acot

auto kyosu::acot = eve::functor<acot_t>

inlineconstexpr

Computes the arc cotangent of the argument.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
  //  regular call
  constexpr auto acot(cayley_dickson_like z)                  noexcept;
  constexpr auto acot(cayley_dickson_like z, eve::value k)    noexcept;
 
  // semantic modifyers
  constexpr auto acot[real_only](Real z)                      noexcept;
  constexpr auto acot[radpi](cayley_dickson_like z)           noexcept;
  constexpr auto acot[rad](cayley_dickson_like 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::acot,
• For complex input, returns elementwise the complex principal value of the arc cotangent of the input as the arc tangent of the inverse of the input.
• For other general cayley_dickson input, returns \(I_z \mathrm{acoth}(z I_z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\).
• The radpi option provides a result in \(\pi\) multiples.
• For two parameters returns the kth branch of acot. If k is not a flint it is truncated before use.

External references

• Wolfram MathWorld: Inverse Cotangent
• 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
            << "<- zref2                  = " << ref2 << std::endl
            << "-> acot(zc)               = " << kyosu::acot(zc) << std::endl
            << "-> acot(ref2)             = " << kyosu::acot(ref2) << std::endl
            << "-> acot(ref2, 1)          = " << kyosu::acot(ref2, 1) << std::endl
            << "-> acot[real_only](ref2)  = " << kyosu::acot[kyosu::real_only](ref2) << std::endl
            << "-> acot[radpi](ref2)      = " << kyosu::acot[kyosu::radpi](ref2) << std::endl;
 
  return 0;
}