asin

kyosu::asin = eve::functor<asin_t>

inlineconstexpr

Computes the arcsine of the argument.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   //  regular call
   template<kyosu::concepts::cayley_dickson_like T> constexpr complexify_t<T> asin(T z) noexcept;  //3
 
   // semantic modifyers
   template<concepts::real T> constexpr complexify_t<T> asin[real_only](T z) noexcept;
}

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, the result will the same as an eve::asin implying a Nan result if the result is not real.

2. Returns the elementwise the complex principal value of the arc sine of the input in the range of a strip unbounded along the imaginary axis and in the interval \([-\pi/2, \pi/2]\) along the real axis.

   special cases are handled as if the operation was implemented by \(-i\; \mathrm{asinh}(z\; i)\)

3. Returns \(-I_z \mathrm{asinh}(z I_z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).

External references

• C++ standard reference: complex asin
• Wolfram MathWorld: InverseSine
• Wikipedia:Inverse trigonometric functions
• DLMF:Inverse trigonometric 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
    << "-> asin(zc)     = " << kyosu::asin(zc)<< std::endl
    << "-> asin(ref2)    = " << kyosu::asin(ref2) << std::endl;
 
  return 0;
}