E.V.E
v2022.09.01

◆ acos

eve::acos = {}
inlineconstexpr

Callable object computing the arc cosine.

Defined in Header

#include <eve/module/math.hpp>

Callable Signatures

namespace eve
{
template< eve::floating_value T >
T acos(T x) noexcept; //1
template< eve::floating_value T >
}
constexpr callable_acos_ acos
Callable object computing the arc cosine.
Definition: acos.hpp:93
Definition: all_of.hpp:22
SIMD-compatible representation of complex numbers.
Definition: complex.hpp:40

Parameters

Return value

  1. Returns the elementwise arc cosine of the input in the range \([0 , \pi]\).

    In particular:

    • If the element is \(1\), \(+0\) is returned.
    • If the element \(|x| > 1\), NaN is returned.
    • If the element is a Nan, NaN is returned.
  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: eve::acos(eve::conj(z)) == eve::conj(std::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 \(NaN+i NaN\)

Example

Real version

#include <eve/module/math.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
wide_ft pf = { 0.0f, 0.99f, -1.0f, -0.5f};
std::cout
<< "---- simd" << '\n'
<< "<- pf = " << pf << '\n'
<< "-> acos(pf) = " << eve::acos(pf) << '\n'
;
float xf = 1.0f;
float yf = eve::nan(eve::as<float>());
std::cout
<< "---- scalar" << '\n'
<< "<- xf = " << xf << '\n'
<< "-> eve::acos(xf) = " << eve::acos(xf) << '\n'
<< "<- yf = " << yf << '\n'
<< "-> eve::acos(yf) = " << eve::acos(yf) << '\n';
return 0;
}
constexpr callable_nan_ nan
Computes the IEEE NaN constant.
Definition: nan.hpp:53
Lightweight type-wrapper.
Definition: as.hpp:29
Wrapper for SIMD registers.
Definition: wide.hpp:65

Complex version

#include <eve/module/complex.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
wide_ft ref = { 0.0f, 1.0f, -1.0f, 0.5f};
wide_ft imf = { 2.0f , -1.0, -5.0, 0.0};
auto z = eve::as_complex_t<wide_ft>(ref, imf);
std::cout
<< "---- simd" << '\n'
<< "<- z = " << z << '\n'
<< "-> acos(z) = " << eve::acos(z) << '\n';
return 0;
}

Semantic Modifiers

  • eve::raw The call raw(acos)(x), call a faster implementation for floating real values which can be slightly less accurate near 1.