ASINH

This function evaluates the arc hyperbolic sine.

Function Return Value

ASINH — Function value. (Output)

Required Arguments

X — Argument for which the arc hyperbolic sine is desired. (Input)

FORTRAN 90 Interface

Generic: ASINH (X)

Specific: The specific interface names are ASINH, DASINH, CASINH, and ZASINH.

FORTRAN 77 Interface

Single: ASINH (X)

Double: The double precision function name is DASINH.

Complex: The complex name is CASINH.

Double Complex:  The double complex name is ZASINH.

Description

The function ASINH(X) computes the inverse hyperbolic sine of x, sinh‑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 ASINH.

Examples

Example 1

In this example, sinh‑1(2.0) is computed and printed.

 

USE ASINH_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = 2.0

VALUE = ASINH(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' ASINH(', F6.3, ') = ', F6.3)

END

Output

 

ASINH( 2.000) = 1.444

Example 2

In this example, sinh‑1(‑1 + i) is computed and printed.

 

USE ASINH_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

COMPLEX VALUE, Z

! Compute

Z = (-1.0, 1.0)

VALUE = ASINH(Z)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) Z, VALUE

99999 FORMAT (' ASINH((', F6.3, ',', F6.3, ')) = (', &

F6.3, ',', F6.3, ')')

END

Output

 

ASINH((-1.000, 1.000)) = (-1.061, 0.666)