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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 nigel 63 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 nigel 41
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 nigel 63 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 nigel 41
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 nigel 43 OP_RECURSE match the pattern recursively
65 nigel 41
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 nigel 63 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 nigel 41
128 nigel 63 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 nigel 43 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 nigel 41
136 nigel 63 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 nigel 41
141 nigel 63
142 nigel 41 Back references
143     ---------------
144    
145 nigel 53 OP_REF is followed by two bytes containing the reference number.
146 nigel 41
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 nigel 43 A pair of non-capturing (round) brackets is wrapped round each expression at
172 nigel 41 compile time, so alternation always happens in the context of brackets.
173 nigel 53
174 nigel 43 Non-capturing brackets use the opcode OP_BRA, while capturing brackets use
175 nigel 41 OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
176 nigel 43 speakers, including myself, can be round, square, curly, or pointy. Hence this
177     usage.]
178 nigel 41
179 nigel 53 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 nigel 41 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 nigel 53 compiled as (abc)(abc)((abc)((abc)(abc)?)?)?. The 99 and 200 bracket limits do
212     not apply to these internally generated brackets.
213 nigel 41
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 nigel 49 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 nigel 41
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 nigel 53 subpattern using the opcode OP_CREF followed by two bytes containing the
241 nigel 63 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 nigel 41
245    
246     Changing options
247     ----------------
248    
249 nigel 63 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 nigel 41
259     Philip Hazel
260 nigel 63 August 2002

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