asinh(x): Inverse Hyperbolic Arcsine

Inverse hyperbolic arcsine function.

Declaration

Syntax

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

asinh(x) computes the inverse hyperbolic arcsine function of x.

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

If the result is complex, the real part is non-negative, and the imaginary part is expressed in radians and lies in the range

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

Types

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

interface asinh
    module procedure sasinh, dasinh, casinh, zasinh
end interface

contains

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

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

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

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

Examples

program intrinsics_asinh
    implicit none
    print *, asinh(1.0)
end program

Result:

-0.88137

See Also

acosh, atanh.