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 are also present in the 7.0 release).

A side effect of this work is 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 is that this is not a big

issue.

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. 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              )

  OP_COMMIT              ) 

  OP_FAIL                ) These are Perl 5.10's "backtracking     

  OP_PRUNE               ) control verbs".                         

  OP_SKIP                )

  OP_THEN                )

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. 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, 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

April 2008