EXTERNAL

SUB dbrent (ax, bx, cx, dum1, dum2, tol, dbrent, xmin)

    ! The function dbrent has been converted to a subroutine
    ! to permit it to return two values: dbrent and xmin.

    DECLARE FUNCTION func, df     ! Supplied by the user

    LET itmax = 100
    LET zeps = 1e-10
    LET a = min(ax, cx)
    LET b = max(ax, cx)
    LET v = bx
    LET w = v
    LET x = v
    LET e = 0
    LET fx = func(x)
    LET fv = fx
    LET fw = fx
    LET dx = df(x)
    LET dv = dx
    LET dw = dx
    FOR iter = 1 to itmax
        LET xm = .5 * (a + b)
        LET tol1 = tol * abs(x) + zeps
        LET tol2 = 2 * tol1
        IF abs(x - xm) <= tol2 - .5 * (b - a) then EXIT FOR

        IF abs(e) > tol1 then
           LET d1 = 2 * (b - a)
           LET d2 = d1
           IF dw <> dx then LET d1 = (w - x) * dx / (dx - dw)
           IF dv <> dx then LET d2 = (v - x) * dx / (dx - dv)
           LET u1 = x + d1
           LET u2 = x + d2
           IF ((a - u1) * (u1 - b) > 0) and (dx * d1 <= 0) then
              LET ok1 = -1
           ELSE
              LET ok1 = 0
           END IF
           IF ((a - u2) * (u2 - b) > 0) and (dx * d2 <= 0) then
              LET ok2 = -1
           ELSE
              LET ok2 = 0
           END IF

           LET olde = e
           LET e = d
           IF ok1=-1 or ok2=-1 then
              IF ok1=-1 and ok2=-1 then
                 IF abs(d1) < abs(d2) then
                    LET d = d1
                 ELSE
                    LET d = d2
                 END IF
              ELSEIF ok1=-1 then
                 LET d = d1
              ELSE
                 LET d = d2
              END IF
              IF abs(d) <= abs(.5 * olde) then
                 IF dx >= 0 then LET e = a - x else LET e = b - x
                 LET d = .5 * e
              ELSE
                 LET u = x + d
                 IF u - a < tol2 or b - u < tol2 then LET d = abs(tol1) * sgn(xm - x)
              END IF
           ELSE
              IF dx >= 0 then LET e = a - x else LET e = b - x
              LET d = .5 * e
           END IF
        ELSE
           IF dx >= 0 then LET e = a - x else LET e = b - x
           LET d = .5 * e
        END IF

        IF abs(d) >= tol1 then
           LET u = x + d
           LET fu = func(u)
        ELSE
           LET u = x + abs(tol1) * sgn(d)
           LET fu = func(u)
           IF fu > fx then EXIT FOR
        END IF

        LET du = df(u)
        IF fu <= fx then
           IF u >= x then LET a = x else LET b = x
           LET v = w
           LET fv = fw
           LET dv = dw
           LET w = x
           LET fw = fx
           LET dw = dx
           LET x = u
           LET fx = fu
           LET dx = du
        ELSE
           IF u < x then LET a = u else LET b = u
           IF fu <= fw or w = x then
              LET v = w
              LET fv = fw
              LET dv = dw
              LET w = u
              LET fw = fu
              LET dw = du
           ELSEIF fu <= fv or v = x or v = w then
              LET v = u
              LET fv = fu
              LET dv = du
           END IF
        END IF
    NEXT iter
    IF iter > itmax then
       PRINT "dbrent exceeded maximum iterations."
    ELSE
       LET xmin = x
       LET dbrent = fx
    END IF

END SUB