| 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 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 data |
| ------------------------------------ |
| |
| OP_THEN is followed by a LINK_SIZE offset, which is the distance back to the |
| start of the current branch. |
| |
| OP_MARK is followed by the mark name, preceded by a one-byte 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. For the first |
| two, the name follows immediately; for OP_THEN_ARG, it follows the LINK_SIZE |
| offset value. |
| |
| |
| 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 2010 |