dlasq6.f

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      SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
     $                   DNM1, DNM2 )
*
*  -- LAPACK routine (version 3.2)                                    --
*
*  -- Contributed by Osni Marques of the Lawrence Berkeley National   --
*  -- Laboratory and Beresford Parlett of the Univ. of California at  --
*  -- Berkeley                                                        --
*  -- November 2008                                                   --
*
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            I0, N0, PP
      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   Z( * )
*     ..
*
*  Purpose
*  =======
*
*  DLASQ6 computes one dqd (shift equal to zero) transform in
*  ping-pong form, with protection against underflow and overflow.
*
*  Arguments
*  =========
*
*  I0    (input) INTEGER
*        First index.
*
*  N0    (input) INTEGER
*        Last index.
*
*  Z     (input) DOUBLE PRECISION array, dimension ( 4*N )
*        Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
*        an extra argument.
*
*  PP    (input) INTEGER
*        PP=0 for ping, PP=1 for pong.
*
*  DMIN  (output) DOUBLE PRECISION
*        Minimum value of d.
*
*  DMIN1 (output) DOUBLE PRECISION
*        Minimum value of d, excluding D( N0 ).
*
*  DMIN2 (output) DOUBLE PRECISION
*        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
*
*  DN    (output) DOUBLE PRECISION
*        d(N0), the last value of d.
*
*  DNM1  (output) DOUBLE PRECISION
*        d(N0-1).
*
*  DNM2  (output) DOUBLE PRECISION
*        d(N0-2).
*
*  =====================================================================
*
*     .. Parameter ..
      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J4, J4P2
      DOUBLE PRECISION   D, EMIN, SAFMIN, TEMP
*     ..
*     .. External Function ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           DLAMCH
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MIN
*     ..
*     .. Executable Statements ..
*
      IF( ( N0-I0-1 ).LE.0 )
     $   RETURN
*
      SAFMIN = DLAMCH( 'Safe minimum' )
      J4 = 4*I0 + PP - 3
      EMIN = Z( J4+4 ) 
      D = Z( J4 )
      DMIN = D
*
      IF( PP.EQ.0 ) THEN
         DO 10 J4 = 4*I0, 4*( N0-3 ), 4
            Z( J4-2 ) = D + Z( J4-1 ) 
            IF( Z( J4-2 ).EQ.ZERO ) THEN
               Z( J4 ) = ZERO
               D = Z( J4+1 )
               DMIN = D
               EMIN = ZERO
            ELSE IF( SAFMIN*Z( J4+1 ).LT.Z( J4-2 ) .AND.
     $               SAFMIN*Z( J4-2 ).LT.Z( J4+1 ) ) THEN
               TEMP = Z( J4+1 ) / Z( J4-2 )
               Z( J4 ) = Z( J4-1 )*TEMP
               D = D*TEMP
            ELSE 
               Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
               D = Z( J4+1 )*( D / Z( J4-2 ) )
            END IF
            DMIN = MIN( DMIN, D )
            EMIN = MIN( EMIN, Z( J4 ) )
   10    CONTINUE
      ELSE
         DO 20 J4 = 4*I0, 4*( N0-3 ), 4
            Z( J4-3 ) = D + Z( J4 ) 
            IF( Z( J4-3 ).EQ.ZERO ) THEN
               Z( J4-1 ) = ZERO
               D = Z( J4+2 )
               DMIN = D
               EMIN = ZERO
            ELSE IF( SAFMIN*Z( J4+2 ).LT.Z( J4-3 ) .AND.
     $               SAFMIN*Z( J4-3 ).LT.Z( J4+2 ) ) THEN
               TEMP = Z( J4+2 ) / Z( J4-3 )
               Z( J4-1 ) = Z( J4 )*TEMP
               D = D*TEMP
            ELSE 
               Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
               D = Z( J4+2 )*( D / Z( J4-3 ) )
            END IF
            DMIN = MIN( DMIN, D )
            EMIN = MIN( EMIN, Z( J4-1 ) )
   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 )
      IF( Z( J4-2 ).EQ.ZERO ) THEN
         Z( J4 ) = ZERO
         DNM1 = Z( J4P2+2 )
         DMIN = DNM1
         EMIN = ZERO
      ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND.
     $         SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN
         TEMP = Z( J4P2+2 ) / Z( J4-2 )
         Z( J4 ) = Z( J4P2 )*TEMP
         DNM1 = DNM2*TEMP
      ELSE
         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
         DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) )
      END IF
      DMIN = MIN( DMIN, DNM1 )
*
      DMIN1 = DMIN
      J4 = J4 + 4
      J4P2 = J4 + 2*PP - 1
      Z( J4-2 ) = DNM1 + Z( J4P2 )
      IF( Z( J4-2 ).EQ.ZERO ) THEN
         Z( J4 ) = ZERO
         DN = Z( J4P2+2 )
         DMIN = DN
         EMIN = ZERO
      ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND.
     $         SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN
         TEMP = Z( J4P2+2 ) / Z( J4-2 )
         Z( J4 ) = Z( J4P2 )*TEMP
         DN = DNM1*TEMP
      ELSE
         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
         DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) )
      END IF
      DMIN = MIN( DMIN, DN )
*
      Z( J4+2 ) = DN
      Z( 4*N0-PP ) = EMIN
      RETURN
*
*     End of DLASQ6
*
      END