dlasq5.f

*> \brief \b DLASQ5
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, DMIN, DMIN1, DMIN2, DN,
*                          DNM1, DNM2, IEEE )
* 
*       .. Scalar Arguments ..
*       LOGICAL            IEEE
*       INTEGER            I0, N0, PP
*       DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   Z( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLASQ5 computes one dqds transform in ping-pong form, one
*> version for IEEE machines another for non IEEE machines.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] I0
*> \verbatim
*>          I0 is INTEGER
*>        First index.
*> \endverbatim
*>
*> \param[in] N0
*> \verbatim
*>          N0 is INTEGER
*>        Last index.
*> \endverbatim
*>
*> \param[in] Z
*> \verbatim
*>          Z is DOUBLE PRECISION array, dimension ( 4*N )
*>        Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
*>        an extra argument.
*> \endverbatim
*>
*> \param[in] PP
*> \verbatim
*>          PP is INTEGER
*>        PP=0 for ping, PP=1 for pong.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION
*>        This is the shift.
*> \endverbatim
*>
*> \param[out] DMIN
*> \verbatim
*>          DMIN is DOUBLE PRECISION
*>        Minimum value of d.
*> \endverbatim
*>
*> \param[out] DMIN1
*> \verbatim
*>          DMIN1 is DOUBLE PRECISION
*>        Minimum value of d, excluding D( N0 ).
*> \endverbatim
*>
*> \param[out] DMIN2
*> \verbatim
*>          DMIN2 is DOUBLE PRECISION
*>        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
*> \endverbatim
*>
*> \param[out] DN
*> \verbatim
*>          DN is DOUBLE PRECISION
*>        d(N0), the last value of d.
*> \endverbatim
*>
*> \param[out] DNM1
*> \verbatim
*>          DNM1 is DOUBLE PRECISION
*>        d(N0-1).
*> \endverbatim
*>
*> \param[out] DNM2
*> \verbatim
*>          DNM2 is DOUBLE PRECISION
*>        d(N0-2).
*> \endverbatim
*>
*> \param[in] IEEE
*> \verbatim
*>          IEEE is LOGICAL
*>        Flag for IEEE or non IEEE arithmetic.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE dlasq5( I0, N0, Z, PP, TAU, DMIN, DMIN1, DMIN2, DN,
     $                   DNM1, DNM2, IEEE )
*
*  -- LAPACK computational routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      LOGICAL            ieee
      INTEGER            i0, n0, pp
      DOUBLE PRECISION   dmin, dmin1, dmin2, dn, dnm1, dnm2, tau
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   z( * )
*     ..
*
*  =====================================================================
*
*     .. Parameter ..
      DOUBLE PRECISION   zero
      parameter( zero = 0.0d0 )
*     ..
*     .. Local Scalars ..
      INTEGER            j4, j4p2
      DOUBLE PRECISION   d, emin, temp
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          min
*     ..
*     .. Executable Statements ..
*
      IF( ( n0-i0-1 ).LE.0 )
     $   RETURN
*
      j4 = 4*i0 + pp - 3
      emin = z( j4+4 ) 
      d = z( j4 ) - tau
      dmin = d
      dmin1 = -z( j4 )
*
      IF( ieee ) THEN
*
*        Code for IEEE arithmetic.
*
         IF( pp.EQ.0 ) THEN
            DO 10 j4 = 4*i0, 4*( n0-3 ), 4
               z( j4-2 ) = d + z( j4-1 ) 
               temp = z( j4+1 ) / z( j4-2 )
               d = d*temp - tau
               dmin = min( dmin, d )
               z( j4 ) = z( j4-1 )*temp
               emin = min( z( j4 ), emin )
   10       CONTINUE
         ELSE
            DO 20 j4 = 4*i0, 4*( n0-3 ), 4
               z( j4-3 ) = d + z( j4 ) 
               temp = z( j4+2 ) / z( j4-3 )
               d = d*temp - tau
               dmin = min( dmin, d )
               z( j4-1 ) = z( j4 )*temp
               emin = min( z( j4-1 ), emin )
   20       CONTINUE
         END IF
*
*        Unroll last two steps. 
*
         dnm2 = d
         dmin2 = dmin
         j4 = 4*( n0-2 ) - pp
         j4p2 = j4 + 2*pp - 1
         z( j4-2 ) = dnm2 + z( j4p2 )
         z( j4 ) = z( j4p2+2 )*( z( j4p2 ) / z( j4-2 ) )
         dnm1 = z( j4p2+2 )*( dnm2 / z( j4-2 ) ) - tau
         dmin = min( dmin, dnm1 )
*
         dmin1 = dmin
         j4 = j4 + 4
         j4p2 = j4 + 2*pp - 1
         z( j4-2 ) = dnm1 + z( j4p2 )
         z( j4 ) = z( j4p2+2 )*( z( j4p2 ) / z( j4-2 ) )
         dn = z( j4p2+2 )*( dnm1 / z( j4-2 ) ) - tau
         dmin = min( dmin, dn )
*
      ELSE
*
*        Code for non IEEE arithmetic.
*
         IF( pp.EQ.0 ) THEN
            DO 30 j4 = 4*i0, 4*( n0-3 ), 4
               z( j4-2 ) = d + z( j4-1 ) 
               IF( d.LT.zero ) THEN
                  RETURN
               ELSE 
                  z( j4 ) = z( j4+1 )*( z( j4-1 ) / z( j4-2 ) )
                  d = z( j4+1 )*( d / z( j4-2 ) ) - tau
               END IF
               dmin = min( dmin, d )
               emin = min( emin, z( j4 ) )
   30       CONTINUE
         ELSE
            DO 40 j4 = 4*i0, 4*( n0-3 ), 4
               z( j4-3 ) = d + z( j4 ) 
               IF( d.LT.zero ) THEN
                  RETURN
               ELSE 
                  z( j4-1 ) = z( j4+2 )*( z( j4 ) / z( j4-3 ) )
                  d = z( j4+2 )*( d / z( j4-3 ) ) - tau
               END IF
               dmin = min( dmin, d )
               emin = min( emin, z( j4-1 ) )
   40       CONTINUE
         END IF
*
*        Unroll last two steps. 
*
         dnm2 = d
         dmin2 = dmin
         j4 = 4*( n0-2 ) - pp
         j4p2 = j4 + 2*pp - 1
         z( j4-2 ) = dnm2 + z( j4p2 )
         IF( dnm2.LT.zero ) THEN
            RETURN
         ELSE
            z( j4 ) = z( j4p2+2 )*( z( j4p2 ) / z( j4-2 ) )
            dnm1 = z( j4p2+2 )*( dnm2 / z( j4-2 ) ) - tau
         END IF
         dmin = min( dmin, dnm1 )
*
         dmin1 = dmin
         j4 = j4 + 4
         j4p2 = j4 + 2*pp - 1
         z( j4-2 ) = dnm1 + z( j4p2 )
         IF( dnm1.LT.zero ) THEN
            RETURN
         ELSE
            z( j4 ) = z( j4p2+2 )*( z( j4p2 ) / z( j4-2 ) )
            dn = z( j4p2+2 )*( dnm1 / z( j4-2 ) ) - tau
         END IF
         dmin = min( dmin, dn )
*
      END IF
*
      z( j4+2 ) = dn
      z( 4*n0-pp ) = emin
      RETURN
*
*     End of DLASQ5
*
      END