1PCRE2MATCHING(3) Library Functions Manual PCRE2MATCHING(3)
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6 PCRE2 - Perl-compatible regular expressions (revised API)
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9 This document describes the two different algorithms that are available
11 in PCRE2 for matching a compiled regular expression against a given
12 subject string. The "standard" algorithm is the one provided by the
13 pcre2_match() function. This works in the same as as Perl's matching
14 function, and provide a Perl-compatible matching operation. The just-
15 in-time (JIT) optimization that is described in the pcre2jit documenta‐
16 tion is compatible with this function.
17 An alternative algorithm is provided by the pcre2_dfa_match() function;
19 it operates in a different way, and is not Perl-compatible. This alter‐
20 native has advantages and disadvantages compared with the standard al‐
21 gorithm, and these are described below.
22 When there is only one possible way in which a given subject string can
24 match a pattern, the two algorithms give the same answer. A difference
25 arises, however, when there are multiple possibilities. For example, if
26 the pattern
27 ^<.*>
29 is matched against the string
31 <something> <something else> <something further>
33 there are three possible answers. The standard algorithm finds only one
35 of them, whereas the alternative algorithm finds all three.
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38 The set of strings that are matched by a regular expression can be rep‐
40 resented as a tree structure. An unlimited repetition in the pattern
41 makes the tree of infinite size, but it is still a tree. Matching the
42 pattern to a given subject string (from a given starting point) can be
43 thought of as a search of the tree. There are two ways to search a
44 tree: depth-first and breadth-first, and these correspond to the two
45 matching algorithms provided by PCRE2.
46
48 In the terminology of Jeffrey Friedl's book "Mastering Regular Expres‐
50 sions", the standard algorithm is an "NFA algorithm". It conducts a
51 depth-first search of the pattern tree. That is, it proceeds along a
52 single path through the tree, checking that the subject matches what is
53 required. When there is a mismatch, the algorithm tries any alterna‐
54 tives at the current point, and if they all fail, it backs up to the
55 previous branch point in the tree, and tries the next alternative
56 branch at that level. This often involves backing up (moving to the
57 left) in the subject string as well. The order in which repetition
58 branches are tried is controlled by the greedy or ungreedy nature of
59 the quantifier.
60 If a leaf node is reached, a matching string has been found, and at
62 that point the algorithm stops. Thus, if there is more than one possi‐
63 ble match, this algorithm returns the first one that it finds. Whether
64 this is the shortest, the longest, or some intermediate length depends
65 on the way the alternations and the greedy or ungreedy repetition quan‐
66 tifiers are specified in the pattern.
67 Because it ends up with a single path through the tree, it is rela‐
69 tively straightforward for this algorithm to keep track of the sub‐
70 strings that are matched by portions of the pattern in parentheses.
71 This provides support for capturing parentheses and backreferences.
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74 This algorithm conducts a breadth-first search of the tree. Starting
76 from the first matching point in the subject, it scans the subject
77 string from left to right, once, character by character, and as it does
78 this, it remembers all the paths through the tree that represent valid
79 matches. In Friedl's terminology, this is a kind of "DFA algorithm",
80 though it is not implemented as a traditional finite state machine (it
81 keeps multiple states active simultaneously).
82 Although the general principle of this matching algorithm is that it
84 scans the subject string only once, without backtracking, there is one
85 exception: when a lookaround assertion is encountered, the characters
86 following or preceding the current point have to be independently in‐
87 spected.
88 The scan continues until either the end of the subject is reached, or
90 there are no more unterminated paths. At this point, terminated paths
91 represent the different matching possibilities (if there are none, the
92 match has failed). Thus, if there is more than one possible match,
93 this algorithm finds all of them, and in particular, it finds the long‐
94 est. The matches are returned in the output vector in decreasing order
95 of length. There is an option to stop the algorithm after the first
96 match (which is necessarily the shortest) is found.
97 Note that the size of vector needed to contain all the results depends
99 on the number of simultaneous matches, not on the number of parentheses
100 in the pattern. Using pcre2_match_data_create_from_pattern() to create
101 the match data block is therefore not advisable when doing DFA match‐
102 ing.
103 Note also that all the matches that are found start at the same point
105 in the subject. If the pattern
106 cat(er(pillar)?)?
108 is matched against the string "the caterpillar catchment", the result
110 is the three strings "caterpillar", "cater", and "cat" that start at
111 the fifth character of the subject. The algorithm does not automati‐
112 cally move on to find matches that start at later positions.
113 PCRE2's "auto-possessification" optimization usually applies to charac‐
115 ter repeats at the end of a pattern (as well as internally). For exam‐
116 ple, the pattern "a\d+" is compiled as if it were "a\d++" because there
117 is no point even considering the possibility of backtracking into the
118 repeated digits. For DFA matching, this means that only one possible
119 match is found. If you really do want multiple matches in such cases,
120 either use an ungreedy repeat ("a\d+?") or set the PCRE2_NO_AUTO_POS‐
121 SESS option when compiling.
122 There are a number of features of PCRE2 regular expressions that are
124 not supported or behave differently in the alternative matching func‐
125 tion. Those that are not supported cause an error if encountered.
126 1. Because the algorithm finds all possible matches, the greedy or un‐
128 greedy nature of repetition quantifiers is not relevant (though it may
129 affect auto-possessification, as just described). During matching,
130 greedy and ungreedy quantifiers are treated in exactly the same way.
131 However, possessive quantifiers can make a difference when what follows
132 could also match what is quantified, for example in a pattern like
133 this:
134 ^a++\w!
136 This pattern matches "aaab!" but not "aaa!", which would be matched by
138 a non-possessive quantifier. Similarly, if an atomic group is present,
139 it is matched as if it were a standalone pattern at the current point,
140 and the longest match is then "locked in" for the rest of the overall
141 pattern.
142 2. When dealing with multiple paths through the tree simultaneously, it
144 is not straightforward to keep track of captured substrings for the
145 different matching possibilities, and PCRE2's implementation of this
146 algorithm does not attempt to do this. This means that no captured sub‐
147 strings are available.
148 3. Because no substrings are captured, backreferences within the pat‐
150 tern are not supported.
151 4. For the same reason, conditional expressions that use a backrefer‐
153 ence as the condition or test for a specific group recursion are not
154 supported.
155 5. Again for the same reason, script runs are not supported.
157 6. Because many paths through the tree may be active, the \K escape se‐
159 quence, which resets the start of the match when encountered (but may
160 be on some paths and not on others), is not supported.
161 7. Callouts are supported, but the value of the capture_top field is
163 always 1, and the value of the capture_last field is always 0.
164 8. The \C escape sequence, which (in the standard algorithm) always
166 matches a single code unit, even in a UTF mode, is not supported in
167 these modes, because the alternative algorithm moves through the sub‐
168 ject string one character (not code unit) at a time, for all active
169 paths through the tree.
170 9. Except for (*FAIL), the backtracking control verbs such as (*PRUNE)
172 are not supported. (*FAIL) is supported, and behaves like a failing
173 negative assertion.
174 10. The PCRE2_MATCH_INVALID_UTF option for pcre2_compile() is not sup‐
176 ported by pcre2_dfa_match().
177
179 The main advantage of the alternative algorithm is that all possible
181 matches (at a single point in the subject) are automatically found, and
182 in particular, the longest match is found. To find more than one match
183 at the same point using the standard algorithm, you have to do kludgy
184 things with callouts.
185 Partial matching is possible with this algorithm, though it has some
187 limitations. The pcre2partial documentation gives details of partial
188 matching and discusses multi-segment matching.
189
191 The alternative algorithm suffers from a number of disadvantages:
193 1. It is substantially slower than the standard algorithm. This is
195 partly because it has to search for all possible matches, but is also
196 because it is less susceptible to optimization.
197 2. Capturing parentheses, backreferences, script runs, and matching
199 within invalid UTF string are not supported.
200 3. Although atomic groups are supported, their use does not provide the
202 performance advantage that it does for the standard algorithm.
203 4. JIT optimization is not supported.
205
207 Philip Hazel
209 Retired from University Computing Service
210 Cambridge, England.
211
213 Last updated: 28 August 2021
215 Copyright (c) 1997-2021 University of Cambridge.
216PCRE2 10.38 28 August 2021 PCRE2MATCHING(3)