This function evaluates the arc hyperbolic cosine.
Function Return Value
ACOSH — Function value. (Output)
Required Arguments
X — Argument for which the arc hyperbolic cosine is desired. (Input)
FORTRAN 90 Interface
Generic: ACOSH (X)
Specific: The specific interface names are ACOSH, DACOSH, CACOSH, and ZACOSH.
FORTRAN 77 Interface
Single: ACOSH (X)
Double: The double precision function name is DACOSH.
Complex: The complex name is CACOSH.
Double Complex: The double complex name is ZACOSH.
Description
The function ACOSH(X) computes the inverse hyperbolic cosine of x, cosh−1x.
For complex arguments, almost all arguments are legal. Only when |z| > b/2 can an overflow occur, where b = AMACH(2) is the largest floating point number. This error is not detected by ACOSH.
Comments
The result of ACOSH(X) is returned on the positive branch. Recall that, like SQRT(X), ACOSH(X) has multiple values.
Example 1
In this example, cosh−1(1.4) is computed and printed.
USE ACOSH_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
REAL VALUE, X
! Compute
X = 1.4
VALUE = ACOSH(X)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) X, VALUE
99999 FORMAT (' ACOSH(', F6.3, ') = ', F6.3)
END
Output
ACOSH( 1.400) = 0.867
Additional Example
Example 2
In this example, cosh−1(1 − i) is computed and printed.
USE ACOSH_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
COMPLEX VALUE, Z
! Compute
Z = (1.0, -1.0)
VALUE = ACOSH(Z)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) Z, VALUE
99999 FORMAT (' ACOSH((', F6.3, ',', F6.3, ')) = (', &
F6.3, ',', F6.3, ')')
END
Output
ACOSH(( 1.000,-1.000)) = (-1.061, 0.905)
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