ACOSH

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.

Examples

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

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)