| 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566 |
- *DECK CASIN
- COMPLEX FUNCTION CASIN (ZINP)
- C***BEGIN PROLOGUE CASIN
- C***PURPOSE Compute the complex arc sine.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C4A
- C***TYPE COMPLEX (CASIN-C)
- C***KEYWORDS ARC SINE, ELEMENTARY FUNCTIONS, FNLIB, TRIGONOMETRIC
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C CASIN(ZINP) calculates the complex trigonometric arc sine of ZINP.
- C The result is in units of radians, and the real part is in the first
- C or fourth quadrant.
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED R1MACH
- C***REVISION HISTORY (YYMMDD)
- C 770701 DATE WRITTEN
- C 890531 Changed all specific intrinsics to generic. (WRB)
- C 890531 REVISION DATE from Version 3.2
- C 891214 Prologue converted to Version 4.0 format. (BAB)
- C***END PROLOGUE CASIN
- COMPLEX ZINP, Z, Z2, SQZP1, CI
- LOGICAL FIRST
- SAVE PI2, PI, CI, NTERMS, RMIN, FIRST
- DATA PI2 /1.5707963267 9489661923E0/
- DATA PI /3.1415926535 8979324E0/
- DATA CI /(0.,1.)/
- DATA FIRST /.TRUE./
- C***FIRST EXECUTABLE STATEMENT CASIN
- IF (FIRST) THEN
- C NTERMS = LOG(EPS)/LOG(RMAX) WHERE RMAX = 0.1
- NTERMS = -0.4343*LOG(R1MACH(3))
- RMIN = SQRT (6.0*R1MACH(3))
- ENDIF
- FIRST = .FALSE.
- C
- Z = ZINP
- R = ABS (Z)
- IF (R.GT.0.1) GO TO 30
- C
- CASIN = Z
- IF (R.LT.RMIN) RETURN
- C
- CASIN = (0.0, 0.0)
- Z2 = Z*Z
- DO 20 I=1,NTERMS
- TWOI = 2*(NTERMS-I) + 1
- CASIN = 1.0/TWOI + TWOI*CASIN*Z2/(TWOI+1.0)
- 20 CONTINUE
- CASIN = Z*CASIN
- RETURN
- C
- 30 IF (REAL(ZINP).LT.0.0) Z = -ZINP
- C
- SQZP1 = SQRT (Z+1.0)
- IF (AIMAG(SQZP1).LT.0.) SQZP1 = -SQZP1
- CASIN = PI2 - CI * LOG (Z + SQZP1*SQRT(Z-1.0))
- C
- IF (REAL(CASIN).GT.PI2) CASIN = PI - CASIN
- IF (REAL(CASIN).LE.(-PI2)) CASIN = -PI - CASIN
- IF (REAL(ZINP).LT.0.) CASIN = -CASIN
- C
- RETURN
- END
|
