diff --git a/SRC/clarrv.f b/SRC/clarrv.f
index dac574d75..ed9ae14fb 100644
--- a/SRC/clarrv.f
+++ b/SRC/clarrv.f
@@ -702,6 +702,10 @@ SUBROUTINE CLARRV( N, VL, VU, D, L, PIVMIN,
      $                       WERR(WBEGIN),WORK( INDWRK ),
      $                       IWORK( IINDWK ), PIVMIN, SPDIAM,
      $                       IN, IINFO )
+                        IF( IINFO.NE.0 ) THEN
+                           INFO = -1
+                           RETURN
+                        END IF
  55                  CONTINUE
 *
                      IF((WBEGIN+NEWLST-1.LT.DOL).OR.
diff --git a/SRC/cstemr.f b/SRC/cstemr.f
index 15dc809d3..8ff54a2d4 100644
--- a/SRC/cstemr.f
+++ b/SRC/cstemr.f
@@ -304,10 +304,11 @@
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
 *>          > 0:  if INFO = 1X, internal error in SLARRE,
-*>                if INFO = 2X, internal error in CLARRV.
+*>                if INFO = 2X, internal error in CLARRV,
+*>                if INFO = 3X, internal error in SLARRJ.
 *>                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
-*>                the nonzero error code returned by SLARRE or
-*>                CLARRV, respectively.
+*>                the nonzero error code returned by SLARRE, CLARRV
+*>                or SLARRJ, respectively.
 *> \endverbatim
 *
 *  Authors:
@@ -752,6 +753,10 @@ SUBROUTINE CSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
      $                   WORK( INDERR+WBEGIN-1 ),
      $                   WORK( INDWRK ), IWORK( IINDWK ), PIVMIN,
      $                   TNRM, IINFO )
+               IF( IINFO.NE.0 ) THEN
+                  INFO = 30 + ABS( IINFO )
+                  RETURN
+               END IF
                IBEGIN = IEND + 1
                WBEGIN = WEND + 1
  39      CONTINUE
diff --git a/SRC/dlarrb.f b/SRC/dlarrb.f
index 38555f818..c3a923aa6 100644
--- a/SRC/dlarrb.f
+++ b/SRC/dlarrb.f
@@ -165,7 +165,11 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          Error flag.
+*>          = 0:  successful exit
+*>          = 1:  the interval around one of the eigenvalues could not
+*>                be widened to contain it: the Sturm counts of the
+*>                representation are inconsistent, as they are when it
+*>                contains a NaN or an Inf.
 *> \endverbatim
 *
 *  Authors:
@@ -274,10 +278,23 @@ SUBROUTINE DLARRB( N, D, LLD, IFIRST, ILAST, RTOL1,
 *
 *        Do while( NEGCNT(LEFT).GT.I-1 )
 *
-         BACK = WERR( II )
+*        The interval is widened by BACK, doubled at every step, until
+*        the Sturm count agrees with the index.  In exact arithmetic
+*        this terminates because the count is 0 below the spectrum and
+*        N above it.  A NaN or an Inf in the representation is never
+*        counted, so the count can stay short of the index; stop once
+*        BACK has overflowed, when no further step can move the
+*        endpoint.  BACK starts at no less than the minimum interval
+*        width so that a zero WERR still makes progress.
+*
+         BACK = MAX( WERR( II ), MNWDTH )
  20      CONTINUE
          NEGCNT = DLANEG( N, D, LLD, LEFT, PIVMIN, R )
          IF( NEGCNT.GT.I-1 ) THEN
+            IF( .NOT.( BACK.LT.TWO*BACK ) ) THEN
+               INFO = 1
+               RETURN
+            END IF
             LEFT = LEFT - BACK
             BACK = TWO*BACK
             GO TO 20
@@ -286,15 +303,18 @@ SUBROUTINE DLARRB( N, D, LLD, IFIRST, ILAST, RTOL1,
 *        Do while( NEGCNT(RIGHT).LT.I )
 *        Compute negcount from dstqds facto L+D+L+^T = L D L^T - RIGHT
 *
-         BACK = WERR( II )
+         BACK = MAX( WERR( II ), MNWDTH )
  50      CONTINUE
-
          NEGCNT = DLANEG( N, D, LLD, RIGHT, PIVMIN, R )
-          IF( NEGCNT.LT.I ) THEN
-             RIGHT = RIGHT + BACK
-             BACK = TWO*BACK
-             GO TO 50
-          END IF
+         IF( NEGCNT.LT.I ) THEN
+            IF( .NOT.( BACK.LT.TWO*BACK ) ) THEN
+               INFO = 1
+               RETURN
+            END IF
+            RIGHT = RIGHT + BACK
+            BACK = TWO*BACK
+            GO TO 50
+         END IF
          WIDTH = HALF*ABS( LEFT - RIGHT )
          TMP = MAX( ABS( LEFT ), ABS( RIGHT ) )
          CVRGD = MAX(RTOL1*GAP,RTOL2*TMP)
diff --git a/SRC/dlarrj.f b/SRC/dlarrj.f
index af3110f6e..5a8a43a81 100644
--- a/SRC/dlarrj.f
+++ b/SRC/dlarrj.f
@@ -137,7 +137,11 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          Error flag.
+*>          = 0:  successful exit
+*>          = 1:  the interval around one of the eigenvalues could not
+*>                be widened to contain it: the Sturm counts of the
+*>                matrix are inconsistent, as they are when it contains
+*>                a NaN or an Inf.
 *> \endverbatim
 *
 *  Authors:
@@ -190,7 +194,7 @@ SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST,
 *     .. Local Scalars ..
       INTEGER            CNT, I, I1, I2, II, ITER, J, K, NEXT, NINT,
      $                   OLNINT, P, PREV, SAVI1
-      DOUBLE PRECISION   DPLUS, FAC, LEFT, MID, RIGHT, S, TMP, WIDTH
+      DOUBLE PRECISION   BACK, DPLUS, LEFT, MID, RIGHT, S, TMP, WIDTH
 *
 *     ..
 *     .. Intrinsic Functions ..
@@ -249,7 +253,16 @@ SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST,
 *
 *           Do while( CNT(LEFT).GT.I-1 )
 *
-            FAC = ONE
+*           The interval is widened by BACK, doubled at every step,
+*           until the Sturm count agrees with the index.  In exact
+*           arithmetic this terminates because the count is 0 below the
+*           spectrum and N above it.  A NaN or an Inf in the matrix is
+*           never counted, so the count can stay short of the index;
+*           stop once BACK has overflowed, when no further step can move
+*           the endpoint.  BACK starts at no less than the minimum
+*           interval width so that a zero WERR still makes progress.
+*
+            BACK = MAX( WERR( II ), TWO*PIVMIN )
  20         CONTINUE
             CNT = 0
             S = LEFT
@@ -260,14 +273,18 @@ SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST,
                IF( DPLUS.LT.ZERO ) CNT = CNT + 1
  30         CONTINUE
             IF( CNT.GT.I-1 ) THEN
-               LEFT = LEFT - WERR( II )*FAC
-               FAC = TWO*FAC
+               IF( .NOT.( BACK.LT.TWO*BACK ) ) THEN
+                  INFO = 1
+                  RETURN
+               END IF
+               LEFT = LEFT - BACK
+               BACK = TWO*BACK
                GO TO 20
             END IF
 *
 *           Do while( CNT(RIGHT).LT.I )
 *
-            FAC = ONE
+            BACK = MAX( WERR( II ), TWO*PIVMIN )
  50         CONTINUE
             CNT = 0
             S = RIGHT
@@ -278,8 +295,12 @@ SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST,
                IF( DPLUS.LT.ZERO ) CNT = CNT + 1
  60         CONTINUE
             IF( CNT.LT.I ) THEN
-               RIGHT = RIGHT + WERR( II )*FAC
-               FAC = TWO*FAC
+               IF( .NOT.( BACK.LT.TWO*BACK ) ) THEN
+                  INFO = 1
+                  RETURN
+               END IF
+               RIGHT = RIGHT + BACK
+               BACK = TWO*BACK
                GO TO 50
             END IF
             NINT = NINT + 1
diff --git a/SRC/dlarrv.f b/SRC/dlarrv.f
index 4cf354ab7..19fe245d4 100644
--- a/SRC/dlarrv.f
+++ b/SRC/dlarrv.f
@@ -698,6 +698,10 @@ SUBROUTINE DLARRV( N, VL, VU, D, L, PIVMIN,
      $                       WERR(WBEGIN),WORK( INDWRK ),
      $                       IWORK( IINDWK ), PIVMIN, SPDIAM,
      $                       IN, IINFO )
+                        IF( IINFO.NE.0 ) THEN
+                           INFO = -1
+                           RETURN
+                        END IF
  55                  CONTINUE
 *
                      IF((WBEGIN+NEWLST-1.LT.DOL).OR.
diff --git a/SRC/dstemr.f b/SRC/dstemr.f
index 71b32ebd3..070a318de 100644
--- a/SRC/dstemr.f
+++ b/SRC/dstemr.f
@@ -287,10 +287,11 @@
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
 *>          > 0:  if INFO = 1X, internal error in DLARRE,
-*>                if INFO = 2X, internal error in DLARRV.
+*>                if INFO = 2X, internal error in DLARRV,
+*>                if INFO = 3X, internal error in DLARRJ.
 *>                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
-*>                the nonzero error code returned by DLARRE or
-*>                DLARRV, respectively.
+*>                the nonzero error code returned by DLARRE, DLARRV
+*>                or DLARRJ, respectively.
 *> \endverbatim
 *
 *  Authors:
@@ -735,6 +736,10 @@ SUBROUTINE DSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
      $                   WORK( INDERR+WBEGIN-1 ),
      $                   WORK( INDWRK ), IWORK( IINDWK ), PIVMIN,
      $                   TNRM, IINFO )
+               IF( IINFO.NE.0 ) THEN
+                  INFO = 30 + ABS( IINFO )
+                  RETURN
+               END IF
                IBEGIN = IEND + 1
                WBEGIN = WEND + 1
  39         CONTINUE
diff --git a/SRC/slarrb.f b/SRC/slarrb.f
index 6e43f126f..efa9e0410 100644
--- a/SRC/slarrb.f
+++ b/SRC/slarrb.f
@@ -165,7 +165,11 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          Error flag.
+*>          = 0:  successful exit
+*>          = 1:  the interval around one of the eigenvalues could not
+*>                be widened to contain it: the Sturm counts of the
+*>                representation are inconsistent, as they are when it
+*>                contains a NaN or an Inf.
 *> \endverbatim
 *
 *  Authors:
@@ -274,10 +278,23 @@ SUBROUTINE SLARRB( N, D, LLD, IFIRST, ILAST, RTOL1,
 *
 *        Do while( NEGCNT(LEFT).GT.I-1 )
 *
-         BACK = WERR( II )
+*        The interval is widened by BACK, doubled at every step, until
+*        the Sturm count agrees with the index.  In exact arithmetic
+*        this terminates because the count is 0 below the spectrum and
+*        N above it.  A NaN or an Inf in the representation is never
+*        counted, so the count can stay short of the index; stop once
+*        BACK has overflowed, when no further step can move the
+*        endpoint.  BACK starts at no less than the minimum interval
+*        width so that a zero WERR still makes progress.
+*
+         BACK = MAX( WERR( II ), MNWDTH )
  20      CONTINUE
          NEGCNT = SLANEG( N, D, LLD, LEFT, PIVMIN, R )
          IF( NEGCNT.GT.I-1 ) THEN
+            IF( .NOT.( BACK.LT.TWO*BACK ) ) THEN
+               INFO = 1
+               RETURN
+            END IF
             LEFT = LEFT - BACK
             BACK = TWO*BACK
             GO TO 20
@@ -286,15 +303,18 @@ SUBROUTINE SLARRB( N, D, LLD, IFIRST, ILAST, RTOL1,
 *        Do while( NEGCNT(RIGHT).LT.I )
 *        Compute negcount from dstqds facto L+D+L+^T = L D L^T - RIGHT
 *
-         BACK = WERR( II )
+         BACK = MAX( WERR( II ), MNWDTH )
  50      CONTINUE
-
          NEGCNT = SLANEG( N, D, LLD, RIGHT, PIVMIN, R )
-          IF( NEGCNT.LT.I ) THEN
-             RIGHT = RIGHT + BACK
-             BACK = TWO*BACK
-             GO TO 50
-          END IF
+         IF( NEGCNT.LT.I ) THEN
+            IF( .NOT.( BACK.LT.TWO*BACK ) ) THEN
+               INFO = 1
+               RETURN
+            END IF
+            RIGHT = RIGHT + BACK
+            BACK = TWO*BACK
+            GO TO 50
+         END IF
          WIDTH = HALF*ABS( LEFT - RIGHT )
          TMP = MAX( ABS( LEFT ), ABS( RIGHT ) )
          CVRGD = MAX(RTOL1*GAP,RTOL2*TMP)
diff --git a/SRC/slarrj.f b/SRC/slarrj.f
index 6cfb2eec8..5fc94ca5f 100644
--- a/SRC/slarrj.f
+++ b/SRC/slarrj.f
@@ -137,7 +137,11 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          Error flag.
+*>          = 0:  successful exit
+*>          = 1:  the interval around one of the eigenvalues could not
+*>                be widened to contain it: the Sturm counts of the
+*>                matrix are inconsistent, as they are when it contains
+*>                a NaN or an Inf.
 *> \endverbatim
 *
 *  Authors:
@@ -190,7 +194,7 @@ SUBROUTINE SLARRJ( N, D, E2, IFIRST, ILAST,
 *     .. Local Scalars ..
       INTEGER            CNT, I, I1, I2, II, ITER, J, K, NEXT, NINT,
      $                   OLNINT, P, PREV, SAVI1
-      REAL               DPLUS, FAC, LEFT, MID, RIGHT, S, TMP, WIDTH
+      REAL               BACK, DPLUS, LEFT, MID, RIGHT, S, TMP, WIDTH
 *
 *     ..
 *     .. Intrinsic Functions ..
@@ -249,7 +253,16 @@ SUBROUTINE SLARRJ( N, D, E2, IFIRST, ILAST,
 *
 *           Do while( CNT(LEFT).GT.I-1 )
 *
-            FAC = ONE
+*           The interval is widened by BACK, doubled at every step,
+*           until the Sturm count agrees with the index.  In exact
+*           arithmetic this terminates because the count is 0 below the
+*           spectrum and N above it.  A NaN or an Inf in the matrix is
+*           never counted, so the count can stay short of the index;
+*           stop once BACK has overflowed, when no further step can move
+*           the endpoint.  BACK starts at no less than the minimum
+*           interval width so that a zero WERR still makes progress.
+*
+            BACK = MAX( WERR( II ), TWO*PIVMIN )
  20         CONTINUE
             CNT = 0
             S = LEFT
@@ -260,14 +273,18 @@ SUBROUTINE SLARRJ( N, D, E2, IFIRST, ILAST,
                IF( DPLUS.LT.ZERO ) CNT = CNT + 1
  30         CONTINUE
             IF( CNT.GT.I-1 ) THEN
-               LEFT = LEFT - WERR( II )*FAC
-               FAC = TWO*FAC
+               IF( .NOT.( BACK.LT.TWO*BACK ) ) THEN
+                  INFO = 1
+                  RETURN
+               END IF
+               LEFT = LEFT - BACK
+               BACK = TWO*BACK
                GO TO 20
             END IF
 *
 *           Do while( CNT(RIGHT).LT.I )
 *
-            FAC = ONE
+            BACK = MAX( WERR( II ), TWO*PIVMIN )
  50         CONTINUE
             CNT = 0
             S = RIGHT
@@ -278,8 +295,12 @@ SUBROUTINE SLARRJ( N, D, E2, IFIRST, ILAST,
                IF( DPLUS.LT.ZERO ) CNT = CNT + 1
  60         CONTINUE
             IF( CNT.LT.I ) THEN
-               RIGHT = RIGHT + WERR( II )*FAC
-               FAC = TWO*FAC
+               IF( .NOT.( BACK.LT.TWO*BACK ) ) THEN
+                  INFO = 1
+                  RETURN
+               END IF
+               RIGHT = RIGHT + BACK
+               BACK = TWO*BACK
                GO TO 50
             END IF
             NINT = NINT + 1
diff --git a/SRC/slarrv.f b/SRC/slarrv.f
index 59ad49770..2734fb0d9 100644
--- a/SRC/slarrv.f
+++ b/SRC/slarrv.f
@@ -698,6 +698,10 @@ SUBROUTINE SLARRV( N, VL, VU, D, L, PIVMIN,
      $                       WERR(WBEGIN),WORK( INDWRK ),
      $                       IWORK( IINDWK ), PIVMIN, SPDIAM,
      $                       IN, IINFO )
+                        IF( IINFO.NE.0 ) THEN
+                           INFO = -1
+                           RETURN
+                        END IF
  55                  CONTINUE
 *
                      IF((WBEGIN+NEWLST-1.LT.DOL).OR.
diff --git a/SRC/sstemr.f b/SRC/sstemr.f
index 8fe8292a5..df8f6e59c 100644
--- a/SRC/sstemr.f
+++ b/SRC/sstemr.f
@@ -287,10 +287,11 @@
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
 *>          > 0:  if INFO = 1X, internal error in SLARRE,
-*>                if INFO = 2X, internal error in SLARRV.
+*>                if INFO = 2X, internal error in SLARRV,
+*>                if INFO = 3X, internal error in SLARRJ.
 *>                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
-*>                the nonzero error code returned by SLARRE or
-*>                SLARRV, respectively.
+*>                the nonzero error code returned by SLARRE, SLARRV
+*>                or SLARRJ, respectively.
 *> \endverbatim
 *
 *  Authors:
@@ -732,6 +733,10 @@ SUBROUTINE SSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
      $                   WORK( INDERR+WBEGIN-1 ),
      $                   WORK( INDWRK ), IWORK( IINDWK ), PIVMIN,
      $                   TNRM, IINFO )
+               IF( IINFO.NE.0 ) THEN
+                  INFO = 30 + ABS( IINFO )
+                  RETURN
+               END IF
                IBEGIN = IEND + 1
                WBEGIN = WEND + 1
  39      CONTINUE
diff --git a/SRC/zlarrv.f b/SRC/zlarrv.f
index 67c1e186a..7bcb99a35 100644
--- a/SRC/zlarrv.f
+++ b/SRC/zlarrv.f
@@ -702,6 +702,10 @@ SUBROUTINE ZLARRV( N, VL, VU, D, L, PIVMIN,
      $                       WERR(WBEGIN),WORK( INDWRK ),
      $                       IWORK( IINDWK ), PIVMIN, SPDIAM,
      $                       IN, IINFO )
+                        IF( IINFO.NE.0 ) THEN
+                           INFO = -1
+                           RETURN
+                        END IF
  55                  CONTINUE
 *
                      IF((WBEGIN+NEWLST-1.LT.DOL).OR.
diff --git a/SRC/zstemr.f b/SRC/zstemr.f
index f8fc18ca1..0ceae2308 100644
--- a/SRC/zstemr.f
+++ b/SRC/zstemr.f
@@ -304,10 +304,11 @@
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
 *>          > 0:  if INFO = 1X, internal error in DLARRE,
-*>                if INFO = 2X, internal error in ZLARRV.
+*>                if INFO = 2X, internal error in ZLARRV,
+*>                if INFO = 3X, internal error in DLARRJ.
 *>                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
-*>                the nonzero error code returned by DLARRE or
-*>                ZLARRV, respectively.
+*>                the nonzero error code returned by DLARRE, ZLARRV
+*>                or DLARRJ, respectively.
 *> \endverbatim
 *
 *  Authors:
@@ -751,6 +752,10 @@ SUBROUTINE ZSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
      $                   WORK( INDERR+WBEGIN-1 ),
      $                   WORK( INDWRK ), IWORK( IINDWK ), PIVMIN,
      $                   TNRM, IINFO )
+               IF( IINFO.NE.0 ) THEN
+                  INFO = 30 + ABS( IINFO )
+                  RETURN
+               END IF
                IBEGIN = IEND + 1
                WBEGIN = WEND + 1
  39      CONTINUE
diff --git a/TESTING/EIG/cchkst.f b/TESTING/EIG/cchkst.f
index 790c7f5f1..f150cebf8 100644
--- a/TESTING/EIG/cchkst.f
+++ b/TESTING/EIG/cchkst.f
@@ -641,12 +641,15 @@ SUBROUTINE CCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
       PARAMETER          ( CREL = .FALSE. )
 *     ..
 *     .. Local Scalars ..
+      CHARACTER          JOBZ
+      INTEGER            JOBNUM
       LOGICAL            BADNN, TRYRAC
       INTEGER            I, IINFO, IL, IMODE, INDE, INDRWK, ITEMP,
      $                   ITYPE, IU, J, JC, JR, JSIZE, JTYPE, LGN,
      $                   LIWEDC, LOG2UI, LRWEDC, LWEDC, M, M2, M3,
      $                   MTYPES, N, NAP, NBLOCK, NERRS, NMATS, NMAX,
      $                   NSPLIT, NTEST, NTESTT
+      REAL               RNAN, RONE
       REAL               ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
      $                   RTUNFL, TEMP1, TEMP2, TEMP3, TEMP4, ULP,
      $                   ULPINV, UNFL, VL, VU
@@ -1954,10 +1957,58 @@ SUBROUTINE CCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
   310 CONTINUE
 *
 *     Summary
+*
+*
+*     CSTEMR must return for a tridiagonal matrix that contains a NaN
+*     instead of widening a bracket forever.  A NaN pivot is never
+*     counted, so the Sturm count of such a matrix never reaches the
+*     index of the wanted eigenvalue, and the widening loops of
+*     SLARRB, which refines the eigenvalues of a representation, and
+*     of SLARRJ, which refines them on the matrix itself when no
+*     eigenvectors are wanted, can only be ended by a bound on the
+*     step.  Any nonnegative INFO is accepted: the test is that the
+*     call returns at all.
+*
+      IF( NMAX.GE.3 .AND. LRWORK.GE.18*NMAX .AND.
+     $    LIWORK.GE.12*NMAX .AND.
+     $    ILAENV( 10, 'CSTEMR', 'VA', 1, 0, 0, 0 ).EQ.1 .AND.
+     $    ILAENV( 11, 'CSTEMR', 'VA', 1, 0, 0, 0 ).EQ.1 ) THEN
+         N = NMAX
+         RONE = ONE
+         RNAN = SQRT( -RONE )
+         DO 330 JOBNUM = 1, 2
+            IF( JOBNUM.EQ.1 ) THEN
+               JOBZ = 'V'
+            ELSE
+               JOBZ = 'N'
+            END IF
+            DO 320 J = 1, N
+               SD( J ) = REAL( J )
+               SE( J ) = ONE / REAL( J+1 )
+  320       CONTINUE
+            SD( 1 ) = RNAN
+            SE( N ) = ZERO
+            VL = ZERO
+            VU = ZERO
+            IL = 0
+            IU = 0
+            TRYRAC = .TRUE.
+            CALL CSTEMR( JOBZ, 'A', N, SD, SE, VL, VU, IL, IU, M,
+     $                   WR, Z, LDU, N, IWORK( 1 ), TRYRAC, RWORK,
+     $                   LRWORK, IWORK( 2*N+1 ), LIWORK-2*N, IINFO )
+            IF( IINFO.LT.0 ) THEN
+               WRITE( NOUNIT, FMT = 9986 )JOBZ, IINFO
+               NERRS = NERRS + 1
+            END IF
+            NTESTT = NTESTT + 1
+  330    CONTINUE
+      END IF
 *
       CALL SLASUM( 'CST', NOUNIT, NERRS, NTESTT )
       RETURN
 *
+ 9986 FORMAT( ' CCHKST: CSTEMR( ', A1, ', A ) on a matrix with a',
+     $      ' NaN returned INFO=', I6 )
  9999 FORMAT( ' CCHKST: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
      $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
 *
diff --git a/TESTING/EIG/dchkst.f b/TESTING/EIG/dchkst.f
index 012aa95d4..4b4599b3d 100644
--- a/TESTING/EIG/dchkst.f
+++ b/TESTING/EIG/dchkst.f
@@ -625,11 +625,14 @@ SUBROUTINE DCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
       PARAMETER          ( SREL = .FALSE. )
 *     ..
 *     .. Local Scalars ..
+      CHARACTER          JOBZ
+      INTEGER            JOBNUM
       LOGICAL            BADNN, TRYRAC
       INTEGER            I, IINFO, IL, IMODE, ITEMP, ITYPE, IU, J, JC,
      $                   JR, JSIZE, JTYPE, LGN, LIWEDC, LOG2UI, LWEDC,
      $                   M, M2, M3, MTYPES, N, NAP, NBLOCK, NERRS,
      $                   NMATS, NMAX, NSPLIT, NTEST, NTESTT
+      DOUBLE PRECISION   RNAN, RONE
       DOUBLE PRECISION   ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
      $                   RTUNFL, TEMP1, TEMP2, TEMP3, TEMP4, ULP,
      $                   ULPINV, UNFL, VL, VU
@@ -1932,10 +1935,57 @@ SUBROUTINE DCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
   310 CONTINUE
 *
 *     Summary
+*
+*
+*     DSTEMR must return for a tridiagonal matrix that contains a NaN
+*     instead of widening a bracket forever.  A NaN pivot is never
+*     counted, so the Sturm count of such a matrix never reaches the
+*     index of the wanted eigenvalue, and the widening loops of
+*     DLARRB, which refines the eigenvalues of a representation, and
+*     of DLARRJ, which refines them on the matrix itself when no
+*     eigenvectors are wanted, can only be ended by a bound on the
+*     step.  Any nonnegative INFO is accepted: the test is that the
+*     call returns at all.
+*
+      IF( NMAX.GE.3 .AND. LWORK.GE.18*NMAX .AND. LIWORK.GE.12*NMAX .AND.
+     $    ILAENV( 10, 'DSTEMR', 'VA', 1, 0, 0, 0 ).EQ.1 .AND.
+     $    ILAENV( 11, 'DSTEMR', 'VA', 1, 0, 0, 0 ).EQ.1 ) THEN
+         N = NMAX
+         RONE = ONE
+         RNAN = SQRT( -RONE )
+         DO 330 JOBNUM = 1, 2
+            IF( JOBNUM.EQ.1 ) THEN
+               JOBZ = 'V'
+            ELSE
+               JOBZ = 'N'
+            END IF
+            DO 320 J = 1, N
+               SD( J ) = DBLE( J )
+               SE( J ) = ONE / DBLE( J+1 )
+  320       CONTINUE
+            SD( 1 ) = RNAN
+            SE( N ) = ZERO
+            VL = ZERO
+            VU = ZERO
+            IL = 0
+            IU = 0
+            TRYRAC = .TRUE.
+            CALL DSTEMR( JOBZ, 'A', N, SD, SE, VL, VU, IL, IU, M,
+     $                   WR, Z, LDU, N, IWORK( 1 ), TRYRAC, WORK,
+     $                   LWORK, IWORK( 2*N+1 ), LIWORK-2*N, IINFO )
+            IF( IINFO.LT.0 ) THEN
+               WRITE( NOUNIT, FMT = 9986 )JOBZ, IINFO
+               NERRS = NERRS + 1
+            END IF
+            NTESTT = NTESTT + 1
+  330    CONTINUE
+      END IF
 *
       CALL DLASUM( 'DST', NOUNIT, NERRS, NTESTT )
       RETURN
 *
+ 9986 FORMAT( ' DCHKST: DSTEMR( ', A1, ', A ) on a matrix with a',
+     $      ' NaN returned INFO=', I6 )
  9999 FORMAT( ' DCHKST: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
      $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
 *
diff --git a/TESTING/EIG/schkst.f b/TESTING/EIG/schkst.f
index c5c7f57c3..d0356f2c2 100644
--- a/TESTING/EIG/schkst.f
+++ b/TESTING/EIG/schkst.f
@@ -625,11 +625,14 @@ SUBROUTINE SCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
       PARAMETER          ( SREL = .FALSE. )
 *     ..
 *     .. Local Scalars ..
+      CHARACTER          JOBZ
+      INTEGER            JOBNUM
       LOGICAL            BADNN, TRYRAC
       INTEGER            I, IINFO, IL, IMODE, ITEMP, ITYPE, IU, J, JC,
      $                   JR, JSIZE, JTYPE, LGN, LIWEDC, LOG2UI, LWEDC,
      $                   M, M2, M3, MTYPES, N, NAP, NBLOCK, NERRS,
      $                   NMATS, NMAX, NSPLIT, NTEST, NTESTT
+      REAL               RNAN, RONE
       REAL               ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
      $                   RTUNFL, TEMP1, TEMP2, TEMP3, TEMP4, ULP,
      $                   ULPINV, UNFL, VL, VU
@@ -1932,10 +1935,57 @@ SUBROUTINE SCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
   310 CONTINUE
 *
 *     Summary
+*
+*
+*     SSTEMR must return for a tridiagonal matrix that contains a NaN
+*     instead of widening a bracket forever.  A NaN pivot is never
+*     counted, so the Sturm count of such a matrix never reaches the
+*     index of the wanted eigenvalue, and the widening loops of
+*     SLARRB, which refines the eigenvalues of a representation, and
+*     of SLARRJ, which refines them on the matrix itself when no
+*     eigenvectors are wanted, can only be ended by a bound on the
+*     step.  Any nonnegative INFO is accepted: the test is that the
+*     call returns at all.
+*
+      IF( NMAX.GE.3 .AND. LWORK.GE.18*NMAX .AND. LIWORK.GE.12*NMAX .AND.
+     $    ILAENV( 10, 'SSTEMR', 'VA', 1, 0, 0, 0 ).EQ.1 .AND.
+     $    ILAENV( 11, 'SSTEMR', 'VA', 1, 0, 0, 0 ).EQ.1 ) THEN
+         N = NMAX
+         RONE = ONE
+         RNAN = SQRT( -RONE )
+         DO 330 JOBNUM = 1, 2
+            IF( JOBNUM.EQ.1 ) THEN
+               JOBZ = 'V'
+            ELSE
+               JOBZ = 'N'
+            END IF
+            DO 320 J = 1, N
+               SD( J ) = REAL( J )
+               SE( J ) = ONE / REAL( J+1 )
+  320       CONTINUE
+            SD( 1 ) = RNAN
+            SE( N ) = ZERO
+            VL = ZERO
+            VU = ZERO
+            IL = 0
+            IU = 0
+            TRYRAC = .TRUE.
+            CALL SSTEMR( JOBZ, 'A', N, SD, SE, VL, VU, IL, IU, M,
+     $                   WR, Z, LDU, N, IWORK( 1 ), TRYRAC, WORK,
+     $                   LWORK, IWORK( 2*N+1 ), LIWORK-2*N, IINFO )
+            IF( IINFO.LT.0 ) THEN
+               WRITE( NOUNIT, FMT = 9986 )JOBZ, IINFO
+               NERRS = NERRS + 1
+            END IF
+            NTESTT = NTESTT + 1
+  330    CONTINUE
+      END IF
 *
       CALL SLASUM( 'SST', NOUNIT, NERRS, NTESTT )
       RETURN
 *
+ 9986 FORMAT( ' SCHKST: SSTEMR( ', A1, ', A ) on a matrix with a',
+     $      ' NaN returned INFO=', I6 )
  9999 FORMAT( ' SCHKST: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
      $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
 *
diff --git a/TESTING/EIG/zchkst.f b/TESTING/EIG/zchkst.f
index 4335e15f0..c43a6496c 100644
--- a/TESTING/EIG/zchkst.f
+++ b/TESTING/EIG/zchkst.f
@@ -641,12 +641,15 @@ SUBROUTINE ZCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
       PARAMETER          ( CREL = .FALSE. )
 *     ..
 *     .. Local Scalars ..
+      CHARACTER          JOBZ
+      INTEGER            JOBNUM
       LOGICAL            BADNN, TRYRAC
       INTEGER            I, IINFO, IL, IMODE, INDE, INDRWK, ITEMP,
      $                   ITYPE, IU, J, JC, JR, JSIZE, JTYPE, LGN,
      $                   LIWEDC, LOG2UI, LRWEDC, LWEDC, M, M2, M3,
      $                   MTYPES, N, NAP, NBLOCK, NERRS, NMATS, NMAX,
      $                   NSPLIT, NTEST, NTESTT
+      DOUBLE PRECISION   RNAN, RONE
       DOUBLE PRECISION   ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
      $                   RTUNFL, TEMP1, TEMP2, TEMP3, TEMP4, ULP,
      $                   ULPINV, UNFL, VL, VU
@@ -1953,10 +1956,58 @@ SUBROUTINE ZCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
   310 CONTINUE
 *
 *     Summary
+*
+*
+*     ZSTEMR must return for a tridiagonal matrix that contains a NaN
+*     instead of widening a bracket forever.  A NaN pivot is never
+*     counted, so the Sturm count of such a matrix never reaches the
+*     index of the wanted eigenvalue, and the widening loops of
+*     DLARRB, which refines the eigenvalues of a representation, and
+*     of DLARRJ, which refines them on the matrix itself when no
+*     eigenvectors are wanted, can only be ended by a bound on the
+*     step.  Any nonnegative INFO is accepted: the test is that the
+*     call returns at all.
+*
+      IF( NMAX.GE.3 .AND. LRWORK.GE.18*NMAX .AND.
+     $    LIWORK.GE.12*NMAX .AND.
+     $    ILAENV( 10, 'ZSTEMR', 'VA', 1, 0, 0, 0 ).EQ.1 .AND.
+     $    ILAENV( 11, 'ZSTEMR', 'VA', 1, 0, 0, 0 ).EQ.1 ) THEN
+         N = NMAX
+         RONE = ONE
+         RNAN = SQRT( -RONE )
+         DO 330 JOBNUM = 1, 2
+            IF( JOBNUM.EQ.1 ) THEN
+               JOBZ = 'V'
+            ELSE
+               JOBZ = 'N'
+            END IF
+            DO 320 J = 1, N
+               SD( J ) = DBLE( J )
+               SE( J ) = ONE / DBLE( J+1 )
+  320       CONTINUE
+            SD( 1 ) = RNAN
+            SE( N ) = ZERO
+            VL = ZERO
+            VU = ZERO
+            IL = 0
+            IU = 0
+            TRYRAC = .TRUE.
+            CALL ZSTEMR( JOBZ, 'A', N, SD, SE, VL, VU, IL, IU, M,
+     $                   WR, Z, LDU, N, IWORK( 1 ), TRYRAC, RWORK,
+     $                   LRWORK, IWORK( 2*N+1 ), LIWORK-2*N, IINFO )
+            IF( IINFO.LT.0 ) THEN
+               WRITE( NOUNIT, FMT = 9986 )JOBZ, IINFO
+               NERRS = NERRS + 1
+            END IF
+            NTESTT = NTESTT + 1
+  330    CONTINUE
+      END IF
 *
       CALL DLASUM( 'ZST', NOUNIT, NERRS, NTESTT )
       RETURN
 *
+ 9986 FORMAT( ' ZCHKST: ZSTEMR( ', A1, ', A ) on a matrix with a',
+     $      ' NaN returned INFO=', I6 )
  9999 FORMAT( ' ZCHKST: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
      $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
 *