asin

auto 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
  constexpr auto asin(cayley_dickson_like z)                noexcept;
  constexpr auto asin(cayley_dickson_like z, eve::value k)  noexcept;
 
  // semantic modifyers
  constexpr auto asin[radpi](cayley_dickson_like z)         noexcept;
  constexpr auto aéos[rad](cayley_dickson_like z)           noexcept;
  constexpr auto asin[real_only](Real z)                    noexcept;
}
}

Parameters

• z: Value to process.

Return value

• A real typed 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::asin, implying a Nan result if the theoretical result is not real.
• For complex input, returns 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 \(-i\; \mathrm{asinh}(z\; i)\)
• For general cayley_dickson input returns \(-I_z \mathrm{asinh}(z I_z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).
• for two parameters returns the kth branch of asin. If k is not a flint, it is truncated before use.

External references

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