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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_SOD match start of data: \A
52 OP_CIRC ^ (start of data, or after \n in multiline)
53 OP_NOT_WORD_BOUNDARY \W
54 OP_WORD_BOUNDARY \w
55 OP_NOT_DIGIT \D
56 OP_DIGIT \d
57 OP_NOT_WHITESPACE \S
58 OP_WHITESPACE \s
59 OP_NOT_WORDCHAR \W
60 OP_WORDCHAR \w
61 OP_EODN match end of data or \n at end: \Z
62 OP_EOD match end of data: \z
63 OP_DOLL $ (end of data, or before \n in multiline)
64 OP_RECURSE match the pattern recursively
65
66
67 Repeating single characters
68 ---------------------------
69
70 The common repeats (*, +, ?) when applied to a single character appear as
71 two-byte items using the following opcodes:
72
73 OP_STAR
74 OP_MINSTAR
75 OP_PLUS
76 OP_MINPLUS
77 OP_QUERY
78 OP_MINQUERY
79
80 Those with "MIN" in their name are the minimizing versions. Each is followed by
81 the character that is to be repeated. Other repeats make use of
82
83 OP_UPTO
84 OP_MINUPTO
85 OP_EXACT
86
87 which are followed by a two-byte count (most significant first) and the
88 repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
89 non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
90 OP_UPTO (or OP_MINUPTO).
91
92
93 Repeating character types
94 -------------------------
95
96 Repeats of things like \d are done exactly as for single characters, except
97 that instead of a character, the opcode for the type is stored in the data
98 byte. The opcodes are:
99
100 OP_TYPESTAR
101 OP_TYPEMINSTAR
102 OP_TYPEPLUS
103 OP_TYPEMINPLUS
104 OP_TYPEQUERY
105 OP_TYPEMINQUERY
106 OP_TYPEUPTO
107 OP_TYPEMINUPTO
108 OP_TYPEEXACT
109
110
111 Matching a character string
112 ---------------------------
113
114 The OP_CHARS opcode is followed by a one-byte count and then that number of
115 characters. If there are more than 255 characters in sequence, successive
116 instances of OP_CHARS are used.
117
118
119 Character classes
120 -----------------
121
122 When characters less than 256 are involved, OP_CLASS is used for a character
123 class. 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 OP_CLASS is followed by a 32-byte bit map containing a 1 bit for every
133 character that is acceptable. The bits are counted from the least significant
134 end of each byte.
135
136 For classes containing characters with values > 255, OP_XCLASS is used. It
137 optionally uses a bit map (if any characters lie within it), followed by a list
138 of pairs and single characters. There is a flag character than indicates
139 whether it's a positive or a negative class.
140
141
142 Back references
143 ---------------
144
145 OP_REF is followed by two bytes containing the reference number.
146
147
148 Repeating character classes and back references
149 -----------------------------------------------
150
151 Single-character classes are handled specially (see above). This applies to
152 OP_CLASS and OP_REF. In both cases, the repeat information follows the base
153 item. The matching code looks at the following opcode to see if it is one of
154
155 OP_CRSTAR
156 OP_CRMINSTAR
157 OP_CRPLUS
158 OP_CRMINPLUS
159 OP_CRQUERY
160 OP_CRMINQUERY
161 OP_CRRANGE
162 OP_CRMINRANGE
163
164 All but the last two are just single-byte items. The others are followed by
165 four bytes of data, comprising the minimum and maximum repeat counts.
166
167
168 Brackets and alternation
169 ------------------------
170
171 A pair of non-capturing (round) brackets is wrapped round each expression at
172 compile time, so alternation always happens in the context of brackets.
173
174 Non-capturing brackets use the opcode OP_BRA, while capturing brackets use
175 OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
176 speakers, including myself, can be round, square, curly, or pointy. Hence this
177 usage.]
178
179 Originally PCRE was limited to 99 capturing brackets (so as not to use up all
180 the opcodes). From release 3.5, there is no limit. What happens is that the
181 first ones, up to EXTRACT_BASIC_MAX are handled with separate opcodes, as
182 above. If there are more, the opcode is set to EXTRACT_BASIC_MAX+1, and the
183 first operation in the bracket is OP_BRANUMBER, followed by a 2-byte bracket
184 number. This opcode is ignored while matching, but is fished out when handling
185 the bracket itself. (They could have all been done like this, but I was making
186 minimal changes.)
187
188 A bracket opcode is followed by two bytes which give the offset to the next
189 alternative OP_ALT or, if there aren't any branches, to the matching KET
190 opcode. Each OP_ALT is followed by two bytes giving the offset to the next one,
191 or to the KET opcode.
192
193 OP_KET is used for subpatterns that do not repeat indefinitely, while
194 OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
195 maximally respectively. All three are followed by two bytes giving (as a
196 positive number) the offset back to the matching BRA opcode.
197
198 If a subpattern is quantified such that it is permitted to match zero times, it
199 is preceded by one of OP_BRAZERO or OP_BRAMINZERO. These are single-byte
200 opcodes which tell the matcher that skipping this subpattern entirely is a
201 valid branch.
202
203 A subpattern with an indefinite maximum repetition is replicated in the
204 compiled data its minimum number of times (or once with a BRAZERO if the
205 minimum is zero), with the final copy terminating with a KETRMIN or KETRMAX as
206 appropriate.
207
208 A subpattern with a bounded maximum repetition is replicated in a nested
209 fashion up to the maximum number of times, with BRAZERO or BRAMINZERO before
210 each replication after the minimum, so that, for example, (abc){2,5} is
211 compiled as (abc)(abc)((abc)((abc)(abc)?)?)?. The 99 and 200 bracket limits do
212 not apply to these internally generated brackets.
213
214
215 Assertions
216 ----------
217
218 Forward assertions are just like other subpatterns, but starting with one of
219 the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes
220 OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion
221 is OP_REVERSE, followed by a two byte count of the number of characters to move
222 back the pointer in the subject string. When operating in UTF-8 mode, the count
223 is a character count rather than a byte count. A separate count is present in
224 each alternative of a lookbehind assertion, allowing them to have different
225 fixed lengths.
226
227
228 Once-only subpatterns
229 ---------------------
230
231 These are also just like other subpatterns, but they start with the opcode
232 OP_ONCE.
233
234
235 Conditional subpatterns
236 -----------------------
237
238 These are like other subpatterns, but they start with the opcode OP_COND. If
239 the condition is a back reference, this is stored at the start of the
240 subpattern using the opcode OP_CREF followed by two bytes containing the
241 reference number. If the condition is "in recursion" (coded as "(?(R)"), the
242 same scheme is used, with a "reference number" of 0xffff. Otherwise, a
243 conditional subpattern always starts with one of the assertions.
244
245
246 Changing options
247 ----------------
248
249 If any of the /i, /m, or /s options are changed within a pattern, an OP_OPT
250 opcode is compiled, followed by one byte containing the new settings of these
251 flags. If there are several alternatives, there is an occurrence of OP_OPT at
252 the start of all those following the first options change, to set appropriate
253 options for the start of the alternative. Immediately after the end of the
254 group there is another such item to reset the flags to their previous values. A
255 change of flag right at the very start of the pattern can be handled entirely
256 at compile time, and so does not cause anything to be put into the compiled
257 data.
258
259 Philip Hazel
260 August 2002

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