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Technical Notes about PCRE -------------------------- These are very rough technical notes that record potentially useful information about PCRE internals. Historical note 1 ----------------- Many years ago I implemented some regular expression functions to an algorithm suggested by Martin Richards. These were not Unix-like in form, and were quite restricted in what they could do by comparison with Perl. The interesting part about the algorithm was that the amount of space required to hold the compiled form of an expression was known in advance. The code to apply an expression did not operate by backtracking, as the original Henry Spencer code and current Perl code does, but instead checked all possibilities simultaneously by keeping a list of current states and checking all of them as it advanced through the subject string. In the terminology of Jeffrey Friedl's book, it was a "DFA algorithm", though it was not a traditional Finite State Machine (FSM). When the pattern was all used up, all remaining states were possible matches, and the one matching the longest subset of the subject string was chosen. This did not necessarily maximize the individual wild portions of the pattern, as is expected in Unix and Perl-style regular expressions. Historical note 2 ----------------- By contrast, the code originally written by Henry Spencer (which was subsequently heavily modified for Perl) compiles the expression twice: once in a dummy mode in order to find out how much store will be needed, and then for real. (The Perl version probably doesn't do this any more; I'm talking about the original library.) The execution function operates by backtracking and maximizing (or, optionally, minimizing in Perl) the amount of the subject that matches individual wild portions of the pattern. This is an "NFA algorithm" in Friedl's terminology. OK, here's the real stuff ------------------------- For the set of functions that form the "basic" PCRE library (which are unrelated to those mentioned above), I tried at first to invent an algorithm that used an amount of store bounded by a multiple of the number of characters in the pattern, to save on compiling time. However, because of the greater complexity in Perl regular expressions, I couldn't do this. In any case, a first pass through the pattern is helpful for other reasons. Computing the memory requirement: how it was -------------------------------------------- Up to and including release 6.7, PCRE worked by running a very degenerate first pass to calculate a maximum store size, and then a second pass to do the real compile - which might use a bit less than the predicted amount of memory. The idea was that this would turn out faster than the Henry Spencer code because the first pass is degenerate and the second pass can just store stuff straight into the vector, which it knows is big enough. Computing the memory requirement: how it is ------------------------------------------- By the time I was working on a potential 6.8 release, the degenerate first pass had become very complicated and hard to maintain. Indeed one of the early things I did for 6.8 was to fix Yet Another Bug in the memory computation. Then I had a flash of inspiration as to how I could run the real compile function in a "fake" mode that enables it to compute how much memory it would need, while actually only ever using a few hundred bytes of working memory, and without too many tests of the mode that might slow it down. So I re-factored the compiling functions to work this way. This got rid of about 600 lines of source. It should make future maintenance and development easier. As this was such a major change, I never released 6.8, instead upping the number to 7.0 (other quite major changes were also present in the 7.0 release). A side effect of this work was that the previous limit of 200 on the nesting depth of parentheses was removed. However, there is a downside: pcre_compile() runs more slowly than before (30% or more, depending on the pattern) because it is doing a full analysis of the pattern. My hope was that this would not be a big issue, and in the event, nobody has commented on it. Traditional matching function ----------------------------- The "traditional", and original, matching function is called pcre_exec(), and it implements an NFA algorithm, similar to the original Henry Spencer algorithm and the way that Perl works. This is not surprising, since it is intended to be as compatible with Perl as possible. This is the function most users of PCRE will use most of the time. Supplementary matching function ------------------------------- From PCRE 6.0, there is also a supplementary matching function called pcre_dfa_exec(). This implements a DFA matching algorithm that searches simultaneously for all possible matches that start at one point in the subject string. (Going back to my roots: see Historical Note 1 above.) This function intreprets the same compiled pattern data as pcre_exec(); however, not all the facilities are available, and those that are do not always work in quite the same way. See the user documentation for details. The algorithm that is used for pcre_dfa_exec() is not a traditional FSM, because it may have a number of states active at one time. More work would be needed at compile time to produce a traditional FSM where only one state is ever active at once. I believe some other regex matchers work this way. Format of compiled patterns --------------------------- The compiled form of a pattern is a vector of bytes, containing items of variable length. The first byte in an item is an opcode, and the length of the item is either implicit in the opcode or contained in the data bytes that follow it. In many cases below LINK_SIZE data values are specified for offsets within the compiled pattern. The default value for LINK_SIZE is 2, but PCRE can be compiled to use 3-byte or 4-byte values for these offsets (impairing the performance). This is necessary only when patterns whose compiled length is greater than 64K are going to be processed. In this description, we assume the "normal" compilation options. Data values that are counts (e.g. for quantifiers) are always just two bytes long. A list of the opcodes follows: Opcodes with no following data ------------------------------ These items are all just one byte long OP_END end of pattern OP_ANY match any one character other than newline OP_ALLANY match any one character, including newline OP_ANYBYTE match any single byte, even in UTF-8 mode OP_SOD match start of data: \A OP_SOM, start of match (subject + offset): \G OP_SET_SOM, set start of match (\K) OP_CIRC ^ (start of data, or after \n in multiline) OP_NOT_WORD_BOUNDARY \W OP_WORD_BOUNDARY \w OP_NOT_DIGIT \D OP_DIGIT \d OP_NOT_HSPACE \H OP_HSPACE \h OP_NOT_WHITESPACE \S OP_WHITESPACE \s OP_NOT_VSPACE \V OP_VSPACE \v OP_NOT_WORDCHAR \W OP_WORDCHAR \w OP_EODN match end of data or \n at end: \Z OP_EOD match end of data: \z OP_DOLL $ (end of data, or before \n in multiline) OP_EXTUNI match an extended Unicode character OP_ANYNL match any Unicode newline sequence OP_ACCEPT ) These are Perl 5.10's "backtracking OP_COMMIT ) control verbs". If OP_ACCEPT is inside OP_FAIL ) capturing parentheses, it may be preceded OP_PRUNE ) by one or more OP_CLOSE, followed by a 2-byte OP_SKIP ) number, indicating which parentheses must be OP_THEN ) closed. Repeating single characters --------------------------- The common repeats (*, +, ?) when applied to a single character use the following opcodes: OP_STAR OP_MINSTAR OP_POSSTAR OP_PLUS OP_MINPLUS OP_POSPLUS OP_QUERY OP_MINQUERY OP_POSQUERY In ASCII mode, these are two-byte items; in UTF-8 mode, the length is variable. Those with "MIN" in their name are the minimizing versions. Those with "POS" in their names are possessive versions. Each is followed by the character that is to be repeated. Other repeats make use of OP_UPTO OP_MINUPTO OP_POSUPTO OP_EXACT which are followed by a two-byte count (most significant first) and the repeated character. OP_UPTO matches from 0 to the given number. A repeat with a non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an OP_UPTO (or OP_MINUPTO or OPT_POSUPTO). Repeating character types ------------------------- Repeats of things like \d are done exactly as for single characters, except that instead of a character, the opcode for the type is stored in the data byte. The opcodes are: OP_TYPESTAR OP_TYPEMINSTAR OP_TYPEPOSSTAR OP_TYPEPLUS OP_TYPEMINPLUS OP_TYPEPOSPLUS OP_TYPEQUERY OP_TYPEMINQUERY OP_TYPEPOSQUERY OP_TYPEUPTO OP_TYPEMINUPTO OP_TYPEPOSUPTO OP_TYPEEXACT Match by Unicode property ------------------------- OP_PROP and OP_NOTPROP are used for positive and negative matches of a character by testing its Unicode property (the \p and \P escape sequences). Each is followed by two bytes that encode the desired property as a type and a value. Repeats of these items use the OP_TYPESTAR etc. set of opcodes, followed by three bytes: OP_PROP or OP_NOTPROP and then the desired property type and value. Matching literal characters --------------------------- The OP_CHAR opcode is followed by a single character that is to be matched casefully. For caseless matching, OP_CHARNC is used. In UTF-8 mode, the character may be more than one byte long. (Earlier versions of PCRE used multi-character strings, but this was changed to allow some new features to be added.) Character classes ----------------- If there is only one character, OP_CHAR or OP_CHARNC is used for a positive class, and OP_NOT for a negative one (that is, for something like [^a]). However, in UTF-8 mode, the use of OP_NOT applies only to characters with values < 128, because OP_NOT is confined to single bytes. Another set of repeating opcodes (OP_NOTSTAR etc.) are used for a repeated, negated, single-character class. The normal ones (OP_STAR etc.) are used for a repeated positive single-character class. When there's more than one character in a class and all the characters are less than 256, OP_CLASS is used for a positive class, and OP_NCLASS for a negative one. In either case, the opcode is followed by a 32-byte bit map containing a 1 bit for every character that is acceptable. The bits are counted from the least significant end of each byte. The reason for having both OP_CLASS and OP_NCLASS is so that, in UTF-8 mode, subject characters with values greater than 256 can be handled correctly. For OP_CLASS they don't match, whereas for OP_NCLASS they do. For classes containing characters with values > 255, OP_XCLASS is used. It optionally uses a bit map (if any characters lie within it), followed by a list of pairs and single characters. There is a flag character than indicates whether it's a positive or a negative class. Back references --------------- OP_REF is followed by two bytes containing the reference number. Repeating character classes and back references ----------------------------------------------- Single-character classes are handled specially (see above). This section applies to OP_CLASS and OP_REF. In both cases, the repeat information follows the base item. The matching code looks at the following opcode to see if it is one of OP_CRSTAR OP_CRMINSTAR OP_CRPLUS OP_CRMINPLUS OP_CRQUERY OP_CRMINQUERY OP_CRRANGE OP_CRMINRANGE All but the last two are just single-byte items. The others are followed by four bytes of data, comprising the minimum and maximum repeat counts. There are no special possessive opcodes for these repeats; a possessive repeat is compiled into an atomic group. Brackets and alternation ------------------------ A pair of non-capturing (round) brackets is wrapped round each expression at compile time, so alternation always happens in the context of brackets. [Note for North Americans: "bracket" to some English speakers, including myself, can be round, square, curly, or pointy. Hence this usage.] Non-capturing brackets use the opcode OP_BRA. Originally PCRE was limited to 99 capturing brackets and it used a different opcode for each one. From release 3.5, the limit was removed by putting the bracket number into the data for higher-numbered brackets. From release 7.0 all capturing brackets are handled this way, using the single opcode OP_CBRA. A bracket opcode is followed by LINK_SIZE bytes which give the offset to the next alternative OP_ALT or, if there aren't any branches, to the matching OP_KET opcode. Each OP_ALT is followed by LINK_SIZE bytes giving the offset to the next one, or to the OP_KET opcode. For capturing brackets, the bracket number immediately follows the offset, always as a 2-byte item. OP_KET is used for subpatterns that do not repeat indefinitely, while OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or maximally respectively. All three are followed by LINK_SIZE bytes giving (as a positive number) the offset back to the matching bracket opcode. If a subpattern is quantified such that it is permitted to match zero times, it is preceded by one of OP_BRAZERO, OP_BRAMINZERO, or OP_SKIPZERO. These are single-byte opcodes that tell the matcher that skipping the following subpattern entirely is a valid branch. In the case of the first two, not skipping the pattern is also valid (greedy and non-greedy). The third is used when a pattern has the quantifier {0,0}. It cannot be entirely discarded, because it may be called as a subroutine from elsewhere in the regex. A subpattern with an indefinite maximum repetition is replicated in the compiled data its minimum number of times (or once with OP_BRAZERO if the minimum is zero), with the final copy terminating with OP_KETRMIN or OP_KETRMAX as appropriate. A subpattern with a bounded maximum repetition is replicated in a nested fashion up to the maximum number of times, with OP_BRAZERO or OP_BRAMINZERO before each replication after the minimum, so that, for example, (abc){2,5} is compiled as (abc)(abc)((abc)((abc)(abc)?)?)?, except that each bracketed group has the same number. When a repeated subpattern has an unbounded upper limit, it is checked to see whether it could match an empty string. If this is the case, the opcode in the final replication is changed to OP_SBRA or OP_SCBRA. This tells the matcher that it needs to check for matching an empty string when it hits OP_KETRMIN or OP_KETRMAX, and if so, to break the loop. Assertions ---------- Forward assertions are just like other subpatterns, but starting with one of the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion is OP_REVERSE, followed by a two byte count of the number of characters to move back the pointer in the subject string. When operating in UTF-8 mode, the count is a character count rather than a byte count. A separate count is present in each alternative of a lookbehind assertion, allowing them to have different fixed lengths. Once-only (atomic) subpatterns ------------------------------ These are also just like other subpatterns, but they start with the opcode OP_ONCE. The check for matching an empty string in an unbounded repeat is handled entirely at runtime, so there is just this one opcode. Conditional subpatterns ----------------------- These are like other subpatterns, but they start with the opcode OP_COND, or OP_SCOND for one that might match an empty string in an unbounded repeat. If the condition is a back reference, this is stored at the start of the subpattern using the opcode OP_CREF followed by two bytes containing the reference number. OP_NCREF is used instead if the reference was generated by name (so that the runtime code knows to check for duplicate names). If the condition is "in recursion" (coded as "(?(R)"), or "in recursion of group x" (coded as "(?(Rx)"), the group number is stored at the start of the subpattern using the opcode OP_RREF or OP_NRREF (cf OP_NCREF), and a value of zero for "the whole pattern". For a DEFINE condition, just the single byte OP_DEF is used (it has no associated data). Otherwise, a conditional subpattern always starts with one of the assertions. Recursion --------- Recursion either matches the current regex, or some subexpression. The opcode OP_RECURSE is followed by an value which is the offset to the starting bracket from the start of the whole pattern. From release 6.5, OP_RECURSE is automatically wrapped inside OP_ONCE brackets (because otherwise some patterns broke it). OP_RECURSE is also used for "subroutine" calls, even though they are not strictly a recursion. Callout ------- OP_CALLOUT is followed by one byte of data that holds a callout number in the range 0 to 254 for manual callouts, or 255 for an automatic callout. In both cases there follows a two-byte value giving the offset in the pattern to the start of the following item, and another two-byte item giving the length of the next item. Changing options ---------------- If any of the /i, /m, or /s options are changed within a pattern, an OP_OPT opcode is compiled, followed by one byte containing the new settings of these flags. If there are several alternatives, there is an occurrence of OP_OPT at the start of all those following the first options change, to set appropriate options for the start of the alternative. Immediately after the end of the group there is another such item to reset the flags to their previous values. A change of flag right at the very start of the pattern can be handled entirely at compile time, and so does not cause anything to be put into the compiled data. Philip Hazel October 2009
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