DLAED6 computes the positive or negative root (closest to the origin)
 of
                  z(1)        z(2)        z(3)
 f(x) =   rho + --------- + ---------- + ---------
                 d(1)-x      d(2)-x      d(3)-x

 It is assumed that

       if ORGATI = .true. the root is between d(2) and d(3);
       otherwise it is between d(1) and d(2)

 This routine will be called by DLAED4 when necessary. In most cases,
 the root sought is the smallest in magnitude, though it might not be
 in some extremely rare situations.

          KNITER is INTEGER
               Refer to DLAED4 for its significance.

          ORGATI is LOGICAL
               If ORGATI is true, the needed root is between d(2) and
               d(3); otherwise it is between d(1) and d(2).  See
               DLAED4 for further details.

          RHO is DOUBLE PRECISION
               Refer to the equation f(x) above.

          D is DOUBLE PRECISION array, dimension (3)
               D satisfies d(1) < d(2) < d(3).

          Z is DOUBLE PRECISION array, dimension (3)
               Each of the elements in z must be positive.

          FINIT is DOUBLE PRECISION
               The value of f at 0. It is more accurate than the one
               evaluated inside this routine (if someone wants to do
               so).

          TAU is DOUBLE PRECISION
               The root of the equation f(x).

          INFO is INTEGER
               = 0: successful exit
               > 0: if INFO = 1, failure to converge

  10/02/03: This version has a few statements commented out for thread
  safety (machine parameters are computed on each entry). SJH.

  05/10/06: Modified from a new version of Ren-Cang Li, use
     Gragg-Thornton-Warner cubic convergent scheme for better stability.