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qpms/amos/zuni1.f

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SUBROUTINE ZUNI1(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL,
* TOL, ELIM, ALIM)
C***BEGIN PROLOGUE ZUNI1
C***REFER TO ZBESI,ZBESK
C
C ZUNI1 COMPUTES I(FNU,Z) BY MEANS OF THE UNIFORM ASYMPTOTIC
C EXPANSION FOR I(FNU,Z) IN -PI/3.LE.ARG Z.LE.PI/3.
C
C FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC
C EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET.
C NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
C FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
C Y(I)=CZERO FOR I=NLAST+1,N
C
C***ROUTINES CALLED ZUCHK,ZUNIK,ZUOIK,D1MACH,AZABS
C***END PROLOGUE ZUNI1
C COMPLEX CFN,CONE,CRSC,CSCL,CSR,CSS,CWRK,CZERO,C1,C2,PHI,RZ,SUM,S1,
C *S2,Y,Z,ZETA1,ZETA2
DOUBLE PRECISION ALIM, APHI, ASCLE, BRY, CONER, CRSC,
* CSCL, CSRR, CSSR, CWRKI, CWRKR, C1R, C2I, C2M, C2R, ELIM, FN,
* FNU, FNUL, PHII, PHIR, RAST, RS1, RZI, RZR, STI, STR, SUMI,
* SUMR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I,
* ZETA1R, ZETA2I, ZETA2R, ZI, ZR, CYR, CYI, D1MACH, AZABS
INTEGER I, IFLAG, INIT, K, KODE, M, N, ND, NLAST, NN, NUF, NW, NZ
DIMENSION BRY(3), YR(N), YI(N), CWRKR(16), CWRKI(16), CSSR(3),
* CSRR(3), CYR(2), CYI(2)
DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 /
C
NZ = 0
ND = N
NLAST = 0
C-----------------------------------------------------------------------
C COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
C NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
C EXP(ALIM)=EXP(ELIM)*TOL
C-----------------------------------------------------------------------
CSCL = 1.0D0/TOL
CRSC = TOL
CSSR(1) = CSCL
CSSR(2) = CONER
CSSR(3) = CRSC
CSRR(1) = CRSC
CSRR(2) = CONER
CSRR(3) = CSCL
BRY(1) = 1.0D+3*D1MACH(1)/TOL
C-----------------------------------------------------------------------
C CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
C-----------------------------------------------------------------------
FN = DMAX1(FNU,1.0D0)
INIT = 0
CALL ZUNIK(ZR, ZI, FN, 1, 1, TOL, INIT, PHIR, PHII, ZETA1R,
* ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI)
IF (KODE.EQ.1) GO TO 10
STR = ZR + ZETA2R
STI = ZI + ZETA2I
RAST = FN/AZABS(STR,STI)
STR = STR*RAST*RAST
STI = -STI*RAST*RAST
S1R = -ZETA1R + STR
S1I = -ZETA1I + STI
GO TO 20
10 CONTINUE
S1R = -ZETA1R + ZETA2R
S1I = -ZETA1I + ZETA2I
20 CONTINUE
RS1 = S1R
IF (DABS(RS1).GT.ELIM) GO TO 130
30 CONTINUE
NN = MIN0(2,ND)
DO 80 I=1,NN
FN = FNU + DBLE(FLOAT(ND-I))
INIT = 0
CALL ZUNIK(ZR, ZI, FN, 1, 0, TOL, INIT, PHIR, PHII, ZETA1R,
* ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI)
IF (KODE.EQ.1) GO TO 40
STR = ZR + ZETA2R
STI = ZI + ZETA2I
RAST = FN/AZABS(STR,STI)
STR = STR*RAST*RAST
STI = -STI*RAST*RAST
S1R = -ZETA1R + STR
S1I = -ZETA1I + STI + ZI
GO TO 50
40 CONTINUE
S1R = -ZETA1R + ZETA2R
S1I = -ZETA1I + ZETA2I
50 CONTINUE
C-----------------------------------------------------------------------
C TEST FOR UNDERFLOW AND OVERFLOW
C-----------------------------------------------------------------------
RS1 = S1R
IF (DABS(RS1).GT.ELIM) GO TO 110
IF (I.EQ.1) IFLAG = 2
IF (DABS(RS1).LT.ALIM) GO TO 60
C-----------------------------------------------------------------------
C REFINE TEST AND SCALE
C-----------------------------------------------------------------------
APHI = AZABS(PHIR,PHII)
RS1 = RS1 + DLOG(APHI)
IF (DABS(RS1).GT.ELIM) GO TO 110
IF (I.EQ.1) IFLAG = 1
IF (RS1.LT.0.0D0) GO TO 60
IF (I.EQ.1) IFLAG = 3
60 CONTINUE
C-----------------------------------------------------------------------
C SCALE S1 IF CABS(S1).LT.ASCLE
C-----------------------------------------------------------------------
S2R = PHIR*SUMR - PHII*SUMI
S2I = PHIR*SUMI + PHII*SUMR
STR = DEXP(S1R)*CSSR(IFLAG)
S1R = STR*DCOS(S1I)
S1I = STR*DSIN(S1I)
STR = S2R*S1R - S2I*S1I
S2I = S2R*S1I + S2I*S1R
S2R = STR
IF (IFLAG.NE.1) GO TO 70
CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
IF (NW.NE.0) GO TO 110
70 CONTINUE
CYR(I) = S2R
CYI(I) = S2I
M = ND - I + 1
YR(M) = S2R*CSRR(IFLAG)
YI(M) = S2I*CSRR(IFLAG)
80 CONTINUE
IF (ND.LE.2) GO TO 100
RAST = 1.0D0/AZABS(ZR,ZI)
STR = ZR*RAST
STI = -ZI*RAST
RZR = (STR+STR)*RAST
RZI = (STI+STI)*RAST
BRY(2) = 1.0D0/BRY(1)
BRY(3) = D1MACH(2)
S1R = CYR(1)
S1I = CYI(1)
S2R = CYR(2)
S2I = CYI(2)
C1R = CSRR(IFLAG)
ASCLE = BRY(IFLAG)
K = ND - 2
FN = DBLE(FLOAT(K))
DO 90 I=3,ND
C2R = S2R
C2I = S2I
S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I)
S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R)
S1R = C2R
S1I = C2I
C2R = S2R*C1R
C2I = S2I*C1R
YR(K) = C2R
YI(K) = C2I
K = K - 1
FN = FN - 1.0D0
IF (IFLAG.GE.3) GO TO 90
STR = DABS(C2R)
STI = DABS(C2I)
C2M = DMAX1(STR,STI)
IF (C2M.LE.ASCLE) GO TO 90
IFLAG = IFLAG + 1
ASCLE = BRY(IFLAG)
S1R = S1R*C1R
S1I = S1I*C1R
S2R = C2R
S2I = C2I
S1R = S1R*CSSR(IFLAG)
S1I = S1I*CSSR(IFLAG)
S2R = S2R*CSSR(IFLAG)
S2I = S2I*CSSR(IFLAG)
C1R = CSRR(IFLAG)
90 CONTINUE
100 CONTINUE
RETURN
C-----------------------------------------------------------------------
C SET UNDERFLOW AND UPDATE PARAMETERS
C-----------------------------------------------------------------------
110 CONTINUE
IF (RS1.GT.0.0D0) GO TO 120
YR(ND) = ZEROR
YI(ND) = ZEROI
NZ = NZ + 1
ND = ND - 1
IF (ND.EQ.0) GO TO 100
CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM)
IF (NUF.LT.0) GO TO 120
ND = ND - NUF
NZ = NZ + NUF
IF (ND.EQ.0) GO TO 100
FN = FNU + DBLE(FLOAT(ND-1))
IF (FN.GE.FNUL) GO TO 30
NLAST = ND
RETURN
120 CONTINUE
NZ = -1
RETURN
130 CONTINUE
IF (RS1.GT.0.0D0) GO TO 120
NZ = N
DO 140 I=1,N
YR(I) = ZEROR
YI(I) = ZEROI
140 CONTINUE
RETURN
END
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