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Subject[RFC] Improved inode number allocation for HTree
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Summary of the problem:

HTree's random relationship between directory entry order and inode order has
been observed to cause increased cache pressure, affecting performance under
certain conditions. Most of this pressure is due to inode table usage, which
is normally several times larger than the directory itself. Even when the
inode table usage is much less than available cache, it may still exceed the
size of the journal file (8 MB by default). Though the journal only becomes
involved when blocks are modified, unfortunately, because of atime updates,
this includes all directory operations. We could suggest to users that they
should disable atime updating if they care about performance, but we ought to
be able to do better than that.

To reduce this cache pressure, what we need to do is make the directory entry
order correspond more closely to the inode number order. It doesn't have to
correspond perfectly in order to show substantial improvement, as Tomas
demonstrated with his recent getdents sorting patch.

Analysis:

To understand why sorting relatively small sections of the directory entries
reduces the cache pressure, we can think about the lifetime of an inode table
block over the course of a directory traversal. This traversal lifetime
extends from when it is first accessed (always a write as noted above) to
when it is last accessed, or the directory traversal finishes. Each inode
table block contains multiple inodes, so if those inodes are accessed
randomly, the traversal lifetime of every inode table block will tend to be
from nearly the beginning of the traversal to nearly the end, and so the load
on the cache will be nearly the same as the number of inode table blocks. If
this load is greater than available cache, various blocks will have to be
written out and reloaded later for further processing. We can call the
period between loading and evicting an inode table block, its "cache period".

The number of times a block must be written/reloaded depends not only on the
number of inode table blocks covered by the directory and the availablity of
cache memory, but on the probable number of the inodes within the block that
will be written during each of the block's cache period. By sorting the
directory chunkwise, the probable number of inodes processed in one cache
period increases, reducing the number of cache periods, in turn reducing disk
seeking and transfer overhead.

To apply the above model to the journal, just substitute "journal period" for
"cache period", where journal period is defined as the time from when a dirty
block first enters the journal to when it is written out to disk.

We can see that local sorting or directory chunks has hardly any effect on
the traversal lifetime of a block; it only reduces the number of cache
periods. The size of the chunk of directory that we sort locally presumably
stays constant, so the probable number of inodes on each inode table block
processed in each cache period approaches one as the directory size
increases. At some point, there is no longer any benefit from sorting, andwe
arrive at that point at rather realistic directory sizes.

We can always do the job perfectly by sorting the whole directory. This
would require changes in every getdents-using application that cares about
performance, to either make the getdents window as big as the directory or to
do the sort in user space. A spinoff benefit of doing the full sort is that
it becomes trivial to detect and eliminate duplicate entries. Higher memory
load is a drawback, as is the work required to update user space programs.
There will also be noticable latency introduced by the sort, which didn't
appear before. If sorting is to be done in user space then we impose the
requirement on all filesystems - even those that do not use inode numbers
internally - that they supply an inode key for sorting, and that the supplied
sorting key be meaningful in terms of cache locality.

Proposed Solution:

What if we could maintain the inodes in the inode table in the same order as
the directory entries, permanently, so that no sorting is required? If we
could do this, the traversal lifetime of each inode table block would be the
same as the number of inodes it contains, and the cache load due to the inode
table would be exactly one block. That is, the directory traversal would
process each inode table block completely before moving on to the next one.
Though the current Ext3 filesystem structure does not support this directly,
we can approximate the effect quite closely within the existing framework.

Due to Ted's recent work, we are already traversing the directory in hash
order, as opposed to physical allocation order, because of the particular
approach adopted to address the telldir/seekdir problem. This is relatively
inexpensive. So now, what we would like to do is make the inode number of
each directory entry increase monotonically, corresponding to monotonically
increasing hash values. We also want to allocate those inode numbers densely
in the inode table, to minimize seeking. If we know beforehand how many
entries the directory will have, this is easy: when we create an entry, we
multiply its hash value by the total number of entries divided by the total
hash range (2**31), add in a base target, and use that as the goal to
allocate a new inode. Due to the randomness of the hash value, we will
sometimes be forced to allocate an inode number out of order, but hopefully
there won't be too many of those, and they won't be very far out of order.
We may also end up with some gaps in the inode table. In fact, we may
intentionally leave some slack in order to reduce the number of out-of-order
allocations. These problems are not serious.

The big problem is that we don't know the number of directory entries ahead
of time. To get around this, we can use the current size of the directory,
rounded up to a power of two as the size estimate. Each time the directory
increases to a new binary size we establish a new region in the inode table,
which will map to the to-be-created half of directory entries, roughly in
order.

Now, consider what happens to a group of directory entries created when the
directory was so small that it mapped to a single inode table block. After a
series of leaf splits, these former neighbors will end up far apart in the
hash order, but their inode numbers will still be ordered monotonically over
a traversal. The traversal lifetime of that group of entries will be nearly
the entire directory traversal, but there is only one such block.

When the directory became larger, some newly created entries were mapped to
two new inode table blocks, the traversal lifetimes of which are roughly half
the entire traversal. There are only two such blocks, and their lifetimes do
not overlap, so these two blocks only generate one block worth of cache load.

So it goes, with each new set of entries of size 2**i generating only one
additional block of cache load. The final cache load is O log2(N), a
pleasingly small number.

A very nice property of this inode allocation strategy is that the ordering
will tend to be reinforced as a directory ages, as opposed to slowly decaying
towards randomness as happens with linear directories.

So this approach is attractive, especially as it can be implemented in a
small number of lines of code. The main outstanding issue I have not
addressed is how to arrange things so that the inode allocation patterns of
neighbouring directories don't interfere with each other too much. I expect
that each time the directory grows to a new power of two size, we need to
scan the inode allocation map for a relatively unpopulated region of that
size and store the region's base in the directory header. Would we need to
store the entire history of allocation bases? Probably not. This aspect
requires further consideration.

Regards,

Daniel

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