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.

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

Additional Example

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)

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