# atanh(x): Inverse Hyperbolic Tangent¶

Inverse hyperbolic tangent function.

## Declaración¶

### Sintaxis¶

retval = atanh(x)
elemental real(p) function atanh(x)
elemental complex(p) function atanh(x)


### Argumentos¶

x the input value, can be real with value greater than or equal to 1 or of type complex.

### Valores devueltos¶

The returned value has the kind of the input value and TYPE may be real or complex.

## Descripción¶

atanh(x) computes the inverse hyperbolic tangent function of x.

The result type and kind are the same as input value x.

If the result is complex, the imaginary part is expressed in radians and lies in the range

$$\frac{-\pi}{2} <= aimag (atanh(x)) <= \frac{\pi}{2}$$

If the result is real, it lies in the range

$$-1.0 < atanh(x) < 1.0$$

## Tipos¶

Supported argument types float, double, complex float, complex double.

interface atanh
module procedure satanh, datanh, catanh, zatanh
end interface

contains

interface
elemental real(sp) function satanh(x)
real(sp), intent(in) :: x
end function

elemental real(dp) function datanh(x)
real(dp), intent(in) :: x
end function

elemental complex(sp) function catanh(x)
complex(sp), intent(in) :: x
end function

elemental complex(dp) function zatanh(x)
complex(dp), intent(in) :: x
end function
end interface


## Ejemplos¶

program intrinsics_atanh
implicit none
print *, atanh(0.0)
end program


Result:

0.0