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
21 algorithm, 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.
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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 greedy and ungreedy repetition quantifiers are specified
66 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
87 inspected.
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 decreasing order of length. There is
95 an option to stop the algorithm after the first match (which is neces‐
96 sarily the shortest) is found.
97 Note that all the matches that are found start at the same point in the
99 subject. If the pattern
100 cat(er(pillar)?)?
102 is matched against the string "the caterpillar catchment", the result
104 is the three strings "caterpillar", "cater", and "cat" that start at
105 the fifth character of the subject. The algorithm does not automati‐
106 cally move on to find matches that start at later positions.
107 PCRE2's "auto-possessification" optimization usually applies to charac‐
109 ter repeats at the end of a pattern (as well as internally). For exam‐
110 ple, the pattern "a\d+" is compiled as if it were "a\d++" because there
111 is no point even considering the possibility of backtracking into the
112 repeated digits. For DFA matching, this means that only one possible
113 match is found. If you really do want multiple matches in such cases,
114 either use an ungreedy repeat ("a\d+?") or set the PCRE2_NO_AUTO_POS‐
115 SESS option when compiling.
116 There are a number of features of PCRE2 regular expressions that are
118 not supported by the alternative matching algorithm. They are as fol‐
119 lows:
120 1. Because the algorithm finds all possible matches, the greedy or
122 ungreedy nature of repetition quantifiers is not relevant (though it
123 may affect auto-possessification, as just described). During matching,
124 greedy and ungreedy quantifiers are treated in exactly the same way.
125 However, possessive quantifiers can make a difference when what follows
126 could also match what is quantified, for example in a pattern like
127 this:
128 ^a++\w!
130 This pattern matches "aaab!" but not "aaa!", which would be matched by
132 a non-possessive quantifier. Similarly, if an atomic group is present,
133 it is matched as if it were a standalone pattern at the current point,
134 and the longest match is then "locked in" for the rest of the overall
135 pattern.
136 2. When dealing with multiple paths through the tree simultaneously, it
138 is not straightforward to keep track of captured substrings for the
139 different matching possibilities, and PCRE2's implementation of this
140 algorithm does not attempt to do this. This means that no captured sub‐
141 strings are available.
142 3. Because no substrings are captured, backreferences within the pat‐
144 tern are not supported, and cause errors if encountered.
145 4. For the same reason, conditional expressions that use a backrefer‐
147 ence as the condition or test for a specific group recursion are not
148 supported.
149 5. Because many paths through the tree may be active, the \K escape
151 sequence, which resets the start of the match when encountered (but may
152 be on some paths and not on others), is not supported. It causes an
153 error if encountered.
154 6. Callouts are supported, but the value of the capture_top field is
156 always 1, and the value of the capture_last field is always 0.
157 7. The \C escape sequence, which (in the standard algorithm) always
159 matches a single code unit, even in a UTF mode, is not supported in
160 these modes, because the alternative algorithm moves through the sub‐
161 ject string one character (not code unit) at a time, for all active
162 paths through the tree.
163 8. Except for (*FAIL), the backtracking control verbs such as (*PRUNE)
165 are not supported. (*FAIL) is supported, and behaves like a failing
166 negative assertion.
167
169 Using the alternative matching algorithm provides the following advan‐
171 tages:
172 1. All possible matches (at a single point in the subject) are automat‐
174 ically found, and in particular, the longest match is found. To find
175 more than one match using the standard algorithm, you have to do kludgy
176 things with callouts.
177 2. Because the alternative algorithm scans the subject string just
179 once, and never needs to backtrack (except for lookbehinds), it is pos‐
180 sible to pass very long subject strings to the matching function in
181 several pieces, checking for partial matching each time. Although it is
182 also possible to do multi-segment matching using the standard algo‐
183 rithm, by retaining partially matched substrings, it is more compli‐
184 cated. The pcre2partial documentation gives details of partial matching
185 and discusses multi-segment matching.
186
188 The alternative algorithm suffers from a number of disadvantages:
190 1. It is substantially slower than the standard algorithm. This is
192 partly because it has to search for all possible matches, but is also
193 because it is less susceptible to optimization.
194 2. Capturing parentheses and backreferences are not supported.
196 3. Although atomic groups are supported, their use does not provide the
198 performance advantage that it does for the standard algorithm.
199
201 Philip Hazel
203 University Computing Service
204 Cambridge, England.
205
207 Last updated: 29 September 2014
209 Copyright (c) 1997-2014 University of Cambridge.
210PCRE2 10.00 29 September 2014 PCRE2MATCHING(3)