pcre-4.0/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 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".) 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, for a number of reasons. 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
-----------------

When characters less than 256 are involved, OP_CLASS is used for a character
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]). However, in 
UTF-8 mode, this 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.

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.

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 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. If the condition is "in recursion" (coded as "(?(R)"), the
same scheme is used, with a "reference number" of 0xffff. Otherwise, a
conditional subpattern always starts with one of the assertions.


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
August 2002
1	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 original Henry Spencer code and current
10	Perl code does, but instead checked all possibilities simultaneously by keeping
11	a list of current states and checking all of them as it advanced through the
12	subject string. (In the terminology of Jeffrey Friedl's book, it was a "DFA
13	algorithm".) When the pattern was all used up, all remaining states were
14	possible matches, and the one matching the longest subset of the subject string
15	was chosen. This did not necessarily maximize the individual wild portions of
16	the pattern, as is 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	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, for a number of reasons. PCRE works by running a very
32	degenerate first pass to calculate a maximum store size, and then a second pass
33	to do the real compile - which may use a bit less than the predicted amount of
34	store. The idea is that this is going to turn out faster because the first pass
35	is degenerate and the second pass can just store stuff straight into the
36	vector. It does make the compiling functions bigger, of course, but they have
37	got quite big anyway to handle all the Perl stuff.
38
39	The compiled form of a pattern is a vector of bytes, containing items of
40	variable length. The first byte in an item is an opcode, and the length of the
41	item is either implicit in the opcode or contained in the data bytes which
42	follow it. A list of all the opcodes follows:
43
44	Opcodes with no following data
45	------------------------------
46
47	These items are all just one byte long
48
49	OP_END end of pattern
50	OP_ANY match any character
51	OP_SOD match start of data: \A
52	OP_CIRC ^ (start of data, or after \n in multiline)
53	OP_NOT_WORD_BOUNDARY \W
54	OP_WORD_BOUNDARY \w
55	OP_NOT_DIGIT \D
56	OP_DIGIT \d
57	OP_NOT_WHITESPACE \S
58	OP_WHITESPACE \s
59	OP_NOT_WORDCHAR \W
60	OP_WORDCHAR \w
61	OP_EODN match end of data or \n at end: \Z
62	OP_EOD match end of data: \z
63	OP_DOLL $ (end of data, or before \n in multiline)
64	OP_RECURSE match the pattern recursively
65
66
67	Repeating single characters
68	---------------------------
69
70	The common repeats (*, +, ?) when applied to a single character appear as
71	two-byte items using the following opcodes:
72
73	OP_STAR
74	OP_MINSTAR
75	OP_PLUS
76	OP_MINPLUS
77	OP_QUERY
78	OP_MINQUERY
79
80	Those with "MIN" in their name are the minimizing versions. Each is followed by
81	the character that is to be repeated. Other repeats make use of
82
83	OP_UPTO
84	OP_MINUPTO
85	OP_EXACT
86
87	which are followed by a two-byte count (most significant first) and the
88	repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
89	non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
90	OP_UPTO (or OP_MINUPTO).
91
92
93	Repeating character types
94	-------------------------
95
96	Repeats of things like \d are done exactly as for single characters, except
97	that instead of a character, the opcode for the type is stored in the data
98	byte. The opcodes are:
99
100	OP_TYPESTAR
101	OP_TYPEMINSTAR
102	OP_TYPEPLUS
103	OP_TYPEMINPLUS
104	OP_TYPEQUERY
105	OP_TYPEMINQUERY
106	OP_TYPEUPTO
107	OP_TYPEMINUPTO
108	OP_TYPEEXACT
109
110
111	Matching a character string
112	---------------------------
113
114	The OP_CHARS opcode is followed by a one-byte count and then that number of
115	characters. If there are more than 255 characters in sequence, successive
116	instances of OP_CHARS are used.
117
118
119	Character classes
120	-----------------
121
122	When characters less than 256 are involved, OP_CLASS is used for a character
123	class. If there is only one character, OP_CHARS is used for a positive class,
124	and OP_NOT for a negative one (that is, for something like [^a]). However, in
125	UTF-8 mode, this applies only to characters with values < 128, because OP_NOT
126	is confined to single bytes.
127
128	Another set of repeating opcodes (OP_NOTSTAR etc.) are used for a repeated,
129	negated, single-character class. The normal ones (OP_STAR etc.) are used for a
130	repeated positive single-character class.
131
132	OP_CLASS is followed by a 32-byte bit map containing a 1 bit for every
133	character that is acceptable. The bits are counted from the least significant
134	end of each byte.
135
136	For classes containing characters with values > 255, OP_XCLASS is used. It
137	optionally uses a bit map (if any characters lie within it), followed by a list
138	of pairs and single characters. There is a flag character than indicates
139	whether it's a positive or a negative class.
140
141
142	Back references
143	---------------
144
145	OP_REF is followed by two bytes containing the reference number.
146
147
148	Repeating character classes and back references
149	-----------------------------------------------
150
151	Single-character classes are handled specially (see above). This applies to
152	OP_CLASS and OP_REF. In both cases, the repeat information follows the base
153	item. The matching code looks at the following opcode to see if it is one of
154
155	OP_CRSTAR
156	OP_CRMINSTAR
157	OP_CRPLUS
158	OP_CRMINPLUS
159	OP_CRQUERY
160	OP_CRMINQUERY
161	OP_CRRANGE
162	OP_CRMINRANGE
163
164	All but the last two are just single-byte items. The others are followed by
165	four bytes of data, comprising the minimum and maximum repeat counts.
166
167
168	Brackets and alternation
169	------------------------
170
171	A pair of non-capturing (round) brackets is wrapped round each expression at
172	compile time, so alternation always happens in the context of brackets.
173
174	Non-capturing brackets use the opcode OP_BRA, while capturing brackets use
175	OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
176	speakers, including myself, can be round, square, curly, or pointy. Hence this
177	usage.]
178
179	Originally PCRE was limited to 99 capturing brackets (so as not to use up all
180	the opcodes). From release 3.5, there is no limit. What happens is that the
181	first ones, up to EXTRACT_BASIC_MAX are handled with separate opcodes, as
182	above. If there are more, the opcode is set to EXTRACT_BASIC_MAX+1, and the
183	first operation in the bracket is OP_BRANUMBER, followed by a 2-byte bracket
184	number. This opcode is ignored while matching, but is fished out when handling
185	the bracket itself. (They could have all been done like this, but I was making
186	minimal changes.)
187
188	A bracket opcode is followed by two bytes which give the offset to the next
189	alternative OP_ALT or, if there aren't any branches, to the matching KET
190	opcode. Each OP_ALT is followed by two bytes giving the offset to the next one,
191	or to the KET opcode.
192
193	OP_KET is used for subpatterns that do not repeat indefinitely, while
194	OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
195	maximally respectively. All three are followed by two bytes giving (as a
196	positive number) the offset back to the matching BRA opcode.
197
198	If a subpattern is quantified such that it is permitted to match zero times, it
199	is preceded by one of OP_BRAZERO or OP_BRAMINZERO. These are single-byte
200	opcodes which tell the matcher that skipping this subpattern entirely is a
201	valid branch.
202
203	A subpattern with an indefinite maximum repetition is replicated in the
204	compiled data its minimum number of times (or once with a BRAZERO if the
205	minimum is zero), with the final copy terminating with a KETRMIN or KETRMAX as
206	appropriate.
207
208	A subpattern with a bounded maximum repetition is replicated in a nested
209	fashion up to the maximum number of times, with BRAZERO or BRAMINZERO before
210	each replication after the minimum, so that, for example, (abc){2,5} is
211	compiled as (abc)(abc)((abc)((abc)(abc)?)?)?. The 99 and 200 bracket limits do
212	not apply to these internally generated brackets.
213
214
215	Assertions
216	----------
217
218	Forward assertions are just like other subpatterns, but starting with one of
219	the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes
220	OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion
221	is OP_REVERSE, followed by a two byte count of the number of characters to move
222	back the pointer in the subject string. When operating in UTF-8 mode, the count
223	is a character count rather than a byte count. A separate count is present in
224	each alternative of a lookbehind assertion, allowing them to have different
225	fixed lengths.
226
227
228	Once-only subpatterns
229	---------------------
230
231	These are also just like other subpatterns, but they start with the opcode
232	OP_ONCE.
233
234
235	Conditional subpatterns
236	-----------------------
237
238	These are like other subpatterns, but they start with the opcode OP_COND. If
239	the condition is a back reference, this is stored at the start of the
240	subpattern using the opcode OP_CREF followed by two bytes containing the
241	reference number. If the condition is "in recursion" (coded as "(?(R)"), the
242	same scheme is used, with a "reference number" of 0xffff. Otherwise, a
243	conditional subpattern always starts with one of the assertions.
244
245
246	Changing options
247	----------------
248
249	If any of the /i, /m, or /s options are changed within a pattern, an OP_OPT
250	opcode is compiled, followed by one byte containing the new settings of these
251	flags. If there are several alternatives, there is an occurrence of OP_OPT at
252	the start of all those following the first options change, to set appropriate
253	options for the start of the alternative. Immediately after the end of the
254	group there is another such item to reset the flags to their previous values. A
255	change of flag right at the very start of the pattern can be handled entirely
256	at compile time, and so does not cause anything to be put into the compiled
257	data.
258
259	Philip Hazel
260	August 2002