This function extends FORTRAN's generic ASIN function to evaluate the complex arc sine.

Function Return Value

ASIN — Complex function value in units of radians and the real part in the first or fourth quadrant.   (Output)

Required Arguments

ZINP — Complex argument for which the arc sine is desired.   (Input)

FORTRAN 90 Interface

Generic:                              ASIN (ZINP)

Specific:                             The specific interface names are CASIN and ZASIN.

FORTRAN 77 Interface

Complex:                            CASIN (ZINP)

Double complex:               The double complex function name is ZASIN.

Description

Almost all arguments are legal. Only when |z| > b/2 can an overflow occur. Here, b = AMACH(2) is the largest floating point number. This error is not detected by ASIN.

See Pennisi (1963, page 126) for reference.

Example

In this example, sin⁻¹(1 − i) is computed and printed.

 

      USE asin_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      COMPLEX    VALUE, Z

!                                 Compute

      Z     = (1.0, -1.0)

      VALUE = ASIN(Z)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) Z, VALUE

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

          F6.3, ',', F6.3, ')')

      END

Output

 

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

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