SUBROUTINE FZERO (F, B, C, R, RE, AE, IFLAG)
      REAL A,ACBS,ACMB,AE,AW,B,C,CMB,ER,FA,FB,FC,FX,FZ,P,Q,R,
     +     RE,RW,T,TOL,Z
      INTEGER IC,IFLAG,KOUNT
C***FIRST EXECUTABLE STATEMENT  FZERO
C
C   ER is two times the computer unit roundoff value which is defined
C   here by the function R1MACH.
C
      ER = 2.0E0 * R1MACH(4)
C
C   Initialize.
C
      Z = R
      IF (R .LE. MIN(B,C)  .OR.  R .GE. MAX(B,C)) Z = C
      RW = MAX(RE,ER)
      AW = MAX(AE,0.E0)
      IC = 0
      T = Z
      FZ = F(T)
      FC = FZ
      T = B
      FB = F(T)
      KOUNT = 2
      IF (SIGN(1.0E0,FZ) .EQ. SIGN(1.0E0,FB)) GO TO 1
      C = Z
      GO TO 2
    1 IF (Z .EQ. C) GO TO 2
      T = C
      FC = F(T)
      KOUNT = 3
      IF (SIGN(1.0E0,FZ) .EQ. SIGN(1.0E0,FC)) GO TO 2
      B = Z
      FB = FZ
    2 A = C
      FA = FC
      ACBS = ABS(B-C)
      FX = MAX(ABS(FB),ABS(FC))
C
    3 IF (ABS(FC) .GE. ABS(FB)) GO TO 4
C
C   Perform interchange.
C
      A = B
      FA = FB
      B = C
      FB = FC
      C = A
      FC = FA
C
    4 CMB = 0.5E0*(C-B)
      ACMB = ABS(CMB)
      TOL = RW*ABS(B) + AW
C
C   Test stopping criterion and function count.
C
      IF (ACMB .LE. TOL) GO TO 10
      IF (FB .EQ. 0.E0) GO TO 11
      IF (KOUNT .GE. 500) GO TO 14
C
C   Calculate new iterate implicitly as B+P/Q, where we arrange
C   P .GE. 0.  The implicit form is used to prevent overflow.
C
      P = (B-A)*FB
      Q = FA - FB
      IF (P .GE. 0.E0) GO TO 5
      P = -P
      Q = -Q
C
C   Update A and check for satisfactory reduction in the size of the
C   bracketing interval.  If not, perform bisection.
C
    5 A = B
      FA = FB
      IC = IC + 1
      IF (IC .LT. 4) GO TO 6
      IF (8.0E0*ACMB .GE. ACBS) GO TO 8
      IC = 0
      ACBS = ACMB
C
C   Test for too small a change.
C
    6 IF (P .GT. ABS(Q)*TOL) GO TO 7
C
C   Increment by TOLerance.
C
      B = B + SIGN(TOL,CMB)
      GO TO 9
C
C   Root ought to be between B and (C+B)/2.
C
    7 IF (P .GE. CMB*Q) GO TO 8
C
C   Use secant rule.
C
      B = B + P/Q
      GO TO 9
C
C   Use bisection (C+B)/2.
C
    8 B = B + CMB
C
C   Have completed computation for new iterate B.
C
    9 T = B
      FB = F(T)
      KOUNT = KOUNT + 1
C
C   Decide whether next step is interpolation or extrapolation.
C
      IF (SIGN(1.0E0,FB) .NE. SIGN(1.0E0,FC)) GO TO 3
      C = A
      FC = FA
      GO TO 3
C
C   Finished.  Process results for proper setting of IFLAG.
C
   10 IF (SIGN(1.0E0,FB) .EQ. SIGN(1.0E0,FC)) GO TO 13
      IF (ABS(FB) .GT. FX) GO TO 12
      IFLAG = 1
      RETURN
   11 IFLAG = 2
      RETURN
   12 IFLAG = 3
      RETURN
   13 IFLAG = 4
      RETURN
   14 IFLAG = 5
      RETURN
      END