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1 nigel 41 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 nigel 43 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 nigel 41
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 nigel 43 OP_RECURSE match the pattern recursively
66 nigel 41
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 nigel 43 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 nigel 41
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 nigel 43 A pair of non-capturing (round) brackets is wrapped round each expression at
165 nigel 41 compile time, so alternation always happens in the context of brackets.
166 nigel 43 Non-capturing brackets use the opcode OP_BRA, while capturing brackets use
167 nigel 41 OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
168 nigel 43 speakers, including myself, can be round, square, curly, or pointy. Hence this
169     usage.]
170 nigel 41
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 nigel 43 February 2000

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