atanh(x): Inverse Hyperbolic Tangent¶

Inverse hyperbolic tangent function.

Declaration¶

Syntax¶

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

Arguments¶

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

Return values¶

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

Description¶

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

\(-1.0 < atanh(x) < 1.0\)

Types¶

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

Examples¶

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

Result:

0.0