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  1Technical Notes about PCRE
  2--------------------------
  3
  4These are very rough technical notes that record potentially useful information 
  5about PCRE internals.
  6
  7Historical note 1
  8-----------------
  9
 10Many years ago I implemented some regular expression functions to an algorithm
 11suggested by Martin Richards. These were not Unix-like in form, and were quite
 12restricted in what they could do by comparison with Perl. The interesting part
 13about the algorithm was that the amount of space required to hold the compiled
 14form of an expression was known in advance. The code to apply an expression did
 15not operate by backtracking, as the original Henry Spencer code and current
 16Perl code does, but instead checked all possibilities simultaneously by keeping
 17a list of current states and checking all of them as it advanced through the
 18subject string. In the terminology of Jeffrey Friedl's book, it was a "DFA
 19algorithm", though it was not a traditional Finite State Machine (FSM). When
 20the pattern was all used up, all remaining states were possible matches, and
 21the one matching the longest subset of the subject string was chosen. This did
 22not necessarily maximize the individual wild portions of the pattern, as is
 23expected in Unix and Perl-style regular expressions.
 24
 25Historical note 2
 26-----------------
 27
 28By contrast, the code originally written by Henry Spencer (which was
 29subsequently heavily modified for Perl) compiles the expression twice: once in
 30a dummy mode in order to find out how much store will be needed, and then for
 31real. (The Perl version probably doesn't do this any more; I'm talking about
 32the original library.) The execution function operates by backtracking and
 33maximizing (or, optionally, minimizing in Perl) the amount of the subject that
 34matches individual wild portions of the pattern. This is an "NFA algorithm" in
 35Friedl's terminology.
 36
 37OK, here's the real stuff
 38-------------------------
 39
 40For the set of functions that form the "basic" PCRE library (which are
 41unrelated to those mentioned above), I tried at first to invent an algorithm
 42that used an amount of store bounded by a multiple of the number of characters
 43in the pattern, to save on compiling time. However, because of the greater
 44complexity in Perl regular expressions, I couldn't do this. In any case, a
 45first pass through the pattern is helpful for other reasons. 
 46
 47Computing the memory requirement: how it was
 48--------------------------------------------
 49
 50Up to and including release 6.7, PCRE worked by running a very degenerate first
 51pass to calculate a maximum store size, and then a second pass to do the real
 52compile - which might use a bit less than the predicted amount of memory. The
 53idea was that this would turn out faster than the Henry Spencer code because
 54the first pass is degenerate and the second pass can just store stuff straight
 55into the vector, which it knows is big enough.
 56
 57Computing the memory requirement: how it is
 58-------------------------------------------
 59
 60By the time I was working on a potential 6.8 release, the degenerate first pass
 61had become very complicated and hard to maintain. Indeed one of the early
 62things I did for 6.8 was to fix Yet Another Bug in the memory computation. Then
 63I had a flash of inspiration as to how I could run the real compile function in
 64a "fake" mode that enables it to compute how much memory it would need, while
 65actually only ever using a few hundred bytes of working memory, and without too
 66many tests of the mode that might slow it down. So I re-factored the compiling
 67functions to work this way. This got rid of about 600 lines of source. It
 68should make future maintenance and development easier. As this was such a major 
 69change, I never released 6.8, instead upping the number to 7.0 (other quite 
 70major changes are also present in the 7.0 release).
 71
 72A side effect of this work is that the previous limit of 200 on the nesting
 73depth of parentheses was removed. However, there is a downside: pcre_compile()
 74runs more slowly than before (30% or more, depending on the pattern) because it
 75is doing a full analysis of the pattern. My hope is that this is not a big
 76issue.
 77
 78Traditional matching function
 79-----------------------------
 80
 81The "traditional", and original, matching function is called pcre_exec(), and 
 82it implements an NFA algorithm, similar to the original Henry Spencer algorithm 
 83and the way that Perl works. Not surprising, since it is intended to be as 
 84compatible with Perl as possible. This is the function most users of PCRE will 
 85use most of the time.
 86
 87Supplementary matching function
 88-------------------------------
 89
 90From PCRE 6.0, there is also a supplementary matching function called 
 91pcre_dfa_exec(). This implements a DFA matching algorithm that searches 
 92simultaneously for all possible matches that start at one point in the subject 
 93string. (Going back to my roots: see Historical Note 1 above.) This function 
 94intreprets the same compiled pattern data as pcre_exec(); however, not all the 
 95facilities are available, and those that are do not always work in quite the 
 96same way. See the user documentation for details.
 97
 98The algorithm that is used for pcre_dfa_exec() is not a traditional FSM, 
 99because it may have a number of states active at one time. More work would be 
100needed at compile time to produce a traditional FSM where only one state is 
101ever active at once. I believe some other regex matchers work this way.
102
103
104Format of compiled patterns
105---------------------------
106
107The compiled form of a pattern is a vector of bytes, containing items of
108variable length. The first byte in an item is an opcode, and the length of the
109item is either implicit in the opcode or contained in the data bytes that
110follow it. 
111
112In many cases below LINK_SIZE data values are specified for offsets within the 
113compiled pattern. The default value for LINK_SIZE is 2, but PCRE can be
114compiled to use 3-byte or 4-byte values for these offsets (impairing the
115performance). This is necessary only when patterns whose compiled length is
116greater than 64K are going to be processed. In this description, we assume the
117"normal" compilation options. Data values that are counts (e.g. for
118quantifiers) are always just two bytes long.
119
120A list of the opcodes follows:
121
122Opcodes with no following data
123------------------------------
124
125These items are all just one byte long
126
127  OP_END                 end of pattern
128  OP_ANY                 match any one character other than newline
129  OP_ALLANY              match any one character, including newline
130  OP_ANYBYTE             match any single byte, even in UTF-8 mode
131  OP_SOD                 match start of data: \A
132  OP_SOM,                start of match (subject + offset): \G
133  OP_SET_SOM,            set start of match (\K) 
134  OP_CIRC                ^ (start of data, or after \n in multiline)
135  OP_NOT_WORD_BOUNDARY   \W
136  OP_WORD_BOUNDARY       \w
137  OP_NOT_DIGIT           \D
138  OP_DIGIT               \d
139  OP_NOT_HSPACE          \H
140  OP_HSPACE              \h  
141  OP_NOT_WHITESPACE      \S
142  OP_WHITESPACE          \s
143  OP_NOT_VSPACE          \V
144  OP_VSPACE              \v  
145  OP_NOT_WORDCHAR        \W
146  OP_WORDCHAR            \w
147  OP_EODN                match end of data or \n at end: \Z
148  OP_EOD                 match end of data: \z
149  OP_DOLL                $ (end of data, or before \n in multiline)
150  OP_EXTUNI              match an extended Unicode character 
151  OP_ANYNL               match any Unicode newline sequence 
152  
153  OP_ACCEPT              )
154  OP_COMMIT              ) 
155  OP_FAIL                ) These are Perl 5.10's "backtracking     
156  OP_PRUNE               ) control verbs".                         
157  OP_SKIP                )
158  OP_THEN                )
159  
160
161Repeating single characters
162---------------------------
163
164The common repeats (*, +, ?) when applied to a single character use the
165following opcodes:
166
167  OP_STAR
168  OP_MINSTAR
169  OP_POSSTAR 
170  OP_PLUS
171  OP_MINPLUS
172  OP_POSPLUS 
173  OP_QUERY
174  OP_MINQUERY
175  OP_POSQUERY 
176
177In ASCII mode, these are two-byte items; in UTF-8 mode, the length is variable.
178Those with "MIN" in their name are the minimizing versions. Those with "POS" in 
179their names are possessive versions. Each is followed by the character that is
180to be repeated. Other repeats make use of
181
182  OP_UPTO
183  OP_MINUPTO
184  OP_POSUPTO 
185  OP_EXACT
186
187which are followed by a two-byte count (most significant first) and the
188repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
189non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
190OP_UPTO (or OP_MINUPTO or OPT_POSUPTO).
191
192
193Repeating character types
194-------------------------
195
196Repeats of things like \d are done exactly as for single characters, except
197that instead of a character, the opcode for the type is stored in the data
198byte. The opcodes are:
199
200  OP_TYPESTAR
201  OP_TYPEMINSTAR
202  OP_TYPEPOSSTAR 
203  OP_TYPEPLUS
204  OP_TYPEMINPLUS
205  OP_TYPEPOSPLUS 
206  OP_TYPEQUERY
207  OP_TYPEMINQUERY
208  OP_TYPEPOSQUERY 
209  OP_TYPEUPTO
210  OP_TYPEMINUPTO
211  OP_TYPEPOSUPTO 
212  OP_TYPEEXACT
213
214
215Match by Unicode property
216-------------------------
217
218OP_PROP and OP_NOTPROP are used for positive and negative matches of a 
219character by testing its Unicode property (the \p and \P escape sequences).
220Each is followed by two bytes that encode the desired property as a type and a 
221value.
222
223Repeats of these items use the OP_TYPESTAR etc. set of opcodes, followed by 
224three bytes: OP_PROP or OP_NOTPROP and then the desired property type and 
225value.
226
227
228Matching literal characters
229---------------------------
230
231The OP_CHAR opcode is followed by a single character that is to be matched 
232casefully. For caseless matching, OP_CHARNC is used. In UTF-8 mode, the 
233character may be more than one byte long. (Earlier versions of PCRE used 
234multi-character strings, but this was changed to allow some new features to be 
235added.)
236
237
238Character classes
239-----------------
240
241If there is only one character, OP_CHAR or OP_CHARNC is used for a positive
242class, and OP_NOT for a negative one (that is, for something like [^a]).
243However, in UTF-8 mode, the use of OP_NOT applies only to characters with
244values < 128, because OP_NOT is confined to single bytes.
245
246Another set of repeating opcodes (OP_NOTSTAR etc.) are used for a repeated,
247negated, single-character class. The normal ones (OP_STAR etc.) are used for a
248repeated positive single-character class.
249
250When there's more than one character in a class and all the characters are less
251than 256, OP_CLASS is used for a positive class, and OP_NCLASS for a negative
252one. In either case, the opcode is followed by a 32-byte bit map containing a 1
253bit for every character that is acceptable. The bits are counted from the least
254significant end of each byte.
255
256The reason for having both OP_CLASS and OP_NCLASS is so that, in UTF-8 mode,
257subject characters with values greater than 256 can be handled correctly. For
258OP_CLASS they don't match, whereas for OP_NCLASS they do.
259
260For classes containing characters with values > 255, OP_XCLASS is used. It
261optionally uses a bit map (if any characters lie within it), followed by a list
262of pairs and single characters. There is a flag character than indicates
263whether it's a positive or a negative class.
264
265
266Back references
267---------------
268
269OP_REF is followed by two bytes containing the reference number.
270
271
272Repeating character classes and back references
273-----------------------------------------------
274
275Single-character classes are handled specially (see above). This section
276applies to OP_CLASS and OP_REF. In both cases, the repeat information follows
277the base item. The matching code looks at the following opcode to see if it is
278one of
279
280  OP_CRSTAR
281  OP_CRMINSTAR
282  OP_CRPLUS
283  OP_CRMINPLUS
284  OP_CRQUERY
285  OP_CRMINQUERY
286  OP_CRRANGE
287  OP_CRMINRANGE
288
289All but the last two are just single-byte items. The others are followed by
290four bytes of data, comprising the minimum and maximum repeat counts. There are 
291no special possessive opcodes for these repeats; a possessive repeat is 
292compiled into an atomic group.
293
294
295Brackets and alternation
296------------------------
297
298A pair of non-capturing (round) brackets is wrapped round each expression at
299compile time, so alternation always happens in the context of brackets.
300
301[Note for North Americans: "bracket" to some English speakers, including
302myself, can be round, square, curly, or pointy. Hence this usage.]
303
304Non-capturing brackets use the opcode OP_BRA. Originally PCRE was limited to 99
305capturing brackets and it used a different opcode for each one. From release
3063.5, the limit was removed by putting the bracket number into the data for
307higher-numbered brackets. From release 7.0 all capturing brackets are handled
308this way, using the single opcode OP_CBRA.
309
310A bracket opcode is followed by LINK_SIZE bytes which give the offset to the
311next alternative OP_ALT or, if there aren't any branches, to the matching
312OP_KET opcode. Each OP_ALT is followed by LINK_SIZE bytes giving the offset to
313the next one, or to the OP_KET opcode. For capturing brackets, the bracket 
314number immediately follows the offset, always as a 2-byte item.
315
316OP_KET is used for subpatterns that do not repeat indefinitely, while
317OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
318maximally respectively. All three are followed by LINK_SIZE bytes giving (as a
319positive number) the offset back to the matching bracket opcode.
320
321If a subpattern is quantified such that it is permitted to match zero times, it
322is preceded by one of OP_BRAZERO, OP_BRAMINZERO, or OP_SKIPZERO. These are
323single-byte opcodes that tell the matcher that skipping the following
324subpattern entirely is a valid branch. In the case of the first two, not 
325skipping the pattern is also valid (greedy and non-greedy). The third is used 
326when a pattern has the quantifier {0,0}. It cannot be entirely discarded, 
327because it may be called as a subroutine from elsewhere in the regex.
328
329A subpattern with an indefinite maximum repetition is replicated in the
330compiled data its minimum number of times (or once with OP_BRAZERO if the
331minimum is zero), with the final copy terminating with OP_KETRMIN or OP_KETRMAX
332as appropriate.
333
334A subpattern with a bounded maximum repetition is replicated in a nested
335fashion up to the maximum number of times, with OP_BRAZERO or OP_BRAMINZERO
336before each replication after the minimum, so that, for example, (abc){2,5} is
337compiled as (abc)(abc)((abc)((abc)(abc)?)?)?, except that each bracketed group 
338has the same number.
339
340When a repeated subpattern has an unbounded upper limit, it is checked to see 
341whether it could match an empty string. If this is the case, the opcode in the 
342final replication is changed to OP_SBRA or OP_SCBRA. This tells the matcher
343that it needs to check for matching an empty string when it hits OP_KETRMIN or
344OP_KETRMAX, and if so, to break the loop.
345
346
347Assertions
348----------
349
350Forward assertions are just like other subpatterns, but starting with one of
351the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes
352OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion
353is OP_REVERSE, followed by a two byte count of the number of characters to move
354back the pointer in the subject string. When operating in UTF-8 mode, the count
355is a character count rather than a byte count. A separate count is present in
356each alternative of a lookbehind assertion, allowing them to have different
357fixed lengths.
358
359
360Once-only (atomic) subpatterns
361------------------------------
362
363These are also just like other subpatterns, but they start with the opcode
364OP_ONCE. The check for matching an empty string in an unbounded repeat is 
365handled entirely at runtime, so there is just this one opcode.
366
367
368Conditional subpatterns
369-----------------------
370
371These are like other subpatterns, but they start with the opcode OP_COND, or
372OP_SCOND for one that might match an empty string in an unbounded repeat. If
373the condition is a back reference, this is stored at the start of the
374subpattern using the opcode OP_CREF followed by two bytes containing the
375reference number. If the condition is "in recursion" (coded as "(?(R)"), or "in
376recursion of group x" (coded as "(?(Rx)"), the group number is stored at the
377start of the subpattern using the opcode OP_RREF, and a value of zero for "the
378whole pattern". For a DEFINE condition, just the single byte OP_DEF is used (it
379has no associated data). Otherwise, a conditional subpattern always starts with
380one of the assertions.
381
382
383Recursion
384---------
385
386Recursion either matches the current regex, or some subexpression. The opcode
387OP_RECURSE is followed by an value which is the offset to the starting bracket
388from the start of the whole pattern. From release 6.5, OP_RECURSE is 
389automatically wrapped inside OP_ONCE brackets (because otherwise some patterns 
390broke it). OP_RECURSE is also used for "subroutine" calls, even though they 
391are not strictly a recursion.
392
393
394Callout
395-------
396
397OP_CALLOUT is followed by one byte of data that holds a callout number in the
398range 0 to 254 for manual callouts, or 255 for an automatic callout. In both 
399cases there follows a two-byte value giving the offset in the pattern to the
400start of the following item, and another two-byte item giving the length of the
401next item.
402
403
404Changing options
405----------------
406
407If any of the /i, /m, or /s options are changed within a pattern, an OP_OPT
408opcode is compiled, followed by one byte containing the new settings of these
409flags. If there are several alternatives, there is an occurrence of OP_OPT at
410the start of all those following the first options change, to set appropriate
411options for the start of the alternative. Immediately after the end of the
412group there is another such item to reset the flags to their previous values. A
413change of flag right at the very start of the pattern can be handled entirely
414at compile time, and so does not cause anything to be put into the compiled
415data.
416
417Philip Hazel
418April 2008