pcre-6.4/doc/Tech.Notes

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,
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.

For the set of functions that forms PCRE (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 needed, in order to find internal flag settings like (?i) at top
level. So PCRE 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
pass 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_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_RECURSE             match the pattern recursively


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, 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 (that is, for something like
[^a]). 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.

OP_CLASS 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.


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 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.


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.

Non-capturing brackets use the opcode OP_BRA, while capturing brackets use
OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
speakers, including myself, can be round, square, curly, or pointy. Hence this
usage.]

Originally PCRE was limited to 99 capturing brackets (so as not to use up all
the opcodes). From release 3.5, there is no limit. What happens is that the
first ones, up to EXTRACT_BASIC_MAX are handled with separate opcodes, as
above. If there are more, the opcode is set to EXTRACT_BASIC_MAX+1, and the
first operation in the bracket is OP_BRANUMBER, followed by a 2-byte bracket
number. This opcode is ignored while matching, but is fished out when handling
the bracket itself. (They could have all been done like this, but I was making
minimal changes.)

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 in a nested
fashion up to the maximum number of times, with BRAZERO or BRAMINZERO before
each replication after the minimum, so that, for example, (abc){2,5} is
compiled as (abc)(abc)((abc)((abc)(abc)?)?)?. The 99 and 200 bracket limits do
not apply to these internally generated brackets.


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 subpatterns
---------------------

These are also just like other subpatterns, but they start with the opcode
OP_ONCE.


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

These are like other subpatterns, but they start with the opcode OP_COND. 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. Otherwise, a conditional subpattern will always start with
one of the assertions.


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

If any of the /i, /m, or /s options are changed within a parenthesized group,
an OP_OPT opcode is compiled, followed by one byte containing the new settings
of these flags. If there are several alternatives in a group, 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. Other changes of flag within the pattern can be
handled entirely at compile time, and so do not cause anything to be put into
the compiled data.


Philip Hazel
August 2001
1	nigel	41	Technical Notes about PCRE
2			--------------------------
3
4			Many years ago I implemented some regular expression functions to an algorithm
5			suggested by Martin Richards. These were not Unix-like in form, and were quite
6			restricted in what they could do by comparison with Perl. The interesting part
7			about the algorithm was that the amount of space required to hold the compiled
8			form of an expression was known in advance. The code to apply an expression did
9			not operate by backtracking, as the Henry Spencer and Perl code does, but
10			instead checked all possibilities simultaneously by keeping a list of current
11			states and checking all of them as it advanced through the subject string. (In
12			the terminology of Jeffrey Friedl's book, it was a "DFA algorithm".) When the
13			pattern was all used up, all remaining states were possible matches, and the
14			one matching the longest subset of the subject string was chosen. This did not
15			necessarily maximize the individual wild portions of the pattern, as is
16			expected in Unix and Perl-style regular expressions.
17
18			By contrast, the code originally written by Henry Spencer and subsequently
19			heavily modified for Perl actually compiles the expression twice: once in a
20			dummy mode in order to find out how much store will be needed, and then for
21			real. The execution function operates by backtracking and maximizing (or,
22			optionally, minimizing in Perl) the amount of the subject that matches
23			individual wild portions of the pattern. This is an "NFA algorithm" in Friedl's
24			terminology.
25
26	nigel	43	For the set of functions that forms PCRE (which are unrelated to those
27			mentioned above), I tried at first to invent an algorithm that used an amount
28			of store bounded by a multiple of the number of characters in the pattern, to
29			save on compiling time. However, because of the greater complexity in Perl
30			regular expressions, I couldn't do this. In any case, a first pass through the
31			pattern is needed, in order to find internal flag settings like (?i) at top
32			level. So PCRE works by running a very degenerate first pass to calculate a
33			maximum store size, and then a second pass to do the real compile - which may
34			use a bit less than the predicted amount of store. The idea is that this is
35			going to turn out faster because the first pass is degenerate and the second
36			pass can just store stuff straight into the vector. It does make the compiling
37			functions bigger, of course, but they have got quite big anyway to handle all
38			the Perl stuff.
39	nigel	41
40			The compiled form of a pattern is a vector of bytes, containing items of
41			variable length. The first byte in an item is an opcode, and the length of the
42			item is either implicit in the opcode or contained in the data bytes which
43			follow it. A list of all the opcodes follows:
44
45			Opcodes with no following data
46			------------------------------
47
48			These items are all just one byte long
49
50			OP_END end of pattern
51			OP_ANY match any character
52			OP_SOD match start of data: \A
53			OP_CIRC ^ (start of data, or after \n in multiline)
54			OP_NOT_WORD_BOUNDARY \W
55			OP_WORD_BOUNDARY \w
56			OP_NOT_DIGIT \D
57			OP_DIGIT \d
58			OP_NOT_WHITESPACE \S
59			OP_WHITESPACE \s
60			OP_NOT_WORDCHAR \W
61			OP_WORDCHAR \w
62			OP_EODN match end of data or \n at end: \Z
63			OP_EOD match end of data: \z
64			OP_DOLL $ (end of data, or before \n in multiline)
65	nigel	43	OP_RECURSE match the pattern recursively
66	nigel	41
67
68			Repeating single characters
69			---------------------------
70
71			The common repeats (*, +, ?) when applied to a single character appear as
72			two-byte items using the following opcodes:
73
74			OP_STAR
75			OP_MINSTAR
76			OP_PLUS
77			OP_MINPLUS
78			OP_QUERY
79			OP_MINQUERY
80
81			Those with "MIN" in their name are the minimizing versions. Each is followed by
82			the character that is to be repeated. Other repeats make use of
83
84			OP_UPTO
85			OP_MINUPTO
86			OP_EXACT
87
88			which are followed by a two-byte count (most significant first) and the
89			repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
90			non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
91			OP_UPTO (or OP_MINUPTO).
92
93
94			Repeating character types
95			-------------------------
96
97			Repeats of things like \d are done exactly as for single characters, except
98			that instead of a character, the opcode for the type is stored in the data
99			byte. The opcodes are:
100
101			OP_TYPESTAR
102			OP_TYPEMINSTAR
103			OP_TYPEPLUS
104			OP_TYPEMINPLUS
105			OP_TYPEQUERY
106			OP_TYPEMINQUERY
107			OP_TYPEUPTO
108			OP_TYPEMINUPTO
109			OP_TYPEEXACT
110
111
112			Matching a character string
113			---------------------------
114
115			The OP_CHARS opcode is followed by a one-byte count and then that number of
116			characters. If there are more than 255 characters in sequence, successive
117			instances of OP_CHARS are used.
118
119
120			Character classes
121			-----------------
122
123			OP_CLASS is used for a character class, provided there are at least two
124			characters in the class. If there is only one character, OP_CHARS is used for a
125			positive class, and OP_NOT for a negative one (that is, for something like
126			[^a]). Another set of repeating opcodes (OP_NOTSTAR etc.) are used for a
127			repeated, negated, single-character class. The normal ones (OP_STAR etc.) are
128			used for a repeated positive single-character class.
129
130	nigel	43	OP_CLASS is followed by a 32-byte bit map containing a 1 bit for every
131			character that is acceptable. The bits are counted from the least significant
132			end of each byte.
133	nigel	41
134
135			Back references
136			---------------
137
138	nigel	53	OP_REF is followed by two bytes containing the reference number.
139	nigel	41
140
141			Repeating character classes and back references
142			-----------------------------------------------
143
144			Single-character classes are handled specially (see above). This applies to
145			OP_CLASS and OP_REF. In both cases, the repeat information follows the base
146			item. The matching code looks at the following opcode to see if it is one of
147
148			OP_CRSTAR
149			OP_CRMINSTAR
150			OP_CRPLUS
151			OP_CRMINPLUS
152			OP_CRQUERY
153			OP_CRMINQUERY
154			OP_CRRANGE
155			OP_CRMINRANGE
156
157			All but the last two are just single-byte items. The others are followed by
158			four bytes of data, comprising the minimum and maximum repeat counts.
159
160
161			Brackets and alternation
162			------------------------
163
164	nigel	43	A pair of non-capturing (round) brackets is wrapped round each expression at
165	nigel	41	compile time, so alternation always happens in the context of brackets.
166	nigel	53
167	nigel	43	Non-capturing brackets use the opcode OP_BRA, while capturing brackets use
168	nigel	41	OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
169	nigel	43	speakers, including myself, can be round, square, curly, or pointy. Hence this
170			usage.]
171	nigel	41
172	nigel	53	Originally PCRE was limited to 99 capturing brackets (so as not to use up all
173			the opcodes). From release 3.5, there is no limit. What happens is that the
174			first ones, up to EXTRACT_BASIC_MAX are handled with separate opcodes, as
175			above. If there are more, the opcode is set to EXTRACT_BASIC_MAX+1, and the
176			first operation in the bracket is OP_BRANUMBER, followed by a 2-byte bracket
177			number. This opcode is ignored while matching, but is fished out when handling
178			the bracket itself. (They could have all been done like this, but I was making
179			minimal changes.)
180
181	nigel	41	A bracket opcode is followed by two bytes which give the offset to the next
182			alternative OP_ALT or, if there aren't any branches, to the matching KET
183			opcode. Each OP_ALT is followed by two bytes giving the offset to the next one,
184			or to the KET opcode.
185
186			OP_KET is used for subpatterns that do not repeat indefinitely, while
187			OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
188			maximally respectively. All three are followed by two bytes giving (as a
189			positive number) the offset back to the matching BRA opcode.
190
191			If a subpattern is quantified such that it is permitted to match zero times, it
192			is preceded by one of OP_BRAZERO or OP_BRAMINZERO. These are single-byte
193			opcodes which tell the matcher that skipping this subpattern entirely is a
194			valid branch.
195
196			A subpattern with an indefinite maximum repetition is replicated in the
197			compiled data its minimum number of times (or once with a BRAZERO if the
198			minimum is zero), with the final copy terminating with a KETRMIN or KETRMAX as
199			appropriate.
200
201			A subpattern with a bounded maximum repetition is replicated in a nested
202			fashion up to the maximum number of times, with BRAZERO or BRAMINZERO before
203			each replication after the minimum, so that, for example, (abc){2,5} is
204	nigel	53	compiled as (abc)(abc)((abc)((abc)(abc)?)?)?. The 99 and 200 bracket limits do
205			not apply to these internally generated brackets.
206	nigel	41
207
208			Assertions
209			----------
210
211			Forward assertions are just like other subpatterns, but starting with one of
212			the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes
213			OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion
214			is OP_REVERSE, followed by a two byte count of the number of characters to move
215	nigel	49	back the pointer in the subject string. When operating in UTF-8 mode, the count
216			is a character count rather than a byte count. A separate count is present in
217			each alternative of a lookbehind assertion, allowing them to have different
218			fixed lengths.
219	nigel	41
220
221			Once-only subpatterns
222			---------------------
223
224			These are also just like other subpatterns, but they start with the opcode
225			OP_ONCE.
226
227
228			Conditional subpatterns
229			-----------------------
230
231			These are like other subpatterns, but they start with the opcode OP_COND. If
232			the condition is a back reference, this is stored at the start of the
233	nigel	53	subpattern using the opcode OP_CREF followed by two bytes containing the
234	nigel	41	reference number. Otherwise, a conditional subpattern will always start with
235			one of the assertions.
236
237
238			Changing options
239			----------------
240
241			If any of the /i, /m, or /s options are changed within a parenthesized group,
242			an OP_OPT opcode is compiled, followed by one byte containing the new settings
243			of these flags. If there are several alternatives in a group, there is an
244			occurrence of OP_OPT at the start of all those following the first options
245			change, to set appropriate options for the start of the alternative.
246			Immediately after the end of the group there is another such item to reset the
247			flags to their previous values. Other changes of flag within the pattern can be
248			handled entirely at compile time, and so do not cause anything to be put into
249			the compiled data.
250
251
252			Philip Hazel
253	nigel	53	August 2001