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1 Technical Notes about PCRE
2 --------------------------
3
4 Many years ago I implemented some regular expression functions to an algorithm
5 suggested by Martin Richards. These were not Unix-like in form, and were quite
6 restricted in what they could do by comparison with Perl. The interesting part
7 about the algorithm was that the amount of space required to hold the compiled
8 form of an expression was known in advance. The code to apply an expression did
9 not operate by backtracking, as the original Henry Spencer code and current
10 Perl code does, but instead checked all possibilities simultaneously by keeping
11 a list of current states and checking all of them as it advanced through the
12 subject string. (In the terminology of Jeffrey Friedl's book, it was a "DFA
13 algorithm".) When the pattern was all used up, all remaining states were
14 possible matches, and the one matching the longest subset of the subject string
15 was chosen. This did not necessarily maximize the individual wild portions of
16 the pattern, as is expected in Unix and Perl-style regular expressions.
17
18 By contrast, the code originally written by Henry Spencer and subsequently
19 heavily modified for Perl actually compiles the expression twice: once in a
20 dummy mode in order to find out how much store will be needed, and then for
21 real. The execution function operates by backtracking and maximizing (or,
22 optionally, minimizing in Perl) the amount of the subject that matches
23 individual wild portions of the pattern. This is an "NFA algorithm" in Friedl's
24 terminology.
25
26 For the set of functions that forms PCRE (which are unrelated to those
27 mentioned above), I tried at first to invent an algorithm that used an amount
28 of store bounded by a multiple of the number of characters in the pattern, to
29 save on compiling time. However, because of the greater complexity in Perl
30 regular expressions, I couldn't do this. In any case, a first pass through the
31 pattern is needed, for a number of reasons. PCRE works by running a very
32 degenerate first pass to calculate a maximum store size, and then a second pass
33 to do the real compile - which may use a bit less than the predicted amount of
34 store. The idea is that this is going to turn out faster because the first pass
35 is degenerate and the second pass can just store stuff straight into the
36 vector. It does make the compiling functions bigger, of course, but they have
37 got quite big anyway to handle all the Perl stuff.
38
39 The compiled form of a pattern is a vector of bytes, containing items of
40 variable length. The first byte in an item is an opcode, and the length of the
41 item is either implicit in the opcode or contained in the data bytes which
42 follow it. A list of all the opcodes follows:
43
44 Opcodes with no following data
45 ------------------------------
46
47 These items are all just one byte long
48
49 OP_END end of pattern
50 OP_ANY match any character
51 OP_ANYBYTE match any single byte, even in UTF-8 mode
52 OP_SOD match start of data: \A
53 OP_SOM, start of match (subject + offset): \G
54 OP_CIRC ^ (start of data, or after \n in multiline)
55 OP_NOT_WORD_BOUNDARY \W
56 OP_WORD_BOUNDARY \w
57 OP_NOT_DIGIT \D
58 OP_DIGIT \d
59 OP_NOT_WHITESPACE \S
60 OP_WHITESPACE \s
61 OP_NOT_WORDCHAR \W
62 OP_WORDCHAR \w
63 OP_EODN match end of data or \n at end: \Z
64 OP_EOD match end of data: \z
65 OP_DOLL $ (end of data, or before \n in multiline)
66
67
68 Repeating single characters
69 ---------------------------
70
71 The common repeats (*, +, ?) when applied to a single character appear as
72 two-byte items using the following opcodes:
73
74 OP_STAR
75 OP_MINSTAR
76 OP_PLUS
77 OP_MINPLUS
78 OP_QUERY
79 OP_MINQUERY
80
81 Those with "MIN" in their name are the minimizing versions. Each is followed by
82 the character that is to be repeated. Other repeats make use of
83
84 OP_UPTO
85 OP_MINUPTO
86 OP_EXACT
87
88 which are followed by a two-byte count (most significant first) and the
89 repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
90 non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
91 OP_UPTO (or OP_MINUPTO).
92
93
94 Repeating character types
95 -------------------------
96
97 Repeats of things like \d are done exactly as for single characters, except
98 that instead of a character, the opcode for the type is stored in the data
99 byte. The opcodes are:
100
101 OP_TYPESTAR
102 OP_TYPEMINSTAR
103 OP_TYPEPLUS
104 OP_TYPEMINPLUS
105 OP_TYPEQUERY
106 OP_TYPEMINQUERY
107 OP_TYPEUPTO
108 OP_TYPEMINUPTO
109 OP_TYPEEXACT
110
111
112 Matching a character string
113 ---------------------------
114
115 The OP_CHARS opcode is followed by a one-byte count and then that number of
116 characters. If there are more than 255 characters in sequence, successive
117 instances of OP_CHARS are used.
118
119
120 Character classes
121 -----------------
122
123 If there is only one character, OP_CHARS is used for a positive class,
124 and OP_NOT for a negative one (that is, for something like [^a]). However, in
125 UTF-8 mode, this applies only to characters with values < 128, because OP_NOT
126 is confined to single bytes.
127
128 Another set of repeating opcodes (OP_NOTSTAR etc.) are used for a repeated,
129 negated, single-character class. The normal ones (OP_STAR etc.) are used for a
130 repeated positive single-character class.
131
132 When there's more than one character in a class and all the characters are less
133 than 256, OP_CLASS is used for a positive class, and OP_NCLASS for a negative
134 one. In either case, the opcode is followed by a 32-byte bit map containing a 1
135 bit for every character that is acceptable. The bits are counted from the least
136 significant end of each byte.
137
138 The reason for having both OP_CLASS and OP_NCLASS is so that, in UTF-8 mode,
139 subject characters with values greater than 256 can be handled correctly. For
140 OP_CLASS they don't match, whereas for OP_NCLASS they do.
141
142 For classes containing characters with values > 255, OP_XCLASS is used. It
143 optionally uses a bit map (if any characters lie within it), followed by a list
144 of pairs and single characters. There is a flag character than indicates
145 whether it's a positive or a negative class.
146
147
148 Back references
149 ---------------
150
151 OP_REF is followed by two bytes containing the reference number.
152
153
154 Repeating character classes and back references
155 -----------------------------------------------
156
157 Single-character classes are handled specially (see above). This applies to
158 OP_CLASS and OP_REF. In both cases, the repeat information follows the base
159 item. The matching code looks at the following opcode to see if it is one of
160
161 OP_CRSTAR
162 OP_CRMINSTAR
163 OP_CRPLUS
164 OP_CRMINPLUS
165 OP_CRQUERY
166 OP_CRMINQUERY
167 OP_CRRANGE
168 OP_CRMINRANGE
169
170 All but the last two are just single-byte items. The others are followed by
171 four bytes of data, comprising the minimum and maximum repeat counts.
172
173
174 Brackets and alternation
175 ------------------------
176
177 A pair of non-capturing (round) brackets is wrapped round each expression at
178 compile time, so alternation always happens in the context of brackets.
179
180 Non-capturing brackets use the opcode OP_BRA, while capturing brackets use
181 OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
182 speakers, including myself, can be round, square, curly, or pointy. Hence this
183 usage.]
184
185 Originally PCRE was limited to 99 capturing brackets (so as not to use up all
186 the opcodes). From release 3.5, there is no limit. What happens is that the
187 first ones, up to EXTRACT_BASIC_MAX are handled with separate opcodes, as
188 above. If there are more, the opcode is set to EXTRACT_BASIC_MAX+1, and the
189 first operation in the bracket is OP_BRANUMBER, followed by a 2-byte bracket
190 number. This opcode is ignored while matching, but is fished out when handling
191 the bracket itself. (They could have all been done like this, but I was making
192 minimal changes.)
193
194 A bracket opcode is followed by two bytes which give the offset to the next
195 alternative OP_ALT or, if there aren't any branches, to the matching KET
196 opcode. Each OP_ALT is followed by two bytes giving the offset to the next one,
197 or to the KET opcode.
198
199 OP_KET is used for subpatterns that do not repeat indefinitely, while
200 OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
201 maximally respectively. All three are followed by two bytes giving (as a
202 positive number) the offset back to the matching BRA opcode.
203
204 If a subpattern is quantified such that it is permitted to match zero times, it
205 is preceded by one of OP_BRAZERO or OP_BRAMINZERO. These are single-byte
206 opcodes which tell the matcher that skipping this subpattern entirely is a
207 valid branch.
208
209 A subpattern with an indefinite maximum repetition is replicated in the
210 compiled data its minimum number of times (or once with a BRAZERO if the
211 minimum is zero), with the final copy terminating with a KETRMIN or KETRMAX as
212 appropriate.
213
214 A subpattern with a bounded maximum repetition is replicated in a nested
215 fashion up to the maximum number of times, with BRAZERO or BRAMINZERO before
216 each replication after the minimum, so that, for example, (abc){2,5} is
217 compiled as (abc)(abc)((abc)((abc)(abc)?)?)?. The 99 and 200 bracket limits do
218 not apply to these internally generated brackets.
219
220
221 Assertions
222 ----------
223
224 Forward assertions are just like other subpatterns, but starting with one of
225 the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes
226 OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion
227 is OP_REVERSE, followed by a two byte count of the number of characters to move
228 back the pointer in the subject string. When operating in UTF-8 mode, the count
229 is a character count rather than a byte count. A separate count is present in
230 each alternative of a lookbehind assertion, allowing them to have different
231 fixed lengths.
232
233
234 Once-only subpatterns
235 ---------------------
236
237 These are also just like other subpatterns, but they start with the opcode
238 OP_ONCE.
239
240
241 Conditional subpatterns
242 -----------------------
243
244 These are like other subpatterns, but they start with the opcode OP_COND. If
245 the condition is a back reference, this is stored at the start of the
246 subpattern using the opcode OP_CREF followed by two bytes containing the
247 reference number. If the condition is "in recursion" (coded as "(?(R)"), the
248 same scheme is used, with a "reference number" of 0xffff. Otherwise, a
249 conditional subpattern always starts with one of the assertions.
250
251
252 Recursion
253 ---------
254
255 Recursion either matches the current regex, or some subexpression. The opcode
256 OP_RECURSE is followed by an value which is the offset to the starting bracket
257 from the start of the whole pattern.
258
259
260 Callout
261 -------
262
263 OP_CALLOUT is followed by one byte of data that holds a callout number in the
264 range 0 to 255.
265
266
267 Changing options
268 ----------------
269
270 If any of the /i, /m, or /s options are changed within a pattern, an OP_OPT
271 opcode is compiled, followed by one byte containing the new settings of these
272 flags. If there are several alternatives, there is an occurrence of OP_OPT at
273 the start of all those following the first options change, to set appropriate
274 options for the start of the alternative. Immediately after the end of the
275 group there is another such item to reset the flags to their previous values. A
276 change of flag right at the very start of the pattern can be handled entirely
277 at compile time, and so does not cause anything to be put into the compiled
278 data.
279
280 Philip Hazel
281 August 2003

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