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.TH PCREMATCHING 3

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.SH NAME

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PCRE  Perlcompatible regular expressions

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.SH "PCRE MATCHING ALGORITHMS"

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.rs

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.sp

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This document describes the two different algorithms that are available in PCRE

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for matching a compiled regular expression against a given subject string. The

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"standard" algorithm is the one provided by the \fBpcre_exec()\fP function.

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This works in the same was as Perl's matching function, and provides a

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Perlcompatible matching operation.

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.P

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An alternative algorithm is provided by the \fBpcre_dfa_exec()\fP function;

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this operates in a different way, and is not Perlcompatible. It has advantages

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and disadvantages compared with the standard algorithm, and these are described

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below.

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.P

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When there is only one possible way in which a given subject string can match a

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pattern, the two algorithms give the same answer. A difference arises, however,

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when there are multiple possibilities. For example, if the pattern

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.sp

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^<.*>

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.sp

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is matched against the string

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.sp

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<something> <something else> <something further>

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.sp

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there are three possible answers. The standard algorithm finds only one of

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them, whereas the alternative algorithm finds all three.

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.

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.SH "REGULAR EXPRESSIONS AS TREES"

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The set of strings that are matched by a regular expression can be represented

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as a tree structure. An unlimited repetition in the pattern makes the tree of

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infinite size, but it is still a tree. Matching the pattern to a given subject

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string (from a given starting point) can be thought of as a search of the tree.

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There are two ways to search a tree: depthfirst and breadthfirst, and these

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correspond to the two matching algorithms provided by PCRE.

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.

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.SH "THE STANDARD MATCHING ALGORITHM"

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.sp

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In the terminology of Jeffrey Friedl's book "Mastering Regular

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Expressions", the standard algorithm is an "NFA algorithm". It conducts a

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depthfirst search of the pattern tree. That is, it proceeds along a single

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path through the tree, checking that the subject matches what is required. When

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there is a mismatch, the algorithm tries any alternatives at the current point,

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and if they all fail, it backs up to the previous branch point in the tree, and

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tries the next alternative branch at that level. This often involves backing up

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(moving to the left) in the subject string as well. The order in which

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repetition branches are tried is controlled by the greedy or ungreedy nature of

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the quantifier.

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.P

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If a leaf node is reached, a matching string has been found, and at that point

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the algorithm stops. Thus, if there is more than one possible match, this

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algorithm returns the first one that it finds. Whether this is the shortest,

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the longest, or some intermediate length depends on the way the greedy and

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ungreedy repetition quantifiers are specified in the pattern.

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.P

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Because it ends up with a single path through the tree, it is relatively

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straightforward for this algorithm to keep track of the substrings that are

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matched by portions of the pattern in parentheses. This provides support for

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capturing parentheses and back references.

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.

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.SH "THE ALTERNATIVE MATCHING ALGORITHM"

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This algorithm conducts a breadthfirst search of the tree. Starting from the

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first matching point in the subject, it scans the subject string from left to

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right, once, character by character, and as it does this, it remembers all the

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paths through the tree that represent valid matches. In Friedl's terminology,

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this is a kind of "DFA algorithm", though it is not implemented as a

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traditional finite state machine (it keeps multiple states active

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simultaneously).

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.P

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The scan continues until either the end of the subject is reached, or there are

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no more unterminated paths. At this point, terminated paths represent the

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different matching possibilities (if there are none, the match has failed).

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Thus, if there is more than one possible match, this algorithm finds all of

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them, and in particular, it finds the longest. In PCRE, there is an option to

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stop the algorithm after the first match (which is necessarily the shortest)

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has been found.

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.P

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Note that all the matches that are found start at the same point in the

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subject. If the pattern

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.sp

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cat(er(pillar)?)

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.sp

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is matched against the string "the caterpillar catchment", the result will be

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the three strings "cat", "cater", and "caterpillar" that start at the fourth

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character of the subject. The algorithm does not automatically move on to find

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matches that start at later positions.

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.P

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There are a number of features of PCRE regular expressions that are not

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supported by the alternative matching algorithm. They are as follows:

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.P

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1. Because the algorithm finds all possible matches, the greedy or ungreedy

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nature of repetition quantifiers is not relevant. Greedy and ungreedy

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quantifiers are treated in exactly the same way. However, possessive

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quantifiers can make a difference when what follows could also match what is

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quantified, for example in a pattern like this:

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.sp

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^a++\ew!

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.sp

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This pattern matches "aaab!" but not "aaa!", which would be matched by a

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nonpossessive quantifier. Similarly, if an atomic group is present, it is

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matched as if it were a standalone pattern at the current point, and the

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longest match is then "locked in" for the rest of the overall pattern.

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.P

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2. When dealing with multiple paths through the tree simultaneously, it is not

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straightforward to keep track of captured substrings for the different matching

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possibilities, and PCRE's implementation of this algorithm does not attempt to

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do this. This means that no captured substrings are available.

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.P

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3. Because no substrings are captured, back references within the pattern are

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not supported, and cause errors if encountered.

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.P

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4. For the same reason, conditional expressions that use a backreference as the

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condition or test for a specific group recursion are not supported.

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.P

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5. Because many paths through the tree may be active, the \eK escape sequence,

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which resets the start of the match when encountered (but may be on some paths

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and not on others), is not supported. It causes an error if encountered.

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.P

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6. Callouts are supported, but the value of the \fIcapture_top\fP field is

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always 1, and the value of the \fIcapture_last\fP field is always 1.

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.P

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7. The \eC escape sequence, which (in the standard algorithm) matches a single

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byte, even in UTF8 mode, is not supported because the alternative algorithm

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moves through the subject string one character at a time, for all active paths

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through the tree.

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.P

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8. None of the backtracking control verbs such as (*PRUNE) are supported.

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.

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.SH "ADVANTAGES OF THE ALTERNATIVE ALGORITHM"

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Using the alternative matching algorithm provides the following advantages:

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.P

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1. All possible matches (at a single point in the subject) are automatically

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found, and in particular, the longest match is found. To find more than one

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match using the standard algorithm, you have to do kludgy things with

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callouts.

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.P

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2. There is much better support for partial matching. The restrictions on the

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content of the pattern that apply when using the standard algorithm for partial

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matching do not apply to the alternative algorithm. For nonanchored patterns,

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the starting position of a partial match is available.

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.P

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3. Because the alternative algorithm scans the subject string just once, and

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never needs to backtrack, it is possible to pass very long subject strings to

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the matching function in several pieces, checking for partial matching each

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time.

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.

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.SH "DISADVANTAGES OF THE ALTERNATIVE ALGORITHM"

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The alternative algorithm suffers from a number of disadvantages:

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.P

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1. It is substantially slower than the standard algorithm. This is partly

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because it has to search for all possible matches, but is also because it is

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less susceptible to optimization.

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.P

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2. Capturing parentheses and back references are not supported.

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.P

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3. Although atomic groups are supported, their use does not provide the

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performance advantage that it does for the standard algorithm.

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.

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.

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.SH AUTHOR

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.sp

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Philip Hazel

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University Computing Service

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Cambridge CB2 3QH, England.

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.

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.SH REVISION

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Last updated: 08 August 2007

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Copyright (c) 19972007 University of Cambridge.

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