What is pikevm?
==============
re1 (http://code.google.com/p/re1/) is "toy regular expression implementation"
by Russel Cox, featuring simplicity and minimal code size unheard of in other
implementations. re2 (http://code.google.com/p/re2/) is "an efficient,
principled regular expression library" by the same author. It is robust,
full-featured, and ... bloated, comparing to re1.
This is implementation of pikevm based on re1.5 which adds features required for
minimalistic real-world use, while sticking to the minimal code size and
memory use.
https://github.com/pfalcon/re1.5
Why?
====
Pikevm guarantees that any input regex will scale O(n) with the size of the
string, thus making it the fastest regex implementation. There is no backtracking
that usually expodes to O(n^k) time and space where k is some constant.
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.
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,
so that the user does not need to waste time taking strlen()
* Highly optimized source code, probably 2x faster than re1.5
* Support for quoted chars in regex. Escapes in brackets.
* Support for ^, $ assertions in regex.
* Support for repetition operator {n} and {n,m} and {n,}.
- Note: cases with 0 are not handled, avoid them, they can easily be replaced.
* Support for Unicode (UTF-8).
* Unlike other engines, the output is byte level offset. (Which is more useful)
* Support for non capture group ?:
* Support for wordend & wordbeg assertions
- Some limitations for word assertions are meta chars like spaces being used
in for expression itself, for example "\< abc" should match " abc" exactly at
that space word boundary but it won't. It's possible to fix this, but it would
require rsplit before word assert, and some dirty logic to check that the character
or class is a space we want to match not assert at. But the code for it was too
dirty and I scrapped it. Syntax for word assertions are like posix C library, not
the pcre "\b" which can be used both in front or back of the word, because there is
no distinction, it makes the implementation potentially even uglier.
* Assert flags like REG_ICASE,REG_NOTEOL,REG_NOTBOL and lookahead inside
negated bracket are implemented here (also shows use case in real world project):
https://github.com/kyx0r/nextvi/blob/master/regex.c
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
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,
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
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.
(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 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.
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.
Currently I removed all dynamic global state from the instructions
fixing any overlow issue at the cost of slight overhead of needing
to look though the nlist states, to prevent their readdition. This
solution is still fast because it affects only nlist + split run on
so most other uses of regex don't suffer big performace penalty.
This does not solve the ambiguity problem with multiple
continuous states though. Finding a fast O(1) solution for continuous
ambiguity is the last thing preventing me to call this regex engine
PERFECT and limitation free. While yet, this is to be invented it
takes a big deal of genius and creativity to make new algorithms
or find improvements in what we already know.
Author and License
==================
licensed under BSD license, just as the original re1.