pcre-3.2/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 this set of functions that forms PCRE, 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 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_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)


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 a single byte 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-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 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 200-bracket limit does 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. 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 one byte 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
January 1999
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 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	For this set of functions that forms PCRE, I tried at first to invent an
27	algorithm that used an amount of store bounded by a multiple of the number of
28	characters in the pattern, to save on compiling time. However, because of the
29	greater complexity in Perl regular expressions, I couldn't do this. In any
30	case, a first pass through the pattern is needed, in order to find internal
31	flag settings like (?i) at top level. So it works by running a very degenerate
32	first pass to calculate a maximum store size, and then a second pass to do the
33	real compile - which may use a bit less than the predicted amount of store. The
34	idea is that this is going to turn out faster because the first pass is
35	degenerate and the second can just store stuff straight into the vector. It
36	does make the compiling functions bigger, of course, but they have got quite
37	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
65
66	Repeating single characters
67	---------------------------
68
69	The common repeats (*, +, ?) when applied to a single character appear as
70	two-byte items using the following opcodes:
71
72	OP_STAR
73	OP_MINSTAR
74	OP_PLUS
75	OP_MINPLUS
76	OP_QUERY
77	OP_MINQUERY
78
79	Those with "MIN" in their name are the minimizing versions. Each is followed by
80	the character that is to be repeated. Other repeats make use of
81
82	OP_UPTO
83	OP_MINUPTO
84	OP_EXACT
85
86	which are followed by a two-byte count (most significant first) and the
87	repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
88	non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
89	OP_UPTO (or OP_MINUPTO).
90
91
92	Repeating character types
93	-------------------------
94
95	Repeats of things like \d are done exactly as for single characters, except
96	that instead of a character, the opcode for the type is stored in the data
97	byte. The opcodes are:
98
99	OP_TYPESTAR
100	OP_TYPEMINSTAR
101	OP_TYPEPLUS
102	OP_TYPEMINPLUS
103	OP_TYPEQUERY
104	OP_TYPEMINQUERY
105	OP_TYPEUPTO
106	OP_TYPEMINUPTO
107	OP_TYPEEXACT
108
109
110	Matching a character string
111	---------------------------
112
113	The OP_CHARS opcode is followed by a one-byte count and then that number of
114	characters. If there are more than 255 characters in sequence, successive
115	instances of OP_CHARS are used.
116
117
118	Character classes
119	-----------------
120
121	OP_CLASS is used for a character class, provided there are at least two
122	characters in the class. If there is only one character, OP_CHARS is used for a
123	positive class, and OP_NOT for a negative one (that is, for something like
124	[^a]). Another set of repeating opcodes (OP_NOTSTAR etc.) are used for a
125	repeated, negated, single-character class. The normal ones (OP_STAR etc.) are
126	used for a repeated positive single-character class.
127
128	OP_CLASS is followed by a 32-byte bit map containing a 1
129	bit for every character that is acceptable. The bits are counted from the least
130	significant end of each byte.
131
132
133	Back references
134	---------------
135
136	OP_REF is followed by a single byte containing the reference number.
137
138
139	Repeating character classes and back references
140	-----------------------------------------------
141
142	Single-character classes are handled specially (see above). This applies to
143	OP_CLASS and OP_REF. In both cases, the repeat information follows the base
144	item. The matching code looks at the following opcode to see if it is one of
145
146	OP_CRSTAR
147	OP_CRMINSTAR
148	OP_CRPLUS
149	OP_CRMINPLUS
150	OP_CRQUERY
151	OP_CRMINQUERY
152	OP_CRRANGE
153	OP_CRMINRANGE
154
155	All but the last two are just single-byte items. The others are followed by
156	four bytes of data, comprising the minimum and maximum repeat counts.
157
158
159	Brackets and alternation
160	------------------------
161
162	A pair of non-identifying (round) brackets is wrapped round each expression at
163	compile time, so alternation always happens in the context of brackets.
164	Non-identifying brackets use the opcode OP_BRA, while identifying brackets use
165	OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
166	speakers, including myself, can be round, square, or curly. Hence this usage.]
167
168	A bracket opcode is followed by two bytes which give the offset to the next
169	alternative OP_ALT or, if there aren't any branches, to the matching KET
170	opcode. Each OP_ALT is followed by two bytes giving the offset to the next one,
171	or to the KET opcode.
172
173	OP_KET is used for subpatterns that do not repeat indefinitely, while
174	OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
175	maximally respectively. All three are followed by two bytes giving (as a
176	positive number) the offset back to the matching BRA opcode.
177
178	If a subpattern is quantified such that it is permitted to match zero times, it
179	is preceded by one of OP_BRAZERO or OP_BRAMINZERO. These are single-byte
180	opcodes which tell the matcher that skipping this subpattern entirely is a
181	valid branch.
182
183	A subpattern with an indefinite maximum repetition is replicated in the
184	compiled data its minimum number of times (or once with a BRAZERO if the
185	minimum is zero), with the final copy terminating with a KETRMIN or KETRMAX as
186	appropriate.
187
188	A subpattern with a bounded maximum repetition is replicated in a nested
189	fashion up to the maximum number of times, with BRAZERO or BRAMINZERO before
190	each replication after the minimum, so that, for example, (abc){2,5} is
191	compiled as (abc)(abc)((abc)((abc)(abc)?)?)?. The 200-bracket limit does not
192	apply to these internally generated brackets.
193
194
195	Assertions
196	----------
197
198	Forward assertions are just like other subpatterns, but starting with one of
199	the opcodes OP_ASSERT or OP_ASSERT_NOT. Backward assertions use the opcodes
200	OP_ASSERTBACK and OP_ASSERTBACK_NOT, and the first opcode inside the assertion
201	is OP_REVERSE, followed by a two byte count of the number of characters to move
202	back the pointer in the subject string. A separate count is present in each
203	alternative of a lookbehind assertion, allowing them to have different fixed
204	lengths.
205
206
207	Once-only subpatterns
208	---------------------
209
210	These are also just like other subpatterns, but they start with the opcode
211	OP_ONCE.
212
213
214	Conditional subpatterns
215	-----------------------
216
217	These are like other subpatterns, but they start with the opcode OP_COND. If
218	the condition is a back reference, this is stored at the start of the
219	subpattern using the opcode OP_CREF followed by one byte containing the
220	reference number. Otherwise, a conditional subpattern will always start with
221	one of the assertions.
222
223
224	Changing options
225	----------------
226
227	If any of the /i, /m, or /s options are changed within a parenthesized group,
228	an OP_OPT opcode is compiled, followed by one byte containing the new settings
229	of these flags. If there are several alternatives in a group, there is an
230	occurrence of OP_OPT at the start of all those following the first options
231	change, to set appropriate options for the start of the alternative.
232	Immediately after the end of the group there is another such item to reset the
233	flags to their previous values. Other changes of flag within the pattern can be
234	handled entirely at compile time, and so do not cause anything to be put into
235	the compiled data.
236
237
238	Philip Hazel
239	January 1999