ASIN

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)