Remove legacy warning for non IEEE 754 compliant machines

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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 @@ SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
 *     .. 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 @@ SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
          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 @@ SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
          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 @@ SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
 *
       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 @@ SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
 *     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

SRC/clals0.f

@@ -392,6 +392,11 @@ SUBROUTINE CLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
      $                ( 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 @@ SUBROUTINE CLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
                   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 )

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:

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:

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.

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:

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: