{1+z^2})\).

External references

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