cuoik.f

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      SUBROUTINE CUOIK(Z, FNU, KODE, IKFLG, N, Y, NUF, TOL, ELIM, ALIM)
C***BEGIN PROLOGUE  CUOIK
C***REFER TO  CBESI,CBESK,CBESH
C
C     CUOIK COMPUTES THE LEADING TERMS OF THE UNIFORM ASYMPTOTIC
C     EXPANSIONS FOR THE I AND K FUNCTIONS AND COMPARES THEM
C     (IN LOGARITHMIC FORM) TO ALIM AND ELIM FOR OVER AND UNDERFLOW
C     WHERE ALIM.LT.ELIM. IF THE MAGNITUDE, BASED ON THE LEADING
C     EXPONENTIAL, IS LESS THAN ALIM OR GREATER THAN -ALIM, THEN
C     THE RESULT IS ON SCALE. IF NOT, THEN A REFINED TEST USING OTHER
C     MULTIPLIERS (IN LOGARITHMIC FORM) IS MADE BASED ON ELIM. HERE
C     EXP(-ELIM)=SMALLEST MACHINE NUMBER*1.0E+3 AND EXP(-ALIM)=
C     EXP(-ELIM)/TOL
C
C     IKFLG=1 MEANS THE I SEQUENCE IS TESTED
C          =2 MEANS THE K SEQUENCE IS TESTED
C     NUF = 0 MEANS THE LAST MEMBER OF THE SEQUENCE IS ON SCALE
C         =-1 MEANS AN OVERFLOW WOULD OCCUR
C     IKFLG=1 AND NUF.GT.0 MEANS THE LAST NUF Y VALUES WERE SET TO ZERO
C             THE FIRST N-NUF VALUES MUST BE SET BY ANOTHER ROUTINE
C     IKFLG=2 AND NUF.EQ.N MEANS ALL Y VALUES WERE SET TO ZERO
C     IKFLG=2 AND 0.LT.NUF.LT.N NOT CONSIDERED. Y MUST BE SET BY
C             ANOTHER ROUTINE
C
C***ROUTINES CALLED  CUCHK,CUNHJ,CUNIK,R1MACH
C***END PROLOGUE  CUOIK
      COMPLEX ARG, ASUM, BSUM, CWRK, CZ, CZERO, PHI, SUM, Y, Z, ZB,
     * ZETA1, ZETA2, ZN, ZR
      REAL AARG, AIC, ALIM, APHI, ASCLE, AX, AY, ELIM, FNN, FNU, GNN,
     * GNU, RCZ, TOL, X, YY
      INTEGER I, IFORM, IKFLG, INIT, KODE, N, NN, NUF, NW
      DIMENSION Y(N), CWRK(16)
      DATA CZERO / (0.0E0,0.0E0) /
      DATA AIC / 1.265512123484645396E+00 /
      NUF = 0
      NN = N
      X = REAL(Z)
      ZR = Z
      IF (X.LT.0.0E0) ZR = -Z
      ZB = ZR
      YY = AIMAG(ZR)
      AX = ABS(X)*1.7321E0
      AY = ABS(YY)
      IFORM = 1
      IF (AY.GT.AX) IFORM = 2
      GNU = AMAX1(FNU,1.0E0)
      IF (IKFLG.EQ.1) GO TO 10
      FNN = FLOAT(NN)
      GNN = FNU + FNN - 1.0E0
      GNU = AMAX1(GNN,FNN)
   10 CONTINUE
C-----------------------------------------------------------------------
C     ONLY THE MAGNITUDE OF ARG AND PHI ARE NEEDED ALONG WITH THE
C     REAL PARTS OF ZETA1, ZETA2 AND ZB. NO ATTEMPT IS MADE TO GET
C     THE SIGN OF THE IMAGINARY PART CORRECT.
C-----------------------------------------------------------------------
      IF (IFORM.EQ.2) GO TO 20
      INIT = 0
      CALL CUNIK(ZR, GNU, IKFLG, 1, TOL, INIT, PHI, ZETA1, ZETA2, SUM,
     * CWRK)
      CZ = -ZETA1 + ZETA2
      GO TO 40
   20 CONTINUE
      ZN = -ZR*CMPLX(0.0E0,1.0E0)
      IF (YY.GT.0.0E0) GO TO 30
      ZN = CONJG(-ZN)
   30 CONTINUE
      CALL CUNHJ(ZN, GNU, 1, TOL, PHI, ARG, ZETA1, ZETA2, ASUM, BSUM)
      CZ = -ZETA1 + ZETA2
      AARG = CABS(ARG)
   40 CONTINUE
      IF (KODE.EQ.2) CZ = CZ - ZB
      IF (IKFLG.EQ.2) CZ = -CZ
      APHI = CABS(PHI)
      RCZ = REAL(CZ)
C-----------------------------------------------------------------------
C     OVERFLOW TEST
C-----------------------------------------------------------------------
      IF (RCZ.GT.ELIM) GO TO 170
      IF (RCZ.LT.ALIM) GO TO 50
      RCZ = RCZ + ALOG(APHI)
      IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*ALOG(AARG) - AIC
      IF (RCZ.GT.ELIM) GO TO 170
      GO TO 100
   50 CONTINUE
C-----------------------------------------------------------------------
C     UNDERFLOW TEST
C-----------------------------------------------------------------------
      IF (RCZ.LT.(-ELIM)) GO TO 60
      IF (RCZ.GT.(-ALIM)) GO TO 100
      RCZ = RCZ + ALOG(APHI)
      IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*ALOG(AARG) - AIC
      IF (RCZ.GT.(-ELIM)) GO TO 80
   60 CONTINUE
      DO 70 I=1,NN
        Y(I) = CZERO
   70 CONTINUE
      NUF = NN
      RETURN
   80 CONTINUE
      ASCLE = 1.0E+3*R1MACH(1)/TOL
      CZ = CZ + CLOG(PHI)
      IF (IFORM.EQ.1) GO TO 90
      CZ = CZ - CMPLX(0.25E0,0.0E0)*CLOG(ARG) - CMPLX(AIC,0.0E0)
   90 CONTINUE
      AX = EXP(RCZ)/TOL
      AY = AIMAG(CZ)
      CZ = CMPLX(AX,0.0E0)*CMPLX(COS(AY),SIN(AY))
      CALL CUCHK(CZ, NW, ASCLE, TOL)
      IF (NW.EQ.1) GO TO 60
  100 CONTINUE
      IF (IKFLG.EQ.2) RETURN
      IF (N.EQ.1) RETURN
C-----------------------------------------------------------------------
C     SET UNDERFLOWS ON I SEQUENCE
C-----------------------------------------------------------------------
  110 CONTINUE
      GNU = FNU + FLOAT(NN-1)
      IF (IFORM.EQ.2) GO TO 120
      INIT = 0
      CALL CUNIK(ZR, GNU, IKFLG, 1, TOL, INIT, PHI, ZETA1, ZETA2, SUM,
     * CWRK)
      CZ = -ZETA1 + ZETA2
      GO TO 130
  120 CONTINUE
      CALL CUNHJ(ZN, GNU, 1, TOL, PHI, ARG, ZETA1, ZETA2, ASUM, BSUM)
      CZ = -ZETA1 + ZETA2
      AARG = CABS(ARG)
  130 CONTINUE
      IF (KODE.EQ.2) CZ = CZ - ZB
      APHI = CABS(PHI)
      RCZ = REAL(CZ)
      IF (RCZ.LT.(-ELIM)) GO TO 140
      IF (RCZ.GT.(-ALIM)) RETURN
      RCZ = RCZ + ALOG(APHI)
      IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*ALOG(AARG) - AIC
      IF (RCZ.GT.(-ELIM)) GO TO 150
  140 CONTINUE
      Y(NN) = CZERO
      NN = NN - 1
      NUF = NUF + 1
      IF (NN.EQ.0) RETURN
      GO TO 110
  150 CONTINUE
      ASCLE = 1.0E+3*R1MACH(1)/TOL
      CZ = CZ + CLOG(PHI)
      IF (IFORM.EQ.1) GO TO 160
      CZ = CZ - CMPLX(0.25E0,0.0E0)*CLOG(ARG) - CMPLX(AIC,0.0E0)
  160 CONTINUE
      AX = EXP(RCZ)/TOL
      AY = AIMAG(CZ)
      CZ = CMPLX(AX,0.0E0)*CMPLX(COS(AY),SIN(AY))
      CALL CUCHK(CZ, NW, ASCLE, TOL)
      IF (NW.EQ.1) GO TO 140
      RETURN
  170 CONTINUE
      NUF = -1
      RETURN
      END