E.V.E
v2022.09.01

◆ cosh

eve::cosh = {}
inlineconstexpr

Callable object computing \(\frac{e^x+e^{-x}}2\).

Defined in Header

#include <eve/module/math.hpp>

Callable Signatures

namespace eve
{
template< eve::floating_value T >
T cosh(T x) noexcept; //1
template< eve::floating_value T >
}
constexpr callable_cosh_ cosh
Callable object computing .
Definition: cosh.hpp:87
Definition: all_of.hpp:22
SIMD-compatible representation of complex numbers.
Definition: complex.hpp:40

Parameters

Return value

  1. Returns the elementwise hyperbolic cosine of the input.

    In particular:

    • If the element is \(\pm0\), 1 is returned.
    • If the element is \(\pm\infty\), \(+\infty\) is returned.
    • If the element is a NaN, NaN is returned.
  2. Returns elementwise the complex value of the hyperbolic cosine of the input.

    • for every z: eve::cosh(eve::conj(z)) == eve::conj(std::cosh(z))
    • for every z: eve::cosh(-z) == eve::cosh(z)
    • If z is \(0\), the result is \(1\)
    • If z is \(i \infty\), the result is \(NaN\)
    • If z is \(i NaN\), the result is \(NaN\)
    • If z is \(x+i \infty\) (for any finite non-zero x), the result is \(NaN+i NaN\)
    • If z is \(x+i NaN\) (for any finite non-zero x), the result is \(NaN+i NaN\)
    • If z is \(\infty+i 0\), the result is \(\infty+i 0\)
    • If z is \(\infty,y\) (for any finite non-zero y), the result is \(\infty \mathrm{cis}\times(y)\)
    • If z is \(\infty+i \infty\), the result is \(\pm \infty+i NaN\) (the sign of the real part is unspecified)
    • If z is \(\infty+i NaN\), the result is \(\infty+i NaN\)
    • If z is \(NaN\), the result is \(NaN\)
    • If z is \(NaN+i y\) (for any finite non-zero y), the result is \(NaN+i NaN\)
    • If z is \(NaN+i NaN\), the result is \(NaN+i NaN\)

    where \(\mathrm{cis}(y) = \cos(y)+i\sin(y)\)

Example

Real version

#include <eve/module/math.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
wide_ft pf = {1.0f, 0.0f, eve::inf(eve::as<float>()), eve::nan(eve::as<float>())};
std::cout << "---- simd" << '\n'
<< "<- pf = " << pf << '\n'
<< "-> cosh(pf) = " << eve::cosh(pf) << '\n'
;
float xf = 3.0f;
std::cout << "---- scalar" << '\n'
<< "<- xf = " << xf << '\n'
<< "-> cosh(xf) = " << eve::cosh(xf) << '\n';
return 0;
}
constexpr callable_nan_ nan
Computes the IEEE NaN constant.
Definition: nan.hpp:53
constexpr callable_inf_ inf
Computes the infinity ieee value.
Definition: inf.hpp:58
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" << std::endl
<< "<- z = " << z << std::endl
<< "-> cosh(z) = " << eve::cosh(z) << std::endl;
return 0;
}