Callable object computing \(\frac{1}{2}\log((1+x)/(1-x))\).
Defined in Header
#include <eve/module/math.hpp>
{
template< eve::floating_value T >
template< eve::floating_value T >
}
constexpr callable_atanh_ atanh
Callable object computing .
Definition: atanh.hpp:85
Definition: all_of.hpp:22
SIMD-compatible representation of complex numbers.
Definition: complex.hpp:40
Parameters
Return value
Returns the elementwise inverse hyperbolic cotangent of the input. The inverse hyperbolic sine is semantically equivalent to \(\frac{1}{2}\log((1+x)/(1-x))\).
In particular:
- If the element is \(\pm1\), \(\pm\infty\) is returned.
- If the element is \(\pm0\), \(\pm0\) is returned.
- If the element is greater than one or a
NaN
, NaN
is returned.
Returns the complex arc hyperbolic sine of z, in the range of a half-strip mathematically unbounded along the real axis and in the interval \(i\times[-\pi/2, \pi/2]\) along the imaginary axis.
- for every z: eve::atanh(eve::conj(z)) == eve::conj(std::atanh(z))
- for every z: eve::atanh(-z) == -eve::atanh(z)
- If z is \(+0\), the result is \(+0\)
- If z is \(NaN\), the result is \(NaN\)
- If z is \(+1\), the result is \(+\infty\)
- If z is \(x+i \infty\) (for any finite positive x), the result is \(+0,\pi/2\)
- If z is \(x+i NaN\) (for any finite nonzero x), the result is \(NaN+i NaN\)
- If z is \(+\infty+i y\) (for any finite positive y), the result is \(i \pi/2\)
- If z is \(+\infty+i \infty\), the result is \(i \pi/2\)
- If z is \(+\infty+i NaN\), the result is \(i NaN\)
- 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 \(i \pi/2\) (the sign of the real part is unspecified)
- If z is \(NaN+i NaN\), the result is \(NaN+i NaN\)
Real version
#include <eve/module/math.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
wide_ft pf = {1.0f, 0.5f, 0.0, -0.5};
std::cout << "---- simd" << '\n'
<< "<- pf = " << pf << '\n'
float xf = 1.0f;
std::cout << "---- scalar" << '\n'
<< "<- xf = " << xf << '\n'
return 0;
}
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
<<
"-> atanh(z) = " <<
eve::atanh(z) << std::endl;
return 0;
}