!>
!> 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.
!> 

KNITER

!>          KNITER is INTEGER
!>               Refer to SLAED4 for its significance.
!> 

ORGATI

!>          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
!>               SLAED4 for further details.
!> 

RHO

!>          RHO is REAL
!>               Refer to the equation f(x) above.
!> 

D

!>          D is REAL array, dimension (3)
!>               D satisfies d(1) < d(2) < d(3).
!> 

Z

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

FINIT

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

TAU

!>          TAU is REAL
!>               The root of the equation f(x).
!> 

INFO

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>  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.
!> 

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA