Attempted to implement TEST_PERMUTATIONS but that went nowhere useful.
Unfortunately test defines don't have a way to represent arrays, and
adding such a representation would be unreasonably complicated.
For practical purposes it's better to just do the permutation generation
inside the tests. Maybe at some point it would be nice to integrate
permutation testing so the state gets hashed somehow as a part of the
test failure, but now is not the time.
Though this is a bit of an ugly fix...
Red edges mess everything up during deletion since we always need to
go down red edges in case we need to do a red flip. This puts our
algorithm into an awkward state.
It would be easier to do away with colors completely when we start
deleting (after all this branch of the tree _will_ be shrinking), but
this conflicts with the ultimate goal of deduplicate rbyd append.
Tree deletion is such a pain. It always seems like an easy addition to
the core algorithm but always comes with problems.
The initial plan for deletes was to iterate through all tags, tombstone,
and then adjust weights as needed. This accomplishes deletes with little
change to the rbyd algorithm, but adds a complex traversal inside the
commit logic. Doable in one commit, but complex. It also risks weird
unintuitive corner cases since the cost of deletion grows with the number
of tags being deleted (O(m log n)).
But this rbyd data structure is a tree, so in theory it's possible to
delete a whole range of tags in a single O(log n) operation.
---
This is a proof-of-concept range deletion algorithm for rbyd trees.
Note, this does not preserve rbyd's balancing properties! But it is no
worse than tombstoning. This is acceptable for littlefs as any
unbalanced trees will be rebalanced during compaction.
The idea is to follow the same underlying dhara algorithm, where we
follow a search path and save any alt pointers not taken, but we follow
both search paths that form the outside of the range, and only keep
outside edges.
For example, a tree:
.-------o-------.
| |
.---o---. .---o---.
| | | |
.-o-. .-o-. .-o-. .-o-.
| | | | | | | |
a b c d e f g h
To delete the range d-e, we would search for d, and search for e:
********o********
* *
.---***** *****---.
| * * |
.-o-. .-*** ***-. .-o-.
| | | * * | | |
a b c d e f g h
And keep the outside edges:
.--- ---.
| |
.-o-. .- -. .-o-.
| | | | | |
a b c f g h
But how do we combine the outside edges? The simpler option is to do
both searches seperately, one after the other. This would end up with a
tree like this:
.---------o
| |
.-o-. .---o
| | | |
a b c o---------.
| |
o---. .-o-.
| | | |
_ f g h
But this horribly throws off the balance of our tree! It's worse than
tombstoning, and gets worse with more tags.
An alternative strategy, which is used here, is to alternate edges as we
descend down the tree. This unfortunately is more complex, and requires
~2x the RAM, but better preserves the balance of our tree. It isn't
perfect, because we lose color information, but we can leave that up to
compaction:
.---------o
| |
.-o-. o---------.
| | | |
a b .---o .-o-.
| | | |
c o---. g h
| |
_ f
I also hope this can be merged into lfs_rbyd_append, deduplicating the
entire core rbyd append algorithm.
The idea behind the full hint is that we may stay on the current search
path, benefiting from a loaded cache. Though this should probably be
benchmarked eventually.
Considered adding --ignore-errors to watch.py, but it doesn't really
make sense with watch.py's implementation. watch.py would need to not update
in realtime, which conflicts with other use cases.
It's quite lucky a spare bit is free in the tag encoding, this means we
don't need a reserved length value as originally planned. We end up using
all of the bits that overlap the alt pointer encoding, which is nice and
unexpected.
In theory spreading rbyd trees across multiple commits shouldn't change
anything, but the whole point of testing is to catch things that are not
in the theory.
This really doesn't need to be this large. The extra 4-bits is not worth
the required extra byte of waste in every commit (CRCs tags are forced
to use a fully expanded leb128 due to a catch-22 issue).
This was a inter-abstraction-layer assumption that won't hold true with
the rbyd blocks.
The whole caching layer probably deserves a rewrite at this point.
It turns out statefulness works quite well with this algorithm (The
prototype was in Haskell, which created some artificial problems. I
think it may have just been too high-level a language for this
near-instruction-level algorithm).
This bias makes it so that tag lookups always find a tag strictly >= the
requested tag, unless we are at the end of the tree.
This makes tree traversal trivial, which is quite nice.
Need to remove ntag now, it's no longer needed.
- Moved alt encoding 0x1 => 0x4, which can lead to slightly better
lookup tables, the perturb bit takes the same place as the color bit,
which means both can be ignored in readonly operations.
- Dropped lfs_rbyd_fetchmatch, asking each lfs_rbyd_fetch to include NULL
isn't that bad.
New encoding:
tags:
iiii iiiiiii iiiiiTT TTTTTTt ttt0tpv
^--------^------^^^- 16-bit id
'------|||- 8-bit type2
'||- 5-bit type1
'|- perturb bit
'- valid bit
llll lllllll lllllll lllllll lllllll
^- n-bit length
alts:
wwww wwwwwww wwwwwww wwwwwww www1dcv
^^^-^- 28-bit weight
'|-|- color bit
'-|- direction bit
'- valid bit
jjjj jjjjjjj jjjjjjj jjjjjjj jjjjjjj
^- n-bit jump
- primitive lfs_rbyd_fetch
- primitive lfs_rbyd_commit
- tag reading/progging and encoding machinery
The tag encoding scheme here uses pairs of leb128s, encoding either
a normal tag:
iiii iiiiiii iiiiiTT TTTTTTt ttttt0v
^--------^------^-^- 16-bit id
'------|-|- 8-bit type2
'-|- 6-bit type1
'- valid bit
llll lllllll lllllll lllllll lllllll
^- n-bit length
Or an alt pointer:
wwww wwwwwww wwwwwww wwwwwww wwwcd1v
^^^-^- 28-bit weight
'|-|- color bit
'-|- direction bit
'- valid bit
jjjj jjjjjjj jjjjjjj jjjjjjj jjjjjjj
^- n-bit jump
Note that two bits overlap the alt pointer dir/color encoding, this
is actually not a problem at all since some tags (crcs/fcrcs) don't
participate in the rbyd tree and can use these bits.
There's a number of benefits to using leb128s, which should probably
be written about, most notably is the abstraction of the device's
word-size. The "n-bits" above can be whatever word size works on the
device, trading off code-size for storage capabilities without breaking
compatibility with other devices. This will eventually be negotiated via
the superblock.
crc32c, with a polynomial of 0x11edc6f41, is generally numerically superior
to the more common crc32 standard. Catching more bit errors across
a wider range of message messages (except 2-bit errors) without any changes
to the underlying algorithm.
Philip Koopman has a large body of work exploring optimal polynomials here:
http://users.ece.cmu.edu/~koopman/crc/crc32.html
And from his experiments we know the maximum message size where we can
still detect a given number of bit errors for each polynomial:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
crc32 0x104c11db7 = ∞ 4294967263 91607 2974 268 171 91 57 34 21 12 10 10 10 - - -
crc32c 0x11edc6f41 = ∞ 2147483615 2147483615 5243 5243 177 177 47 47 20 20 8 8 6 6 1 1
So really crc32c should be prefered where possible. Koopman also has
alternative polynomials with slightly different properties, but crc32c
is already popular enough to have a decent amount of hardware support.
---
Another nice feature of crc32c is that its polynomial has even parity.
It turns out that even-parity polynomials give us the nifty property
parity(crc(m)) == parity(m).
A quick proof:
crc(m) = m(x) x^|P|-1 mod P(x)
parity(m) = m(x) x mod x+1
though note: x mod x+1 = 1, by hand
so:
parity(m) = m(x)*1 mod x+1
= m(x) mod x+1
solving for parity(crc(m)):
parity(crc(m)) = (m(x) x^|P|-1 mod P(x)) mod x+1
note: (a mod b) mod c = a mod c, if c divides b,
aka (a mod b) mod c = a mod c, if b mod c = 0
so if P(x) mod x+1 = 0,
aka if parity(P) = 0:
parity(crc(m)) = m(x) x^|P|-1 mod x+1
but, like before: x^|P|-1 mod x+1 = 1, by hand
so:
parity(crc(m)) = m(x)*1 mod x+1
= m(x) mod x+1
= parity(m)
so if parity(P) = 0:
parity(crc(m)) = parity(m)
This has the potential to replace the 1-bit counter in the metadata tags
with a more general solution that doesn't require extra state.
This of course should never happen normally, two half-orphans requires
two parents, which is disallowed in littlefs for this reason. But it can
happen if there is an outdated half-orphan later in the metadata
linked-list. The two half-orphans can cause the deorphan step to get
stuck, constantly "fixing" the first half-orphan before it has a chance
to remove the problematic, outdated half-orphan later in the list.
The solution here is to do a full check for half-orphans before
restarting the half-orphan loop. This strategy has the potential to
visit more metadata blocks unnecessarily, but avoids situations where
removing a later half-orphan will eventually cause an earlier
half-orphan to resolve itself.
Found with heuristic powerloss testing with test_relocations_reentrant_renames
after 192 nested powerlosses.
Initially I thought the fcrc would be sufficient for all of the
end-of-commit context, since indicating that there is a new commit is a
simple as invalidating the fcrc. But it turns out there are cases that
make this impossible.
The surprising, and actually common, case, is that of an fcrc that
will end up containing a full commit. This is common as soon as the
prog_size is big, as small commits are padded to the prog_size at
minimum.
.------------------. \
| metadata | |
| | |
| | +-.
|------------------| | |
| foward CRC ------------.
|------------------| / | |
| commit CRC -----' |
|------------------| |
| padding | |
| | |
|------------------| \ \ |
| metadata | | | |
| | +-. | |
| | | | +-'
|------------------| / | |
| commit CRC --------' |
|------------------| |
| | /
'------------------'
When the commit + crc is all contained in the fcrc, something silly
happens with the math behind crcs. Everything in the commit gets
canceled out:
crc(m) = m(x) x^|P|-1 mod P(x)
m ++ crc(m) = m(x) x^|P|-1 + (m(x) x^|P|-1 mod P(x))
crc(m ++ crc(m)) = (m(x) x^|P|-1 + (m(x) x^|P|-1 mod P(x))) x^|P|-1 mod P(x)
crc(m ++ crc(m)) = (m(x) x^|P|-1 + m(x) x^|P|-1) x^|P|-1 mod P(x)
crc(m ++ crc(m)) = 0 * x^|P|-1 mod P(x)
This is the reason the crc of a message + naive crc is zero. Even with an
initializer/bit-fiddling, the crc of the whole commit ends up as some
constant.
So no manipulation of the commit can change the fcrc...
But even if this did work, or we changed this scheme to use two
different checksums, it would still require calculating the fcrc of
the whole commit to know if we need to tweak the first bit to invalidate
the unlikely-but-problematic case where we happen to match the fcrc. This
would add a large amount of complexity to the commit code.
It's much simpler and cheaper to keep the 1-bit counter in the tag, even
if it adds another moving part to the system.
This fixes most of the remaining bugs (except one with multiple padding
commits + noop erases in test_badblocks), with some other code tweaks.
The biggest change was dropping reliance on end-of-block commits to know
when to stop parsing commits. We can just continue to parse tags and
rely on the crc for catch bad commits, avoiding a backwards-compatiblity
hiccup. So no new commit tag.
Also renamed nprogcrc -> fcrc and commitcrc -> ccrc and made naming in
the code a bit more consistent.
Previously forward-looking CRCs was just two new CRC types, one for
commits with forward-looking CRCs, one without. These both contained the
CRC needed to complete the current commit (note that the commit CRC
must come last!).
[-- 32 --|-- 32 --|-- 32 --|-- 32 --]
with: [ crc3 tag | nprog size | nprog crc | commit crc ]
without: [ crc2 tag | commit crc ]
This meant there had to be several checks for the two possible structure
sizes, messying up the implementation.
[-- 32 --|-- 32 --|-- 32 --|-- 32 --|-- 32 --]
with: [nprogcrc tag| nprog size | nprog crc | commit tag | commit crc ]
without: [ commit tag | commit crc ]
But we already have a mechanism for storing optional metadata! The
different metadata tags! So why not use a separate tage for the
forward-looking CRC, separate from the commit CRC?
I wasn't sure this would actually help that much, there are still
necessary conditions for wether or not a forward-looking CRC is there,
but in the end it simplified the code quite nicely, and resulted in a ~200 byte
code-cost saving.
- General cleanup from integration, including cleaning up some older
commit code
- Partial-prog tests do not make sense when prog_size == block_size
(there can't be partial-progs!)
- Fixed signed-comparison issue in modified filebd
This change is necessary to handle out-of-order writes found by pjsg's
fuzzing work.
The problem is that it is possible for (non-NOR) block devices to write
pages in any order, or to even write random data in the case of a
power-loss. This breaks littlefs's use of the first bit in a page to
indicate the erase-state.
pjsg notes this behavior is documented in the W25Q here:
https://community.cypress.com/docs/DOC-10507
---
The basic idea here is to CRC the next page, and use this "erase-state CRC" to
check if the next page is erased and ready to accept programs.
.------------------. \ commit
| metadata | |
| | +---.
| | | |
|------------------| | |
| erase-state CRC -----. |
|------------------| | | |
| commit CRC ---|-|-'
|------------------| / |
| padding | | padding (doesn't need CRC)
| | |
|------------------| \ | next prog
| erased? | +-'
| | | |
| v | /
| |
| |
'------------------'
This is made a bit annoying since littlefs doesn't actually store the
page (prog_size) in the superblock, since it doesn't need to know the
size for any other operation. We can work around this by storing both
the CRC and size of the next page when necessary.
Another interesting note is that we don't need to any bit tweaking
information, since we read the next page every time we would need to
know how to clobber the erase-state CRC. And since we only read
prog_size, this works really well with our caching, since the caches
must be a multiple of prog_size.
This also brings back the internal lfs_bd_crc function, in which we can
use some optimizations added to lfs_bd_cmp.
Needs some cleanup but the idea is passing most relevant tests.
The previous cycle detection algorithm (a naive check against the largest
possible tail list) is simple and gets the job done, but has the potential to
take a very long time on disks with many blocks. Brent's algorithm, on
the other hand, takes at most 2x the number of blocks in the tail list.
Originally naive cycle detection was chosen over Floyd's algorithm to
avoid the extra complexity of managing two desynced traversals for every
traversal of the tail list, but Brent's algorithm is very well suited for our
use case, requiring only we keep track of an additional mdir pointer on the
stack as we traverse.
- Added support for negative numbers in the leb16 encoding with an
optional 'w' prefix.
- Changed prettyasserts.py rule to .a.c => .c, allowing other .a.c files
in the future.
- Updated .gitignore with missing generated files (tags, .csv).
- Removed suite-namespacing of test symbols, these are no longer needed.
- Changed test define overrides to have higher priority than explicit
defines encoded in test ids. So:
./runners/bench_runner bench_dir_open:0f1g12gg2b8c8dgg4e0 -DREAD_SIZE=16
Behaves as expected.
Otherwise it's not easy to experiment with known failing test cases.
- Fixed issue where the -b flag ignored explicit test/bench ids.
Driven primarily by a want to compare measurements of different runtime
complexities (it's difficult to fit O(n) and O(log n) on the same plot),
this adds the ability to nest subplots in the same .svg which try to align
as much as possible. This turned out to be surprisingly complicated.
As a part of this, adopted matplotlib's relatively recent
constrained_layout, which behaves much more consistently.
Also dropped --legend-left, no one should really be using that.
Christopher Haster