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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 Henry Spencer and Perl code does, but
10 instead checked all possibilities simultaneously by keeping a list of current
11 states and checking all of them as it advanced through the subject string. (In
12 the terminology of Jeffrey Friedl's book, it was a "DFA algorithm".) When the
13 pattern was all used up, all remaining states were possible matches, and the
14 one matching the longest subset of the subject string was chosen. This did not
15 necessarily maximize the individual wild portions of the pattern, as is
16 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, in order to find internal flag settings like (?i) at top
32 level. So PCRE works by running a very degenerate first pass to calculate a
33 maximum store size, and then a second pass to do the real compile - which may
34 use a bit less than the predicted amount of store. The idea is that this is
35 going to turn out faster because the first pass is degenerate and the second
36 pass can just store stuff straight into the vector. It does make the compiling
37 functions bigger, of course, but they have got quite big anyway to handle all
38 the Perl stuff.
39
40 The compiled form of a pattern is a vector of bytes, containing items of
41 variable length. The first byte in an item is an opcode, and the length of the
42 item is either implicit in the opcode or contained in the data bytes which
43 follow it. A list of all the opcodes follows:
44
45 Opcodes with no following data
46 ------------------------------
47
48 These items are all just one byte long
49
50 OP_END end of pattern
51 OP_ANY match any character
52 OP_SOD match start of data: \A
53 OP_CIRC ^ (start of data, or after \n in multiline)
54 OP_NOT_WORD_BOUNDARY \W
55 OP_WORD_BOUNDARY \w
56 OP_NOT_DIGIT \D
57 OP_DIGIT \d
58 OP_NOT_WHITESPACE \S
59 OP_WHITESPACE \s
60 OP_NOT_WORDCHAR \W
61 OP_WORDCHAR \w
62 OP_EODN match end of data or \n at end: \Z
63 OP_EOD match end of data: \z
64 OP_DOLL $ (end of data, or before \n in multiline)
65 OP_RECURSE match the pattern recursively
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 OP_CLASS is used for a character class, provided there are at least two
124 characters in the class. If there is only one character, OP_CHARS is used for a
125 positive class, and OP_NOT for a negative one (that is, for something like
126 [^a]). Another set of repeating opcodes (OP_NOTSTAR etc.) are used for a
127 repeated, negated, single-character class. The normal ones (OP_STAR etc.) are
128 used for a repeated positive single-character class.
129
130 OP_CLASS is followed by a 32-byte bit map containing a 1 bit for every
131 character that is acceptable. The bits are counted from the least significant
132 end of each byte.
133
134
135 Back references
136 ---------------
137
138 OP_REF is followed by a single byte containing the reference number.
139
140
141 Repeating character classes and back references
142 -----------------------------------------------
143
144 Single-character classes are handled specially (see above). This applies to
145 OP_CLASS and OP_REF. In both cases, the repeat information follows the base
146 item. The matching code looks at the following opcode to see if it is one of
147
148 OP_CRSTAR
149 OP_CRMINSTAR
150 OP_CRPLUS
151 OP_CRMINPLUS
152 OP_CRQUERY
153 OP_CRMINQUERY
154 OP_CRRANGE
155 OP_CRMINRANGE
156
157 All but the last two are just single-byte items. The others are followed by
158 four bytes of data, comprising the minimum and maximum repeat counts.
159
160
161 Brackets and alternation
162 ------------------------
163
164 A pair of non-capturing (round) brackets is wrapped round each expression at
165 compile time, so alternation always happens in the context of brackets.
166 Non-capturing brackets use the opcode OP_BRA, while capturing brackets use
167 OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
168 speakers, including myself, can be round, square, curly, or pointy. Hence this
169 usage.]
170
171 A bracket opcode is followed by two bytes which give the offset to the next
172 alternative OP_ALT or, if there aren't any branches, to the matching KET
173 opcode. Each OP_ALT is followed by two bytes giving the offset to the next one,
174 or to the KET opcode.
175
176 OP_KET is used for subpatterns that do not repeat indefinitely, while
177 OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
178 maximally respectively. All three are followed by two bytes giving (as a
179 positive number) the offset back to the matching BRA opcode.
180
181 If a subpattern is quantified such that it is permitted to match zero times, it
182 is preceded by one of OP_BRAZERO or OP_BRAMINZERO. These are single-byte
183 opcodes which tell the matcher that skipping this subpattern entirely is a
184 valid branch.
185
186 A subpattern with an indefinite maximum repetition is replicated in the
187 compiled data its minimum number of times (or once with a BRAZERO if the
188 minimum is zero), with the final copy terminating with a KETRMIN or KETRMAX as
189 appropriate.
190
191 A subpattern with a bounded maximum repetition is replicated in a nested
192 fashion up to the maximum number of times, with BRAZERO or BRAMINZERO before
193 each replication after the minimum, so that, for example, (abc){2,5} is
194 compiled as (abc)(abc)((abc)((abc)(abc)?)?)?. The 200-bracket limit does not
195 apply to these internally generated brackets.
196
197
198 Assertions
199 ----------
200
201 Forward assertions are just like other subpatterns, but starting with one of
202 the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes
203 OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion
204 is OP_REVERSE, followed by a two byte count of the number of characters to move
205 back the pointer in the subject string. A separate count is present in each
206 alternative of a lookbehind assertion, allowing them to have different fixed
207 lengths.
208
209
210 Once-only subpatterns
211 ---------------------
212
213 These are also just like other subpatterns, but they start with the opcode
214 OP_ONCE.
215
216
217 Conditional subpatterns
218 -----------------------
219
220 These are like other subpatterns, but they start with the opcode OP_COND. If
221 the condition is a back reference, this is stored at the start of the
222 subpattern using the opcode OP_CREF followed by one byte containing the
223 reference number. Otherwise, a conditional subpattern will always start with
224 one of the assertions.
225
226
227 Changing options
228 ----------------
229
230 If any of the /i, /m, or /s options are changed within a parenthesized group,
231 an OP_OPT opcode is compiled, followed by one byte containing the new settings
232 of these flags. If there are several alternatives in a group, there is an
233 occurrence of OP_OPT at the start of all those following the first options
234 change, to set appropriate options for the start of the alternative.
235 Immediately after the end of the group there is another such item to reset the
236 flags to their previous values. Other changes of flag within the pattern can be
237 handled entirely at compile time, and so do not cause anything to be put into
238 the compiled data.
239
240
241 Philip Hazel
242 February 2000

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