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