OpenBLAS/lapack-netlib/SRC/slasq5.f

*> \brief \b SLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*> \htmlonly
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*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE SLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN,
*                          DNM1, DNM2, IEEE, EPS )
* 
*       .. Scalar Arguments ..
*       LOGICAL            IEEE
*       INTEGER            I0, N0, PP
*       REAL               EPS, DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, SIGMA, TAU
*       ..
*       .. Array Arguments ..
*       REAL               Z( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SLASQ5 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 REAL 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 REAL
*>        This is the shift.
*> \endverbatim
*>
*> \param[in] SIGMA
*>          SIGMA is REAL
*>        This is the accumulated shift up to this step.
*> \endverbatim
*>
*> \param[out] DMIN
*> \verbatim
*>          DMIN is REAL
*>        Minimum value of d.
*> \endverbatim
*>
*> \param[out] DMIN1
*> \verbatim
*>          DMIN1 is REAL
*>        Minimum value of d, excluding D( N0 ).
*> \endverbatim
*>
*> \param[out] DMIN2
*> \verbatim
*>          DMIN2 is REAL
*>        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
*> \endverbatim
*>
*> \param[out] DN
*> \verbatim
*>          DN is REAL
*>        d(N0), the last value of d.
*> \endverbatim
*>
*> \param[out] DNM1
*> \verbatim
*>          DNM1 is REAL
*>        d(N0-1).
*> \endverbatim
*>
*> \param[out] DNM2
*> \verbatim
*>          DNM2 is REAL
*>        d(N0-2).
*> \endverbatim
*>
*> \param[in] IEEE
*> \verbatim
*>          IEEE is LOGICAL
*>        Flag for IEEE or non IEEE arithmetic.
*> \endverbatim
*>
*> \param[in] EPS
*> \verbatim
*>         EPS is REAL
*>        This is the value of epsilon used.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2015
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE SLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2,
     $                   DN, DNM1, DNM2, IEEE, EPS )
*
*  -- LAPACK computational routine (version 3.6.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2015
*
*     .. Scalar Arguments ..
      LOGICAL            IEEE
      INTEGER            I0, N0, PP
      REAL               DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU,
     $                   SIGMA, EPS
*     ..
*     .. Array Arguments ..
      REAL               Z( * )
*     ..
*
*  =====================================================================
*
*     .. Parameter ..
      REAL               ZERO, HALF
      PARAMETER          ( ZERO = 0.0E0, HALF = 0.5 )
*     ..
*     .. Local Scalars ..
      INTEGER            J4, J4P2
      REAL               D, EMIN, TEMP, DTHRESH
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MIN
*     ..
*     .. Executable Statements ..
*
      IF( ( N0-I0-1 ).LE.0 )
     $   RETURN
*
      DTHRESH = EPS*(SIGMA+TAU)
      IF( TAU.LT.DTHRESH*HALF ) TAU = ZERO
      IF( TAU.NE.ZERO ) THEN
         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
*
      ELSE
*     This is the version that sets d's to zero if they are small enough
         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 50 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
                  IF( D.LT.DTHRESH ) D = ZERO
                  DMIN = MIN( DMIN, D )
                  Z( J4 ) = Z( J4-1 )*TEMP
                  EMIN = MIN( Z( J4 ), EMIN )
 50            CONTINUE
            ELSE
               DO 60 J4 = 4*I0, 4*( N0-3 ), 4
                  Z( J4-3 ) = D + Z( J4 )
                  TEMP = Z( J4+2 ) / Z( J4-3 )
                  D = D*TEMP - TAU
                  IF( D.LT.DTHRESH ) D = ZERO
                  DMIN = MIN( DMIN, D )
                  Z( J4-1 ) = Z( J4 )*TEMP
                  EMIN = MIN( Z( J4-1 ), EMIN )
 60            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 70 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
                  IF( D.LT.DTHRESH ) D = ZERO
                  DMIN = MIN( DMIN, D )
                  EMIN = MIN( EMIN, Z( J4 ) )
 70            CONTINUE
            ELSE
               DO 80 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
                  IF( D.LT.DTHRESH ) D = ZERO
                  DMIN = MIN( DMIN, D )
                  EMIN = MIN( EMIN, Z( J4-1 ) )
 80            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
*     
      END IF
      Z( J4+2 ) = DN
      Z( 4*N0-PP ) = EMIN
      RETURN
*
*     End of SLASQ5
*
      END