acosh(x): Inverse Hyperbolic Cosine¶

Inverse hyperbolic cosine function.

Declaration¶

Syntax¶

retval = acosh(x)
elemental real(p) function acosh(x)
elemental complex(p) function acosh(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¶

acosh(x) computes the inverse hyperbolic cosine 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 lients in the range

\(-\pi <= img (acosh(x)) <= \pi\)

For real values \(x\) in the domain \(x > 1\), the inverse hyperbolic cosine satisifies:

\(cosh^{-1}(x) = \log(x + \sqrt{(x^2 - 1)})\)

For complex numbers \(x = x + iy\), as well as real values in the domain \(-\infty < z <= 1\), the call \(acosh(z)\) returns complex results.

Types¶

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

interface acosh
    module procedure sacosh, dacosh, cacosh, zacosh
end interface

contains

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

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

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

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

Examples¶

program intrinsics_acosh
implicit none
print *, acosh(1.0)
end program

Result:

0.0