1      SUBROUTINE ZSERI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM,
2     * ALIM)
3C***BEGIN PROLOGUE  ZSERI
4C***REFER TO  ZBESI,ZBESK
5C
6C     ZSERI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY
7C     MEANS OF THE POWER SERIES FOR LARGE CABS(Z) IN THE
8C     REGION CABS(Z).LE.2*SQRT(FNU+1). NZ=0 IS A NORMAL RETURN.
9C     NZ.GT.0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO
10C     DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE
11C     CONDITION CABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE
12C     COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ).
13C
14C***ROUTINES CALLED  DGAMLN,D1MACH,ZUCHK,AZABS,ZDIV,AZLOG,ZMLT
15C***END PROLOGUE  ZSERI
16C     COMPLEX AK1,CK,COEF,CONE,CRSC,CSCL,CZ,CZERO,HZ,RZ,S1,S2,Y,Z
17      DOUBLE PRECISION AA, ACZ, AK, AK1I, AK1R, ALIM, ARM, ASCLE, ATOL,
18     * AZ, CKI, CKR, COEFI, COEFR, CONEI, CONER, CRSCR, CZI, CZR, DFNU,
19     * ELIM, FNU, FNUP, HZI, HZR, RAZ, RS, RTR1, RZI, RZR, S, SS, STI,
20     * STR, S1I, S1R, S2I, S2R, TOL, YI, YR, WI, WR, ZEROI, ZEROR, ZI,
21     * ZR, DGAMLN, D1MACH, AZABS
22      INTEGER I, IB, IDUM, IFLAG, IL, K, KODE, L, M, N, NN, NZ, NW
23      DIMENSION YR(N), YI(N), WR(2), WI(2)
24      DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
25C
26      NZ = 0
27      AZ = AZABS(ZR,ZI)
28      IF (AZ.EQ.0.0D0) GO TO 160
29      ARM = 1.0D+3*D1MACH(1)
30      RTR1 = DSQRT(ARM)
31      CRSCR = 1.0D0
32      IFLAG = 0
33      IF (AZ.LT.ARM) GO TO 150
34      HZR = 0.5D0*ZR
35      HZI = 0.5D0*ZI
36      CZR = ZEROR
37      CZI = ZEROI
38      IF (AZ.LE.RTR1) GO TO 10
39      CALL ZMLT(HZR, HZI, HZR, HZI, CZR, CZI)
40   10 CONTINUE
41      ACZ = AZABS(CZR,CZI)
42      NN = N
43      CALL AZLOG(HZR, HZI, CKR, CKI, IDUM)
44   20 CONTINUE
45      DFNU = FNU + DBLE(FLOAT(NN-1))
46      FNUP = DFNU + 1.0D0
47C-----------------------------------------------------------------------
48C     UNDERFLOW TEST
49C-----------------------------------------------------------------------
50      AK1R = CKR*DFNU
51      AK1I = CKI*DFNU
52      AK = DGAMLN(FNUP,IDUM)
53      AK1R = AK1R - AK
54      IF (KODE.EQ.2) AK1R = AK1R - ZR
55      IF (AK1R.GT.(-ELIM)) GO TO 40
56   30 CONTINUE
57      NZ = NZ + 1
58      YR(NN) = ZEROR
59      YI(NN) = ZEROI
60      IF (ACZ.GT.DFNU) GO TO 190
61      NN = NN - 1
62      IF (NN.EQ.0) RETURN
63      GO TO 20
64   40 CONTINUE
65      IF (AK1R.GT.(-ALIM)) GO TO 50
66      IFLAG = 1
67      SS = 1.0D0/TOL
68      CRSCR = TOL
69      ASCLE = ARM*SS
70   50 CONTINUE
71      AA = DEXP(AK1R)
72      IF (IFLAG.EQ.1) AA = AA*SS
73      COEFR = AA*DCOS(AK1I)
74      COEFI = AA*DSIN(AK1I)
75      ATOL = TOL*ACZ/FNUP
76      IL = MIN0(2,NN)
77      DO 90 I=1,IL
78        DFNU = FNU + DBLE(FLOAT(NN-I))
79        FNUP = DFNU + 1.0D0
80        S1R = CONER
81        S1I = CONEI
82        IF (ACZ.LT.TOL*FNUP) GO TO 70
83        AK1R = CONER
84        AK1I = CONEI
85        AK = FNUP + 2.0D0
86        S = FNUP
87        AA = 2.0D0
88   60   CONTINUE
89        RS = 1.0D0/S
90        STR = AK1R*CZR - AK1I*CZI
91        STI = AK1R*CZI + AK1I*CZR
92        AK1R = STR*RS
93        AK1I = STI*RS
94        S1R = S1R + AK1R
95        S1I = S1I + AK1I
96        S = S + AK
97        AK = AK + 2.0D0
98        AA = AA*ACZ*RS
99        IF (AA.GT.ATOL) GO TO 60
100   70   CONTINUE
101        S2R = S1R*COEFR - S1I*COEFI
102        S2I = S1R*COEFI + S1I*COEFR
103        WR(I) = S2R
104        WI(I) = S2I
105        IF (IFLAG.EQ.0) GO TO 80
106        CALL ZUCHK(S2R, S2I, NW, ASCLE, TOL)
107        IF (NW.NE.0) GO TO 30
108   80   CONTINUE
109        M = NN - I + 1
110        YR(M) = S2R*CRSCR
111        YI(M) = S2I*CRSCR
112        IF (I.EQ.IL) GO TO 90
113        CALL ZDIV(COEFR, COEFI, HZR, HZI, STR, STI)
114        COEFR = STR*DFNU
115        COEFI = STI*DFNU
116   90 CONTINUE
117      IF (NN.LE.2) RETURN
118      K = NN - 2
119      AK = DBLE(FLOAT(K))
120      RAZ = 1.0D0/AZ
121      STR = ZR*RAZ
122      STI = -ZI*RAZ
123      RZR = (STR+STR)*RAZ
124      RZI = (STI+STI)*RAZ
125      IF (IFLAG.EQ.1) GO TO 120
126      IB = 3
127  100 CONTINUE
128      DO 110 I=IB,NN
129        YR(K) = (AK+FNU)*(RZR*YR(K+1)-RZI*YI(K+1)) + YR(K+2)
130        YI(K) = (AK+FNU)*(RZR*YI(K+1)+RZI*YR(K+1)) + YI(K+2)
131        AK = AK - 1.0D0
132        K = K - 1
133  110 CONTINUE
134      RETURN
135C-----------------------------------------------------------------------
136C     RECUR BACKWARD WITH SCALED VALUES
137C-----------------------------------------------------------------------
138  120 CONTINUE
139C-----------------------------------------------------------------------
140C     EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE
141C     UNDERFLOW LIMIT = ASCLE = D1MACH(1)*SS*1.0D+3
142C-----------------------------------------------------------------------
143      S1R = WR(1)
144      S1I = WI(1)
145      S2R = WR(2)
146      S2I = WI(2)
147      DO 130 L=3,NN
148        CKR = S2R
149        CKI = S2I
150        S2R = S1R + (AK+FNU)*(RZR*CKR-RZI*CKI)
151        S2I = S1I + (AK+FNU)*(RZR*CKI+RZI*CKR)
152        S1R = CKR
153        S1I = CKI
154        CKR = S2R*CRSCR
155        CKI = S2I*CRSCR
156        YR(K) = CKR
157        YI(K) = CKI
158        AK = AK - 1.0D0
159        K = K - 1
160        IF (AZABS(CKR,CKI).GT.ASCLE) GO TO 140
161  130 CONTINUE
162      RETURN
163  140 CONTINUE
164      IB = L + 1
165      IF (IB.GT.NN) RETURN
166      GO TO 100
167  150 CONTINUE
168      NZ = N
169      IF (FNU.EQ.0.0D0) NZ = NZ - 1
170  160 CONTINUE
171      YR(1) = ZEROR
172      YI(1) = ZEROI
173      IF (FNU.NE.0.0D0) GO TO 170
174      YR(1) = CONER
175      YI(1) = CONEI
176  170 CONTINUE
177      IF (N.EQ.1) RETURN
178      DO 180 I=2,N
179        YR(I) = ZEROR
180        YI(I) = ZEROI
181  180 CONTINUE
182      RETURN
183C-----------------------------------------------------------------------
184C     RETURN WITH NZ.LT.0 IF CABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE
185C     THE CALCULATION IN CBINU WITH N=N-IABS(NZ)
186C-----------------------------------------------------------------------
187  190 CONTINUE
188      NZ = -NZ
189      RETURN
190      END
191