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pike: improve size calculations

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Kyryl Melekhin
2022-02-17 18:20:06 +00:00
parent 281820d7c9
commit eb01f29134
2 changed files with 131 additions and 144 deletions
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@@ -23,7 +23,7 @@ Features
* UnLike re1.5, here is only pikevm, one file easy to use.
* Unlike re1.5, regexes is compiled to type sized code rather than bytecode,
eliviating the problem of byte overflow in splits/jmps on large regexes.
eliviating the problem of byte overflow in splits/jmps on large regexes.
Currently the type used is int, and every atom in compiled code is aligned
to that.
* Matcher does not take size of string as param, it checks for '\0' instead,
@@ -54,121 +54,103 @@ NOTES
The problem described in this paper has been fixed. Ambiguous matching is correct.
HISTORY:
https://re2c.org/2019_borsotti_trofimovich_efficient_posix_submatch_extraction_on_nfa.pdf
"Cox, 2009 (incorrect). Cox came up with the idea of backward POSIX matching,
which is based on the observation that reversing the longest-match rule
simplifies the handling of iteration subexpressions: instead of maximizing
submatch from the first to the last iteration, one needs to maximize the
iterations in reverse order. This means that the disambiguation is always
based on the most recent iteration, removing the need to remember all previous
iterations (except for the backwards-first, i.e. the last one, which contains
submatch result). The algorithm tracks two pairs of offsets per each submatch
group: the active pair (used for disambiguation) and the result pair. It gives
incorrect results under two conditions: (1) ambiguous matches have equal
offsets on some iteration, and (2) disambiguation happens too late, when
the active offsets have already been updated and the difference between
ambiguous matches is erased. We found that such situations may occur for two
reasons. First, the ε-closure algorithm may compare ambiguous paths after
"Cox, 2009 (incorrect). Cox came up with the idea of backward POSIX matching,
which is based on the observation that reversing the longest-match rule
simplifies the handling of iteration subexpressions: instead of maximizing
submatch from the first to the last iteration, one needs to maximize the
iterations in reverse order. This means that the disambiguation is always
based on the most recent iteration, removing the need to remember all previous
iterations (except for the backwards-first, i.e. the last one, which contains
submatch result). The algorithm tracks two pairs of offsets per each submatch
group: the active pair (used for disambiguation) and the result pair. It gives
incorrect results under two conditions: (1) ambiguous matches have equal
offsets on some iteration, and (2) disambiguation happens too late, when
the active offsets have already been updated and the difference between
ambiguous matches is erased. We found that such situations may occur for two
reasons. First, the ε-closure algorithm may compare ambiguous paths after
their join point, when both paths have a common suffix with tagged
transitions. This is the case with the Cox prototype implementation; for
example, it gives incorrect results for (aa|a)* and string aaaaa. Most of such
failures can be repaired by exploring states in topological order, but a
topological order does not exist in the presence of ε-loops. The second reason
is bounded repetition: ambiguous paths may not have an intermediate join point
at all. For example, in the case of (aaaa|aaa|a){3,4} and string aaaaaaaaaa we
have matches (aaaa)(aaaa)(a)(a) and (aaaa)(aaa)(aaa) with a different number
of iterations. Assuming that the bounded repetition is unrolled by chaining
three sub-automata for (aaaa|aaa|a) and an optional fourth one, by the time
ambiguous paths meet both have active offsets (0,4). Despite the flaw, Cox
algorithm is interesting: if somehow the delayed comparison problem was fixed,
transitions. This is the case with the Cox prototype implementation; for
example, it gives incorrect results for (aa|a)* and string aaaaa. Most of such
failures can be repaired by exploring states in topological order, but a
topological order does not exist in the presence of ε-loops. The second reason
is bounded repetition: ambiguous paths may not have an intermediate join point
at all. For example, in the case of (aaaa|aaa|a){3,4} and string aaaaaaaaaa we
have matches (aaaa)(aaaa)(a)(a) and (aaaa)(aaa)(aaa) with a different number
of iterations. Assuming that the bounded repetition is unrolled by chaining
three sub-automata for (aaaa|aaa|a) and an optional fourth one, by the time
ambiguous paths meet both have active offsets (0,4). Despite the flaw, Cox
algorithm is interesting: if somehow the delayed comparison problem was fixed,
it would work. The algorithm requires O(mt) memory and O(nm^2t) time
(assuming a worst-case optimal closure algorithm), where n is the
length of input, m it the size of RE and t is the number of submatch groups
length of input, m it the size of RE and t is the number of submatch groups
and subexpressions that contain them."
Research has shown that it is possible to disambiguate NFA in polynomial time
but it brings serious performance issues on non ambiguous inputs.
See the branch "disambiguate_paths" on this repo shows what is being
done to solve it and the potential performance costs. In short it
requires tracking the parent of every state added on nlist from clist.
If the state from nlist matches the consumer, the alternative clist
state related to that nlist state gets discarded and the nsub ref
can be decremented (freed). The reason why this problem does not
exist for non ambiguous regexes is because the alternative clist
state will never match due to the next state having a different
consumer. There is no need for any extra handling it gets freed normally.
I decided to not apply this solution here because I think
most use cases for regex are not ambiguious like say regex:
"a{10000}". If you try matching 10000 'a' characters in a row
like that you will have a problem where the stack usage will
jump up to 10000*(subsize) but it will never exceed the size
of regex though, but the number of NFA states will also increase
by the same amount, so at the charater 9999 you will find
9999 redundant nlist states, that will degrade performance
linearly, however it will be very slow compared to uplimited
regex like a+. The cost of this solution is somewhere around
2% general performance decrease (broadly), but a magnitude of
complexity decrease for ambiguous cases, for example
matching 64 characters went down from 30 to 9 microseconds.
Another solution to this problem can be to determine the
ambiguous paths at compile time and flag the inner
states as ambiguous ahead of time, still this can't avoid
having a loop though the alt states as their positioning
in clist can't be precomputed due to the dynamic changes.
but it brings serious performance issues on non ambiguous inputs. See the
branch "disambiguate_paths" on this repo shows what is being done to solve it
and the potential performance costs. In short it requires tracking the parent
of every state added on nlist from clist. If the state from nlist matches
the consumer, the alternative clist state related to that nlist state gets
discarded and the nsub ref can be decremented (freed). The reason why this
problem does not exist for non ambiguous regexes is because the alternative
clist state will never match due to the next state having a different consumer
. There is no need for any extra handling it gets freed normally. I decided
to not apply this solution here because I think most use cases for regex are
not ambiguious like say regex: "a{10000}". If you try matching 10000 'a'
characters in a row like that you will have a problem where the stack usage
will jump up to 10000*(subsize) but it will never exceed the size of regex
though, but the number of NFA states will also increase by the same amount,
so at the charater 9999 you will find 9999 redundant nlist states, that will
degrade performance linearly, however it will be very slow compared to
uplimited regex like a+. The cost of this solution is somewhere around 2%
general performance decrease (broadly), but a magnitude of complexity
decrease for ambiguous cases, for example matching 64 characters went down
from 30 to 9 microseconds. Another solution to this problem can be to
determine the ambiguous paths at compile time and flag the inner states as
ambiguous ahead of time, still this can't avoid having a loop though the alt
states as their positioning in clist can't be precomputed due to the dynamic
changes.
(Comment about O(mt) memory complexity)
This worst case scenario can only happen on ambiguous input, that is why nsubs
size is set to half a MB just in case, this can match 5000000
ambiguous consumers (char, class, any) assuming t is 1. In practice there
is almost never a situation where someone wants to search using regex this
large. Use of alloca() instead of VLA, could remove this limit, I just wish
it was standardized. If you ever wondered about a situation where alloca
is a must, this is the algorithm.
Most of the time memory usage is very low and the space
complexity for non ambigious regex is O(nt) where n is
the number of currently considering alternate paths
in the regex and t is the number of submatch groups.
This worst case scenario can only happen on ambiguous input. Ambiguous
consumers (char, class, any) assuming t is 1. In practice there is almost
never a situation where someone wants to search using regex this large. Most
of the time memory usage is very low and the space complexity for non
ambigious regex is O(nt) where n is the number of currently considering
alternate paths in the regex and t is the number of submatch groups.
This pikevm features an improved submatch extraction
algorithm based on Russ Cox's original design.
I - Kyryl Melekhin have found a way to optimize the tracking
properly of 1st number in the submatch pair. Based on simple
observation of how the NFA is constructed I noticed that
there is no way for addthread1() to ever reach inner SAVE
instructions in the regex, so that leaves tracking 2nd pairs by
addthread1() irrelevant to the final results (except the need to
initialize the sub after allocation). This improved the overall
performance by 25% which is massive considering that at the
time there was nothing else left to can be done to make it faster.
This pikevm implementation features an improved submatch extraction algorithm
based on Russ Cox's original design. I - Kyryl Melekhin have found a way to
optimize the tracking properly of 1st number in the submatch pair. Based on
simple observation of how the NFA is constructed I noticed that there is no
way for addthread1() to ever reach inner SAVE instructions in the regex, so
that leaves tracking 2nd pairs by addthread1() irrelevant to the final
results (except the need to initialize the sub after allocation). This
improved the overall performance by 25% which is massive considering that at
the time there was nothing else left to can be done to make it faster.
What are on##list macros?
Redundant state inside nlist can happen in couple of
ways, and has to do with the (closure) a* (star) operations and
also +. Due to the automata machine design split happens
to be above the next consumed instruction and if that
state gets added onto the list we may segfault or give
wrong submatch result. Rsplit does not have this problem
because it is generated below the consumer instruction, but
it can still add redundant states. Overall this is extremely
difficult to understand or explain, but this is just something
we have to check for. We checked for this using extra int inside
the split instructions, so this left some global state inside the
machine insts. Most of the time we just added to the next
gen number and kept incrementing it forever. This leaves a small
chance of overflowing the int and getting a run on a false state
left from previous use of the regex. Though if overflow never
happens there is no chance of getting a false state. Overflows
like this pose a high security threat, if the hacker knows
how many cycles he needs to overflow the gen variable and get
inconsistent result. It is possible to reset the marks if we
near the overflow, but as you may guess that does not come
for free.
Redundant state inside nlist can happen in couple of ways, and has to do with
the (closure) a* (star) operations and also +. Due to the automata machine
design split happens to be above the next consumed instruction and if that
state gets added onto the list we may segfault or give wrong submatch result.
Rsplit does not have this problem because it is generated below the consumer
instruction, but it can still add redundant states. Overall this is extremely
difficult to understand or explain, but this is just something we have to
check for. We checked for this using extra int inside the split instructions,
so this left some global state inside the machine insts. Most of the time we
just added to the next gen number and kept incrementing it forever. This
leaves a small chance of overflowing the int and getting a run on a false
state left from previous use of the regex. Though if overflow never happens
there is no chance of getting a false state. Overflows like this pose a high
security threat, if the hacker knows how many cycles he needs to overflow the
gen variable and get inconsistent result. It is possible to reset the marks
if we near the overflow, but as you may guess that does not come for free.
Currently I removed all dynamic global state from the instructions
fixing any overlow issue utilizing a sparse set datastructure trick
which abuses the uninitialized varibles. This allows the redundant
states to be excluded in O(1) operation. That said, don't run
valgrind on pikevm as it will go crazy, or find a way to surpress
errors from pikevm.
Currently I removed all dynamic global state from the instructions fixing any
overlow issue utilizing a sparse set datastructure trick which abuses the
uninitialized varibles. This allows the redundant states to be excluded in
O(1) operation. That said, don't run valgrind on pikevm as it will go crazy, or
find a way to surpress errors from pikevm.
Further reading
===============