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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     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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