*> \brief \b DRSCL multiplies a vector by the reciprocal of a real scalar.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DRSCL + dependencies
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*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/drscl.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/drscl.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DRSCL( N, SA, SX, INCX )
*
*       .. Scalar Arguments ..
*       INTEGER            INCX, N
*       DOUBLE PRECISION   SA
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   SX( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DRSCL multiplies an n-element real vector x by the real scalar 1/a.
*> This is done without overflow or underflow as long as
*> the final result x/a does not overflow or underflow.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of components of the vector x.
*> \endverbatim
*>
*> \param[in] SA
*> \verbatim
*>          SA is DOUBLE PRECISION
*>          The scalar a which is used to divide each component of x.
*>          SA must be >= 0, or the subroutine will divide by zero.
*> \endverbatim
*>
*> \param[in,out] SX
*> \verbatim
*>          SX is DOUBLE PRECISION array, dimension
*>                         (1+(N-1)*abs(INCX))
*>          The n-element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*>          INCX is INTEGER
*>          The increment between successive values of the vector SX.
*>          > 0:  SX(1) = X(1) and SX(1+(i-1)*INCX) = x(i),     1< i<= n
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup rscl
*
*  =====================================================================
      SUBROUTINE DRSCL( N, SA, SX, INCX )
*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   SA
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   SX( * )
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            DONE
      DOUBLE PRECISION   BIGNUM, CDEN, CDEN1, CNUM, CNUM1, MUL, SMLNUM
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           DLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           DSCAL
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( N.LE.0 )
     $   RETURN
*
*     Get machine parameters
*
      SMLNUM = DLAMCH( 'S' )
      BIGNUM = ONE / SMLNUM
*
*     Initialize the denominator to SA and the numerator to 1.
*
      CDEN = SA
      CNUM = ONE
*
   10 CONTINUE
      CDEN1 = CDEN*SMLNUM
      CNUM1 = CNUM / BIGNUM
      IF( ABS( CDEN1 ).GT.ABS( CNUM ) .AND. CNUM.NE.ZERO ) THEN
*
*        Pre-multiply X by SMLNUM if CDEN is large compared to CNUM.
*
         MUL = SMLNUM
         DONE = .FALSE.
         CDEN = CDEN1
      ELSE IF( ABS( CNUM1 ).GT.ABS( CDEN ) ) THEN
*
*        Pre-multiply X by BIGNUM if CDEN is small compared to CNUM.
*
         MUL = BIGNUM
         DONE = .FALSE.
         CNUM = CNUM1
      ELSE
*
*        Multiply X by CNUM / CDEN and return.
*
         MUL = CNUM / CDEN
         DONE = .TRUE.
      END IF
*
*     Scale the vector X by MUL
*
      CALL DSCAL( N, MUL, SX, INCX )
*
      IF( .NOT.DONE )
     $   GO TO 10
*
      RETURN
*
*     End of DRSCL
*
      END
