419 lines
18 KiB
Plaintext
419 lines
18 KiB
Plaintext
Technical Notes about PCRE
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--------------------------
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These are very rough technical notes that record potentially useful information
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about PCRE internals.
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Historical note 1
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-----------------
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Many years ago I implemented some regular expression functions to an algorithm
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suggested by Martin Richards. These were not Unix-like in form, and were quite
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restricted in what they could do by comparison with Perl. The interesting part
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about the algorithm was that the amount of space required to hold the compiled
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form of an expression was known in advance. The code to apply an expression did
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not operate by backtracking, as the original Henry Spencer code and current
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Perl code does, but instead checked all possibilities simultaneously by keeping
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a list of current states and checking all of them as it advanced through the
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subject string. In the terminology of Jeffrey Friedl's book, it was a "DFA
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algorithm", though it was not a traditional Finite State Machine (FSM). When
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the pattern was all used up, all remaining states were possible matches, and
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the one matching the longest subset of the subject string was chosen. This did
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not necessarily maximize the individual wild portions of the pattern, as is
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expected in Unix and Perl-style regular expressions.
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Historical note 2
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-----------------
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By contrast, the code originally written by Henry Spencer (which was
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subsequently heavily modified for Perl) compiles the expression twice: once in
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a dummy mode in order to find out how much store will be needed, and then for
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real. (The Perl version probably doesn't do this any more; I'm talking about
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the original library.) The execution function operates by backtracking and
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maximizing (or, optionally, minimizing in Perl) the amount of the subject that
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matches individual wild portions of the pattern. This is an "NFA algorithm" in
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Friedl's terminology.
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OK, here's the real stuff
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-------------------------
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For the set of functions that form the "basic" PCRE library (which are
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unrelated to those mentioned above), I tried at first to invent an algorithm
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that used an amount of store bounded by a multiple of the number of characters
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in the pattern, to save on compiling time. However, because of the greater
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complexity in Perl regular expressions, I couldn't do this. In any case, a
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first pass through the pattern is helpful for other reasons.
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Computing the memory requirement: how it was
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--------------------------------------------
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Up to and including release 6.7, PCRE worked by running a very degenerate first
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pass to calculate a maximum store size, and then a second pass to do the real
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compile - which might use a bit less than the predicted amount of memory. The
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idea was that this would turn out faster than the Henry Spencer code because
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the first pass is degenerate and the second pass can just store stuff straight
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into the vector, which it knows is big enough.
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Computing the memory requirement: how it is
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-------------------------------------------
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By the time I was working on a potential 6.8 release, the degenerate first pass
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had become very complicated and hard to maintain. Indeed one of the early
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things I did for 6.8 was to fix Yet Another Bug in the memory computation. Then
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I had a flash of inspiration as to how I could run the real compile function in
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a "fake" mode that enables it to compute how much memory it would need, while
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actually only ever using a few hundred bytes of working memory, and without too
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many tests of the mode that might slow it down. So I re-factored the compiling
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functions to work this way. This got rid of about 600 lines of source. It
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should make future maintenance and development easier. As this was such a major
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change, I never released 6.8, instead upping the number to 7.0 (other quite
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major changes are also present in the 7.0 release).
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A side effect of this work is that the previous limit of 200 on the nesting
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depth of parentheses was removed. However, there is a downside: pcre_compile()
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runs more slowly than before (30% or more, depending on the pattern) because it
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is doing a full analysis of the pattern. My hope is that this is not a big
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issue.
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Traditional matching function
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-----------------------------
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The "traditional", and original, matching function is called pcre_exec(), and
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it implements an NFA algorithm, similar to the original Henry Spencer algorithm
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and the way that Perl works. Not surprising, since it is intended to be as
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compatible with Perl as possible. This is the function most users of PCRE will
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use most of the time.
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Supplementary matching function
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-------------------------------
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From PCRE 6.0, there is also a supplementary matching function called
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pcre_dfa_exec(). This implements a DFA matching algorithm that searches
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simultaneously for all possible matches that start at one point in the subject
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string. (Going back to my roots: see Historical Note 1 above.) This function
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intreprets the same compiled pattern data as pcre_exec(); however, not all the
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facilities are available, and those that are do not always work in quite the
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same way. See the user documentation for details.
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The algorithm that is used for pcre_dfa_exec() is not a traditional FSM,
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because it may have a number of states active at one time. More work would be
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needed at compile time to produce a traditional FSM where only one state is
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ever active at once. I believe some other regex matchers work this way.
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Format of compiled patterns
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---------------------------
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The compiled form of a pattern is a vector of bytes, containing items of
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variable length. The first byte in an item is an opcode, and the length of the
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item is either implicit in the opcode or contained in the data bytes that
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follow it.
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In many cases below LINK_SIZE data values are specified for offsets within the
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compiled pattern. The default value for LINK_SIZE is 2, but PCRE can be
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compiled to use 3-byte or 4-byte values for these offsets (impairing the
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performance). This is necessary only when patterns whose compiled length is
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greater than 64K are going to be processed. In this description, we assume the
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"normal" compilation options. Data values that are counts (e.g. for
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quantifiers) are always just two bytes long.
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A list of the opcodes follows:
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Opcodes with no following data
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------------------------------
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These items are all just one byte long
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OP_END end of pattern
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OP_ANY match any one character other than newline
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OP_ALLANY match any one character, including newline
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OP_ANYBYTE match any single byte, even in UTF-8 mode
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OP_SOD match start of data: \A
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OP_SOM, start of match (subject + offset): \G
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OP_SET_SOM, set start of match (\K)
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OP_CIRC ^ (start of data, or after \n in multiline)
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OP_NOT_WORD_BOUNDARY \W
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OP_WORD_BOUNDARY \w
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OP_NOT_DIGIT \D
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OP_DIGIT \d
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OP_NOT_HSPACE \H
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OP_HSPACE \h
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OP_NOT_WHITESPACE \S
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OP_WHITESPACE \s
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OP_NOT_VSPACE \V
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OP_VSPACE \v
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OP_NOT_WORDCHAR \W
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OP_WORDCHAR \w
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OP_EODN match end of data or \n at end: \Z
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OP_EOD match end of data: \z
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OP_DOLL $ (end of data, or before \n in multiline)
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OP_EXTUNI match an extended Unicode character
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OP_ANYNL match any Unicode newline sequence
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OP_ACCEPT )
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OP_COMMIT )
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OP_FAIL ) These are Perl 5.10's "backtracking
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OP_PRUNE ) control verbs".
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OP_SKIP )
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OP_THEN )
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Repeating single characters
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---------------------------
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The common repeats (*, +, ?) when applied to a single character use the
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following opcodes:
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OP_STAR
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OP_MINSTAR
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OP_POSSTAR
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OP_PLUS
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OP_MINPLUS
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OP_POSPLUS
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OP_QUERY
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OP_MINQUERY
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OP_POSQUERY
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In ASCII mode, these are two-byte items; in UTF-8 mode, the length is variable.
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Those with "MIN" in their name are the minimizing versions. Those with "POS" in
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their names are possessive versions. Each is followed by the character that is
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to be repeated. Other repeats make use of
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OP_UPTO
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OP_MINUPTO
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OP_POSUPTO
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OP_EXACT
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which are followed by a two-byte count (most significant first) and the
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repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
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non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
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OP_UPTO (or OP_MINUPTO or OPT_POSUPTO).
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Repeating character types
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-------------------------
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Repeats of things like \d are done exactly as for single characters, except
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that instead of a character, the opcode for the type is stored in the data
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byte. The opcodes are:
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OP_TYPESTAR
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OP_TYPEMINSTAR
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OP_TYPEPOSSTAR
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OP_TYPEPLUS
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OP_TYPEMINPLUS
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OP_TYPEPOSPLUS
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OP_TYPEQUERY
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OP_TYPEMINQUERY
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OP_TYPEPOSQUERY
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OP_TYPEUPTO
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OP_TYPEMINUPTO
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OP_TYPEPOSUPTO
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OP_TYPEEXACT
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Match by Unicode property
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-------------------------
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OP_PROP and OP_NOTPROP are used for positive and negative matches of a
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character by testing its Unicode property (the \p and \P escape sequences).
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Each is followed by two bytes that encode the desired property as a type and a
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value.
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Repeats of these items use the OP_TYPESTAR etc. set of opcodes, followed by
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three bytes: OP_PROP or OP_NOTPROP and then the desired property type and
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value.
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Matching literal characters
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---------------------------
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The OP_CHAR opcode is followed by a single character that is to be matched
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casefully. For caseless matching, OP_CHARNC is used. In UTF-8 mode, the
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character may be more than one byte long. (Earlier versions of PCRE used
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multi-character strings, but this was changed to allow some new features to be
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added.)
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Character classes
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-----------------
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If there is only one character, OP_CHAR or OP_CHARNC is used for a positive
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class, and OP_NOT for a negative one (that is, for something like [^a]).
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However, in UTF-8 mode, the use of OP_NOT applies only to characters with
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values < 128, because OP_NOT is confined to single bytes.
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Another set of repeating opcodes (OP_NOTSTAR etc.) are used for a repeated,
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negated, single-character class. The normal ones (OP_STAR etc.) are used for a
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repeated positive single-character class.
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When there's more than one character in a class and all the characters are less
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than 256, OP_CLASS is used for a positive class, and OP_NCLASS for a negative
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one. In either case, the opcode is followed by a 32-byte bit map containing a 1
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bit for every character that is acceptable. The bits are counted from the least
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significant end of each byte.
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The reason for having both OP_CLASS and OP_NCLASS is so that, in UTF-8 mode,
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subject characters with values greater than 256 can be handled correctly. For
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OP_CLASS they don't match, whereas for OP_NCLASS they do.
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For classes containing characters with values > 255, OP_XCLASS is used. It
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optionally uses a bit map (if any characters lie within it), followed by a list
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of pairs and single characters. There is a flag character than indicates
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whether it's a positive or a negative class.
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Back references
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---------------
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OP_REF is followed by two bytes containing the reference number.
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Repeating character classes and back references
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-----------------------------------------------
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Single-character classes are handled specially (see above). This section
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applies to OP_CLASS and OP_REF. In both cases, the repeat information follows
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the base item. The matching code looks at the following opcode to see if it is
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one of
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OP_CRSTAR
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OP_CRMINSTAR
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OP_CRPLUS
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OP_CRMINPLUS
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OP_CRQUERY
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OP_CRMINQUERY
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OP_CRRANGE
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OP_CRMINRANGE
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All but the last two are just single-byte items. The others are followed by
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four bytes of data, comprising the minimum and maximum repeat counts. There are
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no special possessive opcodes for these repeats; a possessive repeat is
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compiled into an atomic group.
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Brackets and alternation
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------------------------
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A pair of non-capturing (round) brackets is wrapped round each expression at
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compile time, so alternation always happens in the context of brackets.
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[Note for North Americans: "bracket" to some English speakers, including
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myself, can be round, square, curly, or pointy. Hence this usage.]
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Non-capturing brackets use the opcode OP_BRA. Originally PCRE was limited to 99
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capturing brackets and it used a different opcode for each one. From release
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3.5, the limit was removed by putting the bracket number into the data for
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higher-numbered brackets. From release 7.0 all capturing brackets are handled
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this way, using the single opcode OP_CBRA.
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A bracket opcode is followed by LINK_SIZE bytes which give the offset to the
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next alternative OP_ALT or, if there aren't any branches, to the matching
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OP_KET opcode. Each OP_ALT is followed by LINK_SIZE bytes giving the offset to
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the next one, or to the OP_KET opcode. For capturing brackets, the bracket
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number immediately follows the offset, always as a 2-byte item.
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OP_KET is used for subpatterns that do not repeat indefinitely, while
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OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
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maximally respectively. All three are followed by LINK_SIZE bytes giving (as a
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positive number) the offset back to the matching bracket opcode.
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If a subpattern is quantified such that it is permitted to match zero times, it
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is preceded by one of OP_BRAZERO, OP_BRAMINZERO, or OP_SKIPZERO. These are
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single-byte opcodes that tell the matcher that skipping the following
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subpattern entirely is a valid branch. In the case of the first two, not
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skipping the pattern is also valid (greedy and non-greedy). The third is used
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when a pattern has the quantifier {0,0}. It cannot be entirely discarded,
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because it may be called as a subroutine from elsewhere in the regex.
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A subpattern with an indefinite maximum repetition is replicated in the
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compiled data its minimum number of times (or once with OP_BRAZERO if the
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minimum is zero), with the final copy terminating with OP_KETRMIN or OP_KETRMAX
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as appropriate.
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A subpattern with a bounded maximum repetition is replicated in a nested
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fashion up to the maximum number of times, with OP_BRAZERO or OP_BRAMINZERO
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before each replication after the minimum, so that, for example, (abc){2,5} is
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compiled as (abc)(abc)((abc)((abc)(abc)?)?)?, except that each bracketed group
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has the same number.
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When a repeated subpattern has an unbounded upper limit, it is checked to see
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whether it could match an empty string. If this is the case, the opcode in the
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final replication is changed to OP_SBRA or OP_SCBRA. This tells the matcher
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that it needs to check for matching an empty string when it hits OP_KETRMIN or
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OP_KETRMAX, and if so, to break the loop.
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Assertions
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----------
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Forward assertions are just like other subpatterns, but starting with one of
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the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes
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OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion
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is OP_REVERSE, followed by a two byte count of the number of characters to move
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back the pointer in the subject string. When operating in UTF-8 mode, the count
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is a character count rather than a byte count. A separate count is present in
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each alternative of a lookbehind assertion, allowing them to have different
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fixed lengths.
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Once-only (atomic) subpatterns
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------------------------------
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These are also just like other subpatterns, but they start with the opcode
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OP_ONCE. The check for matching an empty string in an unbounded repeat is
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handled entirely at runtime, so there is just this one opcode.
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Conditional subpatterns
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-----------------------
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These are like other subpatterns, but they start with the opcode OP_COND, or
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OP_SCOND for one that might match an empty string in an unbounded repeat. If
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the condition is a back reference, this is stored at the start of the
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subpattern using the opcode OP_CREF followed by two bytes containing the
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reference number. If the condition is "in recursion" (coded as "(?(R)"), or "in
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recursion of group x" (coded as "(?(Rx)"), the group number is stored at the
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start of the subpattern using the opcode OP_RREF, and a value of zero for "the
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whole pattern". For a DEFINE condition, just the single byte OP_DEF is used (it
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has no associated data). Otherwise, a conditional subpattern always starts with
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one of the assertions.
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Recursion
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---------
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Recursion either matches the current regex, or some subexpression. The opcode
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OP_RECURSE is followed by an value which is the offset to the starting bracket
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from the start of the whole pattern. From release 6.5, OP_RECURSE is
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automatically wrapped inside OP_ONCE brackets (because otherwise some patterns
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broke it). OP_RECURSE is also used for "subroutine" calls, even though they
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are not strictly a recursion.
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Callout
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-------
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OP_CALLOUT is followed by one byte of data that holds a callout number in the
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range 0 to 254 for manual callouts, or 255 for an automatic callout. In both
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cases there follows a two-byte value giving the offset in the pattern to the
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start of the following item, and another two-byte item giving the length of the
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next item.
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Changing options
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----------------
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If any of the /i, /m, or /s options are changed within a pattern, an OP_OPT
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opcode is compiled, followed by one byte containing the new settings of these
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flags. If there are several alternatives, there is an occurrence of OP_OPT at
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the start of all those following the first options change, to set appropriate
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options for the start of the alternative. Immediately after the end of the
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group there is another such item to reset the flags to their previous values. A
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change of flag right at the very start of the pattern can be handled entirely
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at compile time, and so does not cause anything to be put into the compiled
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data.
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Philip Hazel
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April 2008
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