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OpenLibm/amos/zunk2.f
Viral B. Shah f7c5d2787a Add the amos library
2012-10-29 15:14:32 +05:30

505 lines
17 KiB
Fortran
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SUBROUTINE ZUNK2(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM,
* ALIM)
C***BEGIN PROLOGUE ZUNK2
C***REFER TO ZBESK
C
C ZUNK2 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE
C RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE
C UNIFORM ASYMPTOTIC EXPANSIONS FOR H(KIND,FNU,ZN) AND J(FNU,ZN)
C WHERE ZN IS IN THE RIGHT HALF PLANE, KIND=(3-MR)/2, MR=+1 OR
C -1. HERE ZN=ZR*I OR -ZR*I WHERE ZR=Z IF Z IS IN THE RIGHT
C HALF PLANE OR ZR=-Z IF Z IS IN THE LEFT HALF PLANE. MR INDIC-
C ATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
C NZ=-1 MEANS AN OVERFLOW WILL OCCUR
C
C***ROUTINES CALLED ZAIRY,ZKSCL,ZS1S2,ZUCHK,ZUNHJ,D1MACH,ZABS
C***END PROLOGUE ZUNK2
C COMPLEX AI,ARG,ARGD,ASUM,ASUMD,BSUM,BSUMD,CFN,CI,CIP,CK,CONE,CRSC,
C *CR1,CR2,CS,CSCL,CSGN,CSPN,CSR,CSS,CY,CZERO,C1,C2,DAI,PHI,PHID,RZ,
C *S1,S2,Y,Z,ZB,ZETA1,ZETA1D,ZETA2,ZETA2D,ZN,ZR
DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGDI,
* ARGDR, ARGI, ARGR, ASC, ASCLE, ASUMDI, ASUMDR, ASUMI, ASUMR,
* BRY, BSUMDI, BSUMDR, BSUMI, BSUMR, CAR, CIPI, CIPR, CKI, CKR,
* CONER, CRSC, CR1I, CR1R, CR2I, CR2R, CSCL, CSGNI, CSI,
* CSPNI, CSPNR, CSR, CSRR, CSSR, CYI, CYR, C1I, C1R, C2I, C2M,
* C2R, DAII, DAIR, ELIM, FMR, FN, FNF, FNU, HPI, PHIDI, PHIDR,
* PHII, PHIR, PI, PTI, PTR, RAST, RAZR, RS1, RZI, RZR, SAR, SGN,
* STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, YY, ZBI, ZBR, ZEROI,
* ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZET1DI, ZET1DR, ZET2DI,
* ZET2DR, ZI, ZNI, ZNR, ZR, ZRI, ZRR, D1MACH, ZABS
INTEGER I, IB, IFLAG, IFN, IL, IN, INU, IUF, K, KDFLG, KFLAG, KK,
* KODE, MR, N, NAI, NDAI, NW, NZ, IDUM, J, IPARD, IC
DIMENSION BRY(3), YR(N), YI(N), ASUMR(2), ASUMI(2), BSUMR(2),
* BSUMI(2), PHIR(2), PHII(2), ARGR(2), ARGI(2), ZETA1R(2),
* ZETA1I(2), ZETA2R(2), ZETA2I(2), CYR(2), CYI(2), CIPR(4),
* CIPI(4), CSSR(3), CSRR(3)
DATA ZEROR,ZEROI,CONER,CR1R,CR1I,CR2R,CR2I /
1 0.0D0, 0.0D0, 1.0D0,
1 1.0D0,1.73205080756887729D0 , -0.5D0,-8.66025403784438647D-01 /
DATA HPI, PI, AIC /
1 1.57079632679489662D+00, 3.14159265358979324D+00,
1 1.26551212348464539D+00/
DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4),
* CIPI(4) /
1 1.0D0,0.0D0 , 0.0D0,-1.0D0 , -1.0D0,0.0D0 , 0.0D0,1.0D0 /
C
KDFLG = 1
NZ = 0
C-----------------------------------------------------------------------
C EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN
C THE UNDERFLOW LIMIT
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
BRY(2) = 1.0D0/BRY(1)
BRY(3) = D1MACH(2)
ZRR = ZR
ZRI = ZI
IF (ZR.GE.0.0D0) GO TO 10
ZRR = -ZR
ZRI = -ZI
10 CONTINUE
YY = ZRI
ZNR = ZRI
ZNI = -ZRR
ZBR = ZRR
ZBI = ZRI
INU = INT(SNGL(FNU))
FNF = FNU - DBLE(FLOAT(INU))
ANG = -HPI*FNF
CAR = DCOS(ANG)
SAR = DSIN(ANG)
C2R = HPI*SAR
C2I = -HPI*CAR
KK = MOD(INU,4) + 1
STR = C2R*CIPR(KK) - C2I*CIPI(KK)
STI = C2R*CIPI(KK) + C2I*CIPR(KK)
CSR = CR1R*STR - CR1I*STI
CSI = CR1R*STI + CR1I*STR
IF (YY.GT.0.0D0) GO TO 20
ZNR = -ZNR
ZBI = -ZBI
20 CONTINUE
C-----------------------------------------------------------------------
C K(FNU,Z) IS COMPUTED FROM H(2,FNU,-I*Z) WHERE Z IS IN THE FIRST
C QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY
C CONJUGATION SINCE THE K FUNCTION IS REAL ON THE POSITIVE REAL AXIS
C-----------------------------------------------------------------------
J = 2
DO 80 I=1,N
C-----------------------------------------------------------------------
C J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J
C-----------------------------------------------------------------------
J = 3 - J
FN = FNU + DBLE(FLOAT(I-1))
CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR(J), PHII(J), ARGR(J),
* ARGI(J), ZETA1R(J), ZETA1I(J), ZETA2R(J), ZETA2I(J), ASUMR(J),
* ASUMI(J), BSUMR(J), BSUMI(J))
IF (KODE.EQ.1) GO TO 30
STR = ZBR + ZETA2R(J)
STI = ZBI + ZETA2I(J)
RAST = FN/ZABS(COMPLEX(STR,STI))
STR = STR*RAST*RAST
STI = -STI*RAST*RAST
S1R = ZETA1R(J) - STR
S1I = ZETA1I(J) - STI
GO TO 40
30 CONTINUE
S1R = ZETA1R(J) - ZETA2R(J)
S1I = ZETA1I(J) - ZETA2I(J)
40 CONTINUE
C-----------------------------------------------------------------------
C TEST FOR UNDERFLOW AND OVERFLOW
C-----------------------------------------------------------------------
RS1 = S1R
IF (DABS(RS1).GT.ELIM) GO TO 70
IF (KDFLG.EQ.1) KFLAG = 2
IF (DABS(RS1).LT.ALIM) GO TO 50
C-----------------------------------------------------------------------
C REFINE TEST AND SCALE
C-----------------------------------------------------------------------
APHI = ZABS(COMPLEX(PHIR(J),PHII(J)))
AARG = ZABS(COMPLEX(ARGR(J),ARGI(J)))
RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
IF (DABS(RS1).GT.ELIM) GO TO 70
IF (KDFLG.EQ.1) KFLAG = 1
IF (RS1.LT.0.0D0) GO TO 50
IF (KDFLG.EQ.1) KFLAG = 3
50 CONTINUE
C-----------------------------------------------------------------------
C SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
C EXPONENT EXTREMES
C-----------------------------------------------------------------------
C2R = ARGR(J)*CR2R - ARGI(J)*CR2I
C2I = ARGR(J)*CR2I + ARGI(J)*CR2R
CALL ZAIRY(C2R, C2I, 0, 2, AIR, AII, NAI, IDUM)
CALL ZAIRY(C2R, C2I, 1, 2, DAIR, DAII, NDAI, IDUM)
STR = DAIR*BSUMR(J) - DAII*BSUMI(J)
STI = DAIR*BSUMI(J) + DAII*BSUMR(J)
PTR = STR*CR2R - STI*CR2I
PTI = STR*CR2I + STI*CR2R
STR = PTR + (AIR*ASUMR(J)-AII*ASUMI(J))
STI = PTI + (AIR*ASUMI(J)+AII*ASUMR(J))
PTR = STR*PHIR(J) - STI*PHII(J)
PTI = STR*PHII(J) + STI*PHIR(J)
S2R = PTR*CSR - PTI*CSI
S2I = PTR*CSI + PTI*CSR
STR = DEXP(S1R)*CSSR(KFLAG)
S1R = STR*DCOS(S1I)
S1I = STR*DSIN(S1I)
STR = S2R*S1R - S2I*S1I
S2I = S1R*S2I + S2R*S1I
S2R = STR
IF (KFLAG.NE.1) GO TO 60
CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
IF (NW.NE.0) GO TO 70
60 CONTINUE
IF (YY.LE.0.0D0) S2I = -S2I
CYR(KDFLG) = S2R
CYI(KDFLG) = S2I
YR(I) = S2R*CSRR(KFLAG)
YI(I) = S2I*CSRR(KFLAG)
STR = CSI
CSI = -CSR
CSR = STR
IF (KDFLG.EQ.2) GO TO 85
KDFLG = 2
GO TO 80
70 CONTINUE
IF (RS1.GT.0.0D0) GO TO 320
C-----------------------------------------------------------------------
C FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
C-----------------------------------------------------------------------
IF (ZR.LT.0.0D0) GO TO 320
KDFLG = 1
YR(I)=ZEROR
YI(I)=ZEROI
NZ=NZ+1
STR = CSI
CSI =-CSR
CSR = STR
IF (I.EQ.1) GO TO 80
IF ((YR(I-1).EQ.ZEROR).AND.(YI(I-1).EQ.ZEROI)) GO TO 80
YR(I-1)=ZEROR
YI(I-1)=ZEROI
NZ=NZ+1
80 CONTINUE
I = N
85 CONTINUE
RAZR = 1.0D0/ZABS(COMPLEX(ZRR,ZRI))
STR = ZRR*RAZR
STI = -ZRI*RAZR
RZR = (STR+STR)*RAZR
RZI = (STI+STI)*RAZR
CKR = FN*RZR
CKI = FN*RZI
IB = I + 1
IF (N.LT.IB) GO TO 180
C-----------------------------------------------------------------------
C TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW. SET SEQUENCE TO ZERO
C ON UNDERFLOW.
C-----------------------------------------------------------------------
FN = FNU + DBLE(FLOAT(N-1))
IPARD = 1
IF (MR.NE.0) IPARD = 0
CALL ZUNHJ(ZNR, ZNI, FN, IPARD, TOL, PHIDR, PHIDI, ARGDR, ARGDI,
* ZET1DR, ZET1DI, ZET2DR, ZET2DI, ASUMDR, ASUMDI, BSUMDR, BSUMDI)
IF (KODE.EQ.1) GO TO 90
STR = ZBR + ZET2DR
STI = ZBI + ZET2DI
RAST = FN/ZABS(COMPLEX(STR,STI))
STR = STR*RAST*RAST
STI = -STI*RAST*RAST
S1R = ZET1DR - STR
S1I = ZET1DI - STI
GO TO 100
90 CONTINUE
S1R = ZET1DR - ZET2DR
S1I = ZET1DI - ZET2DI
100 CONTINUE
RS1 = S1R
IF (DABS(RS1).GT.ELIM) GO TO 105
IF (DABS(RS1).LT.ALIM) GO TO 120
C----------------------------------------------------------------------------
C REFINE ESTIMATE AND TEST
C-------------------------------------------------------------------------
APHI = ZABS(COMPLEX(PHIDR,PHIDI))
RS1 = RS1+DLOG(APHI)
IF (DABS(RS1).LT.ELIM) GO TO 120
105 CONTINUE
IF (RS1.GT.0.0D0) GO TO 320
C-----------------------------------------------------------------------
C FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
C-----------------------------------------------------------------------
IF (ZR.LT.0.0D0) GO TO 320
NZ = N
DO 106 I=1,N
YR(I) = ZEROR
YI(I) = ZEROI
106 CONTINUE
RETURN
120 CONTINUE
S1R = CYR(1)
S1I = CYI(1)
S2R = CYR(2)
S2I = CYI(2)
C1R = CSRR(KFLAG)
ASCLE = BRY(KFLAG)
DO 130 I=IB,N
C2R = S2R
C2I = S2I
S2R = CKR*C2R - CKI*C2I + S1R
S2I = CKR*C2I + CKI*C2R + S1I
S1R = C2R
S1I = C2I
CKR = CKR + RZR
CKI = CKI + RZI
C2R = S2R*C1R
C2I = S2I*C1R
YR(I) = C2R
YI(I) = C2I
IF (KFLAG.GE.3) GO TO 130
STR = DABS(C2R)
STI = DABS(C2I)
C2M = DMAX1(STR,STI)
IF (C2M.LE.ASCLE) GO TO 130
KFLAG = KFLAG + 1
ASCLE = BRY(KFLAG)
S1R = S1R*C1R
S1I = S1I*C1R
S2R = C2R
S2I = C2I
S1R = S1R*CSSR(KFLAG)
S1I = S1I*CSSR(KFLAG)
S2R = S2R*CSSR(KFLAG)
S2I = S2I*CSSR(KFLAG)
C1R = CSRR(KFLAG)
130 CONTINUE
180 CONTINUE
IF (MR.EQ.0) RETURN
C-----------------------------------------------------------------------
C ANALYTIC CONTINUATION FOR RE(Z).LT.0.0D0
C-----------------------------------------------------------------------
NZ = 0
FMR = DBLE(FLOAT(MR))
SGN = -DSIGN(PI,FMR)
C-----------------------------------------------------------------------
C CSPN AND CSGN ARE COEFF OF K AND I FUNCIONS RESP.
C-----------------------------------------------------------------------
CSGNI = SGN
IF (YY.LE.0.0D0) CSGNI = -CSGNI
IFN = INU + N - 1
ANG = FNF*SGN
CSPNR = DCOS(ANG)
CSPNI = DSIN(ANG)
IF (MOD(IFN,2).EQ.0) GO TO 190
CSPNR = -CSPNR
CSPNI = -CSPNI
190 CONTINUE
C-----------------------------------------------------------------------
C CS=COEFF OF THE J FUNCTION TO GET THE I FUNCTION. I(FNU,Z) IS
C COMPUTED FROM EXP(I*FNU*HPI)*J(FNU,-I*Z) WHERE Z IS IN THE FIRST
C QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY
C CONJUGATION SINCE THE I FUNCTION IS REAL ON THE POSITIVE REAL AXIS
C-----------------------------------------------------------------------
CSR = SAR*CSGNI
CSI = CAR*CSGNI
IN = MOD(IFN,4) + 1
C2R = CIPR(IN)
C2I = CIPI(IN)
STR = CSR*C2R + CSI*C2I
CSI = -CSR*C2I + CSI*C2R
CSR = STR
ASC = BRY(1)
IUF = 0
KK = N
KDFLG = 1
IB = IB - 1
IC = IB - 1
DO 290 K=1,N
FN = FNU + DBLE(FLOAT(KK-1))
C-----------------------------------------------------------------------
C LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K
C FUNCTION ABOVE
C-----------------------------------------------------------------------
IF (N.GT.2) GO TO 175
172 CONTINUE
PHIDR = PHIR(J)
PHIDI = PHII(J)
ARGDR = ARGR(J)
ARGDI = ARGI(J)
ZET1DR = ZETA1R(J)
ZET1DI = ZETA1I(J)
ZET2DR = ZETA2R(J)
ZET2DI = ZETA2I(J)
ASUMDR = ASUMR(J)
ASUMDI = ASUMI(J)
BSUMDR = BSUMR(J)
BSUMDI = BSUMI(J)
J = 3 - J
GO TO 210
175 CONTINUE
IF ((KK.EQ.N).AND.(IB.LT.N)) GO TO 210
IF ((KK.EQ.IB).OR.(KK.EQ.IC)) GO TO 172
CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIDR, PHIDI, ARGDR,
* ARGDI, ZET1DR, ZET1DI, ZET2DR, ZET2DI, ASUMDR,
* ASUMDI, BSUMDR, BSUMDI)
210 CONTINUE
IF (KODE.EQ.1) GO TO 220
STR = ZBR + ZET2DR
STI = ZBI + ZET2DI
RAST = FN/ZABS(COMPLEX(STR,STI))
STR = STR*RAST*RAST
STI = -STI*RAST*RAST
S1R = -ZET1DR + STR
S1I = -ZET1DI + STI
GO TO 230
220 CONTINUE
S1R = -ZET1DR + ZET2DR
S1I = -ZET1DI + ZET2DI
230 CONTINUE
C-----------------------------------------------------------------------
C TEST FOR UNDERFLOW AND OVERFLOW
C-----------------------------------------------------------------------
RS1 = S1R
IF (DABS(RS1).GT.ELIM) GO TO 280
IF (KDFLG.EQ.1) IFLAG = 2
IF (DABS(RS1).LT.ALIM) GO TO 240
C-----------------------------------------------------------------------
C REFINE TEST AND SCALE
C-----------------------------------------------------------------------
APHI = ZABS(COMPLEX(PHIDR,PHIDI))
AARG = ZABS(COMPLEX(ARGDR,ARGDI))
RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
IF (DABS(RS1).GT.ELIM) GO TO 280
IF (KDFLG.EQ.1) IFLAG = 1
IF (RS1.LT.0.0D0) GO TO 240
IF (KDFLG.EQ.1) IFLAG = 3
240 CONTINUE
CALL ZAIRY(ARGDR, ARGDI, 0, 2, AIR, AII, NAI, IDUM)
CALL ZAIRY(ARGDR, ARGDI, 1, 2, DAIR, DAII, NDAI, IDUM)
STR = DAIR*BSUMDR - DAII*BSUMDI
STI = DAIR*BSUMDI + DAII*BSUMDR
STR = STR + (AIR*ASUMDR-AII*ASUMDI)
STI = STI + (AIR*ASUMDI+AII*ASUMDR)
PTR = STR*PHIDR - STI*PHIDI
PTI = STR*PHIDI + STI*PHIDR
S2R = PTR*CSR - PTI*CSI
S2I = PTR*CSI + PTI*CSR
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 250
CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
IF (NW.EQ.0) GO TO 250
S2R = ZEROR
S2I = ZEROI
250 CONTINUE
IF (YY.LE.0.0D0) S2I = -S2I
CYR(KDFLG) = S2R
CYI(KDFLG) = S2I
C2R = S2R
C2I = S2I
S2R = S2R*CSRR(IFLAG)
S2I = S2I*CSRR(IFLAG)
C-----------------------------------------------------------------------
C ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N
C-----------------------------------------------------------------------
S1R = YR(KK)
S1I = YI(KK)
IF (KODE.EQ.1) GO TO 270
CALL ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NW, ASC, ALIM, IUF)
NZ = NZ + NW
270 CONTINUE
YR(KK) = S1R*CSPNR - S1I*CSPNI + S2R
YI(KK) = S1R*CSPNI + S1I*CSPNR + S2I
KK = KK - 1
CSPNR = -CSPNR
CSPNI = -CSPNI
STR = CSI
CSI = -CSR
CSR = STR
IF (C2R.NE.0.0D0 .OR. C2I.NE.0.0D0) GO TO 255
KDFLG = 1
GO TO 290
255 CONTINUE
IF (KDFLG.EQ.2) GO TO 295
KDFLG = 2
GO TO 290
280 CONTINUE
IF (RS1.GT.0.0D0) GO TO 320
S2R = ZEROR
S2I = ZEROI
GO TO 250
290 CONTINUE
K = N
295 CONTINUE
IL = N - K
IF (IL.EQ.0) RETURN
C-----------------------------------------------------------------------
C RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE
C K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO KEEP
C INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT EXTREMES.
C-----------------------------------------------------------------------
S1R = CYR(1)
S1I = CYI(1)
S2R = CYR(2)
S2I = CYI(2)
CSR = CSRR(IFLAG)
ASCLE = BRY(IFLAG)
FN = DBLE(FLOAT(INU+IL))
DO 310 I=1,IL
C2R = S2R
C2I = S2I
S2R = S1R + (FN+FNF)*(RZR*C2R-RZI*C2I)
S2I = S1I + (FN+FNF)*(RZR*C2I+RZI*C2R)
S1R = C2R
S1I = C2I
FN = FN - 1.0D0
C2R = S2R*CSR
C2I = S2I*CSR
CKR = C2R
CKI = C2I
C1R = YR(KK)
C1I = YI(KK)
IF (KODE.EQ.1) GO TO 300
CALL ZS1S2(ZRR, ZRI, C1R, C1I, C2R, C2I, NW, ASC, ALIM, IUF)
NZ = NZ + NW
300 CONTINUE
YR(KK) = C1R*CSPNR - C1I*CSPNI + C2R
YI(KK) = C1R*CSPNI + C1I*CSPNR + C2I
KK = KK - 1
CSPNR = -CSPNR
CSPNI = -CSPNI
IF (IFLAG.GE.3) GO TO 310
C2R = DABS(CKR)
C2I = DABS(CKI)
C2M = DMAX1(C2R,C2I)
IF (C2M.LE.ASCLE) GO TO 310
IFLAG = IFLAG + 1
ASCLE = BRY(IFLAG)
S1R = S1R*CSR
S1I = S1I*CSR
S2R = CKR
S2I = CKI
S1R = S1R*CSSR(IFLAG)
S1I = S1I*CSSR(IFLAG)
S2R = S2R*CSSR(IFLAG)
S2I = S2I*CSSR(IFLAG)
CSR = CSRR(IFLAG)
310 CONTINUE
RETURN
320 CONTINUE
NZ = -1
RETURN
END
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