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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 this set of functions that forms PCRE, I tried at first to invent an
27 algorithm that used an amount of store bounded by a multiple of the number of
28 characters in the pattern, to save on compiling time. However, because of the
29 greater complexity in Perl regular expressions, I couldn't do this. In any
30 case, a first pass through the pattern is needed, in order to find internal
31 flag settings like (?i) at top level. So it works by running a very degenerate
32 first pass to calculate a maximum store size, and then a second pass to do the
33 real compile - which may use a bit less than the predicted amount of store. The
34 idea is that this is going to turn out faster because the first pass is
35 degenerate and the second can just store stuff straight into the vector. It
36 does make the compiling functions bigger, of course, but they have got quite
37 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
65
66 Repeating single characters
67 ---------------------------
68
69 The common repeats (*, +, ?) when applied to a single character appear as
70 two-byte items using the following opcodes:
71
72 OP_STAR
73 OP_MINSTAR
74 OP_PLUS
75 OP_MINPLUS
76 OP_QUERY
77 OP_MINQUERY
78
79 Those with "MIN" in their name are the minimizing versions. Each is followed by
80 the character that is to be repeated. Other repeats make use of
81
82 OP_UPTO
83 OP_MINUPTO
84 OP_EXACT
85
86 which are followed by a two-byte count (most significant first) and the
87 repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
88 non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
89 OP_UPTO (or OP_MINUPTO).
90
91
92 Repeating character types
93 -------------------------
94
95 Repeats of things like \d are done exactly as for single characters, except
96 that instead of a character, the opcode for the type is stored in the data
97 byte. The opcodes are:
98
99 OP_TYPESTAR
100 OP_TYPEMINSTAR
101 OP_TYPEPLUS
102 OP_TYPEMINPLUS
103 OP_TYPEQUERY
104 OP_TYPEMINQUERY
105 OP_TYPEUPTO
106 OP_TYPEMINUPTO
107 OP_TYPEEXACT
108
109
110 Matching a character string
111 ---------------------------
112
113 The OP_CHARS opcode is followed by a one-byte count and then that number of
114 characters. If there are more than 255 characters in sequence, successive
115 instances of OP_CHARS are used.
116
117
118 Character classes
119 -----------------
120
121 OP_CLASS is used for a character class, provided there are at least two
122 characters in the class. If there is only one character, OP_CHARS is used for a
123 positive class, and OP_NOT for a negative one (that is, for something like
124 [^a]). Another set of repeating opcodes (OP_NOTSTAR etc.) are used for a
125 repeated, negated, single-character class. The normal ones (OP_STAR etc.) are
126 used for a repeated positive single-character class.
127
128 OP_CLASS is followed by a 32-byte bit map containing a 1
129 bit for every character that is acceptable. The bits are counted from the least
130 significant end of each byte.
131
132
133 Back references
134 ---------------
135
136 OP_REF is followed by a single byte containing the reference number.
137
138
139 Repeating character classes and back references
140 -----------------------------------------------
141
142 Single-character classes are handled specially (see above). This applies to
143 OP_CLASS and OP_REF. In both cases, the repeat information follows the base
144 item. The matching code looks at the following opcode to see if it is one of
145
146 OP_CRSTAR
147 OP_CRMINSTAR
148 OP_CRPLUS
149 OP_CRMINPLUS
150 OP_CRQUERY
151 OP_CRMINQUERY
152 OP_CRRANGE
153 OP_CRMINRANGE
154
155 All but the last two are just single-byte items. The others are followed by
156 four bytes of data, comprising the minimum and maximum repeat counts.
157
158
159 Brackets and alternation
160 ------------------------
161
162 A pair of non-identifying (round) brackets is wrapped round each expression at
163 compile time, so alternation always happens in the context of brackets.
164 Non-identifying brackets use the opcode OP_BRA, while identifying brackets use
165 OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
166 speakers, including myself, can be round, square, or curly. Hence this usage.]
167
168 A bracket opcode is followed by two bytes which give the offset to the next
169 alternative OP_ALT or, if there aren't any branches, to the matching KET
170 opcode. Each OP_ALT is followed by two bytes giving the offset to the next one,
171 or to the KET opcode.
172
173 OP_KET is used for subpatterns that do not repeat indefinitely, while
174 OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
175 maximally respectively. All three are followed by two bytes giving (as a
176 positive number) the offset back to the matching BRA opcode.
177
178 If a subpattern is quantified such that it is permitted to match zero times, it
179 is preceded by one of OP_BRAZERO or OP_BRAMINZERO. These are single-byte
180 opcodes which tell the matcher that skipping this subpattern entirely is a
181 valid branch.
182
183 A subpattern with an indefinite maximum repetition is replicated in the
184 compiled data its minimum number of times (or once with a BRAZERO if the
185 minimum is zero), with the final copy terminating with a KETRMIN or KETRMAX as
186 appropriate.
187
188 A subpattern with a bounded maximum repetition is replicated in a nested
189 fashion up to the maximum number of times, with BRAZERO or BRAMINZERO before
190 each replication after the minimum, so that, for example, (abc){2,5} is
191 compiled as (abc)(abc)((abc)((abc)(abc)?)?)?. The 200-bracket limit does not
192 apply to these internally generated brackets.
193
194
195 Assertions
196 ----------
197
198 Forward assertions are just like other subpatterns, but starting with one of
199 the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes
200 OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion
201 is OP_REVERSE, followed by a two byte count of the number of characters to move
202 back the pointer in the subject string. A separate count is present in each
203 alternative of a lookbehind assertion, allowing them to have different fixed
204 lengths.
205
206
207 Once-only subpatterns
208 ---------------------
209
210 These are also just like other subpatterns, but they start with the opcode
211 OP_ONCE.
212
213
214 Conditional subpatterns
215 -----------------------
216
217 These are like other subpatterns, but they start with the opcode OP_COND. If
218 the condition is a back reference, this is stored at the start of the
219 subpattern using the opcode OP_CREF followed by one byte containing the
220 reference number. Otherwise, a conditional subpattern will always start with
221 one of the assertions.
222
223
224 Changing options
225 ----------------
226
227 If any of the /i, /m, or /s options are changed within a parenthesized group,
228 an OP_OPT opcode is compiled, followed by one byte containing the new settings
229 of these flags. If there are several alternatives in a group, there is an
230 occurrence of OP_OPT at the start of all those following the first options
231 change, to set appropriate options for the start of the alternative.
232 Immediately after the end of the group there is another such item to reset the
233 flags to their previous values. Other changes of flag within the pattern can be
234 handled entirely at compile time, and so do not cause anything to be put into
235 the compiled data.
236
237
238 Philip Hazel
239 January 1999

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