Note this is already showing better code reuse, which is a good sign,
though maybe that's just the benefit of reimplementing similar logic
multiple times.
Now both reading and carving end up in the same lfsr_btree_readnext and
lfsr_btree_buildcarve functions for both btrees and shrubs. Both btrees
and shrubs are fundamentally rbyds, so we can share a lot of
functionality as long as we redirect to the correct commit function at
the last minute. This surprising opportunity for deduplication was
noticed while putting together the dbg scripts.
Planned logic (not actual function names):
lfsr_file_readnext -> lfsr_shrub_readnext
| |
| v
'---------> lfsr_btree_readnext
lfsr_file_flushbuffer -> lfsr_shrub_carve ------------.
.---------------------' |
v v
lfsr_file_flushshrub -> lfsr_btree_carve -> lfsr_btree_buildcarve
Though the btree part of the above statement is only a hypothetical at
the moment. Not even the shrubs can survive compaction now.
The reason is the new SLICE tag which needs low-level support in rbyd
compact. SLICE introduces indirect refernces to data located in the same
rbyd, which removes any copying cost associated with coalescing.
Previously, a large coalesce_size risked O(n^2) runtime when
incrementally append small amounts of data, but with SLICEs we can defer
coalescing to compaction time, where the copy is effectively free.
This compaction-time-coalescing is also hypothetical, which is why our
tests are failing. But the theory is promising.
I was originally against this idea because of how it crosses abstraction
layers, requiring some very low-level code that absolutely can not be
omitted in a simpler littlefs driver. But after working on the actual
file writing code for a while I've become convinced the tradeoff is
worth it.
Note coalesce_size will likely still need to be configurable. Data in
fragmenting/sparse btrees is still susceptible to coalescing, and it's
not clear the impacts of internal fragmentation when data sizes approach
the hard block_size/2 limit.
My current thinking is that these are conceptually different types, with
BTREE tags representing the entire btree, and BRANCH tags representing
only the inner btree nodes. We already have multiple btree tags anyways:
btrees attached to files, the mtree, and in the future maybe a bmaptree.
Having separate tags also makes it possible to store a btree in a btree,
though I don't think we'll ever use this functionality.
This also removes the redundant weight field from branches. The
redundant weight field is only a minor cost relative to storage, but it
also takes up a bit of RAM when encoding. Though measurements show this
isn't really significant.
New encodings:
btree encoding: branch encoding:
.---+- -+- -+- -+- -. .---+- -+- -+- -+- -.
| weight | | blocks |
+---+- -+- -+- -+- -+ ' '
| blocks | ' '
' ' +---+- -+- -+- -+- -+
' ' | trunk |
+---+- -+- -+- -+- -+ +---+- -+- -+- -+- -'
| trunk | | cksum |
+---+- -+- -+- -+- -' '---+---+---+---'
| cksum |
'---+---+---+---'
Code/RAM changes:
code stack
before: 30836 2088
after: 30944 (+0.4%) 2080 (-0.4%)
Also reordered other on-disk structs with weight/size, so such structs
always have weight/size as the first field. This may enable some
optimizations around decoding the weight/size without needing to know
the specific type in some cases.
---
This change shouldn't have affected functionality, but it revealed a bug
in a dtree test, where a did gets caught in an mdir split and the split
name makes the did unreachable.
Marking this as a TODO for now. The fix is going to be a bit involved
(fundamental changes to the opened-mdir list), and similar work is
already planned to make removed files work.
This a compromise between padding the tag repr correctly and parsing
speed.
If we don't have to traverse an rbyd (for, say, tree printing), we don't
want to since parsing rbyds can get quite slow when things get big
(remember this is a filesystem!). This makes tag padding a bit of a hard
sell.
Previously this was hardcoded to 22 characters, but with the new file
struct printing it quickly became apparently this would be a problematic
limit:
12288-15711 block w3424 0x1a.0 3424 67 64 79 70 61 69 6e 71 gdypainq
It's interesting to note that this has only become an issue for large
trees, where the weight/size in the tag can be arbitrarily large.
Fortunately we already have the weight of the rbyd after fetch, so we
can use a heuristic similar to the id padding:
tag padding = 21 + nlog10(max(weight,1)+1)
---
Also dropped extra information with the -x/--device flag. It hasn't
really been useful and was implemented inconsistently. Maybe -x/--device
should just be dropped completely...
Previously our lower/upper bounds were initialized to -1..weight. This
made a lot of the math unintuitive and confusing, and it's not really
necessary to support -1 rids (-1 rids arise naturally in order-statistic
trees the can have weight=0).
The tweak here is to use lower/upper bounds initialized to 0..weight,
which makes the math behave as expected. -1 rids naturally arise from
rid = upper-1.
- Added shrub tags to tagrepr
- Modified dbgrbyd.py to use last non-shrub trunk by default
- Tweaked dbgrbyd's log mode to find maximum seen weight for id padding
And by working, I mean you can create inlined trees, just don't
compact/split/move/etc anything. But this does outline the path files
take when writing buffers into inlined trees.
"Inlined trees" in littlefs are entire small rbyd trees embedded as
secondary trees in an mdir's main rbyd tree. When fetching, we can
indicate if a given trunk belongs to the main tree or secondary tree by
setting one of the unused mode bits in the trunk's tag, now called the
"deferred" bit. This bit doesn't need to be included in the alt's "key"
field, so there's no issue with it conflicting with the alt's mode bits.
This requires a bit of tweaking lfsr_rbyd_fetch, since it needs to fall
back to the previous trunk if it discovers the most recent trunk belongs
to an inlined tree. But as a benefit we can leverage the full power of
rbyds in inlined files, including holes, partial updates, etc.
One downside is it looks like these inlined trees may involve more work
in maintining their state correctly, since they need to be sort of
"brought along" when mdirs are compacted, even if they don't actually
have a reference in the mdir yet. But the sheer amount of flexibility
this gives inlined files may make this overhead worth it.
I had never noticed xxd has no header until comparing its output against
dbgblock.py. Turns out these headers aren't really all that useful, and
even sometimes wrong in dbglfs.py.
Now, instead of storing a single contiguous block of config data, config
is stored as tagged metadata like any other attribute.
This allows more flexibility towards adding/removing config in the
future, without cluttering up the config with deprecated entries (see
ATA's "IDENTIFY DEVICE" response).
Most of the config entries are single leb128 limits on various integer
types, with the exception of the magic string and version (major/minor
pair).
---
Note this also includes some semantic changes to the config:
- Limits are stored as size-1. This avoid issues with integer overflow
at extreme ranges.
This was also adopted for block size (block limit) and block count
(disk limit). This deviation between on-disk config and user-facing
config risks confusion, but allows the potential for the full 2^31 range
for these values.
- The default cksum type, crc32c, has been changed to 0.
Originally this was 2 to allow the type to map to the crc width for
crc8, crc16, crc32c, crc64, etc. But dropping this idea and numbering
checksums as they are implemented simplifies things.
May come back to this.
- Storing these configs as attributes opens up of the option of on-disk
defaults when configs are missing.
I'm being a bit conservative with this one, as it's not clear to me if
we should prefer default configs (less code/storage, risk of untested
config parsing) or prefer explicit on-disk configs.
Currently the following have defaults since they seem the most obvious
to me:
- cksum type => defaults to crc32c
- redund type => defaults to parity (TODO, should this default to
no redund?)
- utag_limit => defaults to 0x7f (no special tag decoding)
- uattr_limit => defaults to block_limit (implicit)
This format for mids is a compromise in readability vs debugability.
For example, if our mbid weight is 256 (4KiB blocks), the 19th entry
in the second mdir would be the raw integer 275. With this mid format,
we would print it as 256.19.
The idea is to make it easy to see it's the 19th entry in the mdir while
still making it relatively easy to see that 256.19 and 275 are
equivalent when debugging.
---
The scripts also took some tweaking due to the mid change. Tried to keep
the names consistent, but I don't think it's worthwhile to change too
much of the scripts while they are working.
There is a bit of redundancy here, as we already know the weights of
btree's inner-branches from their parents. But in theory sharing the
same encoding for both the top level btree reference and inner-branches
should offer more chance for deduplication and hopefully less code.
This also moves some members around in the btree encoding so that the
redund blocks are at the beginning. This _might_ simplify decoding of
the variable-length redund blocks at some point.
Current btree encoding:
.----+----+----+----.
| blocks ... redund leb128s (1-20 bytes)
: :
|----+----+----+----|
| trunk ... 1 leb128 (1-5 bytes)
|----+----+----+----|
| weight ... 1 leb128 (1-5 bytes)
|----+----+----+----|
| cksum | 1 le32 (4 bytes)
'----+----+----+----'
This also partially reverts some tag name changes:
- BNAME -> BRANCH
- DMARK -> BOOKMARK
Struct tags, in littlefs, generally encode pointers to different on-disk
data structures. At this point, they've gotten a bit complex, with the
btree struct, for example, containing 1. a block address, 2. the trunk
offset, 3. the weight of the trunk, and 4. a checksum.
Also some future plans:
1. Block redundancy will make it so these pointers may have a variable
number of block addresses to contend with.
2. Different checksum types may make the checksum field itself variable
length, at least on larger builds of littlefs.
This may also happen if we support truncated checksums in littlefs
for storage saving reasons.
Having two variable sized fields becomes a bit of a pain. We can use the
encoded tag size to figure out the size of one of these fields, but not
both.
The change here makes it so the tag size now determines the checksum
size, requiring the redundancy amount to go somewhere else. This makes
it so checksums can be variably sized, and the explicit redundancy
amount avoids the need to parse the leb128s fully to know how many
blocks we're expecting.
But where to put the redundancy amount?
This commit carves out 2-bits from the struct tag to store the amount of
redundancy to allow up to 3 blocks of redundancy:
v0000011 0TTTTTrr
^--^---^-^----^-^- valid bit
'---|-|----|-|- 3-bit mode (0x0 for structs)
'-|----|-|- 4-bit suptype (0x3 for structs)
'----|-|- 0 bit (reserved for leb128)
'-|- 5-bit subtype
'- 2-bit redund
3 blocks may sound extremely limiting, but it's a common limit for
filesystems, 1. because you have to keep in mind each redundant block
adds that much more writing/reading overhead and 2. the fact
that 2^(2^n)-1 is always divisible by 3 makes >3 parity blocks much more
complicated mathematically.
Worst case, if we ever have >3 redundant blocks, we can create new
struct subtypes. Maybe adding extended struct types that prefix the
block addresses with a leb128 encoding the redundancy amount.
---
As a part of this, reorganized the on-disk btree and ecksum encodings to
put the checksum last.
Also split out the btree and inner btree branches as separate struct
types. The btree includes the weight, whereas the weight is implicit in
inner btree branches. This came about after realizing context-specific
prefixes are relatively easy to add thanks to the composability of our
parsers.
This led to some name collisions though:
- BRANCH -> BNAME
- BOOKMARK -> DMARK
This checksum is used to keep track of if we have erased, and not yet
touched, the unused bytes trailing our current commit in the rbyd.
The working theory is that if any prog attempt is made, it will, most
likely, change the checksum of the contents, allowing littlefs to
determine if trailing erased-state is safe to use, even under powerloss.
littlefs can also perturb future data by a single bit, to force this
checksum to always be invalidated during normal operation.
The original name, "forward erased-state checksums (fcksum)", came from the
idea that the checksum "looks forward" into the next commit.
But after using them for a bit, I think the name is unnecessarily
confusing. It, uh, also looks a lot like a swear word. I think
shortening the name to just "erased-state checksums (ecksum)", even
though the previous name is already in use in a release, is reasonable.
---
It's probably hard to believe but the name change from fcrc -> ecrc
really was unrelated to the crc -> cksum change. But boy is it
convenient for avoiding an awkward name. A lot of these name changes
involved sed scripts, so I didn't notice how awkward fcksum would be to
use until writing this commit message.
The reason for this is to move away from the idea that littlefs is
strictly bound to CRCs and make the code more welcoming to other
checksum types, such as SHA256, etc.
Of course, changing the name doesn't really do anything. littlefs
actually _is_ strictly bound to CRCs in a couple ways that other
filesystems aren't. These would need to have workarounds for other
checksum types:
- We leverage the parity-preserving nature of (some) CRCs to not have
to also calculate the parity of metadata in rbyd commits.
- We leverage the linearity of CRCs to retroactively flip the
perturb bit in the cksum tag without needing to recalculate the
checksum. Though the fact we need to do this is because of how we
use parity above, so this may just not be needed for non-CRC
checksums.
- The plans for global-CRCs (not yet implemented) rely heavily on the
mathematical properties of CRC polynomials. This doesn't mean
global-CRCs can't work with other checksums, you would just need to
find a different type of polynomial.
Originally it made sense to name the rbyd ids, well, ids, at least in
the internals of the rbyd functions. But this doesn't work well outside
of the rbyd code, where littlefs has to juggle several different id
types with different purposes:
- rid => rbyd-id, 31-bit index into an rbyd
- bid => btree-id, 31-bit index into a btree
- mid => mdir-id, 15-bit+15-bit index into the mtree
- did => directory-id, 31-bit unique identifier for directories
Even though context makes it clear which id the id refers to in the rbyd
internals, updating the name to rid makes it clearer that these are the
same type of id when looking at code both inside and outside the rbyd
functions.
This implementation is in theory correct, but of course, being untested,
who knows?
Though this does come with remounting added to all of the directory
tests. This effectively tests that all of the directory creation tests
we have so far maintain grm=0 after each unmount-mount cycle. Which is
valuable.
This has, in theory, global-removes (grm) being written out as a part of
of directory creation, but they aren't used in any form and so may not
be being written correctly.
But it did require quite a bit of problem solving to get to this point
(the interactions between mtree splitsand grms is really annoying), so
it's worth a commit.
This makes it now possible to create directories in the new system.
The new system now uses a single global "mtree" to store all metadata
entries in the filesystem. In this system, a directory is simply a range
of metadata entries. This has a number of benefits, but does come with
its own problems:
1. We need to indicate which directory each file belongs to. To do this
the file's name entry has been changed to a tuple of leb128-encoded
directory-id + actual file name:
01 66 69 6c 65 2e 74 78 74 .file.txt
^ '----------+----------'
'------------|------------ leb128 directory-id
'------------ ascii/utf8 name
If we include the directory-id as part of filename comparison, files
should naturally be next to other files in the same directory.
2. We need a way allocate directory-ids for new directories. This turns
out to be a bit more tricky than I expected.
We can't use any mid/bid/rid inherent to the mtree, because these
change on any file creation/deletion. And since we commit the did
into the tree, that's not acceptable.
Initially I though you could just find the largest did and increment,
but this gives you no way to reclaim deleted dids. And sure, deleted
dids have no storage consumption, but eventually you will overflow
the did integer. Since this can suddenly happen in a filesystem
that's been in a steady-state for years, that's pretty unnacceptable.
One solution is to do a simple linear search over the mtree for an
unused did. But with a runtime of O(n^2 log(n)), this raises
performance concerns.
Sidenote: It's interesting to note that the Linux kernel's allocation
of process-ids, a very similar problem, is surprisingly complex and
relies on a radix-tree of bitmaps (struct idr). This suggests I'm not
missing an obvious solution somewhere.
The solution I settled on here is to instead treat the set of dids as
a sort of hash table:
1. Hash the full directory path into a did.
2. Perform a linear search until we have no collision.
leb128(truncate28(crc32c("dir")))
.--------'
v
9e cd c8 30 66 69 6c 65 2e 74 78 74 ...0file.txt
'----+----' '----------+----------'
'-----------------|------------ leb128 directory-id
'------------ ascii/utf8 name
Worst case, this can still exhibit the worst case O(n^2 log(n))
performance when we are close to full dids. However that seems
unlikely to happen in practice, since we don't truncate our hashes,
unlike normal hash tables. An additional 32-bit word for each file
is a small price to pay for a low-chance of collisions.
In the current implementation, I do truncate the hash to 28-bits.
Since we encode the hash with leb128, and hashes are statistically
random, this gives us better usage of the leb128 encoding. However
it does limit a 32-bit littlefs to 256 Mi directories.
Maybe this should be a configurable limit in the future.
But that highlights another benefit of this scheme. It's easy to
change in the future without disk changes.
3. We need a way to know if a directory-id is allocated, even if the
directory is empty.
For this we just introduce a new tag: LFSR_TAG_DSTART, which
is an empty file entry that indicates the directory at the given did
in the mtree is allocated.
To create/delete these atomically with the reference in our parent
directory, we can use the GRM system for atomic renames.
Note this isn't implemented yet.
This is also the first time we finally get around to testing all of the
dname lookup functions, so this did find a few bugs, mostly around
reporting the root correctly.
Now that tree rebalancing is implemented and needed a null terminator
anyways, I think it's clear that the benefit of the alt-always pointers
as trunk terminator has pretty limited value.
Now a null or other tag is needed for every trunk, which simplifies
checks for end-of-trunk.
Alt-always tags are still emitted for deletes, etc, but there their
behavior is implicit, so no special checks are needed. Alt-always tags
are naturally cleaned up as a part of rbyd pruning.
This isn't actually for performance reasons, but to reduce storage
overhead of the rbyd metadata tree, which was showing signs of being
problematic for small block sizes.
Originally, the plan for compaction was to rely on the self-balancing
rbyd append algorithm and simply append each tag to a new tree.
Unfortunately, since each append requires a rewrite of the trunk
(current search path), this introduces ~n*log(n) alts but only uses ~n alts
for the final tree. This really starts to put pressure on small blocks,
where the exponential-ness of the log doesn't kick in and overhead
limits are already tight.
Measuring lfsr_mdir_commit code size, this shows a ~556 byte cost on
thumb: 16416 -> 16972 (+3.4%). Though there are still some optimizations
on the table, this implementation needs a cleanup pass.
alt overhead code cost
rebalance: <= 28*n 16972
append: <= 24*n*log(n) 16416
Note these all assume worst case alt overhead, but we _need_ to assume
worst case for our rbyd estimations, or else the filesystem can get
stuck in unrecoverable compaction states.
Because of the code cost I'm not sure if rebalancing will stay, be
optional, or replace append-compaction completely yet.
Some implementation notes:
- Most tree balancing algorithms rely on true recursion, I suspect
recursion may be a hard requirement in general, but it's hard to find
bounded-ram algorithms.
This solution gets around the ram requirement by leveraging the fact
that our tags exist in a log to build up each layer in the tree
tail-recursively. It's interesting to note that this is a special
case of having little ram but lots of storage.
- Humorously this shouldn't result in a performance improvement. Rbyd
trees result in a worst case 2*log(n) height, and rebalancing gives us
a perfect worst case log(n) height, but, since we need an additional
alt pointer for each node in our tree, things bump back up to 2*log(n).
- Originally the plan was to terminate each node with an alt-always tag,
but during implementation I realized there was no easy way to get the
key that splits the children with awkward tree lookups. As a
workaround each node is terminated with an altle tag that contains the
key followed by an unreachable null tag. This is redundant information,
but makes the algorithm easier to implement.
Fortunately null tags use the smallest tag encoding, which isn't that
small, but that means this wastes at most 4*n bytes.
- Note this preserves the first-tag-always-ends-up-at-off=0x4 rule, which
is necessary for the littlefs magic to end up in a consistent place.
- I've dropped dropping vestigial names for now, which means vestigial
names can remain in btrees indefinitely. Need to revisit this.
Wide tags are a happy accident that fell out of the realization that we
can view all subtypes of a given tag suptype as a range in our rbyd.
Combining this with how natural it is to operate on ranges in an rbyd
allows us to perform operations on an entire range of subtypes as though
it were a single tag.
- lookup wide tag => find the smallest tag with this tag's suptype, O(log(n))
- remove wide tag => remove all tags with this tag's suptype, O(log(n))
- append wide tag => remove all tags with this tag's suptype, and then
append our tag, O(log(n))
This is very useful for littlefs, where we've already been using tag's
subtypes to hold extra type info, and have had to rely on awkward
alternatives such as deleting existing subtypes before writing our new
subtype.
For example, when committing file metadata (not yet implemented), we can
append a wide struct tag to update the metadata while also clearing out any
lingering struct tags from previous commits, all in one rbyd append
operation.
This uses another mode bit in-device to change the behavior of
lfsr_rbyd_commit, of which we have a couple:
vwgrtttt 0TTTTTTT
^^^^---^--------^- valid bit (currently unused, maybe errors?)
'||---|--------|- wide bit, ignores subtype (in-device)
'|---|--------|- grow bit, don't create new id (in-device)
'---|--------|- rm bit, remove this tag (in-device)
'--------|- 4-bit suptype
'- leb128 subtype
This helps with debugging and can avoid weird issues if a file btree
ever accidentally ends up attached to id -1 (due to fs bug).
Though a separate encoding isn't strictly necessary, maybe this should
be reverted at some point.
This replaces unr with null on disk, though note both the rm bit and unr
are used in-device still, they just don't get written to disk.
This removes the need for the rm bit on disk. Since we no longer need to
figure out what's been removed during fetch, we can save this bit for both
internal and future on-disk use.
Special handling of alta allows us to avoid emitting an unr tag (now null) if
the current trunk is truly unreachable. This is minor now, but important
for a theoretical rbyd rebalance operation (planned), which brings the
rbyd overhead down from ~3x to ~2x.
These changes give us two ways to terminate trunks without a tag:
1. With an alta, if the current trunk is unreachable:
altbgt 0x403 w0 0x7b
altbgt 0x402 w0 0x29
alta w0 0x4
2. With a null, if the current trunk is reachable, either for
code convenience or because emitting an alta is impossible (an empty
rbyd for example):
altbgt 0x403 w0 0x7b
altbgt 0x402 w0 0x29
altbgt 0x401 w0 0x4
null
Yet another tag encoding, but hopefully narrowing in on a good long term
design. This change trades a subtype bit for the ability to extend
subtypes indefinitely via leb128 in the future.
The immediate benefit is ~unlimited custom attributes, though I'm not
sure how to make this configurable yet. Extended custom attributes may
have a significant impact on alt tag sizes, so it may be worth
defaulting to only 8-bit custom attributes still.
Tag encoding:
vmmmtttt 0TTTTTTT 0wwwwwww 0sssssss
^--^---^--------^--------^--------^- valid bit
'---|--------|--------|--------|- 3-bit mode
'--------|--------|--------|- 4-bit suptype
'--------|--------|- leb128 subtype
'--------|- leb128 weight
'- leb128 size/jump
This limits subtypes to 7-bits, but this seems very reasonable at the
moment.
This also seems to limit custom attributes to 7-bits, but we can use two
separate suptypes to bring this back up to 8-bits. I was planning to do
this anyways to have separate "user-attributes" and "system-attributes",
so this actually fits in really well.
Optimizing a script? This might sound premature, but the tree rendering
was, uh, quite slow for any decently sized (>1024) btree.
The main reason is that tree generation is quite hacky in places, repeatedly
spitting out multiple copies of the inner node's rbyd trees for example.
Rather than rewrite the tree generation implementation to be smarter,
this just changes all edge representations to namedtuples (which may
reduce memory pressure a bit), and collects them into a Python set.
This has the effect of deduplicating generated edges efficiently, and
improved the rendering performance significantly.
---
I also considered memoizing rbyd tree, but dropped the idea since the
current renderer performs well enough.
This builds on dbgrbyd.py and dbgbtree.py by allowing for quick
debugging of the littlefs mtree, which is a btree of rbyd pairs with a
few bells and whistles.
This also comes with a number of tweaks to dbgrbyd.py and dbgbtree.py,
mostly changing rbyd addresses to support some more mdir friendly
formats.
The syntax for rbyd addresses is starting to converge into a couple
common patterns, which is nice for quickly determining what type of
address you are looking at at a glance:
- 0x12 => An rbyd at block 0x12
- 0x12.34 => An rbyd at block 0x12 with trunk 0x34
- 0x{12,34} => An rbyd at either block 0x12 or block 0x34 (an mdir)
- 0x{12,34}.56 => An rbyd at either block 0x12 or block 0x34 with trunk 0x56
These scripts have also been updated to support any number of blocks in
an rbyd address, for example 0x{12,34,56,78}. This is a bit of future
proofing. >2 blocks in mdirs may be explored in the future for the
increased redundancy.
LFSR_TAG_BNAME => LFSR_TAG_BRANCH
LFSR_TAG_BRANCH => LFSR_TAG_BTREE
Maybe this will be a problem in the future if our branch structure is
not the same as a standalone btree, but I don't really see that
happening.
This work already indicates we need more data-related helper
functions. We shouldn't need this many function calls to do "simple"
operations such as fetch the superconfig if it exists.
This is an absurd optimization that stems from the observation that the
branch encoding for the inner-rbyds in a B-tree is enough information to
jump directly to the trunk of the rbyd without needing an lfsr_rbyd_fetch.
This results in a pretty ridiculous performance jump from O(m log_m(n/m))
to O(log(m) log_m(n/m)).
If the complexity analysis isn't impressive enough, look at some rough
benchmarking of read operations for 4KiB-block, 1K-entry B-trees:
12KiB ^ :: :. :: .: .: :. : .: :. : : .. : : . : .: : : :
| .:: .::.::.:: ::.::::::::::::.::::::::.::::::::::::.
| : :::':: ::'::'::':: :' :':: :'::::::::': ::::::': :
before | ::: ::' :' :' :: :' '' ' ' '' : : : '' ' ' '
| ::: ''
|:
0B :'------------------------------------------------------>
.17KiB ^ ............:::::::::::::::::::::::::::::
| . .....:::::''''''''' ' ' '
| .::::::::::::
after | :':''
|.::
.:'
0B :------------------------------------------------------->
0 1K
In order for this to work, the branch encoding did need to be tweaked
slightly. Before it stored block+off, now it stores block+trunk where
"trunk" is the offset of the entry point into the rbyd tree. Both off
and trunk are enough info to know when to stop fetching, if necessary,
but trunk allows lookups to jump directly into the branches rbyd tree
without a fetch.
With the change to trunk, lfsr_rbyd_fetch has also be extended to allow
fetching of any internal trunks, not just the last trunk in the commit.
This is very useful for dbgrbyd.py, but doesn't currently have a use in
littlefs itself. But it's at least valuable to have the feature available
in case it does become useful.
Note that two cases still requires the slower O(m log_m(n/m)) lookup
with lfsr_rbyd_fetch:
1. Name lookups, since we currently use a linear-search O(m) to find names.
2. Validating B-tree rbyd's, which requires a linear fetch O(m) to
validate the checksums. We will need to do this at least once
after mount.
It's also worth mentioning this will likely have a large impact on B-tree
traversal speed. Which is huge as I am expecting B-tree traversal to be
the main bottleneck once garbage-collection (or its replacement) is
involved.
I've been wanting to make this change for a while now (tag,id => id,tag).
The id,tag order matches the common lexicographic order used for sorting
tuples. Sorting tag,id tuples by their id first is less common.
The reason for this order in the codebase is because all attrs on disk
start with their tag first, since its decoding determines the purpose of
the id field (keep in mind this includes other non-tree tags such as
crcs, alts, etc). But with the move to storing weights instead of tags
on disk, this gives us a clear point to switch from tag,w to id,tag
ordering.
I may be thinking to much about this, but it does affect a significant
amount of the codebase.
While the previous renderer was "technically correct", the attempt to
map rotated alts to their nearest neighbor just made the resulting tree
an unreadable mess.
Now the renderer prunes alts with unreachable edges (like they would be
during lfsr_rbyd_append). And aligns all alts with their destination
trunk. This results in a much more readable, if slightly less accurate,
rendering of the tree.
Example:
$ ./scripts/dbgrbyd.py -B4096 disk 0 -t
rbyd 0x0, rev 1, size 1508, weight 40
off ids tag data (truncated)
0000032a: .-+-> 0 reg w1 1 73 s
00000026: | '-> 1-5 reg w5 1 62 b
00000259: .-------+---> 6-11 reg w6 1 6f o
00000224: | .-+-+-> 12-17 reg w6 1 6e n
0000028e: | | | '-> 18 reg w1 1 70 p
00000076: | | '---> 19-20 reg w2 1 64 d
0000038f: | | .-> 21-22 reg w2 1 75 u
0000041d: | .---+---+-> 23 reg w1 1 78 x
000001f3: | | .-> 24-27 reg w4 1 6d m
00000486: | | .-----+-> 28-29 reg w2 1 7a z
000004f3: | | | .-----> 30-31 reg w2 1 62 b
000004ba: | | | | .---> 32-35 reg w4 1 61 a
0000058d: | | | | | .-> 36-37 reg w2 1 65 e
000005c6: +-+-+-+-+-+-> 38-39 reg w2 1 66 f
Sorting weights instead of ids just had a number of benefits, suggesting
this is a better design:
- Calculating the id and delta of each rbyd trunk is surprisingly
easier - id is now just lower+w-1, and no extra conditions are
needed for unr tags, which just have a weight of zero.
- Removes ambiguity around which id unr tags should be assigned to,
especially unrs that delete ids.
- No more +-1 weirdness when encoding/decoding tag ids - the weight
can be written as-is and -1 ids are infered from their weight and
position in the tree (lower+w-1 = 0+0-1 = -1).
- Weights compress better under leb128 encoding, since they are usually
quite small.
This fixed two notable bugs:
1. Using "altle 0xfff0" to terminate unreachable rbyd trunks threw off
id calculations in lfsr_rbyd_fetch searches. We derive the tag's
id+weight from the lower bound calculated as the sum of all "altle"s
and an always-followed "altle 0xfff0" throws this off.
We _could_ derive the tag's id+weight from the upper bound, inverting
this relationship, but decided to revert back to using "altgt 0" to
terminate unreachable rbyd trunks.
Using the lower bound is more intuitive, and "altgt 0" has the
benifit of supporting variable-length tags if we ever need to adopt
those.
To avoid the previous issues around 0-tag holes (which was the original
motivation for altle 0xfff0), 0-tags are now automatically adjusted
in lfsr_rbyd_lookup, and avoided in lfsr_rbyd_append.
But note! if any implemention tries to look up 0-tags, this will
eventually break! See previous commits for more info.
2. Unfortunately, we can't combine branch updates and weight updates in
lfsr_btree_commit in the general case.
If our btree contains bname tags, the weight is attached to the
bname tag, separately from the branch tag.
Branch updates in lfsr_btree_commit need two separate attrs for the
weight and branch struct for this reason, which is unfortunate.
The amount of extra conditions to make bname+branch pairs work makes
me want to redesign the inner-nodes of the btrees, but I can't think
of a better way to approach the problem.
This "mk" bit must not be written to disk, it would conflict with the
other non-tree tag encodings. But we can use this bit in the context of
lfsr_tag_append to disambiguate tags changing weight from inserting new
tags.
Note that in the context of rbyd compactions, this will make things a bit
weird, since it's no longer just a direct one-to-one copy of each tag.
To make compactions a bit easier, this implementation allows the "mk"
bit to be set on any tag and ignores it when the weight delta is zero.
It turns out that this scheme greatly simplifies the awkward
leaf-split-alt calculation that previously had several if statements to
handle different corner cases, with the caveat that "mk" tags need their
ids adjusted by +1. Added this adjustment directly into lfsr_rbyd_append
for now, so the upper-level interface can be a bit more intuitive.
Though this may need to change later if it is more confusing than
helpful.
This does not work as is due to ambiguity with grows and insertions.
Before, these were disambiguated by seperate grow and attr tags. You
effectively grew the neighboring id before claiming its weight
as yours. But now that the attr itself creates the grow/insertion,
it's ambiguous which one is intended.
I only recently noticed there is enough information in each rbyd trunk
to infer the effective grow/shrinks. This has a number of benefits:
- Cleans up the tag encoding a bit, no longer expecting tag size to
sometimes contain a weight (though this could've been fixed other
ways).
0x6 in the lower nibble now reserved exclusively for in-device tags.
- grow/shrinks can be implicit to any tag. Will attempt to leverage this
in the future.
- The weight of an rbyd can no longer go out-of-sync with itself. While
this _shouldn't_ happen normally, if it does I imagine it'd be very
hard to debug.
Now, there is only one source of knowledge about the weight of the
rbyd: The most recent set of alt-pointers.
Note that remove/unreachable tags now behave _very_ differently when it
comes to weight calculation, remove tags require the tree to make the
tag unreachable. This is a tradeoff for the above.
The main motivation for this was issues fitting a good tag encoding into
14-bits. The extra 2-bits (though really only 1 bit was needed) from
making this not a leb encoding opens up the space from 3 suptypes to
15 suptypes, which is nothing to shake a stick at.
The main downsides:
1. We can't rely on leb encoding for effectively-infinite extensions.
2. We can't shorten small tags (crcs, grows, shrinks) to one byte.
For 1., extending the leb encoding beyond 14-bits is already
unpalatable, because it would increase RAM costs in the tag
encoder/decoder,` which must assume a worst-case tag size, and would likely
add storage cost to every alt pointer, more on this in the next section.
The current encoding is quite generous, so I think it is unlikely we
will exceed the 16-bit encoding space. But even if we do, it's possible
to use a spare bit for an "extended" set of tags in the future.
As for 2., the lack of compression is a downside, but I've realized the
only tags that really matter storage-wise are the alt pointers. In any
rbyds there will be roughly O(m log m) alt pointers, but at most O(m) of
any other tags. What this means is that the encoding of any other tag is
in the noise of the encoding of our alt pointers.
Our alt pointers are already pretty densely packed. But because the
sparse key part of alt-pointers are stored as-is, the worst-case
encoding of in-tree tags likely ends up as the encoding of our
alt-pointers. So going up to 3-byte tags adds a surprisingly large
storage cost.
As a minor plus, le16s should be slightly cheaper to encode/decode. It
should also be slightly easier to debug tags on-disk.
tag encoding:
TTTTtttt ttttTTTv
^--------^--^^- 4+3-bit suptype
'---|- 8-bit subtype
'- valid bit
iiii iiiiiii iiiiiii iiiiiii iiiiiii
^- m-bit id/weight
llll lllllll lllllll lllllll lllllll
^- m-bit length/jump
Also renamed the "mk" tags, since they no longer have special behavior
outside of providing names for entries:
- LFSR_TAG_MK => LFSR_TAG_NAME
- LFSR_TAG_MKBRANCH => LFSR_TAG_BNAME
- LFSR_TAG_MKREG => LFSR_TAG_REG
- LFSR_TAG_MKDIR => LFSR_TAG_DIR
B-trees with names are now working, though this required a number of
changes to the B-tree layout:
1. B-tree no-longer require name entries (LFSR_TAG_MK) on each branch.
This is a nice optimization to the design, since these name entries
just waste space in purely weight-based B-trees, which are probably
going to be most B-trees in the filesystem.
If a name entry is missing, the struct entry, which is required,
should have the effective weight of the entry.
The first entry in every rbyd block is expected to be have no name
entry, since this is the default path for B-tree lookups.
2. The first entry in every rbyd block _may_ have a name entry, which
is ignored. I'm calling these "vestigial names" to make them sound
cooler than they actually are.
These vestigial names show up in a couple complicated B-tree
operations:
- During B-tree split, since pending attributes are calculated before
the split, we need to play out pending attributes into the rbyd
before deciding what name becomes the name of entry in the parent.
This creates a vestigial name which we _could_ immediately remove,
but the remove adds additional size to the must-fit split operation
- During B-tree pop/merge, if we remove the leading no-name entry,
the second, named entry becomes the leading entry. This creates a
vestigial name that _looks_ easy enough to remove when making the
pending attributes for pop/merge, but turns out the be surprisingly
tricky if the parent undergoes a split/merge at the same time.
It may be possible to remove all these vestigial names proactively,
but this adds additional rbyd lookups to figure out the exact tag to
remove, complicates things in a fragile way, and doesn't actually
reduce storage costs until the rbyd is compacted.
The main downside is that these B-trees may be a bit more confusing
to debug.
B-tree remove/merge is the most annoying part of B-trees.
The implementation here follows the same ideas implemented in push/split:
1. Defer splits/merges until compaction.
2. Assume our split/merge will succeed and play it out into the rbyd.
3. On the first sign of failure, revert any unnecessary changes by
appending deletes.
4. Do all of this in a single commit to avoid issues with single-prog
blocks.
Mapping this onto B-tree merge, the condition that triggers merge is
when our rbyd is <1/4 the block_size after compaction, and the condition
that aborts a merge is when our rbyd is >1/2 the block_size, since that
would trigger a split on a later compact.
Weaving this into lfsr_btree_commit is a bit subtle, but relatively
straightforward all things considered.
One downside is it's not physically possible to try merging with both
siblings, so we have to choose just one to attempt a merge. We handle
the corner case of merging the last sibling in a block explicitly, and
in theory the other sibling will eventually trigger a merge during its
own compaction.
Extra annoying are the corner cases with merges in the root rbyd that
make the root rbyd degenerate. We really should avoid a compaction in
this case, as otherwise we would erase a block that we immediately
inline at a significant cost. However determining if our root rbyd is
degenerate is tricky. We can determine a degenerate root with children
by checking if our rbyd's weight matches the B-tree's weight when we
merge. But determining a degenerate root that is a leaf requires
manually looking up both children in lfsr_btree_pop to see if they will
result in a degenerate root. Ugh.
On the bright side, this does all seem to be working now. Which
completes the last of the core B-tree algorithms.
This was a rather simple exercise. lfsr_btree_commit does most of the
work already, so all this needed was setting up the pending attributes
correctly.
Also:
- Tweaked dbgrbyd.py's tree rendering to match dbgbtree.py's.
- Added a print to each B-tree test to help find the resulting B-tree
when debugging.
Changed so there is no 1-to-1 mk-tag/id assumption, any unique ids
create a simulated lifetime to render. This fixes the issue where
grows/shrinks left-aligned ids confused dbgrbyd.py.
As a plus, now dbgrbyd.py can actually handle multi-id grow/shrinks, and
is more robust against out-of-sync grow/shrinks. This sort of lifetime issues
are when you'd want to run dgbrbyd.py, so it's a bit important this is handled
gracefully.
An example:
$ ./scripts/dbgbtree.py -B4096 disk 0xaa -t -i
btree 0xaa.1000, rev 35, weight 278
block ids name tag data
(truncated)
00aa.1000: +-+ 0-16 branch id16 3 7e d4 10 ~..
007e.0854: | |-> 0 inlined id0 1 73 s
| |-> 1 inlined id1 1 74 t
| |-> 2 inlined id2 1 75 u
| |-> 3 inlined id3 1 76 v
| |-> 4 inlined id4 1 77 w
| |-> 5 inlined id5 1 78 x
| |-> 6 inlined id6 1 79 y
| |-> 7 inlined id7 1 7a z
| |-> 8 inlined id8 1 61 a
| |-> 9 inlined id9 1 62 b
...
This added the idea of block+limit addresses such as 0xaa.1000. Added
this as an option to dbgrbyd.py along with a couple other tweaks:
- Added block+limit support (0x<block>.<limit>).
- Fixed in-device representation indentation when trees are present.
- Changed fromtag to implicitly fixup ids/weights off-by-one-ness, this
is consistent with lfs.c.
This involves many, many hacks, but is enough to test the concept
and start looking at how it interacts with different block sizes.
Note only append (lfsr_btree_push on the end) is implemented, and it
makes some assumption about how the ids can interact when splitting
rbyds.
This implements a common B-tree using rbyd's as inner nodes.
Since our rbyds actually map to sorted arrays, this fits together quite
well.
The main caveat/concern is that we can't rely on strict knowledge on the
on-disk size of these things. This first shows up with B-tree insertion,
we can't split in preparation to insert as we descend down the tree.
Normally, this means our B-tree would require recursion in order to keep
track of each parent as we descend down our tree. However, we can
avoid this by not storing our parent, but by looking it up again on each
step of the splitting operation.
This brute-force-ish approach makes our algorithm tail-recursive, so
bounded RAM, but raises our runtime from O(logB(n)) to O(logB(n)^2)
That being said, O(logB(n)^2) is still sublinear, and, thanks to
B-tree's extremely high branching factor, may be insignificant.
