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76 lines
2.2 KiB
Fortran
76 lines
2.2 KiB
Fortran
*DECK CATAN
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COMPLEX FUNCTION CATAN (Z)
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C***BEGIN PROLOGUE CATAN
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C***PURPOSE Compute the complex arc tangent.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C4A
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C***TYPE COMPLEX (CATAN-C)
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C***KEYWORDS ARC TANGENT, 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 CATAN(Z) calculates the complex trigonometric arc tangent of Z.
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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, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 770801 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 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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C 900326 Removed duplicate information from DESCRIPTION section.
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C (WRB)
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C***END PROLOGUE CATAN
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COMPLEX Z, Z2
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LOGICAL FIRST
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SAVE PI2, NTERMS, SQEPS, RMIN, RMAX, FIRST
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DATA PI2 / 1.5707963267 9489661923E0 /
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT CATAN
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IF (FIRST) THEN
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C NTERMS = LOG(EPS)/LOG(RBND) WHERE RBND = 0.1
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NTERMS = -0.4343*LOG(R1MACH(3)) + 1.0
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SQEPS = SQRT(R1MACH(4))
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RMIN = SQRT (3.0*R1MACH(3))
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RMAX = 1.0/R1MACH(3)
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ENDIF
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FIRST = .FALSE.
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C
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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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CATAN = Z
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IF (R.LT.RMIN) RETURN
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C
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CATAN = (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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CATAN = 1.0/TWOI - Z2*CATAN
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20 CONTINUE
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CATAN = Z*CATAN
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RETURN
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C
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30 IF (R.GT.RMAX) GO TO 50
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X = REAL(Z)
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Y = AIMAG(Z)
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R2 = R*R
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IF (R2 .EQ. 1.0 .AND. X .EQ. 0.0) CALL XERMSG ('SLATEC', 'CATAN',
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+ 'Z IS +I OR -I', 2, 2)
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IF (ABS(R2-1.0).GT.SQEPS) GO TO 40
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IF (ABS(CMPLX(1.0, 0.0)+Z*Z) .LT. SQEPS) CALL XERMSG ('SLATEC',
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+ 'CATAN', 'ANSWER LT HALF PRECISION, Z**2 CLOSE TO -1', 1, 1)
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C
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40 XANS = 0.5*ATAN2(2.0*X, 1.0-R2)
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YANS = 0.25*LOG((R2+2.0*Y+1.0)/(R2-2.0*Y+1.0))
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CATAN = CMPLX (XANS, YANS)
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RETURN
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C
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50 CATAN = CMPLX (PI2, 0.)
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IF (REAL(Z).LT.0.0) CATAN = CMPLX(-PI2,0.0)
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RETURN
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C
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END
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