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c996c06e8d
brotli/docs/draft-alakuijala-brotli-07.nroff
Joe Tsai c996c06e8d Use consistent bit ordering and variable names 
If bit-orderings are to be parsed from left-to-right,
then make the bit-strings left-justified.
If bit-orderings are to be parsed from right-to-left,
then make the bit-strings right-justified.

Section 3.1, which describes how prefix codes work
shows prefix codes that are "left-to-right", which
is better for demonstrating how the work. However,
most of the rest of the document uses a "right-to-left"
convention. We should distinctly say at the end of
section 3.1 that we are switching conventions.

Thus, change the prefix code in section 3.5 to be
"right-to-left" to be consistent with sections 9.1
and 9.2.

Also, change the variable names in section 7.3 to
be consistent with those used in section 10.

Also, change the description of MNIBBLES to be
"MNIBBLES - 4", similar to the convention of saying
"MLEN - 1". Beforehand, the phrase
"If MNIBBLES is 0, then ..." was unclear whether it
meant MNIBBLES before the "plus 4" or after.
2015-10-20 14:54:51 -07:00

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.pl 10.0i
.po 0
.ll 7.2i
.lt 7.2i
.nr LL 7.2i
.nr LT 7.2i
.ds LF Alakuijala & Szabadka
.ds RF FORMFEED[Page %]
.ds LH Internet-Draft
.ds RH October 2015
.ds CH Brotli
.ds CF Expires April 6, 2016
.hy 0
.nh
.ad l
.in 0
.nf
.tl 'Network Working Group''J. Alakuijala'
.tl 'Internet-Draft''Z. Szabadka'
.tl 'Intended Status: Informational''Google, Inc'
.tl 'Expires: April 6, 2016''October 2015'
.fi
.ce 2
Brotli Compressed Data Format
draft-alakuijala-brotli-07
.fi
.in 3
.ti 0
Abstract
This specification defines a lossless compressed data format that
compresses data using a combination of the LZ77 algorithm and Huffman
coding, with efficiency comparable to the best currently available
general-purpose compression methods.
.ti 0
Status of this Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at http://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on April 6, 2016.
.ti 0
Copyright Notice
Copyright (c) 2015 IETF Trust and the persons identified as the document
authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(http://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document. Code Components extracted from this document must
include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
.ti 0
Table of Contents
.in 0
.nf
INSERT_TOC_HERE
.fi
.in 3
.bp
.ti 0
1. Introduction
.ti 0
1.1. Purpose
The purpose of this specification is to define a lossless
compressed data format that:
.nf
* Is independent of CPU type, operating system, file system,
and character set, and hence can be used for interchange;
* Can be produced or consumed, even for an arbitrarily long
sequentially presented input data stream, using only an a
priori bounded amount of intermediate storage, and hence
can be used in data communications or similar structures,
such as Unix filters;
* Compresses data with a compression ratio comparable to the
best currently available general-purpose compression methods,
and in particular considerably better than the gzip program;
* Decompresses much faster than current LZMA implementations.
.fi
The data format defined by this specification does not attempt to:
.nf
* Allow random access to compressed data;
* Compress specialized data (e.g., raster graphics) as well
as the best currently available specialized algorithms.
.fi
.ti 0
1.2. Intended audience
This specification is intended for use by software implementers
to compress data into and/or decompress data from the brotli format.
The text of the specification assumes a basic background in
programming at the level of bits and other primitive data
representations. Familiarity with the technique of Huffman coding
is helpful but not required.
This specification uses heavily the notations and terminology
introduced in the DEFLATE format specification [RFC 1951].
For the sake of completeness, we always
include the whole text of the relevant parts of RFC 1951,
therefore familiarity with the DEFLATE format is helpful but not
required.
The compressed data format defined in this specification is
an integral part of the WOFF 2.0 web font file format [WOFF2],
therefore this specification is also intended for implementers of
WOFF 2.0 compressors and decompressors.
.ti 0
1.3. Scope
The specification specifies a method for representing a sequence
of bytes as a (usually shorter) sequence of bits, and a method for
packing the latter bit sequence into bytes.
.ti 0
1.4. Compliance
Unless otherwise indicated below, a compliant decompressor must be
able to accept and decompress any data set that conforms to all
the specifications presented here. A compliant compressor must
produce data sets that conform to all the specifications presented
here.
.ti 0
1.5. Definitions of terms and conventions used
Byte: 8 bits stored or transmitted as a unit (same as an octet).
For this specification, a byte is exactly 8 bits, even on machines
which store a character on a number of bits different from eight.
See below for the numbering of bits within a byte.
String: a sequence of arbitrary bytes.
Bytes stored within a computer do not have a "bit order", since
they are always treated as a unit. However, a byte considered as
an integer between 0 and 255 does have a most- and least-
significant bit, and since we write numbers with the most-
significant digit on the left, we also write bytes with the most-
significant bit on the left. In the diagrams below, we number the
bits of a byte so that bit 0 is the least-significant bit, i.e.,
the bits are numbered:
.nf
+--------+
|76543210|
+--------+
.fi
Within a computer, a number may occupy multiple bytes. All
multi-byte numbers in the format described here are stored with
the least-significant byte first (at the lower memory address).
For example, the decimal number 520 is stored as:
.nf
0 1
+--------+--------+
|00001000|00000010|
+--------+--------+
^ ^
| |
| + more significant byte = 2 x 256
+ less significant byte = 8
.fi
.ti 0
1.5.1. Packing into bytes
This document does not address the issue of the order in which
bits of a byte are transmitted on a bit-sequential medium,
since the final data format described here is byte- rather than
bit-oriented. However, we describe the compressed block format
below as a sequence of data elements of various bit
lengths, not a sequence of bytes. We must therefore specify
how to pack these data elements into bytes to form the final
compressed byte sequence:
.nf
* Data elements are packed into bytes in order of
increasing bit number within the byte, i.e., starting
with the least-significant bit of the byte.
* Data elements other than prefix codes are packed
starting with the least-significant bit of the data
element. These are referred to here as integer values
and are considered unsigned.
* Prefix codes are packed starting with the most-
significant bit of the code.
.fi
In other words, if one were to print out the compressed data as
a sequence of bytes, starting with the first byte at the
*right* margin and proceeding to the *left*, with the most-
significant bit of each byte on the left as usual, one would be
able to parse the result from right-to-left, with fixed-width
elements in the correct MSB-to-LSB order and prefix codes in
bit-reversed order (i.e., with the first bit of the code in the
relative LSB position).
.ti 0
2. Compressed representation overview
A compressed data set consists of a header and a series of meta-
blocks. Each meta-block decompresses to a sequence of 0
to 16,777,216 (16 MiB) uncompressed bytes. The final uncompressed data is
the concatenation of the uncompressed sequences from each meta-block.
The header contains the size of the sliding window that was used during compression.
The decompressor must retain at least that amount of uncompressed data prior to the
current position in the stream, in order to be able to decompress
what follows. The sliding window size is a power of two, minus 16, where
the power is in the range of 10 to 24. The possible sliding window
sizes range from 1 KiB - 16 B to 16 MiB - 16 B.
Each meta-block is compressed using a combination of the LZ77
algorithm (Lempel-Ziv 1977, [LZ77]) and Huffman coding. The
result of Huffman coding is referred to here as a prefix code.
The prefix codes for each meta-block are independent of
those for previous or subsequent meta-blocks; the LZ77 algorithm may
use a reference to a duplicated string occurring in a previous
meta-block, up to the sliding window size of uncompressed bytes before.
In addition, in the brotli format, a string reference may instead refer
to a static dictionary entry.
Each meta-block consists of two parts: a meta-block header that
describes the representation of the compressed data part, and a
compressed data part. The compressed data consists of a series of
commands. Each command consists of two parts: a sequence of literal
bytes (of strings that have not been detected as duplicated within
the sliding window), and a pointer to a duplicated string,
represented as a pair <length, backward distance>. There can be
zero literal bytes in the command. The minimum length of the string to be
duplicated is two, but the last command in the meta-block is permitted to have
only literals and no pointer to a string to duplicate.
Each command in the compressed data is represented using three categories
of prefix codes: one set of prefix codes are for the literal sequence
lengths (also referred to as literal insertion lengths) and backward
copy lengths (that is, a single code word represents two lengths,
one of the literal sequence and one of the backward copy), a separate
set of prefix codes are for literals, and a third set of prefix codes are for
distances. The prefix code descriptions for each meta-block appear in a compact
form just before the compressed data in the meta-block header. The insert and
copy length and distance prefix codes may be followed by extra bits that are
added to the base values determined by the codes. The number of extra bits is
determined by the code.
One meta-block command then appears as a sequence of prefix codes:
Insert and copy length, literal, literal, ..., literal, distance
where the insert and copy defines the number of literals that immediately
follow and the copy length, and the distance defines how far back to go
for the copy, used in combination with the copy length. The resulting
uncompressed data is the sequence of bytes:
literal, literal, ..., literal, copy, copy, ..., copy
where the number of literal bytes and copy bytes are determined by the
insert and copy length code. (The number of bytes copied for a static
dictionary entry can vary from the copy length.)
The last command in the meta-block may end with the last literal if the
total uncompressed length of the meta-block has been satisfied. In
that case there is no distance in the last command, and the copy length is
ignored.
There can be more than one prefix code for each category, where the
prefix code to use for the next element of that category is determined
by the context of the compressed stream that precedes that element.
Part of that context is three current block types, one for each
category. A block type is in the range of 0..255. For each category
there is a count of how many elements of that category remain to be
decoded using the current block type. Once that count is expended,
a new block type and block count is read from the stream immediately
preceding the next element of that category, which will use the new
block type.
The insert and copy block type directly determines which prefix code to
use for the next insert and copy element. For the literal and distance
elements, the respective block type is used in combination with other
context information to determine which prefix code to use for the next
element.
Consider the following
example:
(IaC0, L0, L1, L2, D0)(IaC1, D1)(IaC2, L3, L4, D2)(IaC3, L5, D3)
The meta-block here has four commands, contained in parentheses for clarity,
where each of the three categories of
symbols within these commands can be interpreted using different block types.
Here we separate out each category as its own sequence to show an example of block
types assigned to those elements. Each square-bracketed group is a block that
uses the same block type:
[IaC0, IaC1][IaC2, IaC3] <-- insert-and-copy: block types 0 and 1
[L0, L1][L2, L3, L4][L5] <-- literals: block types 0, 1, and 0
[D0][D1, D2, D3] <-- distances: block types 0 and 1
The subsequent blocks within each block category must have different
block types, but we see that block types can be reused later in the meta-block.
The block types are numbered from 0 to the maximum
block type number of 255 and the first block of each block category
is type 0. The block structure of a meta-block is represented
by the sequence of block-switch commands for each block category,
where a block-switch command is a pair <block type, block count>.
The block-switch commands are represented in the compressed data
before the start of each new block using a prefix code for
block types and a separate prefix code for block counts for
each block category. For the above example the physical layout of the
meta-block is then:
IaC0 L0 L1 LBlockSwitch(1, 3) L2 D0 IaC1 DBlockSwitch(1, 3) D1
IaCBlockSwitch(1, 2) IaC2 L3 L4 D2 IaC3 LBlockSwitch(0, 1) L5 D3
where *BlockSwitch(t, n) switches to block type t for a count of n elements.
Note that in this example DBlockSwitch(1, 3) immediately precedes the
next required distance D1. It does not follow the last distance of
the previous block, D0. Whenever an element of a category is needed,
and the block count for that category has reached zero, then a new
block type and count is read from the stream just before reading that next
element.
The block switch commands for the first blocks of each category are not part
of the meta-block compressed data. Instead the first block type
is defined to be 0, and the first block count for each category is
encoded in the meta-block header. The prefix codes for the block types and counts, a total of
six prefix codes over the three categories, are defined in a compact form in the meta-block
header.
Each category of value (insert-and-copy lengths, literals and distances)
can be encoded with any prefix code from a collection of prefix
codes belonging to the same category appearing in the meta-block header. The
particular prefix code used can depend on two factors: the block
type of the block the value appears in, and the context of the value.
In the case of the literals, the context is the previous two bytes in
the uncompressed data, and in the case of distances, the context is the copy
length from the same command. For insert-and-copy lengths, no context
is used and the prefix code depends only on the block type. In the case
of literals and distances, the context is mapped to a context ID in
the range 0..63 for literals and 0..3 for distances and the matrix
of the prefix code indices for each block type and context ID,
called the context map, is encoded in a compact form in the meta-
block header.
For example, the prefix code to use to decode L2 depends on the
block type (1), and the literal context ID determined by the two uncompressed
bytes that were decoded from L0 and L1.
Similarly, the prefix code to use to decode D0 depends on the block
type (0), and the distance context ID determined by the copy length decoded
from IaC0. The prefix code to use to decode IaC3 depends only on the block
type (1).
In addition to the parts listed above (prefix code for insert-
and-copy lengths, literals, distances, block types and block counts
and the context map), the meta-block header contains the number of
uncompressed bytes coded in the meta-block and two additional parameters used in
the representation of match distances: the number of postfix bits and
the number of direct distance codes.
A compressed meta-block may be marked in the header as the last meta-block,
which terminates the compressed stream.
A meta-block may instead simply store the uncompressed data directly as
bytes on byte boundaries with no coding or matching strings. In this
case the meta-block header information only contains the number of
uncompressed bytes and the indication that the meta-block is uncompressed.
An uncompressed meta-block cannot be the last meta-block.
A meta-block may also be empty, which generates no uncompressed data at all.
An empty meta-block may contain metadata information as bytes starting on byte
boundaries, which are not part of either the sliding window or the uncompressed
data. Thus, these metadata bytes can not be used to create matching strings in
subsequent meta-blocks and are not used as context bytes for literals.
.ti 0
3. Compressed representation of prefix codes
.ti 0
3.1. Introduction to prefix coding
Prefix coding represents symbols from an a priori known alphabet
by bit sequences (codes), one code for each symbol, in a manner
such that different symbols may be represented by bit sequences of
different lengths, but a parser can always parse an encoded string
unambiguously symbol-by-symbol.
We define a prefix code in terms of a binary tree in which the two
edges descending from each non-leaf node are labeled 0 and 1 and
in which the leaf nodes correspond one-for-one with (are labeled
with) the symbols of the alphabet; then the code for a symbol is
the sequence of 0's and 1's on the edges leading from the root to
the leaf labeled with that symbol. For example:
.nf
.KS
/\\ Symbol Code
0 1 ------ ----
/ \\ A 00
/\\ B B 1
0 1 C 011
/ \\ D 010
A /\\
0 1
/ \\
D C
.KE
.fi
A parser can decode the next symbol from the compressed stream
by walking down the tree from the root, at each step choosing the
edge corresponding to the next compressed data bit.
Given an alphabet with known symbol frequencies, the Huffman
algorithm allows the construction of an optimal prefix code (one
which represents strings with those symbol frequencies using the
fewest bits of any possible prefix codes for that alphabet). Such
a prefix code is called a Huffman code. (See [HUFFMAN] in Chapter 5,
references for additional information on Huffman codes.)
Note that in the brotli format, the prefix codes for the
various alphabets must not exceed certain maximum code lengths.
This constraint complicates the algorithm for computing code
lengths from symbol frequencies. Again, see Chapter 5, references
for details.
.ti 0
3.2. Use of prefix coding in the brotli format
The prefix codes used for each alphabet in the brotli format
are canonical prefix codes, which have two additional rules:
.nf
* All codes of a given bit length have lexicographically
consecutive values, in the same order as the symbols they
represent;
* Shorter codes lexicographically precede longer codes.
.fi
We could recode the example above to follow this rule as follows,
assuming that the order of the alphabet is ABCD:
.nf
.KS
Symbol Code
------ ----
A 10
B 0
C 110
D 111
.KE
.fi
I.e., 0 precedes 10 which precedes 11x, and 110 and 111 are
lexicographically consecutive.
Given this rule, we can define the canonical prefix code for an
alphabet just by giving the bit lengths of the codes for each
symbol of the alphabet in order; this is sufficient to determine
the actual codes. In our example, the code is completely defined
by the sequence of bit lengths (2, 1, 3, 3). The following
algorithm generates the codes as integers, intended to be read
from most- to least-significant bit. The code lengths are
initially in tree[I].Len; the codes are produced in tree[I].Code.
.nf
1) Count the number of codes for each code length. Let
bl_count[N] be the number of codes of length N, N >= 1.
2) Find the numerical value of the smallest code for each
code length:
.KS
code = 0;
bl_count[0] = 0;
for (bits = 1; bits <= MAX_BITS; bits++) {
code = (code + bl_count[bits-1]) << 1;
next_code[bits] = code;
}
.KE
3) Assign numerical values to all codes, using consecutive
values for all codes of the same length with the base
values determined at step 2. Codes that are never used
(which have a bit length of zero) must not be assigned a
value.
.KS
for (n = 0; n <= max_code; n++) {
len = tree[n].Len;
if (len != 0) {
tree[n].Code = next_code[len];
next_code[len]++;
}
}
.KE
.fi
Example:
Consider the alphabet ABCDEFGH, with bit lengths (3, 3, 3, 3, 3,
2, 4, 4). After step 1, we have:
.nf
.KS
N bl_count[N]
- -----------
2 1
3 5
4 2
.KE
.fi
Step 2 computes the following next_code values:
.nf
.KS
N next_code[N]
- ------------
1 0
2 0
3 2
4 14
.KE
.fi
Step 3 produces the following code values:
.nf
.KS
Symbol Length Code
------ ------ ----
A 3 010
B 3 011
C 3 100
D 3 101
E 3 110
F 2 00
G 4 1110
H 4 1111
.KE
.fi
The above prefix code contains codes that are parsed from left-to-right
(with MSB on the left). All subsequent prefix codes in this
specification will have codes that are parsed from right-to-left
(with MSB on the right) as they actually appear in the compressed data.
.ti 0
3.3. Alphabet sizes
Prefix codes are used for different purposes in the brotli
format, and each purpose has a different alphabet size. For
literal codes the alphabet size is 256. For insert-and-copy
length codes the alphabet size is 704. For block count codes,
the alphabet size is 26. For distance codes, block type codes and
the prefix codes used in compressing the context map, the
alphabet size is dynamic and is based on parameters defined in
later sections. The following table summarizes the alphabet sizes
for the various prefix codes and the sections where they are defined.
.nf
.KS
+-----------------+------------------------+-------------+
| Prefix code | Alphabet size | Definition |
+-----------------+------------------------+-------------+
| literal | 256 | |
+-----------------+------------------------+-------------+
| distance | 16 + NDIRECT + | Section 4. |
| | (48 << NPOSTFIX) | |
+-----------------+------------------------+-------------+
| insert-and-copy | 704 | Section 5. |
| length | | |
+-----------------+------------------------+-------------+
| block count | 26 | Section 6. |
+-----------------+------------------------+-------------+
| block type | NBLTYPESx + 2, | Section 6. |
| | (where x is I, L or D) | |
+-----------------+------------------------+-------------+
| context map | NTREESx + RLEMAXx | Section 7. |
| | (where x is L or D) | |
+-----------------+------------------------+-------------+
.KE
.fi
.ti 0
3.4. Simple prefix codes
The first two bits of the compressed representation of each
prefix code distinguishes between simple and complex prefix
codes. If this value is 1, then a simple prefix code follows.
Otherwise the value indicates the number of leading zeros.
A simple prefix code can have only up to four symbols with non-
zero code length. The format of the simple prefix code is as
follows:
.nf
2 bits: value of 1 indicates a simple prefix code
2 bits: NSYM - 1, where NSYM = # of symbols coded
NSYM symbols, each encoded using ALPHABET_BITS bits
1 bit: tree-select, present only for NSYM = 4
.fi
The value of ALPHABET_BITS depends on the alphabet of the prefix
code: it is the smallest number of bits that can represent all
symbols in the alphabet. E.g. for the alphabet of literal bytes,
ALPHABET_BITS is 8. The value of each of the NSYM symbols above is
the value of the ALPHABETS_BITS width integer value. (If the integer
value is greater than or equal to the alphabet size, then the stream
should be rejected as invalid.)
Note that the NSYM symbols may not be presented in sorted order. Prefix codes
of the same bit length must be assigned to the symbols in sorted order.
The (non-zero) code lengths of the symbols can be reconstructed as
follows:
.nf
* if NSYM = 1, the code length for the one symbol is zero --
when encoding this symbol in the
compressed data stream using this prefix code, no
actual bits are emitted. Similarly, when decoding a symbol
using this prefix code, no bits are read and the one symbol
is returned.
* if NSYM = 2, both symbols have code length 1.
* if NSYM = 3, the code lengths for the symbols are 1, 2, 2 in
the order they appear in the representation of the simple
prefix code.
* if NSYM = 4, the code lengths (in order of symbols decoded)
depend on the tree-select bit: 2, 2, 2, 2, (tree-select bit 0)
or 1, 2, 3, 3 (tree-select bit 1).
.fi
.ti 0
3.5. Complex prefix codes
A complex prefix code is a canonical prefix code, defined by the
sequence of code lengths, as discussed in Paragraph 3.2, above.
For even greater compactness, the code length sequences themselves
are compressed using a prefix code. The alphabet for code lengths
is as follows:
.nf
0 - 15: Represent code lengths of 0 - 15
16: Copy the previous non-zero code length 3 - 6 times
The next 2 bits indicate repeat length
(0 = 3, ... , 3 = 6)
If this is the first code length, or all previous
code lengths are zero, a code length of 8 is
repeated 3 - 6 times
A repeated code length code of 16 modifies the
repeat count of the previous one as follows:
repeat count = (4 * (repeat count - 2)) +
(3 - 6 on the next 2 bits)
Example: Codes 7, 16 (+2 bits 11), 16 (+2 bits 10)
will expand to 22 code lengths of 7
(1 + 4 * (6 - 2) + 5)
17: Repeat a code length of 0 for 3 - 10 times.
(3 bits of length)
A repeated code length code of 17 modifies the
repeat count of the previous one as follows:
repeat count = (8 * (repeat count - 2)) +
(3 - 10 on the next 3 bits)
.fi
Note that a code of 16 that follows an immediately preceding 16 modifies the
previous repeat count, which becomes the new repeat count. The same is true for
a 17 following a 17. A sequence of three or more 16 codes in a row or three of
more 17 codes in a row is possible, modifying the count each time. Only the
final repeat count is used. The modification only applies if the same code
follows. A 16 repeat does not modify an immediately preceding 17 count, nor
vice versa.
A code length of 0 indicates that the corresponding symbol in the
alphabet will not occur in the compressed data, and should not
participate in the prefix code construction algorithm given
earlier. A complex prefix code must have at least two non-zero
code lengths.
The bit lengths of the prefix code over the code length alphabet
are compressed with the following static prefix code (as it appears
in the compressed data, where the bits are parsed from right-to-left):
.nf
.KS
Symbol Code
------ ----
0 00
1 0111
2 011
3 10
4 01
5 1111
.KE
.fi
We can now define the format of the complex prefix code as
follows:
.nf
2 bits: HSKIP, values of 0, 2 or 3 represent the respective
number of skipped code lengths. The skipped lengths
are taken to be zero. (An HSKIP of 1 indicates a
Simple prefix code.)
Code lengths for symbols in the code length alphabet given
just above, in the order: 1, 2, 3, 4, 0, 5, 17, 6, 16, 7,
8, 9, 10, 11, 12, 13, 14, 15. If HSKIP is 2, then the
code lengths for symbols 1 and 2 are zero, and the first
code length is for symbol 3. If HSKIP is 3, then the code
length for symbol 3 is also zero, and the first code length
is for symbol 4.
The code lengths of code length symbols are between 0 and
5 and they are represented with 2 - 4 bits according to
the static prefix code above. A code length of 0 means
the corresponding code length symbol is not used.
If HSKIP is 2 or 3, a respective number of leading code
lengths are implicit zeros and are not present in the
code lengths sequence above.
If there are at least two non-zero code lengths, any
trailing zero code lengths are omitted, i.e. the last
code length in the sequence must be non-zero. In this
case the sum of (32 >> code length) over all the non-zero
code lengths must equal to 32.
If the lengths have been read for the entire code length
alphabet and there was only one non-zero code length,
then the prefix code has one symbol whose code has zero
length. In this case, that symbol results in no bits
being emitted by the compressor, and no bits consumed by
the decompressor. That single symbol is immediately
returned when this code is decoded.
An example of where this occurs is if the
entire code to be represented has symbols of length 8.
E.g. a literal code that represents all literal values
with equal probability. In this case the single symbol
is 16, which repeats the previous length. The previous
length is taken to be 8 before any code length code
lengths are read.
Sequence of code lengths symbols, encoded using the code
length prefix code. Any trailing 0 or 17 must be
omitted, i.e. the last encoded code length symbol must be
between 1 and 16. The sum of (32768 >> code length) over
all the non-zero code lengths in the alphabet, including
those encoded using repeat code(s) of 16, must equal to
32768. If the number of times to repeat the previous length
or repeat a zero length would result in more lengths in
total than the number of symbols in the alphabet, then the
stream should be rejected as invalid.
.fi
.ti 0
4. Encoding of distances
As described in Section 2, one component of a compressed meta-block
is a sequence of backward distances. In this section we provide the
details to the encoding of distances.
Each distance in the compressed data part of a meta-block is
represented with a pair <distance code, extra bits>. The distance
code and the extra bits are encoded back-to-back, the distance code
is encoded using a prefix code over the distance alphabet,
while the extra bits value is encoded as a fixed-width integer
value. The number of extra bits can be 0 - 24, and it is dependent
on the distance code.
To convert a distance code and associated extra bits to a backward
distance, we need the sequence of past distances and two additional
parameters, the number of "postfix bits", denoted by NPOSTFIX (0..3), and
the number of direct distance codes, denoted by NDIRECT (0..120). Both of
these parameters are encoded in the meta-block header. We will also
use the following derived parameter:
POSTFIX_MASK = ((1 << NPOSTFIX) - 1)
The first 16 distance symbols are special symbols that reference
past distances as follows:
.nf
0: last distance
1: second-to-last distance
2: third-to-last distance
3: fourth-to-last distance
4: last distance - 1
5: last distance + 1
6: last distance - 2
7: last distance + 2
8: last distance - 3
9: last distance + 3
10: second-to-last distance - 1
11: second-to-last distance + 1
12: second-to-last distance - 2
13: second-to-last distance + 2
14: second-to-last distance - 3
15: second-to-last distance + 3
.fi
The ring buffer of four last distances is initialized by the values
16, 15, 11 and 4 (i.e. the fourth-to-last is set to 16, the third-to-last
to 15, the second-to-last to 11 and the last distance to 4) at the
beginning of the *stream* (as opposed to the beginning of the meta-
block) and it is not reset at meta-block boundaries. When a distance
symbol 0 appears, the distance it represents (i.e. the last distance
in the sequence of distances) is not pushed to the ring buffer of
last distances, in other words, the expression "(second, third,
fourth)-to-last distance" means the (second, third, fourth)-to-last
distance that was not represented by a 0 distance symbol. Similarly,
distances that represent static dictionary words (see Section 8.) are
not pushed to the ring buffer of last distances.
The next NDIRECT distance symbols, from 16 to 15 + NDIRECT, represent
distances from 1 to NDIRECT. Neither the distance special symbols, nor
the NDIRECT direct distance symbols are followed by any extra bits.
Distance symbols 16 + NDIRECT and greater all have extra bits, where the
number of extra bits for a distance symbol "dcode" is given by the
following formula:
ndistbits = 1 + ((dcode - NDIRECT - 16) >> (NPOSTFIX + 1))
The maximum number of extra bits is 24, therefore the size of the
distance symbol alphabet is (16 + NDIRECT + (48 << NPOSTFIX)).
Given a distance symbol "dcode" (>= 16 + NDIRECT), and extra bits
"dextra", the backward distance is given by the following formula:
.nf
hcode = (dcode - NDIRECT - 16) >> NPOSTFIX
lcode = (dcode - NDIRECT - 16) & POSTFIX_MASK
offset = ((2 + (hcode & 1)) << ndistbits) - 4;
distance = ((offset + dextra) << NPOSTFIX) + lcode + NDIRECT + 1
.fi
.ti 0
5. Encoding of literal insertion lengths and copy lengths
As described in Section 2, the literal insertion lengths and backward
copy lengths are encoded using a single prefix code. This section
provides the details to this encoding.
Each <insertion length, copy length> pair in the compressed data part
of a meta-block is represented with the following triplet:
<insert-and-copy length code, insert extra bits, copy extra bits>
The insert-and-copy length code, the insert extra bits and the copy
extra bits are encoded back-to-back, the insert-and-copy length code
is encoded using a prefix code over the insert-and-copy length code
alphabet, while the extra bits values are encoded as fixed-width
integer values. The number of insert and copy extra bits can be
0 - 24, and they are dependent on the insert-and-copy length code.
Some of the insert-and-copy length codes also express the fact that
the distance symbol of the distance in the same command is 0, i.e. the
distance component of the command is the same as that of the previous
command. In this case, the distance code and extra bits for the
distance are omitted from the compressed data stream.
We describe the insert-and-copy length code alphabet in terms of the
(not directly used) insert length code and copy length code
alphabets. The symbols of the insert length code alphabet, along with
the number of insert extra bits and the range of the insert lengths
are as follows:
.nf
.KS
Extra Extra Extra
Code Bits Lengths Code Bits Lengths Code Bits Lengths
---- ---- ------ ---- ---- ------- ---- ---- -------
0 0 0 8 2 10-13 16 6 130-193
1 0 1 9 2 14-17 17 7 194-321
2 0 2 10 3 18-25 18 8 322-577
3 0 3 11 3 26-33 19 9 578-1089
4 0 4 12 4 34-49 20 10 1090-2113
5 0 5 13 4 50-65 21 12 2114-6209
6 1 6,7 14 5 66-97 22 14 6210-22593
7 1 8,9 15 5 98-129 23 24 22594-16799809
.KE
.fi
The symbols of the copy length code alphabet, along with the number
of copy extra bits and the range of copy lengths are as follows:
.nf
.KS
Extra Extra Extra
Code Bits Lengths Code Bits Lengths Code Bits Lengths
---- ---- ------ ---- ---- ------- ---- ---- -------
0 0 2 8 1 10,11 16 5 70-101
1 0 3 9 1 12,13 17 5 102-133
2 0 4 10 2 14-17 18 6 134-197
3 0 5 11 2 18-21 19 7 198-325
4 0 6 12 3 22-29 20 8 326-581
5 0 7 13 3 30-37 21 9 582-1093
6 0 8 14 4 38-53 22 10 1094-2117
7 0 9 15 4 54-69 23 24 2118-16779333
.KE
.fi
To convert an insert-and-copy length code to an insert length code
and a copy length code, the following table can be used:
.nf
.KS
Insert
length Copy length code
code 0-7 8-15 16-23
+---------+---------+
| | |
0-7 | 0-63 | 64-127 | <--- distance symbol 0
| | |
+---------+---------+---------+
| | | |
0-7 | 128-191 | 192-255 | 384-447 |
| | | |
+---------+---------+---------+
| | | |
8-15 | 256-319 | 320-383 | 512-575 |
| | | |
+---------+---------+---------+
| | | |
16-23 | 448-511 | 576-639 | 640-703 |
| | | |
+---------+---------+---------+
.KE
.fi
First, look up the cell with the 64 value range containing the
insert-and-copy length code, this gives the insert length code and
the copy length code ranges, both 8 values long. The copy length
code within its range is determined by the lowest 3 bits of the
insert-and-copy length code, and the insert length code within its
range is determined by bits 3-5 (counted from the LSB) of the insert-
and-copy length code. Given the insert length and copy length codes,
the actual insert and copy lengths can be obtained by reading the
number of extra bits given by the tables above.
If the insert-and-copy length code is between 0 and 127, the distance
code of the command is set to zero (the last distance reused).
.ti 0
6. Encoding of block switch commands
As described in Section 2, a block-switch command is a pair
<block type, block count>. These are encoded in the compressed data
part of the meta-block, right before the start of each new block of a
particular block category.
Each block type in the compressed data is represented with a block
type code, encoded using a prefix code over the block type code
alphabet. A block type symbol 0 means that the new block type is the same
as the type of the previous block from the same block category, i.e.
the block type that preceded the current type,
while a block type symbol 1 means that the new block type equals the current
block type plus one. If the current block type is the maximal possible,
then a block type symbol of 1 results in wrapping to a new block type of 0.
Block type symbols 2 - 257
represent block types 0 - 255 respectively. The previous and current block types
are initialized to 1 and 0, respectively, at the end of the
meta-block header.
Since the first block type of each block category is 0, the block
type of the first block switch command is not encoded in
the compressed data. Instead the block count for each category
that has more than one type is encoded in the meta-block header.
Since the end of the meta-block is detected by the number of uncompressed
bytes produced, the block counts for any of the three categories need not
count down to exactly zero at the end of the meta-block.
The number of different block types in each block category, denoted
by NBLTYPESL, NBLTYPESI, and NBLTYPESD for literals, insert-and-copy
lengths and distances, respectively, is encoded in the meta-block
header, and it must equal to the largest block type plus one in that
block category. In other words, the set of literal, insert-and-copy
length and distance block types must be [0..NBLTYPESL-1],
[0..NBLTYPESI-1], and [0..NBLTYPESD-1], respectively. From this it
follows that the alphabet size of literal, insert-and-copy length and
distance block type codes is NBLTYPES + 2, NBLTYPESI + 2 and
NBLTYPESD + 2, respectively.
Each block count in the compressed data is represented with a pair
<block count code, extra bits>. The block count code and the extra
bits are encoded back-to-back, the block count code is encoded using
a prefix code over the block count code alphabet, while the extra
bits value is encoded as a fixed-width integer value. The number of
extra bits can be 0 - 24, and it is dependent on the block count
code. The symbols of the block count code alphabet, along with the
number of extra bits and the range of block counts are as follows:
.nf
.KS
Extra Extra Extra
Code Bits Lengths Code Bits Lengths Code Bits Lengths
---- ---- ------ ---- ---- ------- ---- ---- -------
0 2 1-4 9 4 65-80 18 7 369-496
1 2 5-8 10 4 81-96 19 8 497-752
2 2 9-12 11 4 97-112 20 9 753-1264
3 2 13-16 12 5 113-144 21 10 1265-2288
4 3 17-24 13 5 145-176 22 11 2289-4336
5 3 25-32 14 5 177-208 23 12 4337-8432
6 3 33-40 15 5 209-240 24 13 8433-16624
7 3 41-48 16 6 241-304 25 24 16625-16793840
8 4 49-64 17 6 305-368
.KE
.fi
The first block switch command of each block category is special in
the sense that it is encoded in the meta-block header, and as
described earlier the block type code is omitted, since it is an
implicit zero.
.ti 0
7. Context modeling
As described in Section 2, the prefix tree used to encode a literal
byte or a distance code depends on the context ID and the block type.
This section specifies how to compute the context ID for a particular
literal and distance code, and how to encode the context map that
maps a <context ID, block type> pair to the index of a prefix
code in the array of literal and distance prefix codes.
.ti 0
7.1. Context modes and context ID lookup for literals
The context for encoding the next literal is defined by the last
two bytes in the stream (p1, p2, where p1 is the most recent
byte), regardless if these bytes are produced by backward
references or by literal insertions. At the start of the stream
p1 and p2 are initialized to zero.
There are four methods, called context modes, to compute the
Context ID:
.nf
* LSB6, where the Context ID is the value of six least
significant bits of p1,
* MSB6, where the Context ID is the value of six most
significant bits of p1,
* UTF8, where the Context ID is a complex function of p1, p2,
optimized for text compression, and
* Signed, where Context ID is a complex function of p1, p2,
optimized for compressing sequences of signed integers.
.fi
The Context ID for the UTF8 and Signed context modes is computed
using the following lookup tables Lut0, Lut1, and Lut2.
.nf
Lut0 :=
0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
8, 12, 16, 12, 12, 20, 12, 16, 24, 28, 12, 12, 32, 12, 36, 12,
44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 32, 32, 24, 40, 28, 12,
12, 48, 52, 52, 52, 48, 52, 52, 52, 48, 52, 52, 52, 52, 52, 48,
52, 52, 52, 52, 52, 48, 52, 52, 52, 52, 52, 24, 12, 28, 12, 12,
12, 56, 60, 60, 60, 56, 60, 60, 60, 56, 60, 60, 60, 60, 60, 56,
60, 60, 60, 60, 60, 56, 60, 60, 60, 60, 60, 24, 12, 28, 12, 0,
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3,
2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3,
2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3,
2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3
Lut1 :=
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1,
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1,
1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
Lut2 :=
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7
.fi
The lengths and zlib CRC-32 (ITU-T Recommendation V.42) check values of each
of these tables as a sequence of bytes are as follows:
.nf
Table Length CRC-32
----- ------ ------
Lut0 256 0x8e91efb7
Lut1 256 0xd01a32f4
Lut2 256 0x0dd7a0d6
.fi
Given p1 is the last uncompressed byte and p2 is the second-to-last
uncompressed byte the context IDs can be computed as follows:
.nf
For LSB6 : Context ID = p1 & 0x3f
For MSB6 : Context ID = p1 >> 2
For UTF8 : Context ID = Lut0[p1] | Lut1[p2]
For Signed: Context ID = (Lut2[p1] << 3) | Lut2[p2]
.fi
The context modes LSB6, MSB6, UTF8, and Signed are denoted by
integers 0, 1, 2, 3.
The context mode is defined for each literal block type and they
are stored in a consecutive array of bits in the meta-block
header, always two bits per block type.
.ti 0
7.2. Context ID for distances
The context for encoding a distance code is defined by the copy
length corresponding to the distance. The context IDs are 0, 1, 2,
and 3 for copy lengths 2, 3, 4, and more than 4, respectively.
.ti 0
7.3. Encoding of the context map
There are two context maps, one for literals and one for
distances. The size of the context map is 64 * NBLTYPESL for
literals, and 4 * NBLTYPESD for distances. Each value in the
context map is an integer between 0 and 255, indicating the index
of the prefix code to be used when encoding the next literal or
distance.
The context map is encoded as a one-dimensional array,
CMAPL[0..(64 * NBLTYPESL - 1)] and CMAPD[0..(4 * NBLTYPESD - 1)].
The index of the prefix code for encoding a literal or distance
code with context ID, CIDx, and block type, BTYPE_x, is:
index of literal prefix code = CMAPL[64 * BTYPE_L + CIDL]
index of distance prefix code = CMAPD[4 * BTYPE_D + CIDD]
The values of the context map are encoded with the combination
of run length encoding for zero values and prefix coding. Let
RLEMAX denote the number of run length codes and NTREES denote the
maximum value in the context map plus one. NTREES must equal the
number of different values in the context map, in other words,
the different values in the context map must be the [0..NTREES-1]
interval. The alphabet of the prefix code has the following
RLEMAX + NTREES symbols:
.nf
0: value zero
1: repeat a zero 2 to 3 times, read 1 bit for repeat length
2: repeat a zero 4 to 7 times, read 2 bits for repeat length
...
RLEMAX: repeat a zero (1 << RLEMAX) to (1 << (RLEMAX+1))-1
times, read RLEMAX bits for repeat length
RLEMAX + 1: value 1
...
RLEMAX + NTREES - 1: value NTREES - 1
.fi
If RLEMAX = 0, the run length coding is not used, and the symbols
of the alphabet are directly the values in the context map. We can
now define the format of the context map (the same format is used
for literal and distance context maps):
.nf
1-5 bits: RLEMAX, 0 is encoded with one 0 bit, and values
1 - 16 are encoded with bit pattern xxxx1 (so 01001
is 5)
Prefix code with alphabet size NTREES + RLEMAX
Context map size values encoded with the above prefix code
and run length coding for zero values. If a run length
would result in more lengths in total than the size of
the context map, then the stream should be rejected as
invalid.
1 bit: IMTF bit, if set, we do an inverse move-to-front
transform on the values in the context map to get
the prefix code indexes
.fi
Note that RLEMAX may be larger than the value necessary to represent
the longest sequence of zero values.
For the encoding of NTREES see Section 9.2. We define the
inverse move-to-front transform used in this specification by the
following C language function:
.nf
void InverseMoveToFrontTransform(uint8_t* v, int v_len) {
uint8_t mtf[256];
int i;
for (i = 0; i < 256; ++i) {
mtf[i] = (uint8_t)i;
}
for (i = 0; i < v_len; ++i) {
uint8_t index = v[i];
uint8_t value = mtf[index];
v[i] = value;
for (; index; --index) {
mtf[index] = mtf[index - 1];
}
mtf[0] = value;
}
}
.fi
.ti 0
8. Static dictionary
At any given point during decoding the compressed data, a reference
to a duplicated string in the uncompressed data produced so far has a maximum
backward distance value, which is the minimum of the window size and
the number of uncompressed bytes produced. However, decoding a distance
from the compressed stream, as described in section 4, can produce
distances that are greater than this maximum allowed value. The
difference between these distances and the first invalid distance
value is treated as reference to a word in the static dictionary
given in Appendix A. The copy length for a static dictionary reference
must be between 4 and 24. The static dictionary has three parts:
.nf
* DICT[0..DICTSIZE], an array of bytes
* DOFFSET[0..24], an array of byte offset values for each length
* NDBITS[0..24], an array of bit-depth values for each length
.fi
The number of static dictionary words for a given length is:
.nf
NWORDS[length] = 0 (if length < 4)
NWORDS[length] = (1 << NDBITS[length]) (if length >= 4)
.fi
DOFFSET and DICTSIZE are defined by the following recursion:
.nf
DOFFSET[0] = 0
DOFFSET[length + 1] = DOFFSET[length] + length * NWORDS[length]
DICTSIZE = DOFFSET[24] + 24 * NWORDS[24]
.fi
The offset of a word within the DICT array for a given length and
index is:
offset(length, index) = DOFFSET[length] + index * length
Each static dictionary word has 121 different forms, given by
applying a word transformation to a base word in the DICT array. The
list of word transformations is given in Appendix B. The static
dictionary word for a <length, distance> pair can be reconstructed as
follows:
.nf
word_id = distance - (max allowed distance + 1)
index = word_id % NWORDS[length]
base_word = DICT[offset(length, index)..offset(length, index+1)-1]
transform_id = word_id >> NDBITS[length]
.fi
The string copied to the uncompressed stream is computed by applying the
transformation to the base dictionary word. If transform_id is
greater than 120 or length is smaller than 4 or greater than 24, then
the compressed stream should be rejected as invalid.
Each word transformation has the following form:
transform_i(word) = prefix_i + T_i(word) + suffix_i
where the _i subscript denotes the transform_id above. Each T_i
is one of the following 21 elementary transforms:
.nf
Identity, UppercaseFirst, UppercaseAll,
OmitFirst1, ..., OmitFirst9, OmitLast1, ..., OmitLast9
.fi
The form of these elementary transforms are as follows:
.nf
Identity(word) = word
UppercaseFirst(word) = first UTF-8 character of word upper-cased
UppercaseAll(word) = all UTF-8 characters of word upper-cased
OmitFirstk(word) = the last (length(word) - k) bytes of word, or
empty string if length(word) < k
OmitLastk(word) = the first (length(word) - k) bytes of word, or
empty string if length(word) < k
.fi
For the purposes of UppercaseAll, word is parsed into UTF-8
characters and converted to upper-case by taking 1 - 3 bytes at a time,
using the algorithm below:
.nf
.KS
i = 0
while i < length(word):
if word[i] < 192:
if word[i] >= 97 and word[i] <= 122:
word[i] = word[i] ^ 32
i = i + 1
else if word[i] < 224:
if i + 1 < length(word):
word[i + 1] = word[i + 1] ^ 32
i = i + 2
else:
if i + 2 < length(word):
word[i + 2] = word[i + 2] ^ 5
i = i + 3
.KE
.fi
For UppercaseFirst, the same algorithm is used, but the loop is
executed only once.
Appendix B. contains the list of transformations by specifying the
prefix, elementary transform and suffix components of each of them.
Note that the OmitFirst8 elementary transform is not used in the list
of transformations. The strings in Appendix B. are in C string format
with respect to escape (backslash) characters.
.ti 0
9. Compressed data format
In this section we describe the format of the compressed data set in
terms of the format of the individual data items described in the
previous sections.
.ti 0
9.1. Format of the stream header
The stream header has only the following one field:
.nf
1-7 bits: WBITS, a value in the range 10 - 24, encoded with
the following variable length code (as it appears in
the compressed data, where the bits are parsed from
right-to-left):
Value Bit Pattern
----- -----------
10 0100001
11 0110001
12 1000001
13 1010001
14 1100001
15 1110001
16 0
17 0000001
18 0011
19 0101
20 0111
21 1001
22 1011
23 1101
24 1111
Note that bit pattern 0010001 is invalid and must not
be used.
.fi
The size of the sliding window, which is the maximum value of any
non-dictionary reference backward distance, is given by the
following formula:
window size = (1 << WBITS) - 16
.ti 0
9.2. Format of the meta-block header
A compliant compressed data set has at least one meta-block. Each
meta-block contains a header with information about the
uncompressed length of the meta-block, and a bit signaling if the
meta-block is the last one. The format of the meta-block header is
the following:
.nf
1 bit: ISLAST, set to 1 if this is the last meta-block
1 bit: ISLASTEMPTY, if set to 1, the meta-block is empty;
this field is only present if ISLAST bit is set -- if
it is 1, then the meta-block and the brotli stream ends
at that bit, with any remaining bits in the last byte
of the compressed stream filled with zeros (if the
fill bits are not zero, then the stream should be
rejected as invalid)
2 bits: MNIBBLES - 4, # of nibbles to represent the uncompressed
length. If MNIBBLES is 7, then MNIBBLES is set to 0 and
the meta-block is empty, i.e. it does not generate any
uncompressed data. In this case, the rest of the
meta-block has the following format:
1 bit: reserved, must be zero
2 bits: MSKIPBYTES, # of bytes to represent metadata
length
MSKIPBYTES x 8 bits: MSKIPLEN - 1, where MSKIPLEN is
the number of metadata bytes; this field is
only present if MSKIPBYTES is positive,
otherwise MSKIPLEN is 0 (if MSKIPBYTES is
greater than 1, and the last byte is all
zeros, then the stream should be rejected
as invalid)
0 - 7 bits: fill bits until the next byte boundary,
must be all zeros
MSKIPLEN bytes of metadata, not part of the
uncompressed data or the sliding window
MNIBBLES x 4 bits: MLEN - 1, where MLEN is the length
of the meta-block uncompressed data in bytes (if
MNIBBLES is greater than 4, and the last
nibble is all zeros, then the stream should be
rejected as invalid)
1 bit: ISUNCOMPRESSED, if set to 1, any bits of compressed
data up to the next byte boundary are ignored, and
the rest of the meta-block contains MLEN bytes of
literal data; this field is only present if the
ISLAST bit is not set (if the ignored bits are not
all zeros, the stream should be rejected as invalid)
1-11 bits: NBLTYPESL, # of literal block types, encoded with
the following variable length code (as it appears in
the compressed data, where the bits are parsed from
right-to-left, so 0110111 has the value 12):
Value Bit Pattern
----- -----------
1 0
2 0001
3-4 x0011
5-8 xx0101
9-16 xxx0111
17-32 xxxx1001
33-64 xxxxx1011
65-128 xxxxxx1101
129-256 xxxxxxx1111
Prefix code over the block type code alphabet for literal
block types, appears only if NBLTYPESL >= 2
Prefix code over the block count code alphabet for literal
block counts, appears only if NBLTYPESL >= 2
Block count code + Extra bits for first literal block
count, appears only if NBLTYPESL >= 2
1-11 bits: NBLTYPESI, # of insert-and-copy block types, encoded
with the same variable length code as above
Prefix code over the block type code alphabet for insert-
and-copy block types, only if NBLTYPESI >= 2
Prefix code over the block count code alphabet for insert-
and-copy block counts, only if NBLTYPESI >= 2
Block count code + Extra bits for first insert-and-copy
block count, only if NBLTYPESI >= 2
1-11 bits: NBLTYPESD, # of distance block types, encoded with
the same variable length code as above
Prefix code over the block type code alphabet for distance
block types, appears only if NBLTYPESD >= 2
Prefix code over the block count code alphabet for
distance block counts, only if NBLTYPESD >= 2
Block count code + Extra bits for first distance block
count, only if NBLTYPESD >= 2
2 bits: NPOSTFIX, parameter used in the distance coding
4 bits: four most significant bits of NDIRECT, to get the
actual value of the parameter NDIRECT, left-shift
this four bit number by NPOSTFIX bits
NBLTYPESL x 2 bits: context mode for each literal block type
1-11 bits: NTREESL, # of literal prefix trees, encoded with
the same variable length code as NBLTYPESL
Literal context map, encoded as described in Paragraph 7.3,
appears only if NTREESL >= 2, otherwise the context map
has only zero values
1-11 bits: NTREESD, # of distance prefix trees, encoded with
the same variable length code as NBLTYPESD
Distance context map, encoded as described in Paragraph 7.3,
appears only if NTREESD >= 2, otherwise the context map
has only zero values
NTREESL prefix codes for literals
NBLTYPESI prefix codes for insert-and-copy lengths
NTREESD prefix codes for distances
.fi
.ti 0
9.3. Format of the meta-block data
The compressed data part of a meta-block consists of a series of
commands. Each command has the following format:
.nf
Block type code for next insert-and-copy block type, appears
only if NBLTYPESI >= 2 and the previous insert-and-copy
block count is zero
Block count code + Extra bits for next insert-and-copy
block count, appears only if NBLTYPESI >= 2 and the
previous insert-and-copy block count is zero
Insert-and-copy length, encoded as in section 5, using the
insert-and-copy length prefix code with the current
insert-and-copy block type index
Insert length number of literals, with the following format:
Block type code for next literal block type, appears
only if NBLTYPESL >= 2 and the previous literal
block count is zero
Block count code + Extra bits for next literal block
count, appears only if NBLTYPESL >= 2 and the
previous literal block count is zero
Next byte of the uncompressed data, encoded with the
literal prefix code with the index determined by the
previous two bytes of the uncompressed data, the
current literal block type, and the context map, as
described in Paragraph 7.3.
Block type code for next distance block type, appears only
if NBLTYPESD >= 2 and the previous distance block count
is zero
Block count code + Extra bits for next distance block
length, appears only if NBLTYPESD >= 2 and the previous
distance block count is zero
Distance code, encoded as in section 4, using the distance
prefix code with the current distance block type index,
appears only if the distance code is not an implicit 0,
as indicated by the insert-and-copy length code
.fi
The number of commands in the meta-block is such that the sum of
the uncompressed bytes produced (i.e. the number of literals inserted
plus the number of bytes copied from past data or generated from the
static dictionary) over all the commands gives the uncompressed length,
MLEN encoded in the meta-block header.
If the total number of uncompressed bytes produced after the insert part
of the last command equals MLEN, then the copy length of the last command
is ignored and will not produce any uncompressed output. In this case the
copy length of the last command can have any value. In any other case, if
the number of literals to insert, the copy length, or the resulting
dictionary word length would cause MLEN to be exceeded, then the stream
should be rejected as invalid.
If the last command of the last non-empty meta-block does not end on
a byte boundary, the unused bits in the last byte must be zeros.
.ti 0
10. Decoding algorithm
The decoding algorithm that produces the uncompressed data is as follows:
.nf
read window size
do
read ISLAST bit
if ISLAST
read ISLASTEMPTY bit
if ISLASTEMPTY
break from loop
read MNIBBLES
if MNIBBLES is zero
verify reserved bit is zero
read MSKIPLEN
skip any bits up to the next byte boundary
skip MSKIPLEN bytes
continue to the next meta-block
else
read MLEN
if not ISLAST
read ISUNCOMPRESSED bit
if ISUNCOMPRESSED
skip any bits up to the next byte boundary
copy MLEN bytes of compressed data as literals
continue to the next meta-block
loop for each three block categories (i = L, I, D)
read NBLTYPESi
if NBLTYPESi >= 2
read prefix code for block types, HTREE_BTYPE_i
read prefix code for block counts, HTREE_BLEN_i
read block count, BLEN_i
set block type, BTYPE_i to 0
initialize second-to-last and last block types to 0 and 1
else
set block type, BTYPE_i to 0
set block count, BLEN_i to 268435456
read NPOSTFIX and NDIRECT
read array of literal context modes, CMODE[]
read NTREESL
if NTREESL >= 2
read literal context map, CMAPL[]
else
fill CMAPL[] with zeros
read NTREESD
if NTREESD >= 2
read distance context map, CMAPD[]
else
fill CMAPD[] with zeros
read array of prefix codes for literals, HTREEL[]
read array of prefix codes for insert-and-copy, HTREEI[]
read array of prefix codes for distances, HTREED[]
do
if BLEN_I is zero
read block type using HTREE_BTYPE_I and set BTYPE_I
save previous block type
read block count using HTREE_BLEN_I and set BLEN_I
decrement BLEN_I
read insert and copy length, ILEN, CLEN using HTREEI[BTYPE_I]
loop for ILEN
if BLEN_L is zero
read block type using HTREE_BTYPE_L and set BTYPE_L
save previous block type
read block count using HTREE_BLEN_L and set BLEN_L
decrement BLEN_L
look up context mode CMODE[BTYPE_L]
compute context ID, CIDL from last two uncompressed bytes
read literal using HTREEL[CMAPL[64 * BTYPE_L + CIDL]]
write literal to uncompressed stream
if number of uncompressed bytes produced in the loop for
this meta-block is MLEN, then break from loop (in this
case the copy length is ignored and can have any value)
if distance code is implicit zero from insert-and-copy code
set backward distance to the last distance
else
if BLEN_D is zero
read block type using HTREE_BTYPE_D and set BTYPE_D
save previous block type
read block count using HTREE_BLEN_D and set BLEN_D
decrement BLEN_D
compute context ID, CIDD from CLEN
read distance code using HTREED[CMAPD[4 * BTYPE_D + CIDD]]
compute distance by distance short code substitution
move backwards distance bytes in the uncompressed data and
copy CLEN bytes from this position to the uncompressed
stream, or look up the static dictionary word, transform
the word as directed, and copy the result to the
uncompressed stream
while number of uncompressed bytes for this meta-block < MLEN
while not ISLAST
.fi
If the stream ends before the completion of the last meta-block, then
the stream should be rejected as invalid.
Note that a duplicated string reference may refer to a string in a
previous meta-block, i.e. the backward distance may cross one or
more meta-block boundaries. However a backward copy distance
will not refer past the beginning of the uncompressed stream or the
window size; any such distance is
interpreted as a reference to a static dictionary word. Also note
that the referenced string may overlap the current position, for
example, if the last 2 bytes decoded have values X and Y, a string
reference with <length = 5, distance = 2> adds X,Y,X,Y,X to the
uncompressed stream.
.ti 0
11. Security Considerations
As with any compressed file formats, decompressor implementations should
handle all compressed data byte sequences, not only those that conform to this
specification, where non-conformant compressed data sequences should be discarded.
A possible attack against a system containing a decompressor
implementation (e.g. a web browser) is to exploit a buffer
overflow caused by an invalid compressed data. Therefore decompressor
implementations should perform bound-checking for each memory access
that result from values decoded from the compressed stream.
.ti 0
12. IANA Considerations
The "HTTP Content Coding Registry" has been updated with the
registration below:
.nf
.KS
+----------+----------------------------------------+---------------+
| Name | Description | Reference |
+----------+----------------------------------------+---------------+
| br | Brotli Compressed Data Format | RFCXXXX |
+----------+----------------------------------------+---------------+
.KE
.fi
.ti 0
13. Informative References
.in 14
.ti 3
[HUFFMAN] Huffman, D. A., "A Method for the Construction of Minimum
Redundancy Codes", Proceedings of the Institute of Radio
Engineers, September 1952, Volume 40, Number 9, pp. 1098-1101.
.ti 3
[LZ77] Ziv J., Lempel A., "A Universal Algorithm for Sequential Data
Compression", IEEE Transactions on Information Theory, Vol. 23,
No. 3, pp. 337-343.
.ti 3
[RFC1951] Deutsch, P., "DEFLATE Compressed Data Format Specification
version 1.3", RFC 1951, Aladdin Enterprises, May 1996.
http://www.ietf.org/rfc/rfc1951.txt
.ti 3
[WOFF2] Levantovsky, V. (ed.), Levien, R. (ed.), "WOFF File Format
2.0", W3C WebFonts Working Group, http://www.w3.org/TR/WOFF2/
.in 3
.ti 0
14. Source code
Source code for a C language implementation of a brotli compliant
decompressor and a C++ language implementation of a compressor is
available in the brotli open-source project:
https://github.com/google/brotli
.ti 0
15. Acknowledgments
The authors would like to thank Mark Adler for providing helpful review
comments, validating the specification by writing an independent decompressor
and suggesting improvements to the format and the text of the specification.
.ti 0
Appendix A. Static dictionary data
The hexadecimal form of the DICT array is the following, where the
length is 122,784 bytes and the zlib CRC-32 of the byte sequence is
0x5136cb04.
.in 0
.nf
74696d65646f776e6c6966656c6566746261636b636f64656461746173686f77
6f6e6c7973697465636974796f70656e6a7573746c696b6566726565776f726b
74657874796561726f766572626f64796c6f7665666f726d626f6f6b706c6179
6c6976656c696e6568656c70686f6d65736964656d6f7265776f72646c6f6e67
7468656d7669657766696e64706167656461797366756c6c686561647465726d
656163686172656166726f6d747275656d61726b61626c6575706f6e68696768
646174656c616e646e6577736576656e6e65787463617365626f7468706f7374
757365646d61646568616e6468657265776861746e616d654c696e6b626c6f67
73697a656261736568656c646d616b656d61696e757365722729202b686f6c64
656e6473776974684e65777372656164776572657369676e74616b6568617665
67616d657365656e63616c6c7061746877656c6c706c75736d656e7566696c6d
706172746a6f696e746869736c697374676f6f646e6565647761797377657374
6a6f62736d696e64616c736f6c6f676f72696368757365736c6173747465616d
61726d79666f6f646b696e6777696c6c65617374776172646265737466697265
506167656b6e6f77617761792e706e676d6f76657468616e6c6f616467697665
73656c666e6f74656d756368666565646d616e79726f636b69636f6e6f6e6365
6c6f6f6b6869646564696564486f6d6572756c65686f7374616a6178696e666f
636c75626c6177736c65737368616c66736f6d65737563687a6f6e6531303025
6f6e65736361726554696d6572616365626c7565666f75727765656b66616365
686f706567617665686172646c6f73747768656e7061726b6b65707470617373
73686970726f6f6d48544d4c706c616e54797065646f6e65736176656b656570
666c61676c696e6b736f6c6466697665746f6f6b72617465746f776e6a756d70
746875736461726b6361726466696c6566656172737461796b696c6c74686174
66616c6c6175746f657665722e636f6d74616c6b73686f70766f746564656570
6d6f6465726573747475726e626f726e62616e6466656c6c726f736575726c28
736b696e726f6c65636f6d6561637473616765736d656574676f6c642e6a7067
6974656d7661727966656c747468656e73656e6464726f7056696577636f7079
312e30223c2f613e73746f70656c73656c696573746f75727061636b2e676966
706173746373733f677261796d65616e2667743b7269646573686f746c617465
73616964726f6164766172206665656c6a6f686e7269636b706f727466617374
2755412d646561643c2f623e706f6f7262696c6c74797065552e532e776f6f64
6d7573743270783b496e666f72616e6b7769646577616e7477616c6c6c656164
5b305d3b7061756c776176657375726524282723776169746d61737361726d73
676f65736761696e6c616e6770616964212d2d206c6f636b756e6974726f6f74
77616c6b6669726d77696665786d6c22736f6e6774657374323070786b696e64
726f7773746f6f6c666f6e746d61696c73616665737461726d617073636f7265
7261696e666c6f77626162797370616e736179733470783b3670783b61727473
666f6f747265616c77696b696865617473746570747269706f72672f6c616b65
7765616b746f6c64466f726d6361737466616e7362616e6b7665727972756e73
6a756c797461736b3170783b676f616c67726577736c6f776564676569643d22
736574733570783b2e6a733f3430707869662028736f6f6e736561746e6f6e65
747562657a65726f73656e747265656466616374696e746f676966746861726d
3138707863616d6568696c6c626f6c647a6f6f6d766f69646561737972696e67
66696c6c7065616b696e6974636f73743370783b6a61636b7461677362697473
726f6c6c656469746b6e65776e6561723c212d2d67726f774a534f4e64757479
4e616d6573616c65796f75206c6f74737061696e6a617a7a636f6c6465796573
666973687777772e7269736b7461627370726576313070787269736532357078
426c756564696e673330302c62616c6c666f72646561726e77696c64626f782e
666169726c61636b76657273706169726a756e6574656368696628217069636b
6576696c242822237761726d6c6f7264646f657370756c6c2c30303069646561
647261776875676573706f7466756e646275726e6872656663656c6c6b657973
7469636b686f75726c6f73736675656c31327078737569746465616c52535322
6167656467726579474554226561736561696d736769726c616964733870783b
6e617679677269647469707323393939776172736c61647963617273293b207d
7068703f68656c6c74616c6c77686f6d7a683ae52a2f0d0a2031303068616c6c
2e0a0a413770783b70757368636861743070783b637265772a2f3c2f68617368
37357078666c6174726172652026262074656c6c63616d706f6e746f6c616964
6d697373736b697074656e7466696e656d616c6567657473706c6f743430302c
0d0a0d0a636f6f6c666565742e7068703c62723e657269636d6f737467756964
62656c6c64657363686169726d61746861746f6d2f696d67262338326c75636b
63656e743030303b74696e79676f6e6568746d6c73656c6c6472756746524545
6e6f64656e69636b3f69643d6c6f73656e756c6c7661737477696e6452535320
7765617272656c796265656e73616d6564756b656e6173616361706577697368
67756c665432333a68697473736c6f74676174656b69636b626c757274686579
313570782727293b293b223e6d73696577696e7362697264736f727462657461
7365656b5431383a6f726473747265656d616c6c363070786661726de2809973
626f79735b305d2e27293b22504f5354626561726b696473293b7d7d6d617279
74656e6428554b29717561647a683ae62d73697a2d2d2d2d70726f7027293b0d
6c6966745431393a76696365616e6479646562743e525353706f6f6c6e65636b
626c6f775431363a646f6f726576616c5431373a6c6574736661696c6f72616c
706f6c6c6e6f7661636f6c7367656e6520e28094736f6674726f6d6574696c6c
726f73733c68333e706f75726661646570696e6b3c74723e6d696e69297c2128
6d696e657a683ae862617273686561723030293b6d696c6b202d2d3e69726f6e
667265646469736b77656e74736f696c707574732f6a732f686f6c795432323a
4953424e5432303a6164616d736565733c68323e6a736f6e272c2027636f6e74
5432313a205253536c6f6f70617369616d6f6f6e3c2f703e736f756c4c494e45
666f7274636172745431343a3c68313e38307078212d2d3c3970783b5430343a
6d696b653a34365a6e696365696e6368596f726b726963657a683ae42729293b
707572656d61676570617261746f6e65626f6e643a33375a5f6f665f275d293b
3030302c7a683ae774616e6b79617264626f776c627573683a35365a4a617661
333070780a7c7d0a254333253a33345a6a656666455850496361736876697361
676f6c66736e6f777a683ae9717565722e6373737369636b6d6561746d696e2e
62696e6464656c6c686972657069637372656e743a33365a485454502d323031
666f746f776f6c66454e442078626f783a35345a424f44596469636b3b0a7d0a
657869743a33355a7661727362656174277d293b646965743939393b616e6e65
7d7d3c2f5b695d2e4c616e676b6dc2b277697265746f7973616464737365616c
616c65783b0a097d6563686f6e696e652e6f726730303529746f6e796a657773
73616e646c656773726f6f66303030292032303077696e6567656172646f6773
626f6f74676172796375747374796c6574656d7074696f6e2e786d6c636f636b
67616e672428272e3530707850682e446d697363616c616e6c6f616e6465736b
6d696c657279616e756e697864697363293b7d0a64757374636c6970292e0a0a
373070782d32303044564473375d3e3c7461706564656d6f692b2b2977616765
6575726f7068696c6f707473686f6c65464151736173696e2d3236546c616273
7065747355524c2062756c6b636f6f6b3b7d0d0a484541445b305d2961626272
6a75616e283139386c6573687477696e3c2f693e736f6e79677579736675636b
706970657c2d0a21303032296e646f775b315d3b5b5d3b0a4c6f672073616c74
0d0a090962616e677472696d62617468297b0d0a303070780a7d293b6b6f3aec
6665657361643e0d733a2f2f205b5d3b746f6c6c706c756728297b0a7b0d0a20
2e6a7327323030706475616c626f61742e4a5047293b0a7d71756f74293b0a0a
27293b0a0d0a7d0d323031343230313532303136323031373230313832303139
3230323032303231323032323230323332303234323032353230323632303237
3230323832303239323033303230333132303332323033333230333432303335
3230333632303337323031333230313232303131323031303230303932303038
3230303732303036323030353230303432303033323030323230303132303030
3139393931393938313939373139393631393935313939343139393331393932
3139393131393930313938393139383831393837313938363139383531393834
3139383331393832313938313139383031393739313937383139373731393736
3139373531393734313937333139373231393731313937303139363931393638
3139363731393636313936353139363431393633313936323139363131393630
3139353931393538313935373139353631393535313935343139353331393532
31393531313935303130303031303234313339343030303039393939636f6d6f
6dc3a17365737465657374617065726f746f646f686163656361646161c3b16f
6269656e64c3ad616173c3ad766964616361736f6f74726f666f726f736f6c6f
6f7472616375616c64696a6f7369646f6772616e7469706f74656d6164656265
616c676f7175c3a96573746f6e61646174726573706f636f6361736162616a6f
746f646173696e6f6167756170756573756e6f73616e7465646963656c756973
656c6c616d61796f7a6f6e61616d6f727069736f6f627261636c6963656c6c6f
64696f73686f726163617369d0b7d0b0d0bdd0b0d0bed0bcd180d0b0d180d183
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a58de0a4aee0a4bee0a4a3e0a4b2e0a4bfe0a4aee0a4bfe0a49fe0a587e0a4a1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 number of words for each length is given by the following bit-
depth array:
NDBITS := 0, 0, 0, 0, 10, 10, 11, 11, 10, 10,
10, 10, 10, 9, 9, 8, 7, 7, 8, 7,
7, 6, 6, 5, 5
.fi
.ti 0
Appendix B. List of word transformations
The string literals are in C format, with respect to the use of
backslash escape characters.
In order to generate a length and check value, the transforms can be converted
to a series of bytes, where each transform is the prefix sequence of bytes plus
a terminating zero byte, a single byte value identifying the transform, and the
suffix sequence of bytes plus a terminating zero. The value for the transforms
are 0 for Identity, 1 for UppercaseFirst, 2 for UppercaseAll, 3 to 11 for
OmitFirst1 to OmitFirst9, and 12 to 20 for OmitLast1 to OmitLast9. The byte
sequences that represent the 121 transforms are then concatenated to a single
sequence of bytes. The length of that sequence is 648 bytes, and the zlib CRC
is 0x3d965f81.
.nf
ID Prefix Transform Suffix
-- ------ --------- ------
0 "" Identity ""
1 "" Identity " "
2 " " Identity " "
3 "" OmitFirst1 ""
4 "" UppercaseFirst " "
5 "" Identity " the "
6 " " Identity ""
7 "s " Identity " "
8 "" Identity " of "
9 "" UppercaseFirst ""
10 "" Identity " and "
11 "" OmitFirst2 ""
12 "" OmitLast1 ""
13 ", " Identity " "
14 "" Identity ", "
15 " " UppercaseFirst " "
16 "" Identity " in "
17 "" Identity " to "
18 "e " Identity " "
19 "" Identity "\\""
20 "" Identity "."
21 "" Identity "\\">"
22 "" Identity "\\n"
23 "" OmitLast3 ""
24 "" Identity "]"
25 "" Identity " for "
26 "" OmitFirst3 ""
27 "" OmitLast2 ""
28 "" Identity " a "
29 "" Identity " that "
30 " " UppercaseFirst ""
31 "" Identity ". "
32 "." Identity ""
33 " " Identity ", "
34 "" OmitFirst4 ""
35 "" Identity " with "
36 "" Identity "'"
37 "" Identity " from "
38 "" Identity " by "
39 "" OmitFirst5 ""
40 "" OmitFirst6 ""
41 " the " Identity ""
42 "" OmitLast4 ""
43 "" Identity ". The "
44 "" UppercaseAll ""
45 "" Identity " on "
46 "" Identity " as "
47 "" Identity " is "
48 "" OmitLast7 ""
49 "" OmitLast1 "ing "
50 "" Identity "\\n\\t"
51 "" Identity ":"
52 " " Identity ". "
53 "" Identity "ed "
54 "" OmitFirst9 ""
55 "" OmitFirst7 ""
56 "" OmitLast6 ""
57 "" Identity "("
58 "" UppercaseFirst ", "
59 "" OmitLast8 ""
60 "" Identity " at "
61 "" Identity "ly "
62 " the " Identity " of "
63 "" OmitLast5 ""
64 "" OmitLast9 ""
65 " " UppercaseFirst ", "
66 "" UppercaseFirst "\\""
67 "." Identity "("
68 "" UppercaseAll " "
69 "" UppercaseFirst "\\">"
70 "" Identity "=\\""
71 " " Identity "."
72 ".com/" Identity ""
73 " the " Identity " of the "
74 "" UppercaseFirst "'"
75 "" Identity ". This "
76 "" Identity ","
77 "." Identity " "
78 "" UppercaseFirst "("
79 "" UppercaseFirst "."
80 "" Identity " not "
81 " " Identity "=\\""
82 "" Identity "er "
83 " " UppercaseAll " "
84 "" Identity "al "
85 " " UppercaseAll ""
86 "" Identity "='"
87 "" UppercaseAll "\\""
88 "" UppercaseFirst ". "
89 " " Identity "("
90 "" Identity "ful "
91 " " UppercaseFirst ". "
92 "" Identity "ive "
93 "" Identity "less "
94 "" UppercaseAll "'"
95 "" Identity "est "
96 " " UppercaseFirst "."
97 "" UppercaseAll "\\">"
98 " " Identity "='"
99 "" UppercaseFirst ","
100 "" Identity "ize "
101 "" UppercaseAll "."
102 "\\xc2\\xa0" Identity ""
103 " " Identity ","
104 "" UppercaseFirst "=\\""
105 "" UppercaseAll "=\\""
106 "" Identity "ous "
107 "" UppercaseAll ", "
108 "" UppercaseFirst "='"
109 " " UppercaseFirst ","
110 " " UppercaseAll "=\\""
111 " " UppercaseAll ", "
112 "" UppercaseAll ","
113 "" UppercaseAll "("
114 "" UppercaseAll ". "
115 " " UppercaseAll "."
116 "" UppercaseAll "='"
117 " " UppercaseAll ". "
118 " " UppercaseFirst "=\\""
119 " " UppercaseAll "='"
120 " " UppercaseFirst "='"
.fi
.in 3
.ti 0
Authors' Addresses
.nf
Jyrki Alakuijala
Google, Inc
Email: jyrki@google.com
Zoltan Szabadka
Google, Inc
Email: szabadka@google.com
.fi
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