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```PCRE2MATCHING(3)      DragonFly Library Functions Manual      PCRE2MATCHING(3)

NAME
PCRE2 - Perl-compatible regular expressions (revised API)

PCRE2 MATCHING ALGORITHMS
This document describes the two different algorithms that are available
in PCRE2 for matching a compiled regular expression against a given
subject string. The "standard" algorithm is the one provided by the
pcre2_match() function. This works in the same as as Perl's matching
function, and provide a Perl-compatible matching operation. The just-
in-time (JIT) optimization that is described in the pcre2jit
documentation is compatible with this function.

An alternative algorithm is provided by the pcre2_dfa_match() function;
it operates in a different way, and is not Perl-compatible. This
algorithm, and these are described below.

When there is only one possible way in which a given subject string can
match a pattern, the two algorithms give the same answer. A difference
arises, however, when there are multiple possibilities. For example, if
the pattern

^<.*>

is matched against the string

<something> <something else> <something further>

there are three possible answers. The standard algorithm finds only one
of them, whereas the alternative algorithm finds all three.

REGULAR EXPRESSIONS AS TREES
The set of strings that are matched by a regular expression can be
represented as a tree structure. An unlimited repetition in the pattern
makes the tree of infinite size, but it is still a tree. Matching the
pattern to a given subject string (from a given starting point) can be
thought of as a search of the tree.  There are two ways to search a
tree: depth-first and breadth-first, and these correspond to the two
matching algorithms provided by PCRE2.

THE STANDARD MATCHING ALGORITHM
In the terminology of Jeffrey Friedl's book "Mastering Regular
Expressions", the standard algorithm is an "NFA algorithm". It conducts
a depth-first search of the pattern tree. That is, it proceeds along a
single path through the tree, checking that the subject matches what is
required. When there is a mismatch, the algorithm tries any
alternatives at the current point, and if they all fail, it backs up to
the previous branch point in the tree, and tries the next alternative
branch at that level. This often involves backing up (moving to the
left) in the subject string as well. The order in which repetition
branches are tried is controlled by the greedy or ungreedy nature of
the quantifier.

If a leaf node is reached, a matching string has been found, and at
that point the algorithm stops. Thus, if there is more than one
possible match, this algorithm returns the first one that it finds.
Whether this is the shortest, the longest, or some intermediate length
depends on the way the alternations and the greedy or ungreedy
repetition quantifiers are specified in the pattern.

Because it ends up with a single path through the tree, it is
relatively straightforward for this algorithm to keep track of the
substrings that are matched by portions of the pattern in parentheses.
This provides support for capturing parentheses and backreferences.

THE ALTERNATIVE MATCHING ALGORITHM
This algorithm conducts a breadth-first search of the tree. Starting
from the first matching point in the subject, it scans the subject
string from left to right, once, character by character, and as it does
this, it remembers all the paths through the tree that represent valid
matches. In Friedl's terminology, this is a kind of "DFA algorithm",
though it is not implemented as a traditional finite state machine (it
keeps multiple states active simultaneously).

Although the general principle of this matching algorithm is that it
scans the subject string only once, without backtracking, there is one
exception: when a lookaround assertion is encountered, the characters
following or preceding the current point have to be independently
inspected.

The scan continues until either the end of the subject is reached, or
there are no more unterminated paths. At this point, terminated paths
represent the different matching possibilities (if there are none, the
match has failed).  Thus, if there is more than one possible match,
this algorithm finds all of them, and in particular, it finds the
longest. The matches are returned in the output vector in decreasing
order of length. There is an option to stop the algorithm after the
first match (which is necessarily the shortest) is found.

Note that the size of vector needed to contain all the results depends
on the number of simultaneous matches, not on the number of parentheses
in the pattern. Using pcre2_match_data_create_from_pattern() to create
the match data block is therefore not advisable when doing DFA
matching.

Note also that all the matches that are found start at the same point
in the subject. If the pattern

cat(er(pillar)?)?

is matched against the string "the caterpillar catchment", the result
is the three strings "caterpillar", "cater", and "cat" that start at
the fifth character of the subject. The algorithm does not
automatically move on to find matches that start at later positions.

PCRE2's "auto-possessification" optimization usually applies to
character repeats at the end of a pattern (as well as internally). For
example, the pattern "a\d+" is compiled as if it were "a\d++" because
there is no point even considering the possibility of backtracking into
the repeated digits. For DFA matching, this means that only one
possible match is found. If you really do want multiple matches in such
cases, either use an ungreedy repeat ("a\d+?") or set the
PCRE2_NO_AUTO_POSSESS option when compiling.

There are a number of features of PCRE2 regular expressions that are
not supported or behave differently in the alternative matching
function. Those that are not supported cause an error if encountered.

1. Because the algorithm finds all possible matches, the greedy or
ungreedy nature of repetition quantifiers is not relevant (though it
may affect auto-possessification, as just described). During matching,
greedy and ungreedy quantifiers are treated in exactly the same way.
However, possessive quantifiers can make a difference when what follows
could also match what is quantified, for example in a pattern like
this:

^a++\w!

This pattern matches "aaab!" but not "aaa!", which would be matched by
a non-possessive quantifier. Similarly, if an atomic group is present,
it is matched as if it were a standalone pattern at the current point,
and the longest match is then "locked in" for the rest of the overall
pattern.

2. When dealing with multiple paths through the tree simultaneously, it
is not straightforward to keep track of captured substrings for the
different matching possibilities, and PCRE2's implementation of this
algorithm does not attempt to do this. This means that no captured
substrings are available.

3. Because no substrings are captured, backreferences within the
pattern are not supported.

4. For the same reason, conditional expressions that use a
backreference as the condition or test for a specific group recursion
are not supported.

5. Again for the same reason, script runs are not supported.

6. Because many paths through the tree may be active, the \K escape
sequence, which resets the start of the match when encountered (but may
be on some paths and not on others), is not supported.

7. Callouts are supported, but the value of the capture_top field is
always 1, and the value of the capture_last field is always 0.

8. The \C escape sequence, which (in the standard algorithm) always
matches a single code unit, even in a UTF mode, is not supported in
these modes, because the alternative algorithm moves through the
subject string one character (not code unit) at a time, for all active
paths through the tree.

9. Except for (*FAIL), the backtracking control verbs such as (*PRUNE)
are not supported. (*FAIL) is supported, and behaves like a failing
negative assertion.

10. The PCRE2_MATCH_INVALID_UTF option for pcre2_compile() is not
supported by pcre2_dfa_match().

The main advantage of the alternative algorithm is that all possible
matches (at a single point in the subject) are automatically found, and
in particular, the longest match is found. To find more than one match
at the same point using the standard algorithm, you have to do kludgy
things with callouts.

Partial matching is possible with this algorithm, though it has some
limitations. The pcre2partial documentation gives details of partial
matching and discusses multi-segment matching.

The alternative algorithm suffers from a number of disadvantages:

1. It is substantially slower than the standard algorithm. This is
partly because it has to search for all possible matches, but is also
because it is less susceptible to optimization.

2. Capturing parentheses, backreferences, script runs, and matching
within invalid UTF string are not supported.

3. Although atomic groups are supported, their use does not provide the
performance advantage that it does for the standard algorithm.

4. JIT optimization is not supported.

AUTHOR
Philip Hazel
Retired from University Computing Service
Cambridge, England.

REVISION
Last updated: 28 August 2021
Copyright (c) 1997-2021 University of Cambridge.

PCRE2 10.38                     28 August 2021                PCRE2MATCHING(3)
PCRE2MATCHING(3)      DragonFly Library Functions Manual      PCRE2MATCHING(3)

NAME
PCRE2 - Perl-compatible regular expressions (revised API)

PCRE2 MATCHING ALGORITHMS
This document describes the two different algorithms that are available
in PCRE2 for matching a compiled regular expression against a given
subject string. The "standard" algorithm is the one provided by the
pcre2_match() function. This works in the same as as Perl's matching
function, and provide a Perl-compatible matching operation. The just-
in-time (JIT) optimization that is described in the pcre2jit
documentation is compatible with this function.

An alternative algorithm is provided by the pcre2_dfa_match() function;
it operates in a different way, and is not Perl-compatible. This
algorithm, and these are described below.

When there is only one possible way in which a given subject string can
match a pattern, the two algorithms give the same answer. A difference
arises, however, when there are multiple possibilities. For example, if
the pattern

^<.*>

is matched against the string

<something> <something else> <something further>

there are three possible answers. The standard algorithm finds only one
of them, whereas the alternative algorithm finds all three.

REGULAR EXPRESSIONS AS TREES
The set of strings that are matched by a regular expression can be
represented as a tree structure. An unlimited repetition in the pattern
makes the tree of infinite size, but it is still a tree. Matching the
pattern to a given subject string (from a given starting point) can be
thought of as a search of the tree.  There are two ways to search a
tree: depth-first and breadth-first, and these correspond to the two
matching algorithms provided by PCRE2.

THE STANDARD MATCHING ALGORITHM
In the terminology of Jeffrey Friedl's book "Mastering Regular
Expressions", the standard algorithm is an "NFA algorithm". It conducts
a depth-first search of the pattern tree. That is, it proceeds along a
single path through the tree, checking that the subject matches what is
required. When there is a mismatch, the algorithm tries any
alternatives at the current point, and if they all fail, it backs up to
the previous branch point in the tree, and tries the next alternative
branch at that level. This often involves backing up (moving to the
left) in the subject string as well. The order in which repetition
branches are tried is controlled by the greedy or ungreedy nature of
the quantifier.

If a leaf node is reached, a matching string has been found, and at
that point the algorithm stops. Thus, if there is more than one
possible match, this algorithm returns the first one that it finds.
Whether this is the shortest, the longest, or some intermediate length
depends on the way the alternations and the greedy or ungreedy
repetition quantifiers are specified in the pattern.

Because it ends up with a single path through the tree, it is
relatively straightforward for this algorithm to keep track of the
substrings that are matched by portions of the pattern in parentheses.
This provides support for capturing parentheses and backreferences.

THE ALTERNATIVE MATCHING ALGORITHM
This algorithm conducts a breadth-first search of the tree. Starting
from the first matching point in the subject, it scans the subject
string from left to right, once, character by character, and as it does
this, it remembers all the paths through the tree that represent valid
matches. In Friedl's terminology, this is a kind of "DFA algorithm",
though it is not implemented as a traditional finite state machine (it
keeps multiple states active simultaneously).

Although the general principle of this matching algorithm is that it
scans the subject string only once, without backtracking, there is one
exception: when a lookaround assertion is encountered, the characters
following or preceding the current point have to be independently
inspected.

The scan continues until either the end of the subject is reached, or
there are no more unterminated paths. At this point, terminated paths
represent the different matching possibilities (if there are none, the
match has failed).  Thus, if there is more than one possible match,
this algorithm finds all of them, and in particular, it finds the
longest. The matches are returned in the output vector in decreasing
order of length. There is an option to stop the algorithm after the
first match (which is necessarily the shortest) is found.

Note that the size of vector needed to contain all the results depends
on the number of simultaneous matches, not on the number of parentheses
in the pattern. Using pcre2_match_data_create_from_pattern() to create
the match data block is therefore not advisable when doing DFA
matching.

Note also that all the matches that are found start at the same point
in the subject. If the pattern

cat(er(pillar)?)?

is matched against the string "the caterpillar catchment", the result
is the three strings "caterpillar", "cater", and "cat" that start at
the fifth character of the subject. The algorithm does not
automatically move on to find matches that start at later positions.

PCRE2's "auto-possessification" optimization usually applies to
character repeats at the end of a pattern (as well as internally). For
example, the pattern "a\d+" is compiled as if it were "a\d++" because
there is no point even considering the possibility of backtracking into
the repeated digits. For DFA matching, this means that only one
possible match is found. If you really do want multiple matches in such
cases, either use an ungreedy repeat ("a\d+?") or set the
PCRE2_NO_AUTO_POSSESS option when compiling.

There are a number of features of PCRE2 regular expressions that are
not supported or behave differently in the alternative matching
function. Those that are not supported cause an error if encountered.

1. Because the algorithm finds all possible matches, the greedy or
ungreedy nature of repetition quantifiers is not relevant (though it
may affect auto-possessification, as just described). During matching,
greedy and ungreedy quantifiers are treated in exactly the same way.
However, possessive quantifiers can make a difference when what follows
could also match what is quantified, for example in a pattern like
this:

^a++\w!

This pattern matches "aaab!" but not "aaa!", which would be matched by
a non-possessive quantifier. Similarly, if an atomic group is present,
it is matched as if it were a standalone pattern at the current point,
and the longest match is then "locked in" for the rest of the overall
pattern.

2. When dealing with multiple paths through the tree simultaneously, it
is not straightforward to keep track of captured substrings for the
different matching possibilities, and PCRE2's implementation of this
algorithm does not attempt to do this. This means that no captured
substrings are available.

3. Because no substrings are captured, backreferences within the
pattern are not supported.

4. For the same reason, conditional expressions that use a
backreference as the condition or test for a specific group recursion
are not supported.

5. Again for the same reason, script runs are not supported.

6. Because many paths through the tree may be active, the \K escape
sequence, which resets the start of the match when encountered (but may
be on some paths and not on others), is not supported.

7. Callouts are supported, but the value of the capture_top field is
always 1, and the value of the capture_last field is always 0.

8. The \C escape sequence, which (in the standard algorithm) always
matches a single code unit, even in a UTF mode, is not supported in
these modes, because the alternative algorithm moves through the
subject string one character (not code unit) at a time, for all active
paths through the tree.

9. Except for (*FAIL), the backtracking control verbs such as (*PRUNE)
are not supported. (*FAIL) is supported, and behaves like a failing
negative assertion.

10. The PCRE2_MATCH_INVALID_UTF option for pcre2_compile() is not
supported by pcre2_dfa_match().

The main advantage of the alternative algorithm is that all possible
matches (at a single point in the subject) are automatically found, and
in particular, the longest match is found. To find more than one match
at the same point using the standard algorithm, you have to do kludgy
things with callouts.

Partial matching is possible with this algorithm, though it has some
limitations. The pcre2partial documentation gives details of partial
matching and discusses multi-segment matching.

The alternative algorithm suffers from a number of disadvantages:

1. It is substantially slower than the standard algorithm. This is
partly because it has to search for all possible matches, but is also
because it is less susceptible to optimization.

2. Capturing parentheses, backreferences, script runs, and matching
within invalid UTF string are not supported.

3. Although atomic groups are supported, their use does not provide the
performance advantage that it does for the standard algorithm.

4. JIT optimization is not supported.

AUTHOR
Philip Hazel
Retired from University Computing Service
Cambridge, England.

REVISION
Last updated: 28 August 2021
Copyright (c) 1997-2021 University of Cambridge.

PCRE2 10.38                     28 August 2021                PCRE2MATCHING(3)
```

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