EXTERNAL

SUB brent (ax, bx, cx, dum, tol, brent, xmin)

    ! The original function brent is converted to a subroutine
    ! to permit it to return two values: brent and xmin

    ! The function func must be prepared by the user

    DECLARE FUNCTION func

    LET itmax = 100
    LET cgold = .381966
    LET zeps = 1e-10
    LET a = min(cx, ax)
    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

    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 r = (x - w) * (fx - fv)
           LET q = (x - v) * (fx - fw)
           LET p = (x - v) * q - (x - w) * r
           LET q = 2 * (q - r)
           IF q > 0 then LET p = -p
           LET q = abs(q)
           LET etemp = e
           LET e = d
           LET dum = abs(.5 * q * etemp)
           IF abs(p) < dum and p > q * (a - x) and p < q * (b - x) then
              LET d = p / q
              LET u = x + d
              IF u - a < tol2 or b - u < tol2 then LET d = abs(tol1) * sgn(xm - x)
           ELSE
              IF x >= xm then LET e = a - x else LET e = b - x
              LET d = cgold * e
           END IF
        ELSE
           IF x >= xm then LET e = a - x else LET e = b - x
           LET d = cgold * e
        END IF

        IF abs(d) >= tol1 then
           LET u = x + d
        ELSE
           LET u = x + abs(tol1) * sgn(d)
        END IF
        LET fu = func(u)
        IF fu <= fx then
           IF u >= x then LET a = x else LET b = x
           LET v = w
           LET fv = fw
           LET w = x
           LET fw = fx
           LET x = u
           LET fx = fu
        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 w = u
              LET fw = fu
           ELSEIF fu <= fv or v = x or v = w then
              LET v = u
              LET fv = fu
           END IF
        END IF
    NEXT iter
    IF iter > itmax then
       PRINT "brent exceed maximum iterations."
    ELSE
       LET xmin = x
       LET brent = fx
    END IF

END SUB