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,ZABS 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, ZABS 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/ZABS(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/ZABS(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 = ZABS(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/ZABS(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