kyosu v0.1.0
Complex Without Complexes
 
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◆ acos

kyosu::acos = {}
inlineconstexpr

Computes the acosine of the argument.

Defined in Header

#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
}
constexpr tags::callable_acos acos
Computes the acosine of the argument.
Definition: acos.hpp:101
constexpr tags::callable_atan atan
Computes the arctangent of the argument.
Definition: atan.hpp:86
Main KYOSU namespace.
Definition: types.hpp:14

Parameters

  • z: Value to process.

Return value

  1. a real typed input z is treated as if kyosu::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: kyosu::acos( kyosu::conj(z) ) == kyosu::conj(kyosu::acos(z))
    • If z is \(\pm0\), the result is \(\pi/2\)
    • If z is \(i NaN\), the result is \(\pi/2+ i NaN\)
    • If z is \(x+i\infty\) (for any finite x), the result is \(\pi/2-i\infty\)
    • If z is \(x+i NaN\) (for any nonzero finite x), the result is \(NaN+i NaN\).
    • 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 \(\pm\infty+i NaN\), the result is \(NaN \pm i\infty\) (the sign of the imaginary part is unspecified)
    • If z is \(NaN+i y\) (for any finite y), the result is \(NaN+i NaN\)
    • If z is \(NaN+i\infty\), the result is \(NaN-i\infty\)
    • If z is \(NaN+i NaN\), the result is \(NaN+i NaN\)
  3. Returns \(I_z \mathrm{acosh}(z)\) where \(I_z = \frac{\underline{z}}{|\underline{z}|}\) and \(\underline{z}\) is the pure part of \(z\). template<kyosu::concepts::cayley_dickson T> constexpr T cosh(T z) noexcept; }

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;
}
as_cayley_dickson_n_t< 2, T > complex_t
Type alias for complex numbers.
Definition: complex.hpp:27