Callable object computing \(\frac{e^x-e^{-x}}2\).
Defined in Header
#include <eve/module/math.hpp>
{
template< eve::floating_value T >
}
constexpr callable_sinh_ sinh
Callable object computing .
Definition: sinh.hpp:81
Definition: all_of.hpp:22
Parameters
Return value
Returns the elementwise hyperbolic sine of the input.
In particular:
- If the element is \(\pm0\), \(\pm0\) is returned.
- If the element is \(\pm\infty\), \(\pm\infty\) returned.
- If the element is a
NaN
, NaN
is returned.
Returns elementwise the complex value of the hyperbolic sine of the input.
- for every z:
eve::sinh(eve::conj(z)) == eve::conj(std::sinh(z))
- for every z:
eve::sinh(-z) == -eve::sinh(z)
- If z is \(+0\), the result is \(+0\)
- If z is \(i \infty\), the result is \(i NaN\) (the sign of the real part is unspecified)
- If z is \(i NaN\), the result is \(NaN\)
- If z is \(x+i \infty\) (for any positive finite x), the result is \(NaN+i NaN\)
- If z is \(x+i NaN\) (for any positive finite x), the result is \(NaN+i NaN\)
- If z is \(+\infty\), the result is \(+\infty\)
- If z is \(+\infty+i y\) (for any positive finite y), the result is \(\infty\times cis(y)\)
- 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 \(\pm \infty+i NaN\) (the sign of the real part is unspecified)
- If z is \(NaN\), the result is \(NaN\)
- If z is \(NaN+i y\) (for any finite nonzero y), the result is \(NaN+i NaN\)
where \(\mathrm{cis}(y) = \cos(y)+i\sin(y)\)
Real version
#include <eve/module/math.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
std::cout << "---- simd" << '\n'
<< "<- pf = " << pf << '\n'
;
float xf = 3.0f;
std::cout << "---- scalar" << '\n'
<< "<- xf = " << xf << '\n'
<<
"-> sinh(xf) = " <<
eve::sinh(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
<<
"-> sinh(z) = " <<
eve::sinh(z) << std::endl;
return 0;
}