[PATCH v4 1/2] md raid0/linear: Mark array as 'broken' and fail BIOs if a member is gone

[PATCH v4 1/2] md raid0/linear: Mark array as 'broken' and fail BIOs if a member is gone

[Guilherme G. Piccoli]

Currently md raid0/linear are not provided with any mechanism to validate
if an array member got removed or failed. The driver keeps sending BIOs
regardless of the state of array members, and kernel shows state 'clean'
in the 'array_state' sysfs attribute. This leads to the following
situation: if a raid0/linear array member is removed and the array is
mounted, some user writing to this array won't realize that errors are
happening unless they check dmesg or perform one fsync per written file.
Despite udev signaling the member device is gone, 'mdadm' cannot issue the
STOP_ARRAY ioctl successfully, given the array is mounted.

In other words, no -EIO is returned and writes (except direct ones) appear
normal. Meaning the user might think the wrote data is correctly stored in
the array, but instead garbage was written given that raid0 does stripping
(and so, it requires all its members to be working in order to not corrupt
data). For md/linear, writes to the available members will work fine, but
if the writes go to the missing member(s), it'll cause a file corruption
situation, whereas the portion of the writes to the missing devices aren't
written effectively.

This patch changes this behavior: we check if the block device's gendisk
is UP when submitting the BIO to the array member, and if it isn't, we flag
the md device as MD_BROKEN and fail subsequent I/Os to that device; a read
request to the array requiring data from a valid member is still completed.
While flagging the device as MD_BROKEN, we also show a rate-limited warning
in the kernel log.

A new array state 'broken' was added too: it mimics the state 'clean' in
every aspect, being useful only to distinguish if the array has some member
missing. We rely on the MD_BROKEN flag to put the array in the 'broken'
state. This state cannot be written in 'array_state' as it just shows
one or more members of the array are missing but acts like 'clean', it
wouldn't make sense to write it.

With this patch, the filesystem reacts much faster to the event of missing
array member: after some I/O errors, ext4 for instance aborts the journal
and prevents corruption. Without this change, we're able to keep writing
in the disk and after a machine reboot, e2fsck shows some severe fs errors
that demand fixing. This patch was tested in ext4 and xfs filesystems, and
requires a 'mdadm' counterpart to handle the 'broken' state.

Cc: Song Liu <songliubraving@fb.com>
Reviewed-by: NeilBrown <neilb@suse.de>
Signed-off-by: Guilherme G. Piccoli <gpiccoli@canonical.com>
---

v3 -> v4:
* Use helper is_mddev_broken() to simplify the code on raid0/linear
drivers (thanks Song for the suggestion).
* Use test_and_set_bit() and remove a non-critical path "unlikely"
per Neil's suggestion (thanks Neil).

v2 -> v3:
* Rebased against md-next.
* Merged both patches in a single one (thanks Song for the
suggestion); now we fail BIOs and mark array as MD_BROKEN
when a member is missing. We rely in the MD_BROKEN flag
to set array to 'broken' state.
* Function is_missing_dev() was removed due to the above.

v1 -> v2:
* Added handling for md/linear 'broken' state;
* Check for is_missing_dev() instead of personality (thanks Neil for
the suggestion);
* Changed is_missing_dev() handlers to static;
* Print rate-limited warning in case of more members go away, not only
the first.

Cover-letter from v1:
lore.kernel.org/linux-block/20190729203135.12934-1-gpiccoli@canonical.com


 drivers/md/md-linear.c |  5 +++++
 drivers/md/md.c        | 22 ++++++++++++++++++----
 drivers/md/md.h        | 16 ++++++++++++++++
 drivers/md/raid0.c     |  6 ++++++
 4 files changed, 45 insertions(+), 4 deletions(-)

diff --git a/drivers/md/md-linear.c b/drivers/md/md-linear.c
index 7354466ddc90..c766c559d36d 100644
--- a/drivers/md/md-linear.c
+++ b/drivers/md/md-linear.c
@@ -258,6 +258,11 @@ static bool linear_make_request(struct mddev *mddev, struct bio *bio)
 		     bio_sector < start_sector))
 		goto out_of_bounds;
 
+	if (unlikely(is_mddev_broken(tmp_dev->rdev, "linear"))) {
+		bio_io_error(bio);
+		return true;
+	}
+
 	if (unlikely(bio_end_sector(bio) > end_sector)) {
 		/* This bio crosses a device boundary, so we have to split it */
 		struct bio *split = bio_split(bio, end_sector - bio_sector,
diff --git a/drivers/md/md.c b/drivers/md/md.c
index b46bb143e3c5..73d5a1b04022 100644
--- a/drivers/md/md.c
+++ b/drivers/md/md.c
@@ -376,6 +376,11 @@ static blk_qc_t md_make_request(struct request_queue *q, struct bio *bio)
 	struct mddev *mddev = q->queuedata;
 	unsigned int sectors;
 
+	if (unlikely(test_bit(MD_BROKEN, &mddev->flags)) && (rw == WRITE)) {
+		bio_io_error(bio);
+		return BLK_QC_T_NONE;
+	}
+
 	blk_queue_split(q, &bio);
 
 	if (mddev == NULL || mddev->pers == NULL) {
@@ -4158,12 +4163,17 @@ __ATTR_PREALLOC(resync_start, S_IRUGO|S_IWUSR,
  * active-idle
  *     like active, but no writes have been seen for a while (100msec).
  *
+ * broken
+ *     RAID0/LINEAR-only: same as clean, but array is missing a member.
+ *     It's useful because RAID0/LINEAR mounted-arrays aren't stopped
+ *     when a member is gone, so this state will at least alert the
+ *     user that something is wrong.
  */
 enum array_state { clear, inactive, suspended, readonly, read_auto, clean, active,
-		   write_pending, active_idle, bad_word};
+		   write_pending, active_idle, broken, bad_word};
 static char *array_states[] = {
 	"clear", "inactive", "suspended", "readonly", "read-auto", "clean", "active",
-	"write-pending", "active-idle", NULL };
+	"write-pending", "active-idle", "broken", NULL };
 
 static int match_word(const char *word, char **list)
 {
@@ -4179,7 +4189,7 @@ array_state_show(struct mddev *mddev, char *page)
 {
 	enum array_state st = inactive;
 
-	if (mddev->pers && !test_bit(MD_NOT_READY, &mddev->flags))
+	if (mddev->pers && !test_bit(MD_NOT_READY, &mddev->flags)) {
 		switch(mddev->ro) {
 		case 1:
 			st = readonly;
@@ -4199,7 +4209,10 @@ array_state_show(struct mddev *mddev, char *page)
 				st = active;
 			spin_unlock(&mddev->lock);
 		}
-	else {
+
+		if (test_bit(MD_BROKEN, &mddev->flags) && st == clean)
+			st = broken;
+	} else {
 		if (list_empty(&mddev->disks) &&
 		    mddev->raid_disks == 0 &&
 		    mddev->dev_sectors == 0)
@@ -4313,6 +4326,7 @@ array_state_store(struct mddev *mddev, const char *buf, size_t len)
 		break;
 	case write_pending:
 	case active_idle:
+	case broken:
 		/* these cannot be set */
 		break;
 	}
diff --git a/drivers/md/md.h b/drivers/md/md.h
index 1edcd967eb8e..c5e3ff398b59 100644
--- a/drivers/md/md.h
+++ b/drivers/md/md.h
@@ -251,6 +251,9 @@ enum mddev_flags {
 	MD_NOT_READY,		/* do_md_run() is active, so 'array_state'
 				 * must not report that array is ready yet
 				 */
+	MD_BROKEN,              /* This is used in RAID-0/LINEAR only, to stop
+				 * I/O in case an array member is gone/failed.
+				 */
 };
 
 enum mddev_sb_flags {
@@ -739,6 +742,19 @@ extern void mddev_create_wb_pool(struct mddev *mddev, struct md_rdev *rdev,
 struct md_rdev *md_find_rdev_nr_rcu(struct mddev *mddev, int nr);
 struct md_rdev *md_find_rdev_rcu(struct mddev *mddev, dev_t dev);
 
+static inline bool is_mddev_broken(struct md_rdev *rdev, const char *md_type)
+{
+	int flags = rdev->bdev->bd_disk->flags;
+
+	if (!(flags & GENHD_FL_UP)) {
+		if (!test_and_set_bit(MD_BROKEN, &rdev->mddev->flags))
+			pr_warn("md: %s: %s array has a missing/failed member\n",
+				mdname(rdev->mddev), md_type);
+		return true;
+	}
+	return false;
+}
+
 static inline void rdev_dec_pending(struct md_rdev *rdev, struct mddev *mddev)
 {
 	int faulty = test_bit(Faulty, &rdev->flags);
diff --git a/drivers/md/raid0.c b/drivers/md/raid0.c
index bf5cf184a260..bc422eae2c95 100644
--- a/drivers/md/raid0.c
+++ b/drivers/md/raid0.c
@@ -586,6 +586,12 @@ static bool raid0_make_request(struct mddev *mddev, struct bio *bio)
 
 	zone = find_zone(mddev->private, &sector);
 	tmp_dev = map_sector(mddev, zone, sector, &sector);
+
+	if (unlikely(is_mddev_broken(tmp_dev, "raid0"))) {
+		bio_io_error(bio);
+		return true;
+	}
+
 	bio_set_dev(bio, tmp_dev->bdev);
 	bio->bi_iter.bi_sector = sector + zone->dev_start +
 		tmp_dev->data_offset;
-- 
2.17.1

[PATCH v4 2/2] mdadm: Introduce new array state 'broken' for raid0/linear

[Guilherme G. Piccoli]

Currently if a md raid0/linear array gets one or more members removed while
being mounted, kernel keeps showing state 'clean' in the 'array_state'
sysfs attribute. Despite udev signaling the member device is gone, 'mdadm'
cannot issue the STOP_ARRAY ioctl successfully, given the array is mounted.

Nothing else hints that something is wrong (except that the removed devices
don't show properly in the output of mdadm 'detail' command). There is no
other property to be checked, and if user is not performing reads/writes
to the array, even kernel log is quiet and doesn't give a clue about the
missing member.

This patch is the mdadm counterpart of kernel new array state 'broken'.
The 'broken' state mimics the state 'clean' in every aspect, being useful
only to distinguish if an array has some member missing. All necessary
paths in mdadm were changed to deal with 'broken' state, and in case the
tool runs in a kernel that is not updated, it'll work normally, i.e., it
doesn't require the 'broken' state in order to work.
Also, this patch changes the way the array state is showed in the 'detail'
command (for raid0/linear only) - now it takes the 'array_state' sysfs
attribute into account instead of only rely in the MD_SB_CLEAN flag.

Cc: Jes Sorensen <jes.sorensen@gmail.com>
Cc: NeilBrown <neilb@suse.de>
Cc: Song Liu <songliubraving@fb.com>
Signed-off-by: Guilherme G. Piccoli <gpiccoli@canonical.com>
---

v3 -> v4:
* Changed arrayst from pre-allocated to pointer (thanks Neil
for the suggestion).
* Simplified array size validation in Monitor/Wait() by
using ARRAY_SIZE(), per Neil's suggestion.

v2 -> v3:
* Nothing changed.

v1 -> v2:
* Added handling for md/linear 'broken' state.


 Detail.c  | 14 ++++++++++++--
 Monitor.c |  8 ++++++--
 maps.c    |  1 +
 mdadm.h   |  1 +
 mdmon.h   |  2 +-
 monitor.c |  4 ++--
 6 files changed, 23 insertions(+), 7 deletions(-)

diff --git a/Detail.c b/Detail.c
index ad60434..3e61e37 100644
--- a/Detail.c
+++ b/Detail.c
@@ -81,6 +81,7 @@ int Detail(char *dev, struct context *c)
 	int external;
 	int inactive;
 	int is_container = 0;
+	char *arrayst;
 
 	if (fd < 0) {
 		pr_err("cannot open %s: %s\n",
@@ -485,9 +486,18 @@ int Detail(char *dev, struct context *c)
 			else
 				st = ", degraded";
 
+			if (array.state & (1 << MD_SB_CLEAN)) {
+				if ((array.level == 0) ||
+				    (array.level == LEVEL_LINEAR))
+					arrayst = map_num(sysfs_array_states,
+							  sra->array_state);
+				else
+					arrayst = "clean";
+			} else
+				arrayst = "active";
+
 			printf("             State : %s%s%s%s%s%s \n",
-			       (array.state & (1 << MD_SB_CLEAN)) ?
-			       "clean" : "active", st,
+			       arrayst, st,
 			       (!e || (e->percent < 0 &&
 				       e->percent != RESYNC_PENDING &&
 				       e->percent != RESYNC_DELAYED)) ?
diff --git a/Monitor.c b/Monitor.c
index 036103f..cf0610b 100644
--- a/Monitor.c
+++ b/Monitor.c
@@ -1055,8 +1055,11 @@ int Wait(char *dev)
 	}
 }
 
+/* The state "broken" is used only for RAID0/LINEAR - it's the same as
+ * "clean", but used in case the array has one or more members missing.
+ */
 static char *clean_states[] = {
-	"clear", "inactive", "readonly", "read-auto", "clean", NULL };
+	"clear", "inactive", "readonly", "read-auto", "clean", "broken", NULL };
 
 int WaitClean(char *dev, int verbose)
 {
@@ -1116,7 +1119,8 @@ int WaitClean(char *dev, int verbose)
 			rv = read(state_fd, buf, sizeof(buf));
 			if (rv < 0)
 				break;
-			if (sysfs_match_word(buf, clean_states) <= 4)
+			if (sysfs_match_word(buf, clean_states)
+			    < (int)ARRAY_SIZE(clean_states)-1)
 				break;
 			rv = sysfs_wait(state_fd, &delay);
 			if (rv < 0 && errno != EINTR)
diff --git a/maps.c b/maps.c
index 02a0474..49b7f2c 100644
--- a/maps.c
+++ b/maps.c
@@ -150,6 +150,7 @@ mapping_t sysfs_array_states[] = {
 	{ "read-auto", ARRAY_READ_AUTO },
 	{ "clean", ARRAY_CLEAN },
 	{ "write-pending", ARRAY_WRITE_PENDING },
+	{ "broken", ARRAY_BROKEN },
 	{ NULL, ARRAY_UNKNOWN_STATE }
 };
 
diff --git a/mdadm.h b/mdadm.h
index 43b07d5..c88ceab 100644
--- a/mdadm.h
+++ b/mdadm.h
@@ -373,6 +373,7 @@ struct mdinfo {
 		ARRAY_ACTIVE,
 		ARRAY_WRITE_PENDING,
 		ARRAY_ACTIVE_IDLE,
+		ARRAY_BROKEN,
 		ARRAY_UNKNOWN_STATE,
 	} array_state;
 	struct md_bb bb;
diff --git a/mdmon.h b/mdmon.h
index 818367c..b3d72ac 100644
--- a/mdmon.h
+++ b/mdmon.h
@@ -21,7 +21,7 @@
 extern const char Name[];
 
 enum array_state { clear, inactive, suspended, readonly, read_auto,
-		   clean, active, write_pending, active_idle, bad_word};
+		   clean, active, write_pending, active_idle, broken, bad_word};
 
 enum sync_action { idle, reshape, resync, recover, check, repair, bad_action };
 
diff --git a/monitor.c b/monitor.c
index 81537ed..e0d3be6 100644
--- a/monitor.c
+++ b/monitor.c
@@ -26,7 +26,7 @@
 
 static char *array_states[] = {
 	"clear", "inactive", "suspended", "readonly", "read-auto",
-	"clean", "active", "write-pending", "active-idle", NULL };
+	"clean", "active", "write-pending", "active-idle", "broken", NULL };
 static char *sync_actions[] = {
 	"idle", "reshape", "resync", "recover", "check", "repair", NULL
 };
@@ -476,7 +476,7 @@ static int read_and_act(struct active_array *a, fd_set *fds)
 		a->next_state = clean;
 		ret |= ARRAY_DIRTY;
 	}
-	if (a->curr_state == clean) {
+	if ((a->curr_state == clean) || (a->curr_state == broken)) {
 		a->container->ss->set_array_state(a, 1);
 	}
 	if (a->curr_state == active ||
-- 
2.17.1

Re: [PATCH v4 1/2] md raid0/linear: Mark array as 'broken' and fail BIOs if a member is gone

[Song Liu]

> On Sep 3, 2019, at 12:49 PM, Guilherme G. Piccoli <gpiccoli@canonical.com> wrote:
> 
> Currently md raid0/linear are not provided with any mechanism to validate
> if an array member got removed or failed. The driver keeps sending BIOs
> regardless of the state of array members, and kernel shows state 'clean'
> in the 'array_state' sysfs attribute. This leads to the following
> situation: if a raid0/linear array member is removed and the array is
> mounted, some user writing to this array won't realize that errors are
> happening unless they check dmesg or perform one fsync per written file.
> Despite udev signaling the member device is gone, 'mdadm' cannot issue the
> STOP_ARRAY ioctl successfully, given the array is mounted.
> 
> In other words, no -EIO is returned and writes (except direct ones) appear
> normal. Meaning the user might think the wrote data is correctly stored in
> the array, but instead garbage was written given that raid0 does stripping
> (and so, it requires all its members to be working in order to not corrupt
> data). For md/linear, writes to the available members will work fine, but
> if the writes go to the missing member(s), it'll cause a file corruption
> situation, whereas the portion of the writes to the missing devices aren't
> written effectively.
> 
> This patch changes this behavior: we check if the block device's gendisk
> is UP when submitting the BIO to the array member, and if it isn't, we flag
> the md device as MD_BROKEN and fail subsequent I/Os to that device; a read
> request to the array requiring data from a valid member is still completed.
> While flagging the device as MD_BROKEN, we also show a rate-limited warning
> in the kernel log.
> 
> A new array state 'broken' was added too: it mimics the state 'clean' in
> every aspect, being useful only to distinguish if the array has some member
> missing. We rely on the MD_BROKEN flag to put the array in the 'broken'
> state. This state cannot be written in 'array_state' as it just shows
> one or more members of the array are missing but acts like 'clean', it
> wouldn't make sense to write it.
> 
> With this patch, the filesystem reacts much faster to the event of missing
> array member: after some I/O errors, ext4 for instance aborts the journal
> and prevents corruption. Without this change, we're able to keep writing
> in the disk and after a machine reboot, e2fsck shows some severe fs errors
> that demand fixing. This patch was tested in ext4 and xfs filesystems, and
> requires a 'mdadm' counterpart to handle the 'broken' state.
> 
> Cc: Song Liu <songliubraving@fb.com>
> Reviewed-by: NeilBrown <neilb@suse.de>
> Signed-off-by: Guilherme G. Piccoli <gpiccoli@canonical.com>

Applied to md-next. 

Thanks!

Re: [PATCH v4 1/2] md raid0/linear: Mark array as 'broken' and fail BIOs if a member is gone

[Guilherme G. Piccoli]

On 03/09/2019 18:56, Song Liu wrote:
> [...] 
> Applied to md-next. 
> 
> Thanks!
> 

Thanks a lot Song!
How can we get the mdadm counterpart applied?

Re: [PATCH v4 2/2] mdadm: Introduce new array state 'broken' for raid0/linear

[Song Liu]

> On Sep 3, 2019, at 12:49 PM, Guilherme G. Piccoli <gpiccoli@canonical.com> wrote:
> 
> Currently if a md raid0/linear array gets one or more members removed while
> being mounted, kernel keeps showing state 'clean' in the 'array_state'
> sysfs attribute. Despite udev signaling the member device is gone, 'mdadm'
> cannot issue the STOP_ARRAY ioctl successfully, given the array is mounted.
> 
> Nothing else hints that something is wrong (except that the removed devices
> don't show properly in the output of mdadm 'detail' command). There is no
> other property to be checked, and if user is not performing reads/writes
> to the array, even kernel log is quiet and doesn't give a clue about the
> missing member.
> 
> This patch is the mdadm counterpart of kernel new array state 'broken'.
> The 'broken' state mimics the state 'clean' in every aspect, being useful
> only to distinguish if an array has some member missing. All necessary
> paths in mdadm were changed to deal with 'broken' state, and in case the
> tool runs in a kernel that is not updated, it'll work normally, i.e., it
> doesn't require the 'broken' state in order to work.
> Also, this patch changes the way the array state is showed in the 'detail'
> command (for raid0/linear only) - now it takes the 'array_state' sysfs
> attribute into account instead of only rely in the MD_SB_CLEAN flag.
> 
> Cc: Jes Sorensen <jes.sorensen@gmail.com>
> Cc: NeilBrown <neilb@suse.de>
> Cc: Song Liu <songliubraving@fb.com>
> Signed-off-by: Guilherme G. Piccoli <gpiccoli@canonical.com>

Acked-by: Song Liu <songliubraving@fb.com>

Jes, does this look good?

Thanks,
Song

Re: [PATCH v4 2/2] mdadm: Introduce new array state 'broken' for raid0/linear

[Guilherme G. Piccoli]

On 04/09/2019 12:51, Song Liu wrote:
> [...] 
>>
>> Cc: Jes Sorensen <jes.sorensen@gmail.com>
>> Cc: NeilBrown <neilb@suse.de>
>> Cc: Song Liu <songliubraving@fb.com>
>> Signed-off-by: Guilherme G. Piccoli <gpiccoli@canonical.com>
> 
> Acked-by: Song Liu <songliubraving@fb.com>
> 
> Jes, does this look good?
> 
> Thanks,
> Song
> 

Jes, do you have any comment about this patch? It'd be good having this
code merged before the 5.4 kernel windows ends, since the kernel
counterpart is ready to get merged (it's on Jens' tree).

Thanks in advance,


Guilherme

Re: [PATCH v4 2/2] mdadm: Introduce new array state 'broken' for raid0/linear

[Jes Sorensen]

On 9/3/19 3:49 PM, Guilherme G. Piccoli wrote:
> Currently if a md raid0/linear array gets one or more members removed while
> being mounted, kernel keeps showing state 'clean' in the 'array_state'
> sysfs attribute. Despite udev signaling the member device is gone, 'mdadm'
> cannot issue the STOP_ARRAY ioctl successfully, given the array is mounted.
> 
> Nothing else hints that something is wrong (except that the removed devices
> don't show properly in the output of mdadm 'detail' command). There is no
> other property to be checked, and if user is not performing reads/writes
> to the array, even kernel log is quiet and doesn't give a clue about the
> missing member.
> 
> This patch is the mdadm counterpart of kernel new array state 'broken'.
> The 'broken' state mimics the state 'clean' in every aspect, being useful
> only to distinguish if an array has some member missing. All necessary
> paths in mdadm were changed to deal with 'broken' state, and in case the
> tool runs in a kernel that is not updated, it'll work normally, i.e., it
> doesn't require the 'broken' state in order to work.
> Also, this patch changes the way the array state is showed in the 'detail'
> command (for raid0/linear only) - now it takes the 'array_state' sysfs
> attribute into account instead of only rely in the MD_SB_CLEAN flag.
> 
> Cc: Jes Sorensen <jes.sorensen@gmail.com>
> Cc: NeilBrown <neilb@suse.de>
> Cc: Song Liu <songliubraving@fb.com>
> Signed-off-by: Guilherme G. Piccoli <gpiccoli@canonical.com>
> ---

Applied thanks!

I fixed up one minor nit rather than having to do the merry-go-round by 
email one more time:

> diff --git a/Monitor.c b/Monitor.c
> index 036103f..cf0610b 100644
> --- a/Monitor.c
> +++ b/Monitor.c
[snip]

> @@ -1116,7 +1119,8 @@ int WaitClean(char *dev, int verbose)
>   			rv = read(state_fd, buf, sizeof(buf));
>   			if (rv < 0)
>   				break;
> -			if (sysfs_match_word(buf, clean_states) <= 4)
> +			if (sysfs_match_word(buf, clean_states)
> +			    < (int)ARRAY_SIZE(clean_states)-1)

I moved the < up to the correct line where it belongs, and added spaces 
") - 1)"

Cheers,
Jes

Re: [PATCH v4 2/2] mdadm: Introduce new array state 'broken' for raid0/linear

[Guilherme G. Piccoli]

On 30/09/2019 16:36, Jes Sorensen wrote:
> [...]
> Applied thanks!
> 
> I fixed up one minor nit rather than having to do the merry-go-round by
> email one more time:
> 
>> diff --git a/Monitor.c b/Monitor.c
>> index 036103f..cf0610b 100644
>> --- a/Monitor.c
>> +++ b/Monitor.c
> [snip]
> 
>> @@ -1116,7 +1119,8 @@ int WaitClean(char *dev, int verbose)
>>               rv = read(state_fd, buf, sizeof(buf));
>>               if (rv < 0)
>>                   break;
>> -            if (sysfs_match_word(buf, clean_states) <= 4)
>> +            if (sysfs_match_word(buf, clean_states)
>> +                < (int)ARRAY_SIZE(clean_states)-1)
> 
> I moved the < up to the correct line where it belongs, and added spaces
> ") - 1)"
> 
> Cheers,
> Jes


Thanks a lot Jes, much appreciated!
Cheers,


Guilherme