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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 minimizing in Perl) the amount of the subject that matches individual wild
23 portions of the pattern. This is a "NFA algorithm".
24
25 For this set of functions, I tried at first to invent an algorithm that used an
26 amount of store bounded by a multiple of the number of characters in the
27 pattern, to save on compiling time. However, because of the greater complexity
28 in Perl regular expressions, I couldn't do this. In any case, a first pass
29 through the pattern is needed, in order to find internal flag settings like
30 (?i). So it works by running a very degenerate first pass to calculate a
31 maximum store size, and then a second pass to do the real compile - which may
32 use a bit less than the predicted amount of store. The idea is that this is
33 going to turn out faster because the first pass is degenerate and the second
34 can just store stuff straight into the vector. It does make the compiling
35 functions bigger, of course, but they have got quite big anyway to handle all
36 the Perl stuff.
37
38 The compiled form of a pattern is a vector of bytes, containing items of
39 variable length. The first byte in an item is an opcode, and the length of the
40 item is either implicit in the opcode or contained in the data bytes which
41 follow it. A list of all the opcodes follows:
42
43 Opcodes with no following data
44 ------------------------------
45
46 These items are all just one byte long
47
48 OP_END end of pattern
49 OP_ANY match any character
50 OP_SOD match start of data: \A
51 OP_CIRC ^ (start of data, or after \n in multiline)
52 OP_NOT_WORD_BOUNDARY \W
53 OP_WORD_BOUNDARY \w
54 OP_NOT_DIGIT \D
55 OP_DIGIT \d
56 OP_NOT_WHITESPACE \S
57 OP_WHITESPACE \s
58 OP_NOT_WORDCHAR \W
59 OP_WORDCHAR \w
60 OP_CUT analogue of Prolog's "cut"
61 OP_EOD match end of data: \Z
62 OP_DOLL $ (end of data, or before \n in multiline)
63
64
65 Repeating single characters
66 ---------------------------
67
68 The common repeats (*, +, ?) when applied to a single character appear as
69 two-byte items using the following opcodes:
70
71 OP_STAR
72 OP_MINSTAR
73 OP_PLUS
74 OP_MINPLUS
75 OP_QUERY
76 OP_MINQUERY
77
78 Those with "MIN" in their name are the minimizing versions. Each is followed by
79 the character that is to be repeated. Other repeats make use of
80
81 OP_UPTO
82 OP_MINUPTO
83 OP_EXACT
84
85 which are followed by a two-byte count (most significant first) and the
86 repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
87 non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
88 OP_UPTO (or OP_MINUPTO).
89
90
91 Repeating character types
92 -------------------------
93
94 Repeats of things like \d are done exactly as for single characters, except
95 that instead of a character, the opcode for the type is stored in the data
96 byte. The opcodes are:
97
98 OP_TYPESTAR
99 OP_TYPEMINSTAR
100 OP_TYPEPLUS
101 OP_TYPEMINPLUS
102 OP_TYPEQUERY
103 OP_TYPEMINQUERY
104 OP_TYPEUPTO
105 OP_TYPEMINUPTO
106 OP_TYPEEXACT
107
108
109 Matching a character string
110 ---------------------------
111
112 The OP_CHARS opcode is followed by a one-byte count and then that number of
113 characters. If there are more than 255 characters in sequence, successive
114 instances of OP_CHARS are used.
115
116
117 Character classes
118 -----------------
119
120 OP_CLASS is used for a character class. It is followed by a 32-byte bit map
121 containing a 1 bit for every character that is acceptable. The bits are counted
122 from the least significant end of each byte.
123
124
125 Back references
126 ---------------
127
128 OP_REF is followed by a single byte containing the reference number.
129
130
131 Repeating character classes and back references
132 -----------------------------------------------
133
134 In both cases, the repeat information follows the base item. The matching code
135 looks at the following opcode to see if it is one of
136
137 OP_CRSTAR
138 OP_CRMINSTAR
139 OP_CRPLUS
140 OP_CRMINPLUS
141 OP_CRQUERY
142 OP_CRMINQUERY
143 OP_CRRANGE
144 OP_CRMINRANGE
145
146 All but the last two are just single-byte items. The others are followed by
147 four bytes of data, comprising the minimum and maximum repeat counts.
148
149
150 Brackets and alternation
151 ------------------------
152
153 A pair of non-identifying (round) brackets is wrapped round each expression at
154 compile time, so alternation always happens in the context of brackets.
155 Non-identifying brackets use the opcode OP_BRA, while identifying brackets use
156 OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
157 speakers, including myself, can be round, square, or curly. Hence this usage.]
158
159 A bracket opcode is followed by two bytes which give the offset to the next
160 alternative OP_ALT or, if there aren't any branches, to the matching KET
161 opcode. Each OP_ALT is followed by two bytes giving the offset to the next one,
162 or to the KET opcode.
163
164 OP_KET is used for subpatterns that do not repeat indefinitely, while
165 OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
166 maximally respectively. All three are followed by two bytes giving (as a
167 positive number) the offset back to the matching BRA opcode.
168
169 If a subpattern is quantified such that it is permitted to match zero times, it
170 is preceded by one of OP_BRAZERO or OP_BRAMINZERO. These are single-byte
171 opcodes which tell the matcher that skipping this subpattern entirely is a
172 valid branch.
173
174 A subpattern with an indefinite maximum repetition is replicated in the
175 compiled data its minimum number of times (or once with a BRAZERO if the
176 minimum is zero), with the final copy terminating with a KETRMIN or KETRMAX as
177 appropriate.
178
179 A subpattern with a bounded maximum repetition is replicated up to the maximum
180 number of times, with BRAZERO or BRAMINZERO before each replication after the
181 minimum. In effect, (abc){2,5} becomes (abc)(abc)(abc)?(abc)?(abc)?.
182
183
184 Assertions
185 ----------
186
187 Assertions are just like other subpatterns, but starting with one of the
188 opcodes OP_ASSERT or OP_ASSERT_NOT.
189
190
191 Once-only subpatterns
192 ---------------------
193
194 These are also just like other subpatterns, but they start with the opcode
195 OP_ONCE.
196
197
198 Philip Hazel
199 October 1997

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