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Technical Notes about PCRE
--------------------------

These are very rough technical notes that record potentially useful information 
about PCRE internals.

Historical note 1
-----------------

Many years ago I implemented some regular expression functions to an algorithm
suggested by Martin Richards. These were not Unix-like in form, and were quite
restricted in what they could do by comparison with Perl. The interesting part
about the algorithm was that the amount of space required to hold the compiled
form of an expression was known in advance. The code to apply an expression did
not operate by backtracking, as the original Henry Spencer code and current
Perl code does, but instead checked all possibilities simultaneously by keeping
a list of current states and checking all of them as it advanced through the
subject string. In the terminology of Jeffrey Friedl's book, it was a "DFA
algorithm", though it was not a traditional Finite State Machine (FSM). When
the pattern was all used up, all remaining states were possible matches, and
the one matching the longest subset of the subject string was chosen. This did
not necessarily maximize the individual wild portions of the pattern, as is
expected in Unix and Perl-style regular expressions.

Historical note 2
-----------------

By contrast, the code originally written by Henry Spencer (which was
subsequently heavily modified for Perl) compiles the expression twice: once in
a dummy mode in order to find out how much store will be needed, and then for
real. (The Perl version probably doesn't do this any more; I'm talking about
the original library.) The execution function operates by backtracking and
maximizing (or, optionally, minimizing in Perl) the amount of the subject that
matches individual wild portions of the pattern. This is an "NFA algorithm" in
Friedl's terminology.

OK, here's the real stuff
-------------------------

For the set of functions that form the "basic" PCRE library (which are
unrelated to those mentioned above), I tried at first to invent an algorithm
that used an amount of store bounded by a multiple of the number of characters
in the pattern, to save on compiling time. However, because of the greater
complexity in Perl regular expressions, I couldn't do this. In any case, a
first pass through the pattern is helpful for other reasons.

Computing the memory requirement: how it was
--------------------------------------------

Up to and including release 6.7, PCRE worked by running a very degenerate first
pass to calculate a maximum store size, and then a second pass to do the real
compile - which might use a bit less than the predicted amount of memory. The
idea was that this would turn out faster than the Henry Spencer code because
the first pass is degenerate and the second pass can just store stuff straight
into the vector, which it knows is big enough.

Computing the memory requirement: how it is
-------------------------------------------

By the time I was working on a potential 6.8 release, the degenerate first pass
had become very complicated and hard to maintain. Indeed one of the early
things I did for 6.8 was to fix Yet Another Bug in the memory computation. Then
I had a flash of inspiration as to how I could run the real compile function in
a "fake" mode that enables it to compute how much memory it would need, while
actually only ever using a few hundred bytes of working memory, and without too
many tests of the mode that might slow it down. So I re-factored the compiling
functions to work this way. This got rid of about 600 lines of source. It
should make future maintenance and development easier. As this was such a major 
change, I never released 6.8, instead upping the number to 7.0 (other quite 
major changes were also present in the 7.0 release).

A side effect of this work was that the previous limit of 200 on the nesting
depth of parentheses was removed. However, there is a downside: pcre_compile()
runs more slowly than before (30% or more, depending on the pattern) because it
is doing a full analysis of the pattern. My hope was that this would not be a
big issue, and in the event, nobody has commented on it.

Traditional matching function
-----------------------------

The "traditional", and original, matching function is called pcre_exec(), and 
it implements an NFA algorithm, similar to the original Henry Spencer algorithm 
and the way that Perl works. This is not surprising, since it is intended to be
as compatible with Perl as possible. This is the function most users of PCRE
will use most of the time.

Supplementary matching function
-------------------------------

From PCRE 6.0, there is also a supplementary matching function called 
pcre_dfa_exec(). This implements a DFA matching algorithm that searches 
simultaneously for all possible matches that start at one point in the subject 
string. (Going back to my roots: see Historical Note 1 above.) This function 
intreprets the same compiled pattern data as pcre_exec(); however, not all the 
facilities are available, and those that are do not always work in quite the 
same way. See the user documentation for details.

The algorithm that is used for pcre_dfa_exec() is not a traditional FSM, 
because it may have a number of states active at one time. More work would be 
needed at compile time to produce a traditional FSM where only one state is 
ever active at once. I believe some other regex matchers work this way.

Format of compiled patterns
---------------------------

The compiled form of a pattern is a vector of bytes, containing items of
variable length. The first byte in an item is an opcode, and the length of the
item is either implicit in the opcode or contained in the data bytes that
follow it.

In many cases below LINK_SIZE data values are specified for offsets within the 
compiled pattern. The default value for LINK_SIZE is 2, but PCRE can be
compiled to use 3-byte or 4-byte values for these offsets (impairing the
performance). This is necessary only when patterns whose compiled length is
greater than 64K are going to be processed. In this description, we assume the
"normal" compilation options. Data values that are counts (e.g. for
quantifiers) are always just two bytes long.

A list of the opcodes follows:

Opcodes with no following data
------------------------------

These items are all just one byte long

OP_END                 end of pattern
  OP_ANY                 match any one character other than newline
  OP_ALLANY              match any one character, including newline
  OP_ANYBYTE             match any single byte, even in UTF-8 mode
  OP_SOD                 match start of data: \A
  OP_SOM,                start of match (subject + offset): \G
  OP_SET_SOM,            set start of match (\K) 
  OP_CIRC                ^ (start of data, or after \n in multiline)
  OP_NOT_WORD_BOUNDARY   \W
  OP_WORD_BOUNDARY       \w
  OP_NOT_DIGIT           \D
  OP_DIGIT               \d
  OP_NOT_HSPACE          \H
  OP_HSPACE              \h  
  OP_NOT_WHITESPACE      \S
  OP_WHITESPACE          \s
  OP_NOT_VSPACE          \V
  OP_VSPACE              \v  
  OP_NOT_WORDCHAR        \W
  OP_WORDCHAR            \w
  OP_EODN                match end of data or \n at end: \Z
  OP_EOD                 match end of data: \z
  OP_DOLL                $ (end of data, or before \n in multiline)
  OP_EXTUNI              match an extended Unicode character 
  OP_ANYNL               match any Unicode newline sequence 
  
  OP_ACCEPT              ) These are Perl 5.10's "backtracking    
  OP_COMMIT              ) control verbs". If OP_ACCEPT is inside
  OP_FAIL                ) capturing parentheses, it may be preceded 
  OP_PRUNE               ) by one or more OP_CLOSE, followed by a 2-byte 
  OP_SKIP                ) number, indicating which parentheses must be
  OP_THEN                ) closed.

Repeating single characters
---------------------------

The common repeats (*, +, ?) when applied to a single character use the
following opcodes:

OP_STAR
  OP_MINSTAR
  OP_POSSTAR 
  OP_PLUS
  OP_MINPLUS
  OP_POSPLUS 
  OP_QUERY
  OP_MINQUERY
  OP_POSQUERY

In ASCII mode, these are two-byte items; in UTF-8 mode, the length is variable.
Those with "MIN" in their name are the minimizing versions. Those with "POS" in 
their names are possessive versions. Each is followed by the character that is
to be repeated. Other repeats make use of

OP_UPTO
  OP_MINUPTO
  OP_POSUPTO 
  OP_EXACT

which are followed by a two-byte count (most significant first) and the
repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
OP_UPTO (or OP_MINUPTO or OPT_POSUPTO).

Repeating character types
-------------------------

Repeats of things like \d are done exactly as for single characters, except
that instead of a character, the opcode for the type is stored in the data
byte. The opcodes are:

OP_TYPESTAR
  OP_TYPEMINSTAR
  OP_TYPEPOSSTAR 
  OP_TYPEPLUS
  OP_TYPEMINPLUS
  OP_TYPEPOSPLUS 
  OP_TYPEQUERY
  OP_TYPEMINQUERY
  OP_TYPEPOSQUERY 
  OP_TYPEUPTO
  OP_TYPEMINUPTO
  OP_TYPEPOSUPTO 
  OP_TYPEEXACT

Match by Unicode property
-------------------------

OP_PROP and OP_NOTPROP are used for positive and negative matches of a 
character by testing its Unicode property (the \p and \P escape sequences).
Each is followed by two bytes that encode the desired property as a type and a 
value.

Repeats of these items use the OP_TYPESTAR etc. set of opcodes, followed by 
three bytes: OP_PROP or OP_NOTPROP and then the desired property type and 
value.

Matching literal characters
---------------------------

The OP_CHAR opcode is followed by a single character that is to be matched 
casefully. For caseless matching, OP_CHARNC is used. In UTF-8 mode, the 
character may be more than one byte long. (Earlier versions of PCRE used 
multi-character strings, but this was changed to allow some new features to be 
added.)

Character classes
-----------------

If there is only one character, OP_CHAR or OP_CHARNC is used for a positive
class, and OP_NOT for a negative one (that is, for something like [^a]).
However, in UTF-8 mode, the use of OP_NOT applies only to characters with
values < 128, because OP_NOT is confined to single bytes.

Another set of repeating opcodes (OP_NOTSTAR etc.) are used for a repeated,
negated, single-character class. The normal ones (OP_STAR etc.) are used for a
repeated positive single-character class.

When there's more than one character in a class and all the characters are less
than 256, OP_CLASS is used for a positive class, and OP_NCLASS for a negative
one. In either case, the opcode is followed by a 32-byte bit map containing a 1
bit for every character that is acceptable. The bits are counted from the least
significant end of each byte.

The reason for having both OP_CLASS and OP_NCLASS is so that, in UTF-8 mode,
subject characters with values greater than 256 can be handled correctly. For
OP_CLASS they don't match, whereas for OP_NCLASS they do.

For classes containing characters with values > 255, OP_XCLASS is used. It
optionally uses a bit map (if any characters lie within it), followed by a list
of pairs and single characters. There is a flag character than indicates
whether it's a positive or a negative class.

Back references
---------------

OP_REF is followed by two bytes containing the reference number.

Repeating character classes and back references
-----------------------------------------------

Single-character classes are handled specially (see above). This section
applies to OP_CLASS and OP_REF. In both cases, the repeat information follows
the base item. The matching code looks at the following opcode to see if it is
one of

OP_CRSTAR
  OP_CRMINSTAR
  OP_CRPLUS
  OP_CRMINPLUS
  OP_CRQUERY
  OP_CRMINQUERY
  OP_CRRANGE
  OP_CRMINRANGE

All but the last two are just single-byte items. The others are followed by
four bytes of data, comprising the minimum and maximum repeat counts. There are 
no special possessive opcodes for these repeats; a possessive repeat is 
compiled into an atomic group.

Brackets and alternation
------------------------

A pair of non-capturing (round) brackets is wrapped round each expression at
compile time, so alternation always happens in the context of brackets.

[Note for North Americans: "bracket" to some English speakers, including
myself, can be round, square, curly, or pointy. Hence this usage.]

Non-capturing brackets use the opcode OP_BRA. Originally PCRE was limited to 99
capturing brackets and it used a different opcode for each one. From release
3.5, the limit was removed by putting the bracket number into the data for
higher-numbered brackets. From release 7.0 all capturing brackets are handled
this way, using the single opcode OP_CBRA.

A bracket opcode is followed by LINK_SIZE bytes which give the offset to the
next alternative OP_ALT or, if there aren't any branches, to the matching
OP_KET opcode. Each OP_ALT is followed by LINK_SIZE bytes giving the offset to
the next one, or to the OP_KET opcode. For capturing brackets, the bracket 
number immediately follows the offset, always as a 2-byte item.

OP_KET is used for subpatterns that do not repeat indefinitely, while
OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
maximally respectively. All three are followed by LINK_SIZE bytes giving (as a
positive number) the offset back to the matching bracket opcode.

If a subpattern is quantified such that it is permitted to match zero times, it
is preceded by one of OP_BRAZERO, OP_BRAMINZERO, or OP_SKIPZERO. These are
single-byte opcodes that tell the matcher that skipping the following
subpattern entirely is a valid branch. In the case of the first two, not 
skipping the pattern is also valid (greedy and non-greedy). The third is used 
when a pattern has the quantifier {0,0}. It cannot be entirely discarded, 
because it may be called as a subroutine from elsewhere in the regex.

A subpattern with an indefinite maximum repetition is replicated in the
compiled data its minimum number of times (or once with OP_BRAZERO if the
minimum is zero), with the final copy terminating with OP_KETRMIN or OP_KETRMAX
as appropriate.

A subpattern with a bounded maximum repetition is replicated in a nested
fashion up to the maximum number of times, with OP_BRAZERO or OP_BRAMINZERO
before each replication after the minimum, so that, for example, (abc){2,5} is
compiled as (abc)(abc)((abc)((abc)(abc)?)?)?, except that each bracketed group 
has the same number.

When a repeated subpattern has an unbounded upper limit, it is checked to see 
whether it could match an empty string. If this is the case, the opcode in the 
final replication is changed to OP_SBRA or OP_SCBRA. This tells the matcher
that it needs to check for matching an empty string when it hits OP_KETRMIN or
OP_KETRMAX, and if so, to break the loop.

Assertions
----------

Forward assertions are just like other subpatterns, but starting with one of
the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes
OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion
is OP_REVERSE, followed by a two byte count of the number of characters to move
back the pointer in the subject string. When operating in UTF-8 mode, the count
is a character count rather than a byte count. A separate count is present in
each alternative of a lookbehind assertion, allowing them to have different
fixed lengths.

Once-only (atomic) subpatterns
------------------------------

These are also just like other subpatterns, but they start with the opcode
OP_ONCE. The check for matching an empty string in an unbounded repeat is 
handled entirely at runtime, so there is just this one opcode.

Conditional subpatterns
-----------------------

These are like other subpatterns, but they start with the opcode OP_COND, or
OP_SCOND for one that might match an empty string in an unbounded repeat. If
the condition is a back reference, this is stored at the start of the
subpattern using the opcode OP_CREF followed by two bytes containing the
reference number. OP_NCREF is used instead if the reference was generated by 
name (so that the runtime code knows to check for duplicate names).

If the condition is "in recursion" (coded as "(?(R)"), or "in recursion of
group x" (coded as "(?(Rx)"), the group number is stored at the start of the
subpattern using the opcode OP_RREF or OP_NRREF (cf OP_NCREF), and a value of
zero for "the whole pattern". For a DEFINE condition, just the single byte
OP_DEF is used (it has no associated data). Otherwise, a conditional subpattern
always starts with one of the assertions.

Recursion
---------

Recursion either matches the current regex, or some subexpression. The opcode
OP_RECURSE is followed by an value which is the offset to the starting bracket
from the start of the whole pattern. From release 6.5, OP_RECURSE is 
automatically wrapped inside OP_ONCE brackets (because otherwise some patterns 
broke it). OP_RECURSE is also used for "subroutine" calls, even though they 
are not strictly a recursion.

Callout
-------

OP_CALLOUT is followed by one byte of data that holds a callout number in the
range 0 to 254 for manual callouts, or 255 for an automatic callout. In both 
cases there follows a two-byte value giving the offset in the pattern to the
start of the following item, and another two-byte item giving the length of the
next item.

Changing options
----------------

If any of the /i, /m, or /s options are changed within a pattern, an OP_OPT
opcode is compiled, followed by one byte containing the new settings of these
flags. If there are several alternatives, there is an occurrence of OP_OPT at
the start of all those following the first options change, to set appropriate
options for the start of the alternative. Immediately after the end of the
group there is another such item to reset the flags to their previous values. A
change of flag right at the very start of the pattern can be handled entirely
at compile time, and so does not cause anything to be put into the compiled
data.

Philip Hazel
October 2009

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