acos

kyosu::acos = eve::functor<acos_t>

inlineconstexpr

Computes the arc cosine of the argument.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

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

Parameters

• z: Value to process.

Return value

1. a real typed input z is treated as if complex(z) was entered.
2. Returns elementwise the complex principal value of the arc cosine of the input. Branch cuts exist outside the interval \([-1, +1]\) along the real axis.
   • for every z: acos(conj(z)) == conj(acos(z))
   • If z is \(\pm0\), the result is \(\pi/2\)
   • If z is \(i \textrm{NaN}\), the result is \(\pi/2+ i \textrm{NaN}\)
   • If z is \(x+i\infty\) (for any finite x), the result is \(\pi/2-i\infty\)
   • If z is \(x+i \textrm{NaN}\) (for any nonzero finite x), the result is \(\textrm{NaN}+i \textrm{NaN}\).
   • If z is \(-\infty+i y\) (for any positive finite y), the result is \(\pi-i\infty\)
   • If z is \(+\infty+i y\) (for any positive finite y), the result is \(+0-i\infty\)
   • If z is \(-\infty+i +\infty\), the result is \(3\pi/4-i\infty\)
   • If z is \(\infty+i +\infty\), the result is \(\pi/4-i\infty\)
   • If z is \(\pm\infty+i \textrm{NaN}\), the result is \(\textrm{NaN} \pm i\infty\) (the sign of the imaginary part is unspecified)
   • If z is \(\textrm{NaN}+i y\) (for any finite y), the result is \(\textrm{NaN}+i \textrm{NaN}\)
   • If z is \(\textrm{NaN}+i\infty\), the result is \(\textrm{NaN}-i\infty\)
   • If z is \(\textrm{NaN}+i \textrm{NaN}\), the result is \(\textrm{NaN}+i \textrm{NaN}\)
3. Returns \(I_z \mathrm{acosh}(z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).

External references

• C++ standard reference: complex acos
• Wolfram MathWorld: Inverse Cosine
• Wikipedia: Arc cosinus

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
    << "-> acos(zc)      = " << kyosu::acos(zc)<< std::endl
    << "-> acos(ref2)    = " << kyosu::acos(ref2) << std::endl;
 
  return 0;
}