Remove legacy warning comments and rename variable LAMDA to LAMBDA (Reference-LAPACK PR 852)

lapack-netlib/SRC/cgelsd.f

@@ -60,12 +60,6 @@
 *> singular values which are less than RCOND times the largest singular
 *> value.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/cgesdd.f

@@ -53,12 +53,6 @@
 *>
 *> Note that the routine returns VT = V**H, not V.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/chbevd.f

@@ -41,12 +41,6 @@
 *> a complex Hermitian band matrix A.  If eigenvectors are desired, it
 *> uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/chbevd_2stage.f

@@ -47,12 +47,6 @@
 *> the reduction to tridiagonal.  If eigenvectors are desired, it
 *> uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/chbgvd.f

@@ -46,12 +46,6 @@
 *> and banded, and B is also positive definite.  If eigenvectors are
 *> desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/cheevd.f

@@ -41,12 +41,6 @@
 *> complex Hermitian matrix A.  If eigenvectors are desired, it uses a
 *> divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/cheevd_2stage.f

@@ -46,12 +46,6 @@
 *> the reduction to tridiagonal.  If eigenvectors are desired, it uses a
 *> divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/chegvd.f

@@ -43,12 +43,6 @@
 *> B are assumed to be Hermitian and B is also positive definite.
 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/chpevd.f

@@ -41,12 +41,6 @@
 *> a complex Hermitian matrix A in packed storage.  If eigenvectors are
 *> desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/chpgvd.f

@@ -44,12 +44,6 @@
 *> positive definite.
 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/claed8.f

@@ -18,7 +18,7 @@
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
+*       SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMBDA,
 *                          Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR,
 *                          GIVCOL, GIVNUM, INFO )
 *
@@ -29,7 +29,7 @@
 *       .. Array Arguments ..
 *       INTEGER            GIVCOL( 2, * ), INDX( * ), INDXP( * ),
 *      $                   INDXQ( * ), PERM( * )
-*       REAL               D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ),
+*       REAL               D( * ), DLAMBDA( * ), GIVNUM( 2, * ), W( * ),
 *      $                   Z( * )
 *       COMPLEX            Q( LDQ, * ), Q2( LDQ2, * )
 *       ..
@@ -122,9 +122,9 @@
 *>         destroyed during the updating process.
 *> \endverbatim
 *>
-*> \param[out] DLAMDA
+*> \param[out] DLAMBDA
 *> \verbatim
-*>          DLAMDA is REAL array, dimension (N)
+*>          DLAMBDA is REAL array, dimension (N)
 *>         Contains a copy of the first K eigenvalues which will be used
 *>         by SLAED3 to form the secular equation.
 *> \endverbatim
@@ -222,7 +222,7 @@
 *> \ingroup complexOTHERcomputational
 *
 *  =====================================================================
-      SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
+      SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMBDA,
      $                   Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR,
      $                   GIVCOL, GIVNUM, INFO )
 *
@@ -237,7 +237,7 @@
 *     .. Array Arguments ..
       INTEGER            GIVCOL( 2, * ), INDX( * ), INDXP( * ),
      $                   INDXQ( * ), PERM( * )
-      REAL               D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ),
+      REAL               D( * ), DLAMBDA( * ), GIVNUM( 2, * ), W( * ),
      $                   Z( * )
       COMPLEX            Q( LDQ, * ), Q2( LDQ2, * )
 *     ..
@@ -322,14 +322,14 @@
          INDXQ( I ) = INDXQ( I ) + CUTPNT
    20 CONTINUE
       DO 30 I = 1, N
-         DLAMDA( I ) = D( INDXQ( I ) )
+         DLAMBDA( I ) = D( INDXQ( I ) )
          W( I ) = Z( INDXQ( I ) )
    30 CONTINUE
       I = 1
       J = CUTPNT + 1
-      CALL SLAMRG( N1, N2, DLAMDA, 1, 1, INDX )
+      CALL SLAMRG( N1, N2, DLAMBDA, 1, 1, INDX )
       DO 40 I = 1, N
-         D( I ) = DLAMDA( INDX( I ) )
+         D( I ) = DLAMBDA( INDX( I ) )
          Z( I ) = W( INDX( I ) )
    40 CONTINUE
 *
@@ -438,7 +438,7 @@
          ELSE
             K = K + 1
             W( K ) = Z( JLAM )
-            DLAMDA( K ) = D( JLAM )
+            DLAMBDA( K ) = D( JLAM )
             INDXP( K ) = JLAM
             JLAM = J
          END IF
@@ -450,19 +450,19 @@
 *
       K = K + 1
       W( K ) = Z( JLAM )
-      DLAMDA( K ) = D( JLAM )
+      DLAMBDA( K ) = D( JLAM )
       INDXP( K ) = JLAM
 *
   100 CONTINUE
 *
-*     Sort the eigenvalues and corresponding eigenvectors into DLAMDA
+*     Sort the eigenvalues and corresponding eigenvectors into DLAMBDA
 *     and Q2 respectively.  The eigenvalues/vectors which were not
-*     deflated go into the first K slots of DLAMDA and Q2 respectively,
+*     deflated go into the first K slots of DLAMBDA and Q2 respectively,
 *     while those which were deflated go into the last N - K slots.
 *
       DO 110 J = 1, N
          JP = INDXP( J )
-         DLAMDA( J ) = D( JP )
+         DLAMBDA( J ) = D( JP )
          PERM( J ) = INDXQ( INDX( JP ) )
          CALL CCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 )
   110 CONTINUE
@@ -471,7 +471,7 @@
 *     into the last N - K slots of D and Q respectively.
 *
       IF( K.LT.N ) THEN
-         CALL SCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 )
+         CALL SCOPY( N-K, DLAMBDA( K+1 ), 1, D( K+1 ), 1 )
          CALL CLACPY( 'A', QSIZ, N-K, Q2( 1, K+1 ), LDQ2, Q( 1, K+1 ),
      $                LDQ )
       END IF

lapack-netlib/SRC/clals0.f

@@ -392,6 +392,11 @@
      $                ( POLES( I, 2 ).EQ.ZERO ) ) THEN
                      RWORK( I ) = ZERO
                   ELSE
+*
+*                    Use calls to the subroutine SLAMC3 to enforce the
+*                    parentheses (x+y)+z. The goal is to prevent
+*                    optimizing compilers from doing x+(y+z).
+*
                      RWORK( I ) = POLES( I, 2 )*Z( I ) /
      $                            ( SLAMC3( POLES( I, 2 ), DSIGJ )-
      $                            DIFLJ ) / ( POLES( I, 2 )+DJ )
@@ -470,6 +475,11 @@
                   IF( Z( J ).EQ.ZERO ) THEN
                      RWORK( I ) = ZERO
                   ELSE
+*
+*                    Use calls to the subroutine SLAMC3 to enforce the
+*                    parentheses (x+y)+z. The goal is to prevent optimizing
+*                    compilers from doing x+(y+z).
+*
                      RWORK( I ) = Z( J ) / ( SLAMC3( DSIGJ, -POLES( I+1,
      $                            2 ) )-DIFR( I, 1 ) ) /
      $                            ( DSIGJ+POLES( I, 1 ) ) / DIFR( I, 2 )

lapack-netlib/SRC/clalsd.f

@@ -48,12 +48,6 @@
 *> problem; in this case a minimum norm solution is returned.
 *> The actual singular values are returned in D in ascending order.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/cstedc.f

@@ -43,12 +43,6 @@
 *> be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this
 *> matrix to tridiagonal form.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.  See SLAED3 for details.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dbdsdc.f

@@ -45,13 +45,6 @@
 *> respectively. DBDSDC can be used to compute all singular values,
 *> and optionally, singular vectors or singular vectors in compact form.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.  See DLASD3 for details.
-*>
 *> The code currently calls DLASDQ if singular values only are desired.
 *> However, it can be slightly modified to compute singular values
 *> using the divide and conquer method.

lapack-netlib/SRC/dgelsd.f

@@ -59,12 +59,6 @@
 *> singular values which are less than RCOND times the largest singular
 *> value.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dgesdd.f

@@ -55,12 +55,6 @@
 *>
 *> Note that the routine returns VT = V**T, not V.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dlaed2.f

@@ -18,7 +18,7 @@
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W,
+*       SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMBDA, W,
 *                          Q2, INDX, INDXC, INDXP, COLTYP, INFO )
 *
 *       .. Scalar Arguments ..
@@ -28,7 +28,7 @@
 *       .. Array Arguments ..
 *       INTEGER            COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ),
 *      $                   INDXQ( * )
-*       DOUBLE PRECISION   D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ),
+*       DOUBLE PRECISION   D( * ), DLAMBDA( * ), Q( LDQ, * ), Q2( * ),
 *      $                   W( * ), Z( * )
 *       ..
 *
@@ -123,9 +123,9 @@
 *>         process.
 *> \endverbatim
 *>
-*> \param[out] DLAMDA
+*> \param[out] DLAMBDA
 *> \verbatim
-*>          DLAMDA is DOUBLE PRECISION array, dimension (N)
+*>          DLAMBDA is DOUBLE PRECISION array, dimension (N)
 *>         A copy of the first K eigenvalues which will be used by
 *>         DLAED3 to form the secular equation.
 *> \endverbatim
@@ -148,7 +148,7 @@
 *> \param[out] INDX
 *> \verbatim
 *>          INDX is INTEGER array, dimension (N)
-*>         The permutation used to sort the contents of DLAMDA into
+*>         The permutation used to sort the contents of DLAMBDA into
 *>         ascending order.
 *> \endverbatim
 *>
@@ -207,7 +207,7 @@
 *>  Modified by Francoise Tisseur, University of Tennessee
 *>
 *  =====================================================================
-      SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W,
+      SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMBDA, W,
      $                   Q2, INDX, INDXC, INDXP, COLTYP, INFO )
 *
 *  -- LAPACK computational routine --
@@ -221,7 +221,7 @@
 *     .. Array Arguments ..
       INTEGER            COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ),
      $                   INDXQ( * )
-      DOUBLE PRECISION   D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ),
+      DOUBLE PRECISION   D( * ), DLAMBDA( * ), Q( LDQ, * ), Q2( * ),
      $                   W( * ), Z( * )
 *     ..
 *
@@ -300,9 +300,9 @@
 *     re-integrate the deflated parts from the last pass
 *
       DO 20 I = 1, N
-         DLAMDA( I ) = D( INDXQ( I ) )
+         DLAMBDA( I ) = D( INDXQ( I ) )
    20 CONTINUE
-      CALL DLAMRG( N1, N2, DLAMDA, 1, 1, INDXC )
+      CALL DLAMRG( N1, N2, DLAMBDA, 1, 1, INDXC )
       DO 30 I = 1, N
          INDX( I ) = INDXQ( INDXC( I ) )
    30 CONTINUE
@@ -324,11 +324,11 @@
          DO 40 J = 1, N
             I = INDX( J )
             CALL DCOPY( N, Q( 1, I ), 1, Q2( IQ2 ), 1 )
-            DLAMDA( J ) = D( I )
+            DLAMBDA( J ) = D( I )
             IQ2 = IQ2 + N
    40    CONTINUE
          CALL DLACPY( 'A', N, N, Q2, N, Q, LDQ )
-         CALL DCOPY( N, DLAMDA, 1, D, 1 )
+         CALL DCOPY( N, DLAMBDA, 1, D, 1 )
          GO TO 190
       END IF
 *
@@ -421,7 +421,7 @@
             PJ = NJ
          ELSE
             K = K + 1
-            DLAMDA( K ) = D( PJ )
+            DLAMBDA( K ) = D( PJ )
             W( K ) = Z( PJ )
             INDXP( K ) = PJ
             PJ = NJ
@@ -433,7 +433,7 @@
 *     Record the last eigenvalue.
 *
       K = K + 1
-      DLAMDA( K ) = D( PJ )
+      DLAMBDA( K ) = D( PJ )
       W( K ) = Z( PJ )
       INDXP( K ) = PJ
 *
@@ -470,9 +470,9 @@
          PSM( CT ) = PSM( CT ) + 1
   130 CONTINUE
 *
-*     Sort the eigenvalues and corresponding eigenvectors into DLAMDA
+*     Sort the eigenvalues and corresponding eigenvectors into DLAMBDA
 *     and Q2 respectively.  The eigenvalues/vectors which were not
-*     deflated go into the first K slots of DLAMDA and Q2 respectively,
+*     deflated go into the first K slots of DLAMBDA and Q2 respectively,
 *     while those which were deflated go into the last N - K slots.
 *
       I = 1

lapack-netlib/SRC/dlaed3.f

@@ -18,7 +18,7 @@
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX,
+*       SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMBDA, Q2, INDX,
 *                          CTOT, W, S, INFO )
 *
 *       .. Scalar Arguments ..
@@ -27,7 +27,7 @@
 *       ..
 *       .. Array Arguments ..
 *       INTEGER            CTOT( * ), INDX( * )
-*       DOUBLE PRECISION   D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ),
+*       DOUBLE PRECISION   D( * ), DLAMBDA( * ), Q( LDQ, * ), Q2( * ),
 *      $                   S( * ), W( * )
 *       ..
 *
@@ -44,12 +44,6 @@
 *> being combined by the matrix of eigenvectors of the K-by-K system
 *> which is solved here.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:
@@ -104,14 +98,12 @@
 *>          RHO >= 0 required.
 *> \endverbatim
 *>
-*> \param[in,out] DLAMDA
+*> \param[in] DLAMBDA
 *> \verbatim
-*>          DLAMDA is DOUBLE PRECISION array, dimension (K)
+*>          DLAMBDA is DOUBLE PRECISION array, dimension (K)
 *>          The first K elements of this array contain the old roots
 *>          of the deflated updating problem.  These are the poles
-*>          of the secular equation. May be changed on output by
-*>          having lowest order bit set to zero on Cray X-MP, Cray Y-MP,
-*>          Cray-2, or Cray C-90, as described above.
+*>          of the secular equation.
 *> \endverbatim
 *>
 *> \param[in] Q2
@@ -180,7 +172,7 @@
 *>  Modified by Francoise Tisseur, University of Tennessee
 *>
 *  =====================================================================
-      SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX,
+      SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMBDA, Q2, INDX,
      $                   CTOT, W, S, INFO )
 *
 *  -- LAPACK computational routine --
@@ -193,7 +185,7 @@
 *     ..
 *     .. Array Arguments ..
       INTEGER            CTOT( * ), INDX( * )
-      DOUBLE PRECISION   D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ),
+      DOUBLE PRECISION   D( * ), DLAMBDA( * ), Q( LDQ, * ), Q2( * ),
      $                   S( * ), W( * )
 *     ..
 *
@@ -208,8 +200,8 @@
       DOUBLE PRECISION   TEMP
 *     ..
 *     .. External Functions ..
-      DOUBLE PRECISION   DLAMC3, DNRM2
-      EXTERNAL           DLAMC3, DNRM2
+      DOUBLE PRECISION   DNRM2
+      EXTERNAL           DNRM2
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DCOPY, DGEMM, DLACPY, DLAED4, DLASET, XERBLA
@@ -240,29 +232,9 @@
       IF( K.EQ.0 )
      $   RETURN
 *
-*     Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can
-*     be computed with high relative accuracy (barring over/underflow).
-*     This is a problem on machines without a guard digit in
-*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
-*     The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I),
-*     which on any of these machines zeros out the bottommost
-*     bit of DLAMDA(I) if it is 1; this makes the subsequent
-*     subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation
-*     occurs. On binary machines with a guard digit (almost all
-*     machines) it does not change DLAMDA(I) at all. On hexadecimal
-*     and decimal machines with a guard digit, it slightly
-*     changes the bottommost bits of DLAMDA(I). It does not account
-*     for hexadecimal or decimal machines without guard digits
-*     (we know of none). We use a subroutine call to compute
-*     2*DLAMBDA(I) to prevent optimizing compilers from eliminating
-*     this code.
-*
-      DO 10 I = 1, K
-         DLAMDA( I ) = DLAMC3( DLAMDA( I ), DLAMDA( I ) ) - DLAMDA( I )
-   10 CONTINUE
 *
       DO 20 J = 1, K
-         CALL DLAED4( K, J, DLAMDA, W, Q( 1, J ), RHO, D( J ), INFO )
+         CALL DLAED4( K, J, DLAMBDA, W, Q( 1, J ), RHO, D( J ), INFO )
 *
 *        If the zero finder fails, the computation is terminated.
 *
@@ -293,10 +265,10 @@
       CALL DCOPY( K, Q, LDQ+1, W, 1 )
       DO 60 J = 1, K
          DO 40 I = 1, J - 1
-            W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) )
+            W( I ) = W( I )*( Q( I, J )/( DLAMBDA( I )-DLAMBDA( J ) ) )
    40    CONTINUE
          DO 50 I = J + 1, K
-            W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) )
+            W( I ) = W( I )*( Q( I, J )/( DLAMBDA( I )-DLAMBDA( J ) ) )
    50    CONTINUE
    60 CONTINUE
       DO 70 I = 1, K

lapack-netlib/SRC/dlaed8.f

@@ -19,7 +19,7 @@
 *  ===========
 *
 *       SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO,
-*                          CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR,
+*                          CUTPNT, Z, DLAMBDA, Q2, LDQ2, W, PERM, GIVPTR,
 *                          GIVCOL, GIVNUM, INDXP, INDX, INFO )
 *
 *       .. Scalar Arguments ..
@@ -30,7 +30,7 @@
 *       .. Array Arguments ..
 *       INTEGER            GIVCOL( 2, * ), INDX( * ), INDXP( * ),
 *      $                   INDXQ( * ), PERM( * )
-*       DOUBLE PRECISION   D( * ), DLAMDA( * ), GIVNUM( 2, * ),
+*       DOUBLE PRECISION   D( * ), DLAMBDA( * ), GIVNUM( 2, * ),
 *      $                   Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * )
 *       ..
 *
@@ -141,9 +141,9 @@
 *>         process.
 *> \endverbatim
 *>
-*> \param[out] DLAMDA
+*> \param[out] DLAMBDA
 *> \verbatim
-*>          DLAMDA is DOUBLE PRECISION array, dimension (N)
+*>          DLAMBDA is DOUBLE PRECISION array, dimension (N)
 *>         A copy of the first K eigenvalues which will be used by
 *>         DLAED3 to form the secular equation.
 *> \endverbatim
@@ -238,7 +238,7 @@
 *
 *  =====================================================================
       SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO,
-     $                   CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR,
+     $                   CUTPNT, Z, DLAMBDA, Q2, LDQ2, W, PERM, GIVPTR,
      $                   GIVCOL, GIVNUM, INDXP, INDX, INFO )
 *
 *  -- LAPACK computational routine --
@@ -253,7 +253,7 @@
 *     .. Array Arguments ..
       INTEGER            GIVCOL( 2, * ), INDX( * ), INDXP( * ),
      $                   INDXQ( * ), PERM( * )
-      DOUBLE PRECISION   D( * ), DLAMDA( * ), GIVNUM( 2, * ),
+      DOUBLE PRECISION   D( * ), DLAMBDA( * ), GIVNUM( 2, * ),
      $                   Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * )
 *     ..
 *
@@ -339,14 +339,14 @@
          INDXQ( I ) = INDXQ( I ) + CUTPNT
    20 CONTINUE
       DO 30 I = 1, N
-         DLAMDA( I ) = D( INDXQ( I ) )
+         DLAMBDA( I ) = D( INDXQ( I ) )
          W( I ) = Z( INDXQ( I ) )
    30 CONTINUE
       I = 1
       J = CUTPNT + 1
-      CALL DLAMRG( N1, N2, DLAMDA, 1, 1, INDX )
+      CALL DLAMRG( N1, N2, DLAMBDA, 1, 1, INDX )
       DO 40 I = 1, N
-         D( I ) = DLAMDA( INDX( I ) )
+         D( I ) = DLAMBDA( INDX( I ) )
          Z( I ) = W( INDX( I ) )
    40 CONTINUE
 *
@@ -464,7 +464,7 @@
          ELSE
             K = K + 1
             W( K ) = Z( JLAM )
-            DLAMDA( K ) = D( JLAM )
+            DLAMBDA( K ) = D( JLAM )
             INDXP( K ) = JLAM
             JLAM = J
          END IF
@@ -476,26 +476,26 @@
 *
       K = K + 1
       W( K ) = Z( JLAM )
-      DLAMDA( K ) = D( JLAM )
+      DLAMBDA( K ) = D( JLAM )
       INDXP( K ) = JLAM
 *
   110 CONTINUE
 *
-*     Sort the eigenvalues and corresponding eigenvectors into DLAMDA
+*     Sort the eigenvalues and corresponding eigenvectors into DLAMBDA
 *     and Q2 respectively.  The eigenvalues/vectors which were not
-*     deflated go into the first K slots of DLAMDA and Q2 respectively,
+*     deflated go into the first K slots of DLAMBDA and Q2 respectively,
 *     while those which were deflated go into the last N - K slots.
 *
       IF( ICOMPQ.EQ.0 ) THEN
          DO 120 J = 1, N
             JP = INDXP( J )
-            DLAMDA( J ) = D( JP )
+            DLAMBDA( J ) = D( JP )
             PERM( J ) = INDXQ( INDX( JP ) )
   120    CONTINUE
       ELSE
          DO 130 J = 1, N
             JP = INDXP( J )
-            DLAMDA( J ) = D( JP )
+            DLAMBDA( J ) = D( JP )
             PERM( J ) = INDXQ( INDX( JP ) )
             CALL DCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 )
   130    CONTINUE
@@ -506,9 +506,9 @@
 *
       IF( K.LT.N ) THEN
          IF( ICOMPQ.EQ.0 ) THEN
-            CALL DCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 )
+            CALL DCOPY( N-K, DLAMBDA( K+1 ), 1, D( K+1 ), 1 )
          ELSE
-            CALL DCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 )
+            CALL DCOPY( N-K, DLAMBDA( K+1 ), 1, D( K+1 ), 1 )
             CALL DLACPY( 'A', QSIZ, N-K, Q2( 1, K+1 ), LDQ2,
      $                   Q( 1, K+1 ), LDQ )
          END IF

lapack-netlib/SRC/dlaed9.f

@@ -18,15 +18,15 @@
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
-*                          S, LDS, INFO )
+*       SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMBDA,
+*                          W, S, LDS, INFO )
 *
 *       .. Scalar Arguments ..
 *       INTEGER            INFO, K, KSTART, KSTOP, LDQ, LDS, N
 *       DOUBLE PRECISION   RHO
 *       ..
 *       .. Array Arguments ..
-*       DOUBLE PRECISION   D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ),
+*       DOUBLE PRECISION   D( * ), DLAMBDA( * ), Q( LDQ, * ), S( LDS, * ),
 *      $                   W( * )
 *       ..
 *
@@ -96,9 +96,9 @@
 *>          RHO >= 0 required.
 *> \endverbatim
 *>
-*> \param[in] DLAMDA
+*> \param[in] DLAMBDA
 *> \verbatim
-*>          DLAMDA is DOUBLE PRECISION array, dimension (K)
+*>          DLAMBDA is DOUBLE PRECISION array, dimension (K)
 *>          The first K elements of this array contain the old roots
 *>          of the deflated updating problem.  These are the poles
 *>          of the secular equation.
@@ -151,8 +151,8 @@
 *> at Berkeley, USA
 *
 *  =====================================================================
-      SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
-     $                   S, LDS, INFO )
+      SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMBDA,
+     $                   W, S, LDS, INFO )
 *
 *  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
@@ -163,7 +163,7 @@
       DOUBLE PRECISION   RHO
 *     ..
 *     .. Array Arguments ..
-      DOUBLE PRECISION   D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ),
+      DOUBLE PRECISION   D( * ), DLAMBDA( * ), Q( LDQ, * ), S( LDS, * ),
      $                   W( * )
 *     ..
 *
@@ -174,8 +174,8 @@
       DOUBLE PRECISION   TEMP
 *     ..
 *     .. External Functions ..
-      DOUBLE PRECISION   DLAMC3, DNRM2
-      EXTERNAL           DLAMC3, DNRM2
+      DOUBLE PRECISION   DNRM2
+      EXTERNAL           DNRM2
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DCOPY, DLAED4, XERBLA
@@ -212,30 +212,9 @@
 *
       IF( K.EQ.0 )
      $   RETURN
-*
-*     Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can
-*     be computed with high relative accuracy (barring over/underflow).
-*     This is a problem on machines without a guard digit in
-*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
-*     The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I),
-*     which on any of these machines zeros out the bottommost
-*     bit of DLAMDA(I) if it is 1; this makes the subsequent
-*     subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation
-*     occurs. On binary machines with a guard digit (almost all
-*     machines) it does not change DLAMDA(I) at all. On hexadecimal
-*     and decimal machines with a guard digit, it slightly
-*     changes the bottommost bits of DLAMDA(I). It does not account
-*     for hexadecimal or decimal machines without guard digits
-*     (we know of none). We use a subroutine call to compute
-*     2*DLAMBDA(I) to prevent optimizing compilers from eliminating
-*     this code.
-*
-      DO 10 I = 1, N
-         DLAMDA( I ) = DLAMC3( DLAMDA( I ), DLAMDA( I ) ) - DLAMDA( I )
-   10 CONTINUE
 *
       DO 20 J = KSTART, KSTOP
-         CALL DLAED4( K, J, DLAMDA, W, Q( 1, J ), RHO, D( J ), INFO )
+         CALL DLAED4( K, J, DLAMBDA, W, Q( 1, J ), RHO, D( J ), INFO )
 *
 *        If the zero finder fails, the computation is terminated.
 *
@@ -261,10 +240,10 @@
       CALL DCOPY( K, Q, LDQ+1, W, 1 )
       DO 70 J = 1, K
          DO 50 I = 1, J - 1
-            W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) )
+            W( I ) = W( I )*( Q( I, J )/( DLAMBDA( I )-DLAMBDA( J ) ) )
    50    CONTINUE
          DO 60 I = J + 1, K
-            W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) )
+            W( I ) = W( I )*( Q( I, J )/( DLAMBDA( I )-DLAMBDA( J ) ) )
    60    CONTINUE
    70 CONTINUE
       DO 80 I = 1, K

lapack-netlib/SRC/dlals0.f

@@ -389,6 +389,11 @@
      $                ( POLES( I, 2 ).EQ.ZERO ) ) THEN
                      WORK( I ) = ZERO
                   ELSE
+*
+*                    Use calls to the subroutine DLAMC3 to enforce the
+*                    parentheses (x+y)+z. The goal is to prevent
+*                    optimizing compilers from doing x+(y+z).
+*
                      WORK( I ) = POLES( I, 2 )*Z( I ) /
      $                           ( DLAMC3( POLES( I, 2 ), DSIGJ )-
      $                           DIFLJ ) / ( POLES( I, 2 )+DJ )
@@ -440,6 +445,11 @@
                   IF( Z( J ).EQ.ZERO ) THEN
                      WORK( I ) = ZERO
                   ELSE
+*
+*                    Use calls to the subroutine DLAMC3 to enforce the
+*                    parentheses (x+y)+z. The goal is to prevent
+*                    optimizing compilers from doing x+(y+z).
+*
                      WORK( I ) = Z( J ) / ( DLAMC3( DSIGJ, -POLES( I+1,
      $                           2 ) )-DIFR( I, 1 ) ) /
      $                           ( DSIGJ+POLES( I, 1 ) ) / DIFR( I, 2 )

lapack-netlib/SRC/dlalsd.f

@@ -47,12 +47,6 @@
 *> problem; in this case a minimum norm solution is returned.
 *> The actual singular values are returned in D in ascending order.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dlas2.f

@@ -93,9 +93,7 @@
 *>  infinite.
 *>
 *>  Overflow will not occur unless the largest singular value itself
-*>  overflows, or is within a few ulps of overflow. (On machines with
-*>  partial overflow, like the Cray, overflow may occur if the largest
-*>  singular value is within a factor of 2 of overflow.)
+*>  overflows, or is within a few ulps of overflow.
 *>
 *>  Underflow is harmless if underflow is gradual. Otherwise, results
 *>  may correspond to a matrix modified by perturbations of size near

lapack-netlib/SRC/dlasd3.f

@@ -44,13 +44,6 @@
 *> appropriate calls to DLASD4 and then updates the singular
 *> vectors by matrix multiplication.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
-*>
 *> DLASD3 is called from DLASD1.
 *> \endverbatim
 *
@@ -103,7 +96,7 @@
 *>         The leading dimension of the array Q.  LDQ >= K.
 *> \endverbatim
 *>
-*> \param[in,out] DSIGMA
+*> \param[in] DSIGMA
 *> \verbatim
 *>          DSIGMA is DOUBLE PRECISION array, dimension(K)
 *>         The first K elements of this array contain the old roots
@@ -249,8 +242,8 @@
       DOUBLE PRECISION   RHO, TEMP
 *     ..
 *     .. External Functions ..
-      DOUBLE PRECISION   DLAMC3, DNRM2
-      EXTERNAL           DLAMC3, DNRM2
+      DOUBLE PRECISION   DNRM2
+      EXTERNAL           DNRM2
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DCOPY, DGEMM, DLACPY, DLASCL, DLASD4, XERBLA
@@ -310,27 +303,6 @@
          RETURN
       END IF
 *
-*     Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can
-*     be computed with high relative accuracy (barring over/underflow).
-*     This is a problem on machines without a guard digit in
-*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
-*     The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I),
-*     which on any of these machines zeros out the bottommost
-*     bit of DSIGMA(I) if it is 1; this makes the subsequent
-*     subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation
-*     occurs. On binary machines with a guard digit (almost all
-*     machines) it does not change DSIGMA(I) at all. On hexadecimal
-*     and decimal machines with a guard digit, it slightly
-*     changes the bottommost bits of DSIGMA(I). It does not account
-*     for hexadecimal or decimal machines without guard digits
-*     (we know of none). We use a subroutine call to compute
-*     2*DSIGMA(I) to prevent optimizing compilers from eliminating
-*     this code.
-*
-      DO 20 I = 1, K
-         DSIGMA( I ) = DLAMC3( DSIGMA( I ), DSIGMA( I ) ) - DSIGMA( I )
-   20 CONTINUE
-*
 *     Keep a copy of Z.
 *
       CALL DCOPY( K, Z, 1, Q, 1 )

lapack-netlib/SRC/dlasd8.f

@@ -121,14 +121,12 @@
 *>          The leading dimension of DIFR, must be at least K.
 *> \endverbatim
 *>
-*> \param[in,out] DSIGMA
+*> \param[in] DSIGMA
 *> \verbatim
 *>          DSIGMA is DOUBLE PRECISION array, dimension ( K )
 *>          On entry, the first K elements of this array contain the old
 *>          roots of the deflated updating problem.  These are the poles
 *>          of the secular equation.
-*>          On exit, the elements of DSIGMA may be very slightly altered
-*>          in value.
 *> \endverbatim
 *>
 *> \param[out] WORK
@@ -227,27 +225,6 @@
          RETURN
       END IF
 *
-*     Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can
-*     be computed with high relative accuracy (barring over/underflow).
-*     This is a problem on machines without a guard digit in
-*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
-*     The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I),
-*     which on any of these machines zeros out the bottommost
-*     bit of DSIGMA(I) if it is 1; this makes the subsequent
-*     subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation
-*     occurs. On binary machines with a guard digit (almost all
-*     machines) it does not change DSIGMA(I) at all. On hexadecimal
-*     and decimal machines with a guard digit, it slightly
-*     changes the bottommost bits of DSIGMA(I). It does not account
-*     for hexadecimal or decimal machines without guard digits
-*     (we know of none). We use a subroutine call to compute
-*     2*DLAMBDA(I) to prevent optimizing compilers from eliminating
-*     this code.
-*
-      DO 10 I = 1, K
-         DSIGMA( I ) = DLAMC3( DSIGMA( I ), DSIGMA( I ) ) - DSIGMA( I )
-   10 CONTINUE
-*
 *     Book keeping.
 *
       IWK1 = 1
@@ -312,6 +289,11 @@
             DSIGJP = -DSIGMA( J+1 )
          END IF
          WORK( J ) = -Z( J ) / DIFLJ / ( DSIGMA( J )+DJ )
+*
+*        Use calls to the subroutine DLAMC3 to enforce the parentheses
+*        (x+y)+z. The goal is to prevent optimizing compilers
+*        from doing x+(y+z).
+*
          DO 60 I = 1, J - 1
             WORK( I ) = Z( I ) / ( DLAMC3( DSIGMA( I ), DSIGJ )-DIFLJ )
      $                   / ( DSIGMA( I )+DJ )

lapack-netlib/SRC/dlasv2.f

@@ -124,9 +124,7 @@
 *>  infinite.
 *>
 *>  Overflow will not occur unless the largest singular value itself
-*>  overflows or is within a few ulps of overflow. (On machines with
-*>  partial overflow, like the Cray, overflow may occur if the largest
-*>  singular value is within a factor of 2 of overflow.)
+*>  overflows or is within a few ulps of overflow.
 *>
 *>  Underflow is harmless if underflow is gradual. Otherwise, results
 *>  may correspond to a matrix modified by perturbations of size near

lapack-netlib/SRC/dsbevd.f

@@ -40,12 +40,6 @@
 *> a real symmetric band matrix A. If eigenvectors are desired, it uses
 *> a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dsbevd_2stage.f

@@ -45,12 +45,6 @@
 *> the reduction to tridiagonal. If eigenvectors are desired, it uses
 *> a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dsbgvd.f

@@ -43,12 +43,6 @@
 *> banded, and B is also positive definite.  If eigenvectors are
 *> desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dspevd.f

@@ -40,12 +40,6 @@
 *> of a real symmetric matrix A in packed storage. If eigenvectors are
 *> desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dspgvd.f

@@ -44,12 +44,6 @@
 *> positive definite.
 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dstedc.f

@@ -42,12 +42,6 @@
 *> found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this
 *> matrix to tridiagonal form.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.  See DLAED3 for details.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dstevd.f

@@ -40,12 +40,6 @@
 *> real symmetric tridiagonal matrix. If eigenvectors are desired, it
 *> uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dsyevd.f

@@ -40,13 +40,6 @@
 *> real symmetric matrix A. If eigenvectors are desired, it uses a
 *> divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
-*>
 *> Because of large use of BLAS of level 3, DSYEVD needs N**2 more
 *> workspace than DSYEVX.
 *> \endverbatim

lapack-netlib/SRC/dsyevd_2stage.f

@@ -45,12 +45,6 @@
 *> the reduction to tridiagonal. If eigenvectors are desired, it uses a
 *> divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/dsygvd.f

@@ -42,12 +42,6 @@
 *> B are assumed to be symmetric and B is also positive definite.
 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/sbdsdc.f

@@ -45,13 +45,6 @@
 *> respectively. SBDSDC can be used to compute all singular values,
 *> and optionally, singular vectors or singular vectors in compact form.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.  See SLASD3 for details.
-*>
 *> The code currently calls SLASDQ if singular values only are desired.
 *> However, it can be slightly modified to compute singular values
 *> using the divide and conquer method.

lapack-netlib/SRC/sgelsd.f

@@ -59,12 +59,6 @@
 *> singular values which are less than RCOND times the largest singular
 *> value.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/sgesdd.f

@@ -55,12 +55,6 @@
 *>
 *> Note that the routine returns VT = V**T, not V.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/slaed2.f

@@ -18,7 +18,7 @@
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W,
+*       SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMBDA, W,
 *                          Q2, INDX, INDXC, INDXP, COLTYP, INFO )
 *
 *       .. Scalar Arguments ..
@@ -28,7 +28,7 @@
 *       .. Array Arguments ..
 *       INTEGER            COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ),
 *      $                   INDXQ( * )
-*       REAL               D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ),
+*       REAL               D( * ), DLAMBDA( * ), Q( LDQ, * ), Q2( * ),
 *      $                   W( * ), Z( * )
 *       ..
 *
@@ -123,9 +123,9 @@
 *>         process.
 *> \endverbatim
 *>
-*> \param[out] DLAMDA
+*> \param[out] DLAMBDA
 *> \verbatim
-*>          DLAMDA is REAL array, dimension (N)
+*>          DLAMBDA is REAL array, dimension (N)
 *>         A copy of the first K eigenvalues which will be used by
 *>         SLAED3 to form the secular equation.
 *> \endverbatim
@@ -148,7 +148,7 @@
 *> \param[out] INDX
 *> \verbatim
 *>          INDX is INTEGER array, dimension (N)
-*>         The permutation used to sort the contents of DLAMDA into
+*>         The permutation used to sort the contents of DLAMBDA into
 *>         ascending order.
 *> \endverbatim
 *>
@@ -207,7 +207,7 @@
 *>  Modified by Francoise Tisseur, University of Tennessee
 *>
 *  =====================================================================
-      SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W,
+      SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMBDA, W,
      $                   Q2, INDX, INDXC, INDXP, COLTYP, INFO )
 *
 *  -- LAPACK computational routine --
@@ -221,7 +221,7 @@
 *     .. Array Arguments ..
       INTEGER            COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ),
      $                   INDXQ( * )
-      REAL               D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ),
+      REAL               D( * ), DLAMBDA( * ), Q( LDQ, * ), Q2( * ),
      $                   W( * ), Z( * )
 *     ..
 *
@@ -300,9 +300,9 @@
 *     re-integrate the deflated parts from the last pass
 *
       DO 20 I = 1, N
-         DLAMDA( I ) = D( INDXQ( I ) )
+         DLAMBDA( I ) = D( INDXQ( I ) )
    20 CONTINUE
-      CALL SLAMRG( N1, N2, DLAMDA, 1, 1, INDXC )
+      CALL SLAMRG( N1, N2, DLAMBDA, 1, 1, INDXC )
       DO 30 I = 1, N
          INDX( I ) = INDXQ( INDXC( I ) )
    30 CONTINUE
@@ -324,11 +324,11 @@
          DO 40 J = 1, N
             I = INDX( J )
             CALL SCOPY( N, Q( 1, I ), 1, Q2( IQ2 ), 1 )
-            DLAMDA( J ) = D( I )
+            DLAMBDA( J ) = D( I )
             IQ2 = IQ2 + N
    40    CONTINUE
          CALL SLACPY( 'A', N, N, Q2, N, Q, LDQ )
-         CALL SCOPY( N, DLAMDA, 1, D, 1 )
+         CALL SCOPY( N, DLAMBDA, 1, D, 1 )
          GO TO 190
       END IF
 *
@@ -421,7 +421,7 @@
             PJ = NJ
          ELSE
             K = K + 1
-            DLAMDA( K ) = D( PJ )
+            DLAMBDA( K ) = D( PJ )
             W( K ) = Z( PJ )
             INDXP( K ) = PJ
             PJ = NJ
@@ -433,7 +433,7 @@
 *     Record the last eigenvalue.
 *
       K = K + 1
-      DLAMDA( K ) = D( PJ )
+      DLAMBDA( K ) = D( PJ )
       W( K ) = Z( PJ )
       INDXP( K ) = PJ
 *
@@ -470,9 +470,9 @@
          PSM( CT ) = PSM( CT ) + 1
   130 CONTINUE
 *
-*     Sort the eigenvalues and corresponding eigenvectors into DLAMDA
+*     Sort the eigenvalues and corresponding eigenvectors into DLAMBDA
 *     and Q2 respectively.  The eigenvalues/vectors which were not
-*     deflated go into the first K slots of DLAMDA and Q2 respectively,
+*     deflated go into the first K slots of DLAMBDA and Q2 respectively,
 *     while those which were deflated go into the last N - K slots.
 *
       I = 1

lapack-netlib/SRC/slaed3.f

@@ -18,7 +18,7 @@
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX,
+*       SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMBDA, Q2, INDX,
 *                          CTOT, W, S, INFO )
 *
 *       .. Scalar Arguments ..
@@ -27,7 +27,7 @@
 *       ..
 *       .. Array Arguments ..
 *       INTEGER            CTOT( * ), INDX( * )
-*       REAL               D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ),
+*       REAL               D( * ), DLAMBDA( * ), Q( LDQ, * ), Q2( * ),
 *      $                   S( * ), W( * )
 *       ..
 *
@@ -44,12 +44,6 @@
 *> being combined by the matrix of eigenvectors of the K-by-K system
 *> which is solved here.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:
@@ -104,14 +98,12 @@
 *>          RHO >= 0 required.
 *> \endverbatim
 *>
-*> \param[in,out] DLAMDA
+*> \param[in] DLAMBDA
 *> \verbatim
-*>          DLAMDA is REAL array, dimension (K)
+*>          DLAMBDA is REAL array, dimension (K)
 *>          The first K elements of this array contain the old roots
 *>          of the deflated updating problem.  These are the poles
-*>          of the secular equation. May be changed on output by
-*>          having lowest order bit set to zero on Cray X-MP, Cray Y-MP,
-*>          Cray-2, or Cray C-90, as described above.
+*>          of the secular equation.
 *> \endverbatim
 *>
 *> \param[in] Q2
@@ -180,7 +172,7 @@
 *>  Modified by Francoise Tisseur, University of Tennessee
 *>
 *  =====================================================================
-      SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX,
+      SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMBDA, Q2, INDX,
      $                   CTOT, W, S, INFO )
 *
 *  -- LAPACK computational routine --
@@ -193,7 +185,7 @@
 *     ..
 *     .. Array Arguments ..
       INTEGER            CTOT( * ), INDX( * )
-      REAL               D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ),
+      REAL               D( * ), DLAMBDA( * ), Q( LDQ, * ), Q2( * ),
      $                   S( * ), W( * )
 *     ..
 *
@@ -208,8 +200,8 @@
       REAL               TEMP
 *     ..
 *     .. External Functions ..
-      REAL               SLAMC3, SNRM2
-      EXTERNAL           SLAMC3, SNRM2
+      REAL               SNRM2
+      EXTERNAL           SNRM2
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           SCOPY, SGEMM, SLACPY, SLAED4, SLASET, XERBLA
@@ -239,30 +231,9 @@
 *
       IF( K.EQ.0 )
      $   RETURN
-*
-*     Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can
-*     be computed with high relative accuracy (barring over/underflow).
-*     This is a problem on machines without a guard digit in
-*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
-*     The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I),
-*     which on any of these machines zeros out the bottommost
-*     bit of DLAMDA(I) if it is 1; this makes the subsequent
-*     subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation
-*     occurs. On binary machines with a guard digit (almost all
-*     machines) it does not change DLAMDA(I) at all. On hexadecimal
-*     and decimal machines with a guard digit, it slightly
-*     changes the bottommost bits of DLAMDA(I). It does not account
-*     for hexadecimal or decimal machines without guard digits
-*     (we know of none). We use a subroutine call to compute
-*     2*DLAMBDA(I) to prevent optimizing compilers from eliminating
-*     this code.
-*
-      DO 10 I = 1, K
-         DLAMDA( I ) = SLAMC3( DLAMDA( I ), DLAMDA( I ) ) - DLAMDA( I )
-   10 CONTINUE
 *
       DO 20 J = 1, K
-         CALL SLAED4( K, J, DLAMDA, W, Q( 1, J ), RHO, D( J ), INFO )
+         CALL SLAED4( K, J, DLAMBDA, W, Q( 1, J ), RHO, D( J ), INFO )
 *
 *        If the zero finder fails, the computation is terminated.
 *
@@ -293,10 +264,10 @@
       CALL SCOPY( K, Q, LDQ+1, W, 1 )
       DO 60 J = 1, K
          DO 40 I = 1, J - 1
-            W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) )
+            W( I ) = W( I )*( Q( I, J )/( DLAMBDA( I )-DLAMBDA( J ) ) )
    40    CONTINUE
          DO 50 I = J + 1, K
-            W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) )
+            W( I ) = W( I )*( Q( I, J )/( DLAMBDA( I )-DLAMBDA( J ) ) )
    50    CONTINUE
    60 CONTINUE
       DO 70 I = 1, K

lapack-netlib/SRC/slaed8.f

@@ -19,7 +19,7 @@
 *  ===========
 *
 *       SUBROUTINE SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO,
-*                          CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR,
+*                          CUTPNT, Z, DLAMBDA, Q2, LDQ2, W, PERM, GIVPTR,
 *                          GIVCOL, GIVNUM, INDXP, INDX, INFO )
 *
 *       .. Scalar Arguments ..
@@ -30,7 +30,7 @@
 *       .. Array Arguments ..
 *       INTEGER            GIVCOL( 2, * ), INDX( * ), INDXP( * ),
 *      $                   INDXQ( * ), PERM( * )
-*       REAL               D( * ), DLAMDA( * ), GIVNUM( 2, * ),
+*       REAL               D( * ), DLAMBDA( * ), GIVNUM( 2, * ),
 *      $                   Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * )
 *       ..
 *
@@ -141,9 +141,9 @@
 *>         process.
 *> \endverbatim
 *>
-*> \param[out] DLAMDA
+*> \param[out] DLAMBDA
 *> \verbatim
-*>          DLAMDA is REAL array, dimension (N)
+*>          DLAMBDA is REAL array, dimension (N)
 *>         A copy of the first K eigenvalues which will be used by
 *>         SLAED3 to form the secular equation.
 *> \endverbatim
@@ -238,7 +238,7 @@
 *
 *  =====================================================================
       SUBROUTINE SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO,
-     $                   CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR,
+     $                   CUTPNT, Z, DLAMBDA, Q2, LDQ2, W, PERM, GIVPTR,
      $                   GIVCOL, GIVNUM, INDXP, INDX, INFO )
 *
 *  -- LAPACK computational routine --
@@ -253,7 +253,7 @@
 *     .. Array Arguments ..
       INTEGER            GIVCOL( 2, * ), INDX( * ), INDXP( * ),
      $                   INDXQ( * ), PERM( * )
-      REAL               D( * ), DLAMDA( * ), GIVNUM( 2, * ),
+      REAL               D( * ), DLAMBDA( * ), GIVNUM( 2, * ),
      $                   Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * )
 *     ..
 *
@@ -339,14 +339,14 @@
          INDXQ( I ) = INDXQ( I ) + CUTPNT
    20 CONTINUE
       DO 30 I = 1, N
-         DLAMDA( I ) = D( INDXQ( I ) )
+         DLAMBDA( I ) = D( INDXQ( I ) )
          W( I ) = Z( INDXQ( I ) )
    30 CONTINUE
       I = 1
       J = CUTPNT + 1
-      CALL SLAMRG( N1, N2, DLAMDA, 1, 1, INDX )
+      CALL SLAMRG( N1, N2, DLAMBDA, 1, 1, INDX )
       DO 40 I = 1, N
-         D( I ) = DLAMDA( INDX( I ) )
+         D( I ) = DLAMBDA( INDX( I ) )
          Z( I ) = W( INDX( I ) )
    40 CONTINUE
 *
@@ -464,7 +464,7 @@
          ELSE
             K = K + 1
             W( K ) = Z( JLAM )
-            DLAMDA( K ) = D( JLAM )
+            DLAMBDA( K ) = D( JLAM )
             INDXP( K ) = JLAM
             JLAM = J
          END IF
@@ -476,26 +476,26 @@
 *
       K = K + 1
       W( K ) = Z( JLAM )
-      DLAMDA( K ) = D( JLAM )
+      DLAMBDA( K ) = D( JLAM )
       INDXP( K ) = JLAM
 *
   110 CONTINUE
 *
-*     Sort the eigenvalues and corresponding eigenvectors into DLAMDA
+*     Sort the eigenvalues and corresponding eigenvectors into DLAMBDA
 *     and Q2 respectively.  The eigenvalues/vectors which were not
-*     deflated go into the first K slots of DLAMDA and Q2 respectively,
+*     deflated go into the first K slots of DLAMBDA and Q2 respectively,
 *     while those which were deflated go into the last N - K slots.
 *
       IF( ICOMPQ.EQ.0 ) THEN
          DO 120 J = 1, N
             JP = INDXP( J )
-            DLAMDA( J ) = D( JP )
+            DLAMBDA( J ) = D( JP )
             PERM( J ) = INDXQ( INDX( JP ) )
   120    CONTINUE
       ELSE
          DO 130 J = 1, N
             JP = INDXP( J )
-            DLAMDA( J ) = D( JP )
+            DLAMBDA( J ) = D( JP )
             PERM( J ) = INDXQ( INDX( JP ) )
             CALL SCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 )
   130    CONTINUE
@@ -506,9 +506,9 @@
 *
       IF( K.LT.N ) THEN
          IF( ICOMPQ.EQ.0 ) THEN
-            CALL SCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 )
+            CALL SCOPY( N-K, DLAMBDA( K+1 ), 1, D( K+1 ), 1 )
          ELSE
-            CALL SCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 )
+            CALL SCOPY( N-K, DLAMBDA( K+1 ), 1, D( K+1 ), 1 )
             CALL SLACPY( 'A', QSIZ, N-K, Q2( 1, K+1 ), LDQ2,
      $                   Q( 1, K+1 ), LDQ )
          END IF

lapack-netlib/SRC/slaed9.f

@@ -18,15 +18,15 @@
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
-*                          S, LDS, INFO )
+*       SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMBDA,
+*                          W, S, LDS, INFO )
 *
 *       .. Scalar Arguments ..
 *       INTEGER            INFO, K, KSTART, KSTOP, LDQ, LDS, N
 *       REAL               RHO
 *       ..
 *       .. Array Arguments ..
-*       REAL               D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ),
+*       REAL               D( * ), DLAMBDA( * ), Q( LDQ, * ), S( LDS, * ),
 *      $                   W( * )
 *       ..
 *
@@ -96,9 +96,9 @@
 *>          RHO >= 0 required.
 *> \endverbatim
 *>
-*> \param[in] DLAMDA
+*> \param[in] DLAMBDA
 *> \verbatim
-*>          DLAMDA is REAL array, dimension (K)
+*>          DLAMBDA is REAL array, dimension (K)
 *>          The first K elements of this array contain the old roots
 *>          of the deflated updating problem.  These are the poles
 *>          of the secular equation.
@@ -151,8 +151,8 @@
 *> at Berkeley, USA
 *
 *  =====================================================================
-      SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
-     $                   S, LDS, INFO )
+      SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMBDA,
+     $                   W, S, LDS, INFO )
 *
 *  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
@@ -163,7 +163,7 @@
       REAL               RHO
 *     ..
 *     .. Array Arguments ..
-      REAL               D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ),
+      REAL               D( * ), DLAMBDA( * ), Q( LDQ, * ), S( LDS, * ),
      $                   W( * )
 *     ..
 *
@@ -174,8 +174,8 @@
       REAL               TEMP
 *     ..
 *     .. External Functions ..
-      REAL               SLAMC3, SNRM2
-      EXTERNAL           SLAMC3, SNRM2
+      REAL               SNRM2
+      EXTERNAL           SNRM2
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           SCOPY, SLAED4, XERBLA
@@ -212,30 +212,9 @@
 *
       IF( K.EQ.0 )
      $   RETURN
-*
-*     Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can
-*     be computed with high relative accuracy (barring over/underflow).
-*     This is a problem on machines without a guard digit in
-*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
-*     The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I),
-*     which on any of these machines zeros out the bottommost
-*     bit of DLAMDA(I) if it is 1; this makes the subsequent
-*     subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation
-*     occurs. On binary machines with a guard digit (almost all
-*     machines) it does not change DLAMDA(I) at all. On hexadecimal
-*     and decimal machines with a guard digit, it slightly
-*     changes the bottommost bits of DLAMDA(I). It does not account
-*     for hexadecimal or decimal machines without guard digits
-*     (we know of none). We use a subroutine call to compute
-*     2*DLAMBDA(I) to prevent optimizing compilers from eliminating
-*     this code.
-*
-      DO 10 I = 1, N
-         DLAMDA( I ) = SLAMC3( DLAMDA( I ), DLAMDA( I ) ) - DLAMDA( I )
-   10 CONTINUE
 *
       DO 20 J = KSTART, KSTOP
-         CALL SLAED4( K, J, DLAMDA, W, Q( 1, J ), RHO, D( J ), INFO )
+         CALL SLAED4( K, J, DLAMBDA, W, Q( 1, J ), RHO, D( J ), INFO )
 *
 *        If the zero finder fails, the computation is terminated.
 *
@@ -261,10 +240,10 @@
       CALL SCOPY( K, Q, LDQ+1, W, 1 )
       DO 70 J = 1, K
          DO 50 I = 1, J - 1
-            W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) )
+            W( I ) = W( I )*( Q( I, J )/( DLAMBDA( I )-DLAMBDA( J ) ) )
    50    CONTINUE
          DO 60 I = J + 1, K
-            W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) )
+            W( I ) = W( I )*( Q( I, J )/( DLAMBDA( I )-DLAMBDA( J ) ) )
    60    CONTINUE
    70 CONTINUE
       DO 80 I = 1, K

lapack-netlib/SRC/slals0.f

@@ -389,6 +389,11 @@
      $                ( POLES( I, 2 ).EQ.ZERO ) ) THEN
                      WORK( I ) = ZERO
                   ELSE
+*
+*                    Use calls to the subroutine SLAMC3 to enforce the
+*                    parentheses (x+y)+z. The goal is to prevent
+*                    optimizing compilers from doing x+(y+z).
+*
                      WORK( I ) = POLES( I, 2 )*Z( I ) /
      $                           ( SLAMC3( POLES( I, 2 ), DSIGJ )-
      $                           DIFLJ ) / ( POLES( I, 2 )+DJ )
@@ -440,6 +445,11 @@
                   IF( Z( J ).EQ.ZERO ) THEN
                      WORK( I ) = ZERO
                   ELSE
+*
+*                    Use calls to the subroutine SLAMC3 to enforce the
+*                    parentheses (x+y)+z. The goal is to prevent
+*                    optimizing compilers from doing x+(y+z).
+*
                      WORK( I ) = Z( J ) / ( SLAMC3( DSIGJ, -POLES( I+1,
      $                           2 ) )-DIFR( I, 1 ) ) /
      $                           ( DSIGJ+POLES( I, 1 ) ) / DIFR( I, 2 )

lapack-netlib/SRC/slalsd.f

@@ -47,12 +47,6 @@
 *> problem; in this case a minimum norm solution is returned.
 *> The actual singular values are returned in D in ascending order.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/slas2.f

@@ -93,9 +93,7 @@
 *>  infinite.
 *>
 *>  Overflow will not occur unless the largest singular value itself
-*>  overflows, or is within a few ulps of overflow. (On machines with
-*>  partial overflow, like the Cray, overflow may occur if the largest
-*>  singular value is within a factor of 2 of overflow.)
+*>  overflows, or is within a few ulps of overflow.
 *>
 *>  Underflow is harmless if underflow is gradual. Otherwise, results
 *>  may correspond to a matrix modified by perturbations of size near

lapack-netlib/SRC/slasd3.f

@@ -44,13 +44,6 @@
 *> appropriate calls to SLASD4 and then updates the singular
 *> vectors by matrix multiplication.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
-*>
 *> SLASD3 is called from SLASD1.
 *> \endverbatim
 *
@@ -103,7 +96,7 @@
 *>         The leading dimension of the array Q.  LDQ >= K.
 *> \endverbatim
 *>
-*> \param[in,out] DSIGMA
+*> \param[in] DSIGMA
 *> \verbatim
 *>          DSIGMA is REAL array, dimension(K)
 *>         The first K elements of this array contain the old roots
@@ -249,8 +242,8 @@
       REAL               RHO, TEMP
 *     ..
 *     .. External Functions ..
-      REAL               SLAMC3, SNRM2
-      EXTERNAL           SLAMC3, SNRM2
+      REAL               SNRM2
+      EXTERNAL           SNRM2
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           SCOPY, SGEMM, SLACPY, SLASCL, SLASD4, XERBLA
@@ -310,27 +303,6 @@
          RETURN
       END IF
 *
-*     Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can
-*     be computed with high relative accuracy (barring over/underflow).
-*     This is a problem on machines without a guard digit in
-*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
-*     The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I),
-*     which on any of these machines zeros out the bottommost
-*     bit of DSIGMA(I) if it is 1; this makes the subsequent
-*     subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation
-*     occurs. On binary machines with a guard digit (almost all
-*     machines) it does not change DSIGMA(I) at all. On hexadecimal
-*     and decimal machines with a guard digit, it slightly
-*     changes the bottommost bits of DSIGMA(I). It does not account
-*     for hexadecimal or decimal machines without guard digits
-*     (we know of none). We use a subroutine call to compute
-*     2*DSIGMA(I) to prevent optimizing compilers from eliminating
-*     this code.
-*
-      DO 20 I = 1, K
-         DSIGMA( I ) = SLAMC3( DSIGMA( I ), DSIGMA( I ) ) - DSIGMA( I )
-   20 CONTINUE
-*
 *     Keep a copy of Z.
 *
       CALL SCOPY( K, Z, 1, Q, 1 )

lapack-netlib/SRC/slasd8.f

@@ -121,14 +121,12 @@
 *>          The leading dimension of DIFR, must be at least K.
 *> \endverbatim
 *>
-*> \param[in,out] DSIGMA
+*> \param[in] DSIGMA
 *> \verbatim
 *>          DSIGMA is REAL array, dimension ( K )
 *>          On entry, the first K elements of this array contain the old
 *>          roots of the deflated updating problem.  These are the poles
 *>          of the secular equation.
-*>          On exit, the elements of DSIGMA may be very slightly altered
-*>          in value.
 *> \endverbatim
 *>
 *> \param[out] WORK
@@ -227,27 +225,6 @@
          RETURN
       END IF
 *
-*     Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can
-*     be computed with high relative accuracy (barring over/underflow).
-*     This is a problem on machines without a guard digit in
-*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
-*     The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I),
-*     which on any of these machines zeros out the bottommost
-*     bit of DSIGMA(I) if it is 1; this makes the subsequent
-*     subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation
-*     occurs. On binary machines with a guard digit (almost all
-*     machines) it does not change DSIGMA(I) at all. On hexadecimal
-*     and decimal machines with a guard digit, it slightly
-*     changes the bottommost bits of DSIGMA(I). It does not account
-*     for hexadecimal or decimal machines without guard digits
-*     (we know of none). We use a subroutine call to compute
-*     2*DLAMBDA(I) to prevent optimizing compilers from eliminating
-*     this code.
-*
-      DO 10 I = 1, K
-         DSIGMA( I ) = SLAMC3( DSIGMA( I ), DSIGMA( I ) ) - DSIGMA( I )
-   10 CONTINUE
-*
 *     Book keeping.
 *
       IWK1 = 1
@@ -312,6 +289,11 @@
             DSIGJP = -DSIGMA( J+1 )
          END IF
          WORK( J ) = -Z( J ) / DIFLJ / ( DSIGMA( J )+DJ )
+*
+*        Use calls to the subroutine SLAMC3 to enforce the parentheses
+*        (x+y)+z. The goal is to prevent optimizing compilers
+*        from doing x+(y+z).
+*
          DO 60 I = 1, J - 1
             WORK( I ) = Z( I ) / ( SLAMC3( DSIGMA( I ), DSIGJ )-DIFLJ )
      $                   / ( DSIGMA( I )+DJ )

lapack-netlib/SRC/slasv2.f

@@ -124,9 +124,7 @@
 *>  infinite.
 *>
 *>  Overflow will not occur unless the largest singular value itself
-*>  overflows or is within a few ulps of overflow. (On machines with
-*>  partial overflow, like the Cray, overflow may occur if the largest
-*>  singular value is within a factor of 2 of overflow.)
+*>  overflows or is within a few ulps of overflow.
 *>
 *>  Underflow is harmless if underflow is gradual. Otherwise, results
 *>  may correspond to a matrix modified by perturbations of size near

lapack-netlib/SRC/ssbevd.f

@@ -40,12 +40,6 @@
 *> a real symmetric band matrix A. If eigenvectors are desired, it uses
 *> a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/ssbevd_2stage.f

@@ -45,12 +45,6 @@
 *> the reduction to tridiagonal. If eigenvectors are desired, it uses
 *> a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/ssbgvd.f

@@ -43,12 +43,6 @@
 *> banded, and B is also positive definite.  If eigenvectors are
 *> desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/sspevd.f

@@ -40,12 +40,6 @@
 *> of a real symmetric matrix A in packed storage. If eigenvectors are
 *> desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/sspgvd.f

@@ -44,12 +44,6 @@
 *> positive definite.
 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/sstedc.f

@@ -42,12 +42,6 @@
 *> found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this
 *> matrix to tridiagonal form.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.  See SLAED3 for details.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/sstevd.f

@@ -40,12 +40,6 @@
 *> real symmetric tridiagonal matrix. If eigenvectors are desired, it
 *> uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/ssyevd.f

@@ -40,13 +40,6 @@
 *> real symmetric matrix A. If eigenvectors are desired, it uses a
 *> divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
-*>
 *> Because of large use of BLAS of level 3, SSYEVD needs N**2 more
 *> workspace than SSYEVX.
 *> \endverbatim

lapack-netlib/SRC/ssyevd_2stage.f

@@ -45,12 +45,6 @@
 *> the reduction to tridiagonal. If eigenvectors are desired, it uses a
 *> divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/ssygvd.f

@@ -42,12 +42,6 @@
 *> B are assumed to be symmetric and B is also positive definite.
 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zgelsd.f

@@ -60,12 +60,6 @@
 *> singular values which are less than RCOND times the largest singular
 *> value.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zgesdd.f

@@ -53,12 +53,6 @@
 *>
 *> Note that the routine returns VT = V**H, not V.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zhbevd.f

@@ -41,12 +41,6 @@
 *> a complex Hermitian band matrix A.  If eigenvectors are desired, it
 *> uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zhbevd_2stage.f

@@ -47,12 +47,6 @@
 *> the reduction to tridiagonal.  If eigenvectors are desired, it
 *> uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zhbgvd.f

@@ -46,12 +46,6 @@
 *> and banded, and B is also positive definite.  If eigenvectors are
 *> desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zheevd.f

@@ -41,12 +41,6 @@
 *> complex Hermitian matrix A.  If eigenvectors are desired, it uses a
 *> divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zheevd_2stage.f

@@ -46,12 +46,6 @@
 *> the reduction to tridiagonal.  If eigenvectors are desired, it uses a
 *> divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zhegvd.f

@@ -43,12 +43,6 @@
 *> B are assumed to be Hermitian and B is also positive definite.
 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zhpevd.f

@@ -41,12 +41,6 @@
 *> a complex Hermitian matrix A in packed storage.  If eigenvectors are
 *> desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zhpgvd.f

@@ -44,12 +44,6 @@
 *> positive definite.
 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
 *>
-*> The divide and conquer algorithm makes very mild assumptions about
-*> floating point arithmetic. It will work on machines with a guard
-*> digit in add/subtract, or on those binary machines without guard
-*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zlaed8.f

@@ -18,7 +18,7 @@
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
+*       SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMBDA,
 *                          Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR,
 *                          GIVCOL, GIVNUM, INFO )
 *
@@ -29,7 +29,7 @@
 *       .. Array Arguments ..
 *       INTEGER            GIVCOL( 2, * ), INDX( * ), INDXP( * ),
 *      $                   INDXQ( * ), PERM( * )
-*       DOUBLE PRECISION   D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ),
+*       DOUBLE PRECISION   D( * ), DLAMBDA( * ), GIVNUM( 2, * ), W( * ),
 *      $                   Z( * )
 *       COMPLEX*16         Q( LDQ, * ), Q2( LDQ2, * )
 *       ..
@@ -122,9 +122,9 @@
 *>         destroyed during the updating process.
 *> \endverbatim
 *>
-*> \param[out] DLAMDA
+*> \param[out] DLAMBDA
 *> \verbatim
-*>          DLAMDA is DOUBLE PRECISION array, dimension (N)
+*>          DLAMBDA is DOUBLE PRECISION array, dimension (N)
 *>         Contains a copy of the first K eigenvalues which will be used
 *>         by DLAED3 to form the secular equation.
 *> \endverbatim
@@ -222,7 +222,7 @@
 *> \ingroup complex16OTHERcomputational
 *
 *  =====================================================================
-      SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
+      SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMBDA,
      $                   Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR,
      $                   GIVCOL, GIVNUM, INFO )
 *
@@ -237,7 +237,7 @@
 *     .. Array Arguments ..
       INTEGER            GIVCOL( 2, * ), INDX( * ), INDXP( * ),
      $                   INDXQ( * ), PERM( * )
-      DOUBLE PRECISION   D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ),
+      DOUBLE PRECISION   D( * ), DLAMBDA( * ), GIVNUM( 2, * ), W( * ),
      $                   Z( * )
       COMPLEX*16         Q( LDQ, * ), Q2( LDQ2, * )
 *     ..
@@ -322,14 +322,14 @@
          INDXQ( I ) = INDXQ( I ) + CUTPNT
    20 CONTINUE
       DO 30 I = 1, N
-         DLAMDA( I ) = D( INDXQ( I ) )
+         DLAMBDA( I ) = D( INDXQ( I ) )
          W( I ) = Z( INDXQ( I ) )
    30 CONTINUE
       I = 1
       J = CUTPNT + 1
-      CALL DLAMRG( N1, N2, DLAMDA, 1, 1, INDX )
+      CALL DLAMRG( N1, N2, DLAMBDA, 1, 1, INDX )
       DO 40 I = 1, N
-         D( I ) = DLAMDA( INDX( I ) )
+         D( I ) = DLAMBDA( INDX( I ) )
          Z( I ) = W( INDX( I ) )
    40 CONTINUE
 *
@@ -438,7 +438,7 @@
          ELSE
             K = K + 1
             W( K ) = Z( JLAM )
-            DLAMDA( K ) = D( JLAM )
+            DLAMBDA( K ) = D( JLAM )
             INDXP( K ) = JLAM
             JLAM = J
          END IF
@@ -450,19 +450,19 @@
 *
       K = K + 1
       W( K ) = Z( JLAM )
-      DLAMDA( K ) = D( JLAM )
+      DLAMBDA( K ) = D( JLAM )
       INDXP( K ) = JLAM
 *
   100 CONTINUE
 *
-*     Sort the eigenvalues and corresponding eigenvectors into DLAMDA
+*     Sort the eigenvalues and corresponding eigenvectors into DLAMBDA
 *     and Q2 respectively.  The eigenvalues/vectors which were not
-*     deflated go into the first K slots of DLAMDA and Q2 respectively,
+*     deflated go into the first K slots of DLAMBDA and Q2 respectively,
 *     while those which were deflated go into the last N - K slots.
 *
       DO 110 J = 1, N
          JP = INDXP( J )
-         DLAMDA( J ) = D( JP )
+         DLAMBDA( J ) = D( JP )
          PERM( J ) = INDXQ( INDX( JP ) )
          CALL ZCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 )
   110 CONTINUE
@@ -471,7 +471,7 @@
 *     into the last N - K slots of D and Q respectively.
 *
       IF( K.LT.N ) THEN
-         CALL DCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 )
+         CALL DCOPY( N-K, DLAMBDA( K+1 ), 1, D( K+1 ), 1 )
          CALL ZLACPY( 'A', QSIZ, N-K, Q2( 1, K+1 ), LDQ2, Q( 1, K+1 ),
      $                LDQ )
       END IF

lapack-netlib/SRC/zlals0.f

@@ -392,6 +392,11 @@
      $                ( POLES( I, 2 ).EQ.ZERO ) ) THEN
                      RWORK( I ) = ZERO
                   ELSE
+*
+*                    Use calls to the subroutine DLAMC3 to enforce the
+*                    parentheses (x+y)+z. The goal is to prevent
+*                    optimizing compilers from doing x+(y+z).
+*
                      RWORK( I ) = POLES( I, 2 )*Z( I ) /
      $                            ( DLAMC3( POLES( I, 2 ), DSIGJ )-
      $                            DIFLJ ) / ( POLES( I, 2 )+DJ )
@@ -470,6 +475,11 @@
                   IF( Z( J ).EQ.ZERO ) THEN
                      RWORK( I ) = ZERO
                   ELSE
+*
+*                    Use calls to the subroutine DLAMC3 to enforce the
+*                    parentheses (x+y)+z. The goal is to prevent
+*                    optimizing compilers from doing x+(y+z).
+*
                      RWORK( I ) = Z( J ) / ( DLAMC3( DSIGJ, -POLES( I+1,
      $                            2 ) )-DIFR( I, 1 ) ) /
      $                            ( DSIGJ+POLES( I, 1 ) ) / DIFR( I, 2 )

lapack-netlib/SRC/zlalsd.f

@@ -48,12 +48,6 @@
 *> problem; in this case a minimum norm solution is returned.
 *> The actual singular values are returned in D in ascending order.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zstedc.f

@@ -43,12 +43,6 @@
 *> be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this
 *> matrix to tridiagonal form.
 *>
-*> This code makes very mild assumptions about floating point
-*> arithmetic. It will work on machines with a guard digit in
-*> add/subtract, or on those binary machines without guard digits
-*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
-*> It could conceivably fail on hexadecimal or decimal machines
-*> without guard digits, but we know of none.  See DLAED3 for details.
 *> \endverbatim
 *
 *  Arguments: