268 lines
8.5 KiB
FortranFixed
268 lines
8.5 KiB
FortranFixed
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SUBROUTINE ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL,
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* TOL, ELIM, ALIM)
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C***BEGIN PROLOGUE ZUNI2
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C***REFER TO ZBESI,ZBESK
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C
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C ZUNI2 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF
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C UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I
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C OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO.
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C
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C FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC
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C EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET.
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C NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
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C FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
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C Y(I)=CZERO FOR I=NLAST+1,N
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C
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C***ROUTINES CALLED ZAIRY,ZUCHK,ZUNHJ,ZUOIK,D1MACH,ZABS
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C***END PROLOGUE ZUNI2
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C COMPLEX AI,ARG,ASUM,BSUM,CFN,CI,CID,CIP,CONE,CRSC,CSCL,CSR,CSS,
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C *CZERO,C1,C2,DAI,PHI,RZ,S1,S2,Y,Z,ZB,ZETA1,ZETA2,ZN
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DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGI,
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* ARGR, ASCLE, ASUMI, ASUMR, BRY, BSUMI, BSUMR, CIDI, CIPI, CIPR,
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* CONER, CRSC, CSCL, CSRR, CSSR, C1R, C2I, C2M, C2R, DAII,
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* DAIR, ELIM, FN, FNU, FNUL, HPI, PHII, PHIR, RAST, RAZ, RS1, RZI,
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* RZR, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZBI, ZBR, ZEROI,
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* ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, ZNI, ZNR, ZR, CYR,
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* CYI, D1MACH, ZABS, CAR, SAR
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INTEGER I, IFLAG, IN, INU, J, K, KODE, N, NAI, ND, NDAI, NLAST,
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* NN, NUF, NW, NZ, IDUM
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DIMENSION BRY(3), YR(N), YI(N), CIPR(4), CIPI(4), CSSR(3),
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* CSRR(3), CYR(2), CYI(2)
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DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 /
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DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4),
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* CIPI(4)/ 1.0D0,0.0D0, 0.0D0,1.0D0, -1.0D0,0.0D0, 0.0D0,-1.0D0/
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DATA HPI, AIC /
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1 1.57079632679489662D+00, 1.265512123484645396D+00/
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C
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NZ = 0
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ND = N
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NLAST = 0
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C-----------------------------------------------------------------------
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C COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
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C NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
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C EXP(ALIM)=EXP(ELIM)*TOL
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C-----------------------------------------------------------------------
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CSCL = 1.0D0/TOL
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CRSC = TOL
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CSSR(1) = CSCL
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CSSR(2) = CONER
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CSSR(3) = CRSC
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CSRR(1) = CRSC
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CSRR(2) = CONER
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CSRR(3) = CSCL
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BRY(1) = 1.0D+3*D1MACH(1)/TOL
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C-----------------------------------------------------------------------
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C ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI
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C-----------------------------------------------------------------------
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ZNR = ZI
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ZNI = -ZR
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ZBR = ZR
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ZBI = ZI
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CIDI = -CONER
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INU = INT(SNGL(FNU))
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ANG = HPI*(FNU-DBLE(FLOAT(INU)))
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C2R = DCOS(ANG)
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C2I = DSIN(ANG)
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CAR = C2R
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SAR = C2I
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IN = INU + N - 1
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IN = MOD(IN,4) + 1
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STR = C2R*CIPR(IN) - C2I*CIPI(IN)
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C2I = C2R*CIPI(IN) + C2I*CIPR(IN)
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C2R = STR
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IF (ZI.GT.0.0D0) GO TO 10
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ZNR = -ZNR
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ZBI = -ZBI
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CIDI = -CIDI
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C2I = -C2I
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10 CONTINUE
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C-----------------------------------------------------------------------
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C CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
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C-----------------------------------------------------------------------
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FN = DMAX1(FNU,1.0D0)
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CALL ZUNHJ(ZNR, ZNI, FN, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R,
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* ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
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IF (KODE.EQ.1) GO TO 20
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STR = ZBR + ZETA2R
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STI = ZBI + ZETA2I
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RAST = FN/ZABS(STR,STI)
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STR = STR*RAST*RAST
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STI = -STI*RAST*RAST
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S1R = -ZETA1R + STR
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S1I = -ZETA1I + STI
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GO TO 30
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20 CONTINUE
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S1R = -ZETA1R + ZETA2R
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S1I = -ZETA1I + ZETA2I
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30 CONTINUE
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RS1 = S1R
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IF (DABS(RS1).GT.ELIM) GO TO 150
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40 CONTINUE
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NN = MIN0(2,ND)
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DO 90 I=1,NN
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FN = FNU + DBLE(FLOAT(ND-I))
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CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR, PHII, ARGR, ARGI,
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* ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
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IF (KODE.EQ.1) GO TO 50
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STR = ZBR + ZETA2R
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STI = ZBI + ZETA2I
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RAST = FN/ZABS(STR,STI)
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STR = STR*RAST*RAST
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STI = -STI*RAST*RAST
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S1R = -ZETA1R + STR
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S1I = -ZETA1I + STI + DABS(ZI)
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GO TO 60
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50 CONTINUE
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S1R = -ZETA1R + ZETA2R
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S1I = -ZETA1I + ZETA2I
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60 CONTINUE
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C-----------------------------------------------------------------------
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C TEST FOR UNDERFLOW AND OVERFLOW
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C-----------------------------------------------------------------------
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RS1 = S1R
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IF (DABS(RS1).GT.ELIM) GO TO 120
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IF (I.EQ.1) IFLAG = 2
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IF (DABS(RS1).LT.ALIM) GO TO 70
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C-----------------------------------------------------------------------
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C REFINE TEST AND SCALE
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C-----------------------------------------------------------------------
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C-----------------------------------------------------------------------
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APHI = ZABS(PHIR,PHII)
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AARG = ZABS(ARGR,ARGI)
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RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
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IF (DABS(RS1).GT.ELIM) GO TO 120
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IF (I.EQ.1) IFLAG = 1
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IF (RS1.LT.0.0D0) GO TO 70
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IF (I.EQ.1) IFLAG = 3
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70 CONTINUE
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C-----------------------------------------------------------------------
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C SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
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C EXPONENT EXTREMES
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C-----------------------------------------------------------------------
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CALL ZAIRY(ARGR, ARGI, 0, 2, AIR, AII, NAI, IDUM)
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CALL ZAIRY(ARGR, ARGI, 1, 2, DAIR, DAII, NDAI, IDUM)
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STR = DAIR*BSUMR - DAII*BSUMI
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STI = DAIR*BSUMI + DAII*BSUMR
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STR = STR + (AIR*ASUMR-AII*ASUMI)
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STI = STI + (AIR*ASUMI+AII*ASUMR)
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S2R = PHIR*STR - PHII*STI
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S2I = PHIR*STI + PHII*STR
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STR = DEXP(S1R)*CSSR(IFLAG)
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S1R = STR*DCOS(S1I)
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S1I = STR*DSIN(S1I)
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STR = S2R*S1R - S2I*S1I
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S2I = S2R*S1I + S2I*S1R
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S2R = STR
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IF (IFLAG.NE.1) GO TO 80
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CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
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IF (NW.NE.0) GO TO 120
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80 CONTINUE
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IF (ZI.LE.0.0D0) S2I = -S2I
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STR = S2R*C2R - S2I*C2I
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S2I = S2R*C2I + S2I*C2R
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S2R = STR
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CYR(I) = S2R
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CYI(I) = S2I
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J = ND - I + 1
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YR(J) = S2R*CSRR(IFLAG)
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YI(J) = S2I*CSRR(IFLAG)
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STR = -C2I*CIDI
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C2I = C2R*CIDI
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C2R = STR
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90 CONTINUE
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IF (ND.LE.2) GO TO 110
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RAZ = 1.0D0/ZABS(ZR,ZI)
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STR = ZR*RAZ
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STI = -ZI*RAZ
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RZR = (STR+STR)*RAZ
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RZI = (STI+STI)*RAZ
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BRY(2) = 1.0D0/BRY(1)
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BRY(3) = D1MACH(2)
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S1R = CYR(1)
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S1I = CYI(1)
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S2R = CYR(2)
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S2I = CYI(2)
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C1R = CSRR(IFLAG)
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ASCLE = BRY(IFLAG)
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K = ND - 2
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FN = DBLE(FLOAT(K))
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DO 100 I=3,ND
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C2R = S2R
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C2I = S2I
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S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I)
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S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R)
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S1R = C2R
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S1I = C2I
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C2R = S2R*C1R
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C2I = S2I*C1R
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YR(K) = C2R
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YI(K) = C2I
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K = K - 1
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FN = FN - 1.0D0
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IF (IFLAG.GE.3) GO TO 100
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STR = DABS(C2R)
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STI = DABS(C2I)
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C2M = DMAX1(STR,STI)
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IF (C2M.LE.ASCLE) GO TO 100
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IFLAG = IFLAG + 1
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ASCLE = BRY(IFLAG)
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S1R = S1R*C1R
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S1I = S1I*C1R
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S2R = C2R
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S2I = C2I
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S1R = S1R*CSSR(IFLAG)
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S1I = S1I*CSSR(IFLAG)
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S2R = S2R*CSSR(IFLAG)
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S2I = S2I*CSSR(IFLAG)
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C1R = CSRR(IFLAG)
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100 CONTINUE
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110 CONTINUE
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RETURN
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120 CONTINUE
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IF (RS1.GT.0.0D0) GO TO 140
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C-----------------------------------------------------------------------
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C SET UNDERFLOW AND UPDATE PARAMETERS
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C-----------------------------------------------------------------------
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YR(ND) = ZEROR
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YI(ND) = ZEROI
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NZ = NZ + 1
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ND = ND - 1
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IF (ND.EQ.0) GO TO 110
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CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM)
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IF (NUF.LT.0) GO TO 140
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ND = ND - NUF
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NZ = NZ + NUF
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IF (ND.EQ.0) GO TO 110
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FN = FNU + DBLE(FLOAT(ND-1))
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IF (FN.LT.FNUL) GO TO 130
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C FN = CIDI
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C J = NUF + 1
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C K = MOD(J,4) + 1
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C S1R = CIPR(K)
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C S1I = CIPI(K)
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C IF (FN.LT.0.0D0) S1I = -S1I
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C STR = C2R*S1R - C2I*S1I
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C C2I = C2R*S1I + C2I*S1R
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C C2R = STR
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IN = INU + ND - 1
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IN = MOD(IN,4) + 1
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C2R = CAR*CIPR(IN) - SAR*CIPI(IN)
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C2I = CAR*CIPI(IN) + SAR*CIPR(IN)
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IF (ZI.LE.0.0D0) C2I = -C2I
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GO TO 40
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130 CONTINUE
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NLAST = ND
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RETURN
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140 CONTINUE
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NZ = -1
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RETURN
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150 CONTINUE
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IF (RS1.GT.0.0D0) GO TO 140
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NZ = N
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DO 160 I=1,N
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YR(I) = ZEROR
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YI(I) = ZEROI
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160 CONTINUE
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RETURN
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END
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