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Technical Notes about PCRE
--------------------------
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 Henry Spencer 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".) 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.
By contrast, the code originally written by Henry Spencer and subsequently
heavily modified for Perl actually 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 execution function operates by backtracking and maximizing (or
minimizing in Perl) the amount of the subject that matches individual wild
portions of the pattern. This is a "NFA algorithm".
For this set of functions, 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 needed, in order to find internal flag settings like
(?i). So it works by running a very degenerate first pass to calculate a
maximum store size, and then a second pass to do the real compile - which may
use a bit less than the predicted amount of store. The idea is that this is
going to turn out faster because the first pass is degenerate and the second
can just store stuff straight into the vector. It does make the compiling
functions bigger, of course, but they have got quite big anyway to handle all
the Perl stuff.
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 which
follow it. A list of all 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 character
OP_SOD match start of data: \A
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_WHITESPACE \S
OP_WHITESPACE \s
OP_NOT_WORDCHAR \W
OP_WORDCHAR \w
OP_CUT analogue of Prolog's "cut"
OP_EOD match end of data: \Z
OP_DOLL $ (end of data, or before \n in multiline)
Repeating single characters
---------------------------
The common repeats (*, +, ?) when applied to a single character appear as
two-byte items using the following opcodes:
OP_STAR
OP_MINSTAR
OP_PLUS
OP_MINPLUS
OP_QUERY
OP_MINQUERY
Those with "MIN" in their name are the minimizing versions. Each is followed by
the character that is to be repeated. Other repeats make use of
OP_UPTO
OP_MINUPTO
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).
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_TYPEPLUS
OP_TYPEMINPLUS
OP_TYPEQUERY
OP_TYPEMINQUERY
OP_TYPEUPTO
OP_TYPEMINUPTO
OP_TYPEEXACT
Matching a character string
---------------------------
The OP_CHARS opcode is followed by a one-byte count and then that number of
characters. If there are more than 255 characters in sequence, successive
instances of OP_CHARS are used.
Character classes
-----------------
OP_CLASS is used for a character class, and OP_NEGCLASS for a negated character
class, provided there are at least two characters in the class. If there is
only one character, OP_CHARS is used for a positive class, and OP_NOT for a
negative one. A set of repeating opcodes (OP_NOTSTAR etc.) are used for a
repeated, negated, single-character class.
Both OP_CLASS and OP_NEGCLASS are 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 two opcodes is to cope with
negated character classes when caseless matching is specified at run time but
not at compile time. If it is specified at compile time, the bit map is built
appropriately. This is the only time that a distinction is made between
OP_CLASS and OP_NEGCLASS, when the bit map was built in a caseful manner but
matching must be caseless. For OP_CLASS, a character matches if either of its
cases is in the bit map, but for OP_NEGCLASS, both of them must be present.
Back references
---------------
OP_REF is followed by a single byte containing the reference number.
Repeating character classes and 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
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.
Brackets and alternation
------------------------
A pair of non-identifying (round) brackets is wrapped round each expression at
compile time, so alternation always happens in the context of brackets.
Non-identifying brackets use the opcode OP_BRA, while identifying brackets use
OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
speakers, including myself, can be round, square, or curly. Hence this usage.]
A bracket opcode is followed by two bytes which give the offset to the next
alternative OP_ALT or, if there aren't any branches, to the matching KET
opcode. Each OP_ALT is followed by two bytes giving the offset to the next one,
or to the KET opcode.
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 two bytes giving (as a
positive number) the offset back to the matching BRA opcode.
If a subpattern is quantified such that it is permitted to match zero times, it
is preceded by one of OP_BRAZERO or OP_BRAMINZERO. These are single-byte
opcodes which tell the matcher that skipping this subpattern entirely is a
valid branch.
A subpattern with an indefinite maximum repetition is replicated in the
compiled data its minimum number of times (or once with a BRAZERO if the
minimum is zero), with the final copy terminating with a KETRMIN or KETRMAX as
appropriate.
A subpattern with a bounded maximum repetition is replicated up to the maximum
number of times, with BRAZERO or BRAMINZERO before each replication after the
minimum. In effect, (abc){2,5} becomes (abc)(abc)(abc)?(abc)?(abc)?.
Assertions
----------
Assertions are just like other subpatterns, but starting with one of the
opcodes OP_ASSERT or OP_ASSERT_NOT.
Once-only subpatterns
---------------------
These are also just like other subpatterns, but they start with the opcode
OP_ONCE.
Philip Hazel
December 1997
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