Fix integer overflow in DBDSQR

As noted in lapack issue 135, an integer overflow in the calculation of the iteration limit could lead to an immediate return without any iterations having been performed if the input matrix is sufficiently big.

lapack-netlib/SRC/dbdsqr.f

@@ -214,6 +214,16 @@
 *>          through the inner loop exceeds MAXITR*N**2.
 *> \endverbatim
 *
+*> \par Note:
+*  ===========
+*>
+*> \verbatim
+*>  Bug report from Cezary Dendek.
+*>  On March 23rd 2017, the INTEGER variable MAXIT = MAXITR*N**2 is
+*>  removed since it can overflow pretty easily (for N larger or equal
+*>  than 18,919). We instead use MAXITDIVN = MAXITR*N.
+*> \endverbatim
+*
 *  Authors:
 *  ========
 *
@@ -266,8 +276,8 @@
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LOWER, ROTATE
-      INTEGER            I, IDIR, ISUB, ITER, J, LL, LLL, M, MAXIT, NM1,
-     $                   NM12, NM13, OLDLL, OLDM
+      INTEGER            I, IDIR, ISUB, ITER, ITERDIVN, J, LL, LLL, M,
+     $                   MAXITDIVN, NM1, NM12, NM13, OLDLL, OLDM
       DOUBLE PRECISION   ABSE, ABSS, COSL, COSR, CS, EPS, F, G, H, MU,
      $                   OLDCS, OLDSN, R, SHIFT, SIGMN, SIGMX, SINL,
      $                   SINR, SLL, SMAX, SMIN, SMINL, SMINOA,
@@ -300,7 +310,7 @@
       ELSE IF( NRU.LT.0 ) THEN
          INFO = -4
       ELSE IF( NCC.LT.0 ) THEN
-         INFO = -5
+         INFO = -5NM1, 
       ELSE IF( ( NCVT.EQ.0 .AND. LDVT.LT.1 ) .OR.
      $         ( NCVT.GT.0 .AND. LDVT.LT.MAX( 1, N ) ) ) THEN
          INFO = -9
@@ -412,8 +422,9 @@
 *     (MAXIT is the maximum number of passes through the inner
 *     loop permitted before nonconvergence signalled.)
 *
-      MAXIT = MAXITR*N*N
-      ITER = 0
+      MAXITDIVN = MAXITR*N
+      ITERDIVN = 0
+      ITER = -1
       OLDLL = -1
       OLDM = -1
 *
@@ -429,8 +440,13 @@
 *
       IF( M.LE.1 )
      $   GO TO 160
-      IF( ITER.GT.MAXIT )
+*     
+      IF( ITER.GE.N ) THEN
+         ITER = ITER - N
+         ITERDIVN = ITERDIVN + 1
+         IF (ITERDIVN.GE.MAXITDIVN )
      $   GO TO 200
+      ENDIF
 *
 *     Find diagonal block of matrix to work on
 *