Technical Notes about PCRE2
---------------------------

These are very rough technical notes that record potentially useful information
about PCRE2 internals. PCRE2 is a library based on the original PCRE library,
but with a revised (and incompatible) API. To avoid confusion, the original
library is referred to as PCRE1 below. For information about testing PCRE2, see
the pcre2test documentation and the comment at the head of the RunTest file.

PCRE1 releases were up to 8.3x when PCRE2 was developed. The 8.xx series will
continue for bugfixes if necessary. PCRE2 releases started at 10.00 to avoid
confusion with PCRE1.


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
PCRE2 and 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 formed the original PCRE1 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.


Support for 16-bit and 32-bit data strings
-------------------------------------------

The library can be compiled in any combination of 8-bit, 16-bit or 32-bit
modes, creating up to three different libraries. In the description that
follows, the word "short" is used for a 16-bit data quantity, and the phrase
"code unit" is used for a quantity that is a byte in 8-bit mode, a short in
16-bit mode and a 32-bit word in 32-bit mode. The names of PCRE2 functions are
given in generic form, without the _8, _16, or _32 suffix.


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

Up to and including release 6.7, PCRE1 worked by running a very degenerate
first pass to calculate a maximum memory requirement, 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 memory, 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 refactored 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 was a downside: compiling ran
more slowly than before (30% or more, depending on the pattern) because it now
did 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.

At release 8.34, a limit on the nesting depth of parentheses was re-introduced
(default 250, settable at build time) so as to put a limit on the amount of
system stack used by the compile function, which uses recursive function calls
for nested parenthesized groups. This is a safety feature for environments with
small stacks where the patterns are provided by users.

History repeated itself for release 10.20. A number of bugs relating to named 
subpatterns had been discovered by fuzzers. Most of these were related to the 
handling of forward references when it was not known if the named pattern was
unique. (References to non-unique names use a different opcode and more
memory.) The use of duplicate group numbers (the (?| facility) also caused
issues. 

To get around these problems I adopted a new approach by adding a third pass,
really a "pre-pass", over the pattern, which does nothing other than identify
all the named subpatterns and their corresponding group numbers. This means 
that the actual compile (both pre-pass and real compile) have full knowledge of 
group names and numbers throughout. Several dozen lines of messy code were 
eliminated, though the new pre-pass is not short (skipping over [] classes is 
complicated).


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

The "traditional", and original, matching function is called pcre2_match(), 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 PCRE2
will use most of the time. If PCRE2 is compiled with just-in-time (JIT)
support, and studying a compiled pattern with JIT is successful, the JIT code
is run instead of the normal pcre2_match() code, but the result is the same.


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

There is also a supplementary matching function called pcre2_dfa_match(). 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 pcre2_match(); 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 pcre2_dfa_match() 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. JIT
support is not available for this kind of matching.


Changeable options
------------------

The /i, /m, or /s options (PCRE2_CASELESS, PCRE2_MULTILINE, PCRE2_DOTALL, and
some others) may change in the middle of patterns. Their processing is handled
entirely at compile time by generating different opcodes for the different
settings. The runtime functions do not need to keep track of an options state.


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

The compiled form of a pattern is a vector of unsigned code units (bytes in
8-bit mode, shorts in 16-bit mode, 32-bit words in 32-bit mode), containing
items of variable length. The first code unit in an item contains an opcode,
and the length of the item is either implicit in the opcode or contained in the
data that follows it.

In many cases listed below, LINK_SIZE data values are specified for offsets
within the compiled pattern. LINK_SIZE always specifies a number of bytes. The
default value for LINK_SIZE is 2, except for the 32-bit library, where it can
only be 4. The 8-bit library can be compiled to used 3-byte or 4-byte values,
and the 16-bit library can be compiled to use 4-byte values, though this
impairs performance. Specifing a LINK_SIZE larger than 2 for these libraries is
necessary only when patterns whose compiled length is greater than 64K code
units are going to be processed. When a LINK_SIZE value uses more than one code
unit, the most significant unit is first.

In this description, we assume the "normal" compilation options. Data values
that are counts (e.g. quantifiers) are always two bytes long in 8-bit mode
(most significant byte first), or one code unit in 16-bit and 32-bit modes.


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

These items are all just one unit 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 code unit, even in UTF-8/16 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)
  OP_CIRCM               ^ multiline mode (start of data or after newline)
  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 newline at end: \Z
  OP_EOD                 match end of data: \z
  OP_DOLL                $ (end of data, or before final newline)
  OP_DOLLM               $ multiline mode (end of data or before newline)
  OP_EXTUNI              match an extended Unicode grapheme cluster
  OP_ANYNL               match any Unicode newline sequence

  OP_ASSERT_ACCEPT       )
  OP_ACCEPT              ) These are Perl 5.10's "backtracking control
  OP_COMMIT              ) verbs". If OP_ACCEPT is inside capturing
  OP_FAIL                ) parentheses, it may be preceded by one or more
  OP_PRUNE               ) OP_CLOSE, each followed by a count that
  OP_SKIP                ) indicates which parentheses must be closed.
  OP_THEN                )

OP_ASSERT_ACCEPT is used when (*ACCEPT) is encountered within an assertion.
This ends the assertion, not the entire pattern match. The assertion (?!) is 
always optimized to OP_FAIL.


Backtracking control verbs with optional data
---------------------------------------------

(*THEN) without an argument generates the opcode OP_THEN and no following data.
OP_MARK is followed by the mark name, preceded by a length in one code unit,
and followed by a binary zero. For (*PRUNE), (*SKIP), and (*THEN) with
arguments, the opcodes OP_PRUNE_ARG, OP_SKIP_ARG, and OP_THEN_ARG are used,
with the name following in the same format as OP_MARK.


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

The OP_CHAR opcode is followed by a single character that is to be matched
casefully. For caseless matching, OP_CHARI is used. In UTF-8 or UTF-16 modes,
the character may be more than one code unit long. In UTF-32 mode, characters
are always exactly one code unit long.

If there is only one character in a character class, OP_CHAR or OP_CHARI is
used for a positive class, and OP_NOT or OP_NOTI for a negative one (that is,
for something like [^a]).


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

The common repeats (*, +, ?), when applied to a single character, use the
following opcodes, which come in caseful and caseless versions:

  Caseful         Caseless
  OP_STAR         OP_STARI
  OP_MINSTAR      OP_MINSTARI
  OP_POSSTAR      OP_POSSTARI
  OP_PLUS         OP_PLUSI
  OP_MINPLUS      OP_MINPLUSI
  OP_POSPLUS      OP_POSPLUSI
  OP_QUERY        OP_QUERYI
  OP_MINQUERY     OP_MINQUERYI
  OP_POSQUERY     OP_POSQUERYI

Each opcode is followed by the character that is to be repeated. In ASCII or
UTF-32 modes, these are two-code-unit items; in UTF-8 or UTF-16 modes, the
length is variable. Those with "MIN" in their names are the minimizing
versions. Those with "POS" in their names are possessive versions. Other kinds
of repeat make use of these opcodes:

  Caseful         Caseless
  OP_UPTO         OP_UPTOI
  OP_MINUPTO      OP_MINUPTOI
  OP_POSUPTO      OP_POSUPTOI
  OP_EXACT        OP_EXACTI

Each of these is followed by a count and then the repeated character. The count
is two bytes long in 8-bit mode (most significant byte first), or one code unit
in 16-bit and 32-bit modes.

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).

Another set of matching repeating opcodes (called OP_NOTSTAR, OP_NOTSTARI,
etc.) are used for repeated, negated, single-character classes such as [^a]*.
The normal single-character opcodes (OP_STAR, etc.) are used for repeated
positive single-character classes.


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 (e.g. OP_DIGIT) is stored
in the next code unit. 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 code units that encode the desired property as a type
and a value. The types are a set of #defines of the form PT_xxx, and the values
are enumerations of the form ucp_xx, defined in the pcre2_ucp.h source file.
The value is relevant only for PT_GC (General Category), PT_PC (Particular
Category), and PT_SC (Script).

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


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

If there is only one character in a class, OP_CHAR or OP_CHARI is used for a
positive class, and OP_NOT or OP_NOTI for a negative one (that is, for
something like [^a]).

A set of repeating opcodes (called OP_NOTSTAR etc.) are used for repeated,
negated, single-character classes. The normal single-character opcodes
(OP_STAR, etc.) are used for repeated positive single-character classes.

When there is more than one character in a class, and all the code points 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 (16-short,
8-word) bit map containing a 1 bit for every character that is acceptable. The
bits are counted from the least significant end of each unit. In caseless mode,
bits for both cases are set.

The reason for having both OP_CLASS and OP_NCLASS is so that, in UTF-8 and
16-bit and 32-bit modes, subject characters with values greater than 255 can be
handled correctly. For OP_CLASS they do not match, whereas for OP_NCLASS they
do.

For classes containing characters with values greater than 255 or that contain
\p or \P, OP_XCLASS is used. It optionally uses a bit map if any acceptable
code points are less than 256, followed by a list of pairs (for a range) and/or
single characters and/or properties. In caseless mode, both cases are
explicitly listed.

OP_XCLASS is followed by a LINK_SIZE value containing the total length of the
opcode and its data. This is followed by a code unit containing flag bits:
XCL_NOT indicates that this is a negative class, and XCL_MAP indicates that a
bit map is present. There follows the bit map, if XCL_MAP is set, and then a
sequence of items coded as follows:

  XCL_END      marks the end of the list
  XCL_SINGLE   one character follows
  XCL_RANGE    two characters follow
  XCL_PROP     a Unicode property (type, value) follows
  XCL_NOTPROP  a Unicode property (type, value) follows

If a range starts with a code point less than 256 and ends with one greater
than 255, it is split into two ranges, with characters less than 256 being
indicated in the bit map, and the rest with XCL_RANGE.

When XCL_NOT is set, the bit map, if present, contains bits for characters that
are allowed (exactly as for OP_NCLASS), but the list of items that follow it
specifies characters and properties that are not allowed.


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

OP_REF (caseful) or OP_REFI (caseless) is followed by a count containing the
reference number when the reference is to a unique capturing group (either by
number or by name). When named groups are used, there may be more than one
group with the same name. In this case, a reference to such a group by name
generates OP_DNREF or OP_DNREFI. These are followed by two counts: the index
(not the byte offset) in the group name table of the first entry for the
required name, followed by the number of groups with the same name. The
matching code can then search for the first one that is set.


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

Single-character classes are handled specially (see above). This section
applies to other classes and also to back references. 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 these:

  OP_CRSTAR
  OP_CRMINSTAR
  OP_CRPOSSTAR
  OP_CRPLUS
  OP_CRMINPLUS
  OP_CRPOSPLUS
  OP_CRQUERY
  OP_CRMINQUERY
  OP_CRPOSQUERY
  OP_CRRANGE
  OP_CRMINRANGE
  OP_CRPOSRANGE

All but the last three are single-code-unit items, with no data. The others are
followed by the minimum and maximum repeat counts.


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 rather than
"parentheses".]

Non-capturing brackets use the opcode OP_BRA, capturing brackets use OP_CBRA. A
bracket opcode is followed by a LINK_SIZE value which gives 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 a LINK_SIZE value giving the offset
to the next one, or to the OP_KET opcode. For capturing brackets, the bracket
number is a count that immediately follows the offset.

OP_KET is used for subpatterns that do not repeat indefinitely, and OP_KETRMIN
and OP_KETRMAX are used for indefinite repetitions, minimally or maximally
respectively (see below for possessive repetitions). All three are followed by
a LINK_SIZE value 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-unit opcodes that tell the matcher that skipping the following
subpattern entirely is a valid match. 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 pattern.

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.


Possessive brackets
-------------------

When a repeated group (capturing or non-capturing) is marked as possessive by
the "+" notation, e.g. (abc)++, different opcodes are used. Their names all
have POS on the end, e.g. OP_BRAPOS instead of OP_BRA and OP_SCBRAPOS instead
of OP_SCBRA. The end of such a group is marked by OP_KETRPOS. If the minimum
repetition is zero, the group is preceded by OP_BRAPOSZERO.


Once-only (atomic) groups
-------------------------

These are just like other subpatterns, but they start with the opcode
OP_ONCE or OP_ONCE_NC. The former is used when there are no capturing brackets
within the atomic group; the latter when there are. The distinction is needed
for when there is a backtrack to before the group - any captures within the
group must be reset, so it is necessary to retain backtracking points inside
the group, even after it is complete, in order to do this. When there are no
captures in an atomic group, all the backtracking can be discarded when it is
complete. This is more efficient, and also uses less stack.

The check for matching an empty string in an unbounded repeat is handled
entirely at runtime, so there are just these two opcodes for atomic groups.


Assertions
----------

Forward assertions are also 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 count of the number of characters to move back the
pointer in the subject string. In ASCII or UTF-32 mode, the count is also the
number of code units, but in UTF-8/16 mode each character may occupy more than
one code unit. A separate count is present in each alternative of a lookbehind
assertion, allowing them to have different (but fixed) lengths.


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 a count containing the
reference number, provided that the reference is to a unique capturing group.
If the reference was by name and there is more than one group with that name,
OP_DNCREF is used instead. It is followed by two counts: the index in the group
names table, and the number of groups with the same name. The allows the
matcher to check if any group with the given name is set.

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 (with a value of RREF_ANY (0xffff) for "the
whole pattern") or OP_DNRREF (with data as for OP_DNCREF).

For a DEFINE condition, OP_FALSE is used (with no associated data). During
compilation, however, a DEFINE condition is coded as OP_DEFINE so that, when
the conditional group is complete, there can be a check to ensure that it
contains only one top-level branch. Once this has happened, the opcode is
changed to OP_FALSE, so the matcher never sees OP_DEFINE.

There is a special PCRE2-specific condition of the form (VERSION[>]=x.y), which
tests the PCRE2 version number. This compiles into one of the opcodes OP_TRUE
or OP_FALSE.

If a condition is not a back reference, recursion test, DEFINE, or VERSION, it
must start with an assertion, whose opcode normally immediately follows OP_COND
or OP_SCOND. However, if automatic callouts are enabled, a callout is inserted
immediately before the assertion. It is also possible to insert a manual
callout at this point. Only assertion conditions may have callouts preceding
the condition.

A condition that is the negative assertion (?!) is optimized to OP_FAIL in all 
parts of the pattern, so this is another opcode that may appear as a condition. 
It is treated the same as OP_FALSE.


Recursion
---------

Recursion either matches the current pattern, or some subexpression. The opcode
OP_RECURSE is followed by a LINK_SIZE value that is the offset to the starting
bracket from the start of the whole pattern. OP_RECURSE is also used for
"subroutine" calls, even though they are not strictly a recursion. Repeated
recursions are automatically wrapped inside OP_ONCE brackets, because otherwise
some patterns broke them. A non-repeated recursion is not wrapped in OP_ONCE
brackets, but it is nevertheless still treated as an atomic group.


Callout
-------

A callout can nowadays have either a numerical argument or a string argument.
These use OP_CALLOUT or OP_CALLOUT_STR, respectively. In each case these are
followed by two LINK_SIZE values giving the offset in the pattern string to the
start of the following item, and another count giving the length of this item.
These values make it possible for pcre2test to output useful tracing
information using callouts.

In the case of a numeric callout, after these two values there is a single code
unit containing the callout number, in the range 0-255, with 255 being used for
callouts that are automatically inserted as a result of the PCRE2_AUTO_CALLOUT
option. Thus, this opcode item is of fixed length:

  [OP_CALLOUT] [PATTERN_OFFSET] [PATTERN_LENGTH] [NUMBER]

For callouts with string arguments, OP_CALLOUT_STR has three more data items:
a LINK_SIZE value giving the complete length of the entire opcode item, a
LINK_SIZE item containing the offset within the pattern string to the start of
the string argument, and the string itself, preceded by its starting delimiter
and followed by a binary zero. When a callout function is called, a pointer to
the actual string is passed, but the delimiter can be accessed as string[-1] if
the application needs it. In the 8-bit library, the callout in /X(?C'abc')Y/ is
compiled as the following bytes (decimal numbers represent binary values):

  [OP_CALLOUT]  [0] [10]  [0] [1]  [0] [14]  [0] [5] ['] [a] [b] [c] [0]
                --------  -------  --------  -------
                   |         |        |         |
                   ------- LINK_SIZE items ------

Opcode table checking
---------------------

The last opcode that is defined in pcre2_internal.h is OP_TABLE_LENGTH. This is
not a real opcode, but is used to check that tables indexed by opcode are the
correct length, in order to catch updating errors.

Philip Hazel
June 2015