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