SLAED6 - compute 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


SYNOPSIS

       SUBROUTINE SLAED6( KNITER, ORGATI, RHO, D, Z, FINIT,  TAU,
                          INFO )

           LOGICAL        ORGATI

           INTEGER        INFO, KNITER

           REAL           FINIT, RHO, TAU

           REAL           D( 3 ), Z( 3 )


PURPOSE

       SLAED6  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 SLAED4 when necessary. In
       most cases, the root sought is the smallest in  magnitude,
       though  it might not be in some extremely rare situations.


ARGUMENTS

       KNITER       (input) INTEGER
                    Refer to SLAED4 for its significance.

       ORGATI       (input) 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 SLAED4 for further details.

       RHO          (input) REAL
                    Refer to the equation f(x) above.

       D            (input) REAL array, dimension (3)
                    D satisfies d(1) < d(2) < d(3).

       Z            (input) REAL array, dimension (3)
                    Each of the elements in z must be positive.

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

                    The root of the equation f(x).

       INFO         (output) INTEGER
                    = 0: successful exit
                    > 0: if INFO = 1, failure to converge


FURTHER DETAILS

       Based on contributions by
          Ren-Cang Li, Computer Science Division,  University  of
       California
          at Berkeley, USA


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