code/trunk/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
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. It 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
-----------------------------------------------

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
October 1997
1	nigel	3	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			minimizing in Perl) the amount of the subject that matches individual wild
23			portions of the pattern. This is a "NFA algorithm".
24
25			For this set of functions, I tried at first to invent an algorithm that used an
26			amount of store bounded by a multiple of the number of characters in the
27			pattern, to save on compiling time. However, because of the greater complexity
28			in Perl regular expressions, I couldn't do this. In any case, a first pass
29			through the pattern is needed, in order to find internal flag settings like
30			(?i). So it works by running a very degenerate first pass to calculate a
31			maximum store size, and then a second pass to do the real compile - which may
32			use a bit less than the predicted amount of store. The idea is that this is
33			going to turn out faster because the first pass is degenerate and the second
34			can just store stuff straight into the vector. It does make the compiling
35			functions bigger, of course, but they have got quite big anyway to handle all
36			the Perl stuff.
37
38			The compiled form of a pattern is a vector of bytes, containing items of
39			variable length. The first byte in an item is an opcode, and the length of the
40			item is either implicit in the opcode or contained in the data bytes which
41			follow it. A list of all the opcodes follows:
42
43			Opcodes with no following data
44			------------------------------
45
46			These items are all just one byte long
47
48			OP_END end of pattern
49			OP_ANY match any character
50			OP_SOD match start of data: \A
51			OP_CIRC ^ (start of data, or after \n in multiline)
52			OP_NOT_WORD_BOUNDARY \W
53			OP_WORD_BOUNDARY \w
54			OP_NOT_DIGIT \D
55			OP_DIGIT \d
56			OP_NOT_WHITESPACE \S
57			OP_WHITESPACE \s
58			OP_NOT_WORDCHAR \W
59			OP_WORDCHAR \w
60			OP_CUT analogue of Prolog's "cut"
61			OP_EOD match end of data: \Z
62			OP_DOLL $ (end of data, or before \n in multiline)
63
64
65			Repeating single characters
66			---------------------------
67
68			The common repeats (*, +, ?) when applied to a single character appear as
69			two-byte items using the following opcodes:
70
71			OP_STAR
72			OP_MINSTAR
73			OP_PLUS
74			OP_MINPLUS
75			OP_QUERY
76			OP_MINQUERY
77
78			Those with "MIN" in their name are the minimizing versions. Each is followed by
79			the character that is to be repeated. Other repeats make use of
80
81			OP_UPTO
82			OP_MINUPTO
83			OP_EXACT
84
85			which are followed by a two-byte count (most significant first) and the
86			repeated character. OP_UPTO matches from 0 to the given number. A repeat with a
87			non-zero minimum and a fixed maximum is coded as an OP_EXACT followed by an
88			OP_UPTO (or OP_MINUPTO).
89
90
91			Repeating character types
92			-------------------------
93
94			Repeats of things like \d are done exactly as for single characters, except
95			that instead of a character, the opcode for the type is stored in the data
96			byte. The opcodes are:
97
98			OP_TYPESTAR
99			OP_TYPEMINSTAR
100			OP_TYPEPLUS
101			OP_TYPEMINPLUS
102			OP_TYPEQUERY
103			OP_TYPEMINQUERY
104			OP_TYPEUPTO
105			OP_TYPEMINUPTO
106			OP_TYPEEXACT
107
108
109			Matching a character string
110			---------------------------
111
112			The OP_CHARS opcode is followed by a one-byte count and then that number of
113			characters. If there are more than 255 characters in sequence, successive
114			instances of OP_CHARS are used.
115
116
117			Character classes
118			-----------------
119
120			OP_CLASS is used for a character class. It is followed by a 32-byte bit map
121			containing a 1 bit for every character that is acceptable. The bits are counted
122			from the least significant end of each byte.
123
124
125			Back references
126			---------------
127
128			OP_REF is followed by a single byte containing the reference number.
129
130
131			Repeating character classes and back references
132			-----------------------------------------------
133
134			In both cases, the repeat information follows the base item. The matching code
135			looks at the following opcode to see if it is one of
136
137			OP_CRSTAR
138			OP_CRMINSTAR
139			OP_CRPLUS
140			OP_CRMINPLUS
141			OP_CRQUERY
142			OP_CRMINQUERY
143			OP_CRRANGE
144			OP_CRMINRANGE
145
146			All but the last two are just single-byte items. The others are followed by
147			four bytes of data, comprising the minimum and maximum repeat counts.
148
149
150			Brackets and alternation
151			------------------------
152
153			A pair of non-identifying (round) brackets is wrapped round each expression at
154			compile time, so alternation always happens in the context of brackets.
155			Non-identifying brackets use the opcode OP_BRA, while identifying brackets use
156			OP_BRA+1, OP_BRA+2, etc. [Note for North Americans: "bracket" to some English
157			speakers, including myself, can be round, square, or curly. Hence this usage.]
158
159			A bracket opcode is followed by two bytes which give the offset to the next
160			alternative OP_ALT or, if there aren't any branches, to the matching KET
161			opcode. Each OP_ALT is followed by two bytes giving the offset to the next one,
162			or to the KET opcode.
163
164			OP_KET is used for subpatterns that do not repeat indefinitely, while
165			OP_KETRMIN and OP_KETRMAX are used for indefinite repetitions, minimally or
166			maximally respectively. All three are followed by two bytes giving (as a
167			positive number) the offset back to the matching BRA opcode.
168
169			If a subpattern is quantified such that it is permitted to match zero times, it
170			is preceded by one of OP_BRAZERO or OP_BRAMINZERO. These are single-byte
171			opcodes which tell the matcher that skipping this subpattern entirely is a
172			valid branch.
173
174			A subpattern with an indefinite maximum repetition is replicated in the
175			compiled data its minimum number of times (or once with a BRAZERO if the
176			minimum is zero), with the final copy terminating with a KETRMIN or KETRMAX as
177			appropriate.
178
179			A subpattern with a bounded maximum repetition is replicated up to the maximum
180			number of times, with BRAZERO or BRAMINZERO before each replication after the
181			minimum. In effect, (abc){2,5} becomes (abc)(abc)(abc)?(abc)?(abc)?.
182
183
184			Assertions
185			----------
186
187			Assertions are just like other subpatterns, but starting with one of the
188			opcodes OP_ASSERT or OP_ASSERT_NOT.
189
190
191			Once-only subpatterns
192			---------------------
193
194			These are also just like other subpatterns, but they start with the opcode
195			OP_ONCE.
196
197
198			Philip Hazel
199			October 1997