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Technical Notes about PCRE -------------------------- These are very rough technical notes that record potentially useful information about PCRE internals. For information about testing PCRE, see the pcretest documentation and the comment at the head of the RunTest file. 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. Support for 16-bit and 32-bit data strings ------------------------------------------- From release 8.30, PCRE supports 16-bit as well as 8-bit data strings; and from release 8.32, PCRE supports 32-bit data strings. The library can be compiled in any combination of 8-bit, 16-bit or 32-bit modes, creating different libraries. In the description that follows, the word "short" is used for a 16-bit data quantity, and the word "unit" is used for a quantity that is a byte in 8-bit mode, a short in 16-bit mode and a 32-bit unsigned integer in 32-bit mode. However, so as not to over-complicate the text, the names of PCRE functions are given in 8-bit form only. 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 refactored 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. From release 8.20, if PCRE is compiled with just-in-time (JIT) support, and studying a compiled pattern with JIT is successful, the JIT code is run instead of the normal pcre_exec() code, but the result is the same. 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. Changeable options ------------------ The /i, /m, or /s options (PCRE_CASELESS, PCRE_MULTILINE, PCRE_DOTALL) may change in the middle of patterns. From PCRE 8.13, their processing is handled entirely at compile time by generating different opcodes for the different settings. The runtime functions do not need to keep track of an options state any more. Format of compiled patterns --------------------------- The compiled form of a pattern is a vector of units (bytes in 8-bit mode, or shorts in 16-bit mode, 32-bit unsigned integers in 32-bit mode), containing items of variable length. The first unit in an item contains an opcode, and the length of the item is either implicit in the opcode or contained in the data that follows it. In many cases listed below, LINK_SIZE data values are specified for offsets within the compiled pattern. LINK_SIZE always specifies a number of bytes. The default value for LINK_SIZE is 2, but PCRE can be compiled to use 3-byte or 4-byte values for these offsets, although this impairs the performance. (3-byte LINK_SIZE values are available only in 8-bit mode.) Specifing a LINK_SIZE larger than 2 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 (one short in 16-bit mode). Opcodes with no following data ------------------------------ These items are all just one unit 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) OP_CIRCM ^ multiline mode (start of data or after newline) 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 final newline) OP_DOLLM $ multiline mode (end of data or before newline) OP_EXTUNI match an extended Unicode character OP_ANYNL match any Unicode newline sequence OP_ACCEPT ) These are Perl 5.10's "backtracking control OP_COMMIT ) verbs". If OP_ACCEPT is inside capturing OP_FAIL ) parentheses, it may be preceded by one or more OP_PRUNE ) OP_CLOSE, followed by a 2-byte number, OP_SKIP ) indicating which parentheses must be closed. Backtracking control verbs with (optional) data ----------------------------------------------- (*THEN) without an argument generates the opcode OP_THEN and no following data. OP_MARK is followed by the mark name, preceded by a one-unit length, and followed by a binary zero. For (*PRUNE), (*SKIP), and (*THEN) with arguments, the opcodes OP_PRUNE_ARG, OP_SKIP_ARG, and OP_THEN_ARG are used, with the name following in the same format. Matching literal characters --------------------------- The OP_CHAR opcode is followed by a single character that is to be matched casefully. For caseless matching, OP_CHARI is used. In UTF-8 or UTF-16 modes, the character may be more than one unit long. In UTF-32 mode, characters are always exactly one unit long. Repeating single characters --------------------------- The common repeats (*, +, ?), when applied to a single character, use the following opcodes, which come in caseful and caseless versions: Caseful Caseless OP_STAR OP_STARI OP_MINSTAR OP_MINSTARI OP_POSSTAR OP_POSSTARI OP_PLUS OP_PLUSI OP_MINPLUS OP_MINPLUSI OP_POSPLUS OP_POSPLUSI OP_QUERY OP_QUERYI OP_MINQUERY OP_MINQUERYI OP_POSQUERY OP_POSQUERYI Each opcode is followed by the character that is to be repeated. In ASCII mode, these are two-unit items; in UTF-8 or UTF-16 modes, the length is variable; in UTF-32 mode these are one-unit items. Those with "MIN" in their names are the minimizing versions. Those with "POS" in their names are possessive versions. Other repeats make use of these opcodes: Caseful Caseless OP_UPTO OP_UPTOI OP_MINUPTO OP_MINUPTOI OP_POSUPTO OP_POSUPTOI OP_EXACT OP_EXACTI Each of these is followed by a two-byte (one short) count (most significant byte first in 8-bit mode) and then 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 unit. 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 units 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 units: OP_PROP or OP_NOTPROP, and then the desired property type and value. Character classes ----------------- If there is only one character in the class, OP_CHAR or OP_CHARI is used for a positive class, and OP_NOT or OP_NOTI for a negative one (that is, for something like [^a]). Another set of 13 repeating opcodes (called OP_NOTSTAR etc.) are used for repeated, negated, single-character classes. The normal single-character opcodes (OP_STAR, etc.) are used for repeated positive single-character classes. When there is 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 (16-short) bit map containing a 1 bit for every character that is acceptable. The bits are counted from the least significant end of each unit. In caseless mode, bits for both cases are set. The reason for having both OP_CLASS and OP_NCLASS is so that, in UTF-8/16/32 mode, subject characters with values greater than 255 can be handled correctly. For OP_CLASS they do not match, whereas for OP_NCLASS they do. For classes containing characters with values greater than 255, OP_XCLASS is used. It optionally uses a bit map (if any characters lie within it), followed by a list of pairs (for a range) and single characters. In caseless mode, both cases are explicitly listed. There is a flag character than indicates whether it is a positive or a negative class. Back references --------------- OP_REF (caseful) or OP_REFI (caseless) is followed by two bytes (one short) 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[I]. 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-unit items. The others are followed by four bytes (two shorts) 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 rather than "parentheses".] 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 (one short) item. OP_KET is used for subpatterns that do not repeat indefinitely, and OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or maximally respectively (see below for possessive repetitions). 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-unit 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. Possessive brackets ------------------- When a repeated group (capturing or non-capturing) is marked as possessive by the "+" notation, e.g. (abc)++, different opcodes are used. Their names all have POS on the end, e.g. OP_BRAPOS instead of OP_BRA and OP_SCPBRPOS instead of OP_SCBRA. The end of such a group is marked by OP_KETRPOS. If the minimum repetition is zero, the group is preceded by OP_BRAPOSZERO. 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 (one short) count of the number of characters to move back the pointer in the subject string. In ASCII mode, the count is a number of units, but in UTF-8/16 mode each character may occupy more than one unit; in UTF-32 mode each character occupies exactly one unit. 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 (one short) 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 unit 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 unit 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 (one short) value giving the offset in the pattern to the start of the following item, and another two-byte (one short) item giving the length of the next item. Philip Hazel February 2012

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