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)
