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J. Alakuijala
Z. Szabadka
______ _______ _______ _______ _________
( __ \ ( ____ )( ___ )( ____ \\__ __/
| ( \ )| ( )|| ( ) || ( \/ ) (
| | ) || (____)|| (___) || (__ | |
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(______/ |/ \__/|/ \||/ )_(
DRAFT of
Brotli Compression Algorithm Compressed Data Format Specification 1.0
Status of This Memo
This memo provides information for the Internet community. This memo
does not specify an Internet standard of any kind. Distribution of
this memo is unlimited.
Notices
Copyright (c) 2013 J. Alakuijala and Z. Szabadka
Permission is granted to copy and distribute this document for any
purpose and without charge, including translations into other
languages and incorporation into compilations, provided that the
copyright notice and this notice are preserved, and that any
substantive changes or deletions from the original are clearly
marked.
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.
1. Introduction
1.1. Purpose
The purpose of this specification is to define a lossless
compressed data format that:
* 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 efficiency comparable to the best
currently available general-purpose compression methods,
and in particular considerably better than the gzip program;
* Decompresses much faster than the LZMA implementations.
The data format defined by this specification does not attempt to:
* Allow random access to compressed data;
* Compress specialized data (e.g., raster graphics) as well
as the best currently available specialized algorithms.
1.2. Intended audience
This specification is intended for use by software implementers
to compress data into and/or decompress data from "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, see
reference [3] below). 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.
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.
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.
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:
+--------+
|76543210|
+--------+
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:
0 1
+--------+--------+
|00001000|00000010|
+--------+--------+
^ ^
| |
| + more significant byte = 2 x 256
+ less significant byte = 8
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:
* 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 Huffman codes are packed
starting with the least-significant bit of the data
element.
* Huffman codes are packed starting with the most-
significant bit of the code.
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 Huffman codes in
bit-reversed order (i.e., with the first bit of the code in the
relative LSB position).
2. Compressed representation overview
A compressed data set consists of a header and a series of meta-
blocks corresponding to successive meta-blocks of input data. The
meta-block sizes are limited to bytes and the maximum meta-block size
is 268,435,456 bytes.
The header contains the size of a sliding window on the input data
that is sufficient to keep on the intermediate storage at any given
point during decoding the stream.
Each meta-block is compressed using a combination of the LZ77
algorithm (Lempel-Ziv 1977, see reference [2] below) and Huffman
coding. The Huffman trees for each block are independent of those for
previous or subsequent blocks; the LZ77 algorithm may use a
reference to a duplicated string occurring in a previous meta-block,
up to sliding window size input bytes before.
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>.
Each command in the compressed data is represented using three kinds
of Huffman codes: one kind of code tree 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
kind of code tree for literals, and a third kind of code tree for
distances. The code trees for each meta-block appear in a compact
form just before the compressed data in the meta-block header.
The sequence of each type of value in the representation of a command
(insert-and-copy lengths, literals and distances) within a meta-
block is further divided into blocks. In the "brotli" format, blocks
are not contiguous chunks of compressed data, but rather the pieces
of compressed data belonging to a block are interleaved with pieces
of data belonging to other blocks. Each meta-block can be logically
decomposed into a series of insert-and-copy length blocks, a series
of literal blocks and a series of distance blocks. These are also
called the three block categories: a meta-block has a series of
blocks for each block category. Note that the physical structure of
the meta-block is a series of commands, while the three series of
blocks is the logical structure. Consider the following example:
(IaC0, L0, L1, L2, D0)(IaC1, D1)(IaC2, L3, L4, D2)(IaC3, L5, D3)
The meta-block here has 4 commands, and each three types of symbols
within these commands can be rearranged for example into the
following logical block structure:
[IaC0, IaC1][IaC2, IaC3] <-- block types 0 and 1
[L0, L1][L2, L3, L4][L5] <-- block types 0, 1, and 0
[D0][D1, D2, D3] <-- block types 0 and 1
The subsequent blocks within each block category must have different
block types, but blocks further away in the block sequence can have
the same types. The block types are numbered from 0 to the maximum
block type number of 255 and the first block of each block category
must have 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 length>.
The block-switch commands are represented in the compressed data
before the start of each new block using a Huffman code tree for
block types and a separate Huffman code tree for block lengths for
each block category. In the above example the physical layout of the
meta-block is the following:
IaC0 L0 L1 LBlockSwitch(1, 3) L2 D0 IaC1 DBlockSwitch(1, 1) D1
IaCBlockSwitch(1, 2) IaC2 L3 L4 D2 IaC3 LBlockSwitch(0, 1) D3
Note that the block switch commands for the first blocks are not part
of the meta-block compressed data part, they are encoded in the meta-
block header. The code trees for block types and lengths (total of
six Huffman code trees) appear in a compact form in the meta-block
header.
Each type of value (insert-and-copy lengths, literals and distances)
can be encoded with any Huffman tree from a collection of Huffman
trees of the same kind appearing in the meta-block header. The
particular Huffman tree 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 input 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 Huffman tree depends only on the block type (in fact,
the index of the Huffman tree is the block type number). In the case
of literals and distances, the context is mapped to a context ID in
the rage [0, 63] for literals and [0, 3] for distances and the matrix
of the Huffman tree indices for each block type and context ID,
called the context map, is encoded in a compact form in the meta-
block header.
In addition to the parts listed above (Huffman code trees for insert-
and-copy lengths, literals, distances, block types and block lengths
and the context map), the meta-block header contains the number of
input bytes in the meta-block and two additional parameters used in
the representation of copy distances (number of "postfix bits" and
number of direct distance codes).
3. Compressed representation of Huffman codes
3.1. Introduction to prefix and Huffman 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:
/\ Symbol Code
0 1 ------ ----
/ \ A 00
/\ B B 1
0 1 C 011
/ \ D 010
A /\
0 1
/ \
D C
A parser can decode the next symbol from an encoded input stream
by walking down the tree from the root, at each step choosing the
edge corresponding to the next input 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 code is called a Huffman code. (See reference [1] in Chapter 5,
references for additional information on Huffman codes.)
Note that in the "brotli" format, the Huffman 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.
3.2. Use of Huffman coding in the "brotli" format
The Huffman codes used for each alphabet in the "brotli" format
are canonical Huffman codes, which have two additional rules:
* 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.
We could recode the example above to follow this rule as follows,
assuming that the order of the alphabet is ABCD:
Symbol Code
------ ----
A 10
B 0
C 110
D 111
I.e., 0 precedes 10 which precedes 11x, and 110 and 111 are
lexicographically consecutive.
Given this rule, we can define the canonical Huffman 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.
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:
code = 0;
bl_count[0] = 0;
for (bits = 1; bits <= MAX_BITS; bits++) {
code = (code + bl_count[bits-1]) << 1;
next_code[bits] = code;
}
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.
for (n = 0; n <= max_code; n++) {
len = tree[n].Len;
if (len != 0) {
tree[n].Code = next_code[len];
next_code[len]++;
}
}
Example:
Consider the alphabet ABCDEFGH, with bit lengths (3, 3, 3, 3, 3,
2, 4, 4). After step 1, we have:
N bl_count[N]
- -----------
2 1
3 5
4 2
Step 2 computes the following next_code values:
N next_code[N]
- ------------
1 0
2 0
3 2
4 14
Step 3 produces the following code values:
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
3.3. Alphabet sizes
Huffman 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 length codes,
the alphabet size is 26. For distance codes, block type codes and
the Huffman codes used in compressing the context map, the
alphabet size is dynamic and is based on other parameters.
3.4. Simple Huffman codes
The first two bits of the compressed representation of each
Huffman code distinguishes between simple and complex Huffman
codes. If this value is 1, then a simple Huffman code follows.
Otherwise the value indicates the number of leading zeros.
A simple Huffman code can have only up to four symbols with non-
zero code length. The format of the simple Huffman code is as
follows:
2 bits: value of 1 indicates a simple Huffman code
2 bits: NSYM - 1, where NSYM = # of symbols with non-zero
code length
NSYM symbols, each encoded using ALPHABET_BITS bits
1 bit: tree-select, present only for NSYM = 4
The value of ALPHABET_BITS depends on the alphabet of the Huffman
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 machine integer representing
the symbol modulo the alphabet size of the Huffman code.
The (non-zero) code lengths of the symbols can be reconstructed as
follows:
* if NSYM = 1, the code length for the one symbol is one at
this stage, but only to distinguish it from the other zero
code length symbols, when encoding this symbol in the
compressed data stream using this Huffman code later, no
actual bits are emitted. Similarly, when decoding a symbol
using this Huffman 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
Huffman 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).
3.5. Complex Huffman codes
A complex Huffman code is a canonical Huffman 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 Huffman code. The alphabet for code lengths
is as follows:
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)
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 Huffman code construction algorithm given
earlier. A complex Huffman code must have at least two non-zero
code lengths.
The bit lengths of the Huffman code over the code length alphabet
are compressed with the following static Huffman code:
Symbol Code
------ ----
0 00
1 1110
2 110
3 01
4 10
5 1111
We can now define the format of the complex Huffman code as
follows:
2 bits: HSKIP, values of 0, 2 or 3 represent the respective
number of leading zeros. (Value of 1 indicates the
Simple Huffman 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
The code lengths of code length symbols are between 0 and
5 and they are represented with 2 - 5 bits according to
the static Huffman 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.
Sequence of code lengths symbols, encoded using the code
length Huffman 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.
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 Huffman code over the distance code alphabet,
while the extra bits value is encoded as a fixed-width machine
integer. 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, and
the number of direct distance codes, denoted by NDIRECT. 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 codes are special short codes that reference
past distances as follows:
0: last distance
1: second last distance
2: third last distance
3: fourth 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 last distance - 1
11: second last distance + 1
12: second last distance - 2
13: second last distance + 2
14: second last distance - 3
15: second last distance + 3
The ring-buffer of four last distances is initialized by the values
16, 15, 11 and 4 (i.e. the fourth last is set to 16, the third last
to 15, the second 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
code 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) last distance" means the (second, third, fourth) last
distance that was not represented by a 0 distance code. Similarly,
distances that represent static dictionary words (see Section 8.) are
not pushed to the ringbuffer of last distances.
The next NDIRECT distance codes, from 16 to 15 + NDIRECT, represent
distances from 1 to NDIRECT. Neither the distance short codes, nor
the NDIRECT direct distance codes have any extra bits.
Distance codes 16 + NDIRECT and greater all have extra bits, the
number of extra bits for a distance code "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 code alphabet is (16 + NDIRECT + (48 << NPOSTFIX)).
Given a distance code "dcode" (>= 16 + NDIRECT), and extra bits
"dextra", the backward distance is given by the following formula:
hcode = (dcode - NDIRECT - 16) >> NPOSTFIX
lcode = (dcode - NDIRECT - 16) & POSTFIX_MASK
offset = ((2 + (hcode & 1)) << ndistbits) - 4;
distance = ((offset + dextra) << NPOSTFIX) + lcode + NDIRECT + 1
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 Huffman 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 Huffman code over the insert-and-copy length code
alphabet, while the extra bits values are encoded as fixed-width
machine integers. 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 code 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:
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
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:
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
To convert an insert-and-copy length code to an insert length code
and a copy length code, the following table can be used:
Insert
length Copy length code
code 0-7 8-15 16-23
+---------+---------+
| | |
0-7 | 0-63 | 64-127 | <--- distance code 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 |
| | | |
+---------+---------+---------+
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).
6. Encoding of block switch commands
As described in Section 2, a block-switch command is a pair
<block type, block length>. 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 Huffman code over the block type code
alphabet. A block type code 0 means that the block type is the same
as the type of the second last block from the same block category,
while a block type code 1 means that the block type equals the last
block type plus one. If the last block type is the maximal possible,
then a block type code 1 means block type 0. Block type codes 2 - 257
represent block types 0 - 255. The second last and last block types
are initialized with 0 and 1, respectively, at the beginning of each
meta-block.
The first block type of each block category must be 0 and the block
type of the first block switch command is therefore not encoded in
the compressed data.
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 length in the compressed data is represented with a pair
<block length code, extra bits>. The block length code and the extra
bits are encoded back-to-back, the block length code is encoded using
a Huffman code over the block length code alphabet, while the extra
bits value is encoded as a fixed-width machine integer. The number of
extra bits can be 0 - 24, and it is dependent on the block length
code. The symbols of the block length code alphabet, along with the
number of extra bits and the range of block lengths are as follows:
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
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.
7. Context modeling
As described in Section 2, the Huffman 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 Huffman
tree in the array of literal and distance Huffman trees.
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.
There are four methods, called context modes, to compute the
Context ID:
* MSB6, where the Context ID is the value of six most
significant bits of p1,
* LSB6, where the Context ID is the value of six least
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.
The Context ID for the UTF8 and Signed context modes is computed
using the following lookup tables Lut0, Lut1, and Lut2.
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
Given p1 is the last decoded byte and p2 is the second last
decoded byte the context IDs can be computed as follows:
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]
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.
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.
7.3. Encoding of the context map
There are two kinds of context maps, for literals and 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 Huffman tree 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 Huffman tree for encoding a literal or distance
code with context ID "cid" and block type "bltype" is
index of literal Huffman tree = CMAPL[bltype * 64 + cid]
index of distance Huffman tree = CMAPD[bltype * 4 + cid]
The values of the context map are encoded with the combination
of run length encoding for zero values and Huffman 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 Huffman code has the following
RLEMAX + NTREES symbols:
0: value zero
1: repeat a zero 2-3 times, read 1 bit for repeat length
2: repeat a zero 4-7 times, read 2 bits for repeat length
...
RLEMAX: repeat a zero (2^RLEMAX)-(2^(RLEMAX+1) - 1) times,
read RLEMAX bits for repeat length
RLEMAX + 1: value 1
...
RLEMAX + NTREES - 1: value NTREES - 1
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):
1-5 bits: RLEMAX, 0 is encoded with one 0 bit, and values
1 - 16 are encoded with bit pattern 1xxxx
Huffman code with alphabet size NTREES + RLEMAX
Context map size values encoded with the above Huffman code
and run length coding for zero values
1 bit: IMTF bit, if set, we do an inverse move-to-front
transform on the values in the context map to get
the Huffman code indexes
For the encoding of NTREES see Section 9.2.
8. Static dictionary
At any given point during decoding the compressed data, a reference
to a duplicated string in the output produced so far has a maximum
backward distance value, which is the minimum of the window size and
the number of output bytes produced. However, decoding a distance
from the input 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 maximum valid copy length for a static
dictionary reference is 24. The static dictionary has three parts:
* 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
The number of static dictionary words for a given length is:
NWORDS[length] = 0 (if length < 3)
NWORDS[length] = (1 << NDBITS[lengths]) (if length >= 3)
DOFFSET and DICTSIZE are defined by the following recursion:
DOFFSET[0] = 0
DOFFSET[length + 1] = DOFFSET[length] + length * NWORDS[length]
DICTSIZE = DOFFSET[24] + 24 * NWORDS[24]
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 NTRANSFORMS 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:
word_id = distance - (max allowed distance + 1)
index = word_id % NWORDS[length]
base_word = DICT[offset(length, index)..offset(length, index+1))
transform_id = word_id >> NDBITS[length]
The string copied to the output stream is computed by applying the
transformation to the base dictionary word. If transform_id is
greater than NTRANSFORMS - 1 or length is greater than 24, the
compressed data set is invalid and must be discarded.
Each word transformation has the follwing 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 12 elementary transforms:
Identity, Omit1, ..., Omit9, UppercaseFirst, UppercaseAll
The form of these elementary transforms are as follows:
Identity(word) = word
Omitk(word) = the first (length(word) - k) bytes of word, or
empty string if length(word) < k
UppercaseFirst(word) = first UTF-8 character of word upper-cased
UppercaseAll(word) = all UTF-8 characters of word upper-cased
For the purposes of UppercaseAll, word is parsed into UTF-8
characters an coverted to upper-case by taking 1 - 3 bytes at a time,
using the algorithm below:
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
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.
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.
9.1. Format of the stream header
The stream header has only the following one field:
1-4 bits: WBITS, a value in the range 16 - 24, value 16 is
encoded with one 0 bit, and values 17 - 24 are
encoded with bit pattern 1xxx
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
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:
1 bit: ISLAST, set to 1 if this is the last meta-block
1 bit: ISEMPTY, set to 1 if the meta-block is empty, this
field is only present if ISLAST bit is set, since
only the last meta-block can be empty
2 bits: MNIBBLES - 4, where MNIBBLES is # of nibbles to
represent the length
MNIBBLES x 4 bits: MLEN - 1, where MLEN is the length
of the meta-block in the input data in bytes
1 bit: ISUNCOMPRESSED, if set to 1, any bits of input 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 ISLAST bit is not set
1-11 bits: NBLTYPESL, # of literal block types, encoded with
the following variable length code:
Value Bit Pattern
----- -----------
1 0
2 1000
3-4 1001x
5-8 1010xx
9-16 1011xxx
17-32 1100xxxx
33-64 1101xxxxx
65-128 1110xxxxxx
129-256 1111xxxxxxx
Huffman code over the block type code alphabet for literal
block types, appears only if NBLTYPESL >= 2
Huffman code over the block length code alphabet for literal
block lengths, appears only if NBLTYPESL >= 2
Block length code + Extra bits for first literal block
length, appears only if NBLTYPESL >= 2
1-11 bits: NBLTYPESI, # of insert-and-copy block types, encoded
with the same variable length code as above
Huffman code over the block type code alphabet for insert-
and-copy block types, only if NBLTYPESI >= 2
Huffman code over the block length code alphabet for insert-
and-copy block lengths, only if NBLTYPESI >= 2
Block length code + Extra bits for first insert-and-copy
block length, only if NBLTYPESI >= 2
1-11 bits: NBLTYPESD, # of distance block types, encoded with
the same variable length code as above
Huffman code over the block type code alphabet for distance
block types, appears only if NBLTYPESD >= 2
Huffman code over the block length code alphabet for
distance block lengths, only if NBLTYPESD >= 2
Block length code + Extra bits for first distance block
length, 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 Huffman 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 Huffman 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 Huffman codes for literals
NBLTYPESI Huffman codes for insert-and-copy lengths
NTREESD Huffman codes for distances
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:
Block type code for next insert-and-copy block type, appears
only if NBLTYPESI >= 2 and the previous insert-and-copy
block has ended
Block length code + Extra bits for next insert-and-copy
block length, appears only if NBLTYPESI >= 2 and the
previous insert and-copy block has ended
Insert-and-copy length, encoded as in section 5, using the
insert-and-copy length Huffman 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 has ended
Block length code + Extra bits for next literal block
length, appears only if NBLTYPESL >= 2 and the
previous literal block has ended
Next byte of the input data, encoded with the literal
Huffman code with the index determined by the
previuos two bytes of the input 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 has
ended
Block length code + Extra bits for next distance block
length, appears only if NBLTYPESD >= 2 and the previous
distance block has ended
Distance code, encoded as in section 4, using the distance
Huffman 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
The number of commands in the meta-block is such that the sum of
insert lengths and copy lengths over all the commands gives the
uncompressed length, MLEN encoded in the meta-block header.
10. Decoding algorithm
The decoding algorithm that produces the output data is as follows:
read window size
do
read ISLAST bit
if ISLAST
read ISEMPTY bit
if ISEMPTY
break from loop
read MLEN
if not ISLAST
read ISUNCOMPRESSED bit
if ISUNCOMPRESSED
skip any bits up to the next byte boundary
copy MLEN bytes of input to the output stream
continue to the next meta-block
loop for each three block categories (i = L, I, D)
read NBLTYPESi
if NBLTYPESi >= 2
read Huffman code for block types, HTREE_BTYPE_i
read Huffman code for block lengths, HTREE_BLEN_i
read block length, BLEN_i
set block type, BTYPE_i to 0
initialize second last and last block types to 0 and 1
else
set block type, BTYPE_i to 0
set block length, 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 Huffman codes for literals, HTREEL[]
read array of Huffman codes for insert-and-copy, HTREEI[]
read array of Huffman codes for distances, HTREED[]
do
if BLEN_I is zero
read block type using HTREE_BTYPE_I and set BTYPE_I
read block length using HTREE_BLEN_I and set BLEN_I
decrement BLEN_I
read insert and copy length, ILEN, CLEN with HTREEI[BTYPE_I]
loop for ILEN
if BLEN_L is zero
read block type using HTREE_BTYPE_L and set BTYPE_L
read block length 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 bytes of output
read literal using HTREEL[CMAPL[64 * BTYPE_L + CIDL]]
copy literal to output stream
if number of output bytes produced in the loop is MLEN
break from loop
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
read block length using HTREE_BLEN_D and set BLEN_D
decrement BLEN_D
compute context ID, CIDD from CLEN
read distance code with HTREED[CMAPD[4 * BTYPE_D + CIDD]]
compute distance by distance short code substitution
move backwards distance bytes in the output stream, and
copy CLEN bytes from this position to the output stream,
or look up the static dictionary word and copy it to the
output stram
while number of output bytes produced in the loop < MLEN
while not ISLAST
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
cannot refer past the beginning of the output stream and it can
not be greater than the window size; any such distance must be
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
output stream.
11. References
[1] 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.
[2] Ziv J., Lempel A., "A Universal Algorithm for Sequential Data
Compression", IEEE Transactions on Information Theory, Vol. 23,
No. 3, pp. 337-343.
[3] Deutsch, P., "DEFLATE Compressed Data Format Specification
version 1.3", RFC 1951, Aladdin Enterprises, May 1996.
http://www.ietf.org/rfc/rfc1951.txt
12. 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/ directory within the font-compression-
reference open-source project:
https://code.google.com/p/font-compression-reference/source/browse/
Appendix A. Static dictionary data
The hexadecimal form of the DICT array is the following: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7472616e736974696f6e616c2f2f454e2268746d6c342f6c6f6f73652e647464
223e7868746d6c312f4454442f7868746d6c31616c6c6f775472616e73706172
656e6379617269612d6175746f636f6d706c6574653c626c6f636b71756f7465
20636c617373616c6c6f777472616e73706172656e6379616c6c6f7773637269
70746163636573733c656e636c6f73757265206c656e67746867415f676f6f67
6c6546696c6c536c6f746973557365724f7074696f6e734f70656e676f6f676c
655f6166735f616470616765676f6f676c655f6166735f636c69656e74676c6f
62616c526567697374657255524c676574437573746f6d4164436f6e66696767
6f6f676c655f61645f6368616e6e656c735f71657572795f6865616465725f77
316765745f636f6d6d656e745f636f756e74696e746572636570744d65737361
676573676f6f676c655f636f6c6f725f6c696e6b676f6f676c655f636f6c6f72
5f7465787467415f676f6f676c6546657463684164736d656e755f335f646874
6d6c5f6e65773167657454696d657a6f6e654f66667365747365744f6e4c6f61
6443616c6c6261636b5f5f636865636b41644c6f636174696f6e6d616b655f61
6a61785f726571756573746e636f6465496d616765526573697a65726375725f
74656d706c6174655f6e616d656a6f62536561726368416464506172616d696e
6372656d656e74616c5f706978656c676f6f676c655f7461675f706172616d73
656e636f64696e673d227574662d38223f3e656e636f64696e673d225554462d
38223f3e636f6e74656e743d22746578742f68746d6c676f6f676c655f616673
5f6368616e6e656c656e636f6465555249436f6d706f6e656e746f6e72656164
7973746174656368616e67656f70656e496e666f57696e646f7748746d6c6c61
72677572615f696465616c5f70616765656e61626c654c696e6b547261636b69
6e6776616c6f725f70726f706f7263696f6e616c6c777274655f636c65616e75
705f776f7264616a6178436f6e74726f6c546f6f6c6b6974686173685f706f72
745f616c6c5f6c69737462617463684170706c79436865636b426f7862617365
5f70726963655f6164645f666565657461726765745365617263685175657279
6574617267657442616e6e65724964656e74736561726368436f6d706c657465
6455524c7265676973746572496e744d6573736167656f6e756e6c6f61645f66
756e6374696f6e7373686f774d657373616765436f6e74656e746f70656e6564
5f696e666f5f77696e646f776d796a666c617368333669306d6f64756c656578
7463616c5f636f6f6b69655f706174686574617267657442616e6e6572537479
6c65696e69744c616e677561676553656c656374657461726765744361744b65
79776f72647374656c65636f6d6d756e69636174696f6e736368617261637465
726973746963616c6c79d091d18ad0bbd0b3d0b0d180d181d0bad0b8d0b1d18a
d0bbd0b3d0b0d180d181d0bad0b8d0a4d0b5d0b4d0b5d180d0b0d186d0b8d0b8
d0bdd0b5d181d0bad0bed0bbd18cd0bad0bed181d0bed0bed0b1d189d0b5d0bd
d0b8d0b5d181d0bed0bed0b1d189d0b5d0bdd0b8d18fd0bfd180d0bed0b3d180
d0b0d0bcd0bcd18bd09ed182d0bfd180d0b0d0b2d0b8d182d18cd0b1d0b5d181
d0bfd0bbd0b0d182d0bdd0bed0bcd0b0d182d0b5d180d0b8d0b0d0bbd18bd0bf
d0bed0b7d0b2d0bed0bbd18fd0b5d182d0bfd0bed181d0bbd0b5d0b4d0bdd0b8
d0b5d180d0b0d0b7d0bbd0b8d187d0bdd18bd185d0bfd180d0bed0b4d183d0ba
d186d0b8d0b8d0bfd180d0bed0b3d180d0b0d0bcd0bcd0b0d0bfd0bed0bbd0bd
d0bed181d182d18cd18ed0bdd0b0d185d0bed0b4d0b8d182d181d18fd0b8d0b7
d0b1d180d0b0d0bdd0bdd0bed0b5d0bdd0b0d181d0b5d0bbd0b5d0bdd0b8d18f
d0b8d0b7d0bcd0b5d0bdd0b5d0bdd0b8d18fd0bad0b0d182d0b5d0b3d0bed180
d0b8d0b8d090d0bbd0b5d0bad181d0b0d0bdd0b4d180e0a4a6e0a58de0a4b5e0
a4bee0a4b0e0a4bee0a4aee0a588e0a4a8e0a581e0a485e0a4b2e0a4aae0a58d
e0a4b0e0a4a6e0a4bee0a4a8e0a4ade0a4bee0a4b0e0a4a4e0a580e0a4afe0a4
85e0a4a8e0a581e0a4a6e0a587e0a4b6e0a4b9e0a4bfe0a4a8e0a58de0a4a6e0
a580e0a487e0a482e0a4a1e0a4bfe0a4afe0a4bee0a4a6e0a4bfe0a4b2e0a58d
e0a4b2e0a580e0a485e0a4a7e0a4bfe0a495e0a4bee0a4b0e0a4b5e0a580e0a4
a1e0a4bfe0a4afe0a58be0a49ae0a4bfe0a49fe0a58de0a4a0e0a587e0a4b8e0
a4aee0a4bee0a49ae0a4bee0a4b0e0a49ce0a482e0a495e0a58de0a4b6e0a4a8
e0a4a6e0a581e0a4a8e0a4bfe0a4afe0a4bee0a4aae0a58de0a4b0e0a4afe0a5
8be0a497e0a485e0a4a8e0a581e0a4b8e0a4bee0a4b0e0a491e0a4a8e0a4b2e0
a4bee0a487e0a4a8e0a4aae0a4bee0a4b0e0a58de0a49fe0a580e0a4b6e0a4b0
e0a58de0a4a4e0a58be0a482e0a4b2e0a58be0a495e0a4b8e0a4ade0a4bee0a4
abe0a4bce0a58de0a4b2e0a588e0a4b6e0a4b6e0a4b0e0a58de0a4a4e0a587e0
a482e0a4aae0a58de0a4b0e0a4a6e0a587e0a4b6e0a4aae0a58de0a4b2e0a587
e0a4afe0a4b0e0a495e0a587e0a482e0a4a6e0a58de0a4b0e0a4b8e0a58de0a4
a5e0a4bfe0a4a4e0a4bfe0a489e0a4a4e0a58de0a4aae0a4bee0a4a6e0a489e0
a4a8e0a58de0a4b9e0a587e0a482e0a49ae0a4bfe0a49fe0a58de0a4a0e0a4be
e0a4afe0a4bee0a4a4e0a58de0a4b0e0a4bee0a49ce0a58de0a4afe0a4bee0a4
a6e0a4bee0a4aae0a581e0a4b0e0a4bee0a4a8e0a587e0a49ce0a58be0a4a1e0
a4bce0a587e0a482e0a485e0a4a8e0a581e0a4b5e0a4bee0a4a6e0a4b6e0a58d
e0a4b0e0a587e0a4a3e0a580e0a4b6e0a4bfe0a495e0a58de0a4b7e0a4bee0a4
b8e0a4b0e0a495e0a4bee0a4b0e0a580e0a4b8e0a482e0a497e0a58de0a4b0e0
a4b9e0a4aae0a4b0e0a4bfe0a4a3e0a4bee0a4aee0a4ace0a58de0a4b0e0a4be
e0a482e0a4a1e0a4ace0a49ae0a58de0a49ae0a58be0a482e0a489e0a4aae0a4
b2e0a4ace0a58de0a4a7e0a4aee0a482e0a4a4e0a58de0a4b0e0a580e0a4b8e0
a482e0a4aae0a4b0e0a58de0a495e0a489e0a4aee0a58de0a4aee0a580e0a4a6
e0a4aee0a4bee0a4a7e0a58de0a4afe0a4aee0a4b8e0a4b9e0a4bee0a4afe0a4
a4e0a4bee0a4b6e0a4ace0a58de0a4a6e0a58be0a482e0a4aee0a580e0a4a1e0
a4bfe0a4afe0a4bee0a486e0a488e0a4aae0a580e0a48fe0a4b2e0a4aee0a58b
e0a4ace0a4bee0a487e0a4b2e0a4b8e0a482e0a496e0a58de0a4afe0a4bee0a4
86e0a4aae0a4b0e0a587e0a4b6e0a4a8e0a485e0a4a8e0a581e0a4ace0a482e0
a4a7e0a4ace0a4bee0a49ce0a4bce0a4bee0a4b0e0a4a8e0a4b5e0a580e0a4a8
e0a4a4e0a4aee0a4aae0a58de0a4b0e0a4aee0a581e0a496e0a4aae0a58de0a4
b0e0a4b6e0a58de0a4a8e0a4aae0a4b0e0a4bfe0a4b5e0a4bee0a4b0e0a4a8e0
a581e0a495e0a4b8e0a4bee0a4a8e0a4b8e0a4aee0a4b0e0a58de0a4a5e0a4a8
e0a486e0a4afe0a58be0a49ce0a4bfe0a4a4e0a4b8e0a58be0a4aee0a4b5e0a4
bee0a4b0d8a7d984d985d8b4d8a7d8b1d983d8a7d8aad8a7d984d985d986d8aa
d8afd98ad8a7d8aad8a7d984d983d985d8a8d98ad988d8aad8b1d8a7d984d985
d8b4d8a7d987d8afd8a7d8aad8b9d8afd8afd8a7d984d8b2d988d8a7d8b1d8b9
d8afd8afd8a7d984d8b1d8afd988d8afd8a7d984d8a5d8b3d984d8a7d985d98a
d8a9d8a7d984d981d988d8aad988d8b4d988d8a8d8a7d984d985d8b3d8a7d8a8
d982d8a7d8aad8a7d984d985d8b9d984d988d985d8a7d8aad8a7d984d985d8b3
d984d8b3d984d8a7d8aad8a7d984d8acd8b1d8a7d981d98ad983d8b3d8a7d984
d8a7d8b3d984d8a7d985d98ad8a9d8a7d984d8a7d8aad8b5d8a7d984d8a7d8aa
7075626c696320222d2f2f7733632f2f6474642d7472616e736974696f6e616c
2e647464223e3c68746d6c3e3c686561643e3c7469746c653e676f6f676c655f
6166735f7172795f63747874676f6f676c655f636f6c6f725f626f7264657263
7573746f6d536561726368436f6e74726f6c656e61626c6553696e676c655265
7175657374637573746f6d5365617263684f7074696f6e733c3f786d6c207665
7273696f6e3d22312e3022203c696e70757420747970653d2268696464656e22
676574456c656d656e747342795461674e616d657772697465496e6c696e6550
6c6163656d656e7470705f67656d6975735f6964656e746966696572636f6f6b
6965416c657274446973706c61796564676f6f676c655f636f6e76657273696f
6e5f69646e61766261725f70617373776f72645f68696e746e61766261725f75
7365726e616d655f626c75726f7074696f6e616c5a6970436f756e7472696573
77696e646f775f6c6f636174696f6e5f68726566676f6f676c655f637573746f
6d5f706172616d736a626d5f6c61737473686f7274656e656475726c636f6c6c
656374696f6e4669656c6473496e666f706f7274756775c3aa7320284575726f
70657529d0a3d0bad180d0b0d197d0bdd181d18cd0bad0b0d183d0bad180d0b0
d197d0bdd181d18cd0bad0b0d0a0d0bed181d181d0b8d0b9d181d0bad0bed0b9
d0bcd0b0d182d0b5d180d0b8d0b0d0bbd0bed0b2d0b8d0bdd184d0bed180d0bc
d0b0d186d0b8d0b8d183d0bfd180d0b0d0b2d0bbd0b5d0bdd0b8d18fd0bdd0b5
d0bed0b1d185d0bed0b4d0b8d0bcd0bed0b8d0bdd184d0bed180d0bcd0b0d186
d0b8d18fd098d0bdd184d0bed180d0bcd0b0d186d0b8d18fd0a0d0b5d181d0bf
d183d0b1d0bbd0b8d0bad0b8d0bad0bed0bbd0b8d187d0b5d181d182d0b2d0be
d0b8d0bdd184d0bed180d0bcd0b0d186d0b8d18ed182d0b5d180d180d0b8d182
d0bed180d0b8d0b8d0b4d0bed181d182d0b0d182d0bed187d0bdd0bed8a7d984
d985d8aad988d8a7d8acd8afd988d986d8a7d984d8a7d8b4d8aad8b1d8a7d983
d8a7d8aad8a7d984d8a7d982d8aad8b1d8a7d8add8a7d8aa7365744f70656e53
656374696f6e73436f6f6b69656e61766261725f757365726e616d655f666f63
75736f75746c696e655768696c65416e696d6174696e67e0b8a0e0b8b2e0b8a9
e0b8b2e0b984e0b897e0b8a2e183a5e18390e183a0e18397e183a3e1839ae183
98e6ada3e9ab94e4b8ade696872028e7b981e9ab9429e0a4a8e0a4bfe0a4b0e0
a58de0a4a6e0a587e0a4b6e0a4a1e0a4bee0a489e0a4a8e0a4b2e0a58be0a4a1
e0a495e0a58de0a4b7e0a587e0a4a4e0a58de0a4b0e0a49ce0a4bee0a4a8e0a4
95e0a4bee0a4b0e0a580e0a4b8e0a482e0a4ace0a482e0a4a7e0a4bfe0a4a4e0
a4b8e0a58de0a4a5e0a4bee0a4aae0a4a8e0a4bee0a4b8e0a58de0a4b5e0a580
e0a495e0a4bee0a4b0e0a4b8e0a482e0a4b8e0a58de0a495e0a4b0e0a4a3e0a4
b8e0a4bee0a4aee0a497e0a58de0a4b0e0a580e0a49ae0a4bfe0a49fe0a58de0
a4a0e0a58be0a482e0a4b5e0a4bfe0a49ce0a58de0a49ee0a4bee0a4a8e0a485
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a8e0a58de0a4a8e0a497e0a4bee0a4a1e0a4bfe0a4afe0a4bee0a481e0a495e0
a58de0a4afe0a58be0a482e0a495e0a4bfe0a4b8e0a581e0a4b0e0a495e0a58d
e0a4b7e0a4bee0a4aae0a4b9e0a581e0a481e0a49ae0a4a4e0a580e0a4aae0a5
8de0a4b0e0a4ace0a482e0a4a7e0a4a8e0a49fe0a4bfe0a4aae0a58de0a4aae0
a4a3e0a580e0a495e0a58de0a4b0e0a4bfe0a495e0a587e0a49fe0a4aae0a58d
e0a4b0e0a4bee0a4b0e0a482e0a4ade0a4aae0a58de0a4b0e0a4bee0a4aae0a5
8de0a4a4e0a4aee0a4bee0a4b2e0a4bfe0a495e0a58be0a482e0a4b0e0a4abe0
a4bce0a58de0a4a4e0a4bee0a4b0e0a4a8e0a4bfe0a4b0e0a58de0a4aee0a4be
e0a4a3e0a4b2e0a4bfe0a4aee0a4bfe0a49fe0a587e0a4a122687474703a2f2f
7777772e77332e6f72672f54522f3c6c696e6b2072656c3d227374796c657368
6565742270656e64696e675f616e616c79746963735f76617273735f71657572
795f6865616465725f775f6f626a5f31735f71657572795f6865616465725f77
5f6f626a5f3270705f67656d6975735f686974636f6c6c6563746f72676f6f67
6c655f616e616c79746963735f7561636374637265617465446f63756d656e74
467261676d656e74676574456c656d656e74734279436c6173734e616d65706f
7274756775c3aa732028646f2042726173696c29d0bed180d0b3d0b0d0bdd0b8
d0b7d0b0d186d0b8d0b8d0b2d0bed0b7d0bcd0bed0b6d0bdd0bed181d182d18c
d0bed0b1d180d0b0d0b7d0bed0b2d0b0d0bdd0b8d18fd180d0b5d0b3d0b8d181
d182d180d0b0d186d0b8d0b8d0b2d0bed0b7d0bcd0bed0b6d0bdd0bed181d182
d0b8d0bed0b1d18fd0b7d0b0d182d0b5d0bbd18cd0bdd0b06d6f7573655f6f76
65725f7374617475735f6172726179676f6f676c655f636f6e76657273696f6e
5f6c6162656c7868746d6c31312f4454442f7868746d6c31312e647464226874
74702d65717569763d22436f6e74656e742d54797065d0b4d0b5d18fd182d0b5
d0bbd18cd0bdd0bed181d182d0b8d181d0bed0bed182d0b2d0b5d182d181d182
d0b2d0b8d0b8d0bfd180d0bed0b8d0b7d0b2d0bed0b4d181d182d0b2d0b0d0b1
d0b5d0b7d0bed0bfd0b0d181d0bdd0bed181d182d0b8e0a4aae0a581e0a4b8e0
a58de0a4a4e0a4bfe0a495e0a4bee0a495e0a4bee0a482e0a497e0a58de0a4b0
e0a587e0a4b8e0a489e0a4a8e0a58de0a4b9e0a58be0a482e0a4a8e0a587e0a4
b5e0a4bfe0a4a7e0a4bee0a4a8e0a4b8e0a4ade0a4bee0a4abe0a4bfe0a495e0
a58de0a4b8e0a4bfe0a482e0a497e0a4b8e0a581e0a4b0e0a495e0a58de0a4b7
e0a4bfe0a4a4e0a495e0a589e0a4aae0a580e0a4b0e0a4bee0a487e0a49fe0a4
b5e0a4bfe0a49ce0a58de0a49ee0a4bee0a4aae0a4a8e0a495e0a4bee0a4b0e0
a58de0a4b0e0a4b5e0a4bee0a488e0a4b8e0a495e0a58de0a4b0e0a4bfe0a4af
e0a4a4e0a4be
The number of words for each length is given by the following bit-
depth array:
NDBITS := 0, 0, 0, 9, 10, 10, 11, 9, 10, 9,
9, 8, 9, 6, 7, 7, 6, 5, 7, 3,
5, 5, 4, 1, 4,
Appendix B. List of word transformations
ID Prefix Transform Suffix
-- ------ --------- ------
0 "" Identity ""
1 "" Identity " "
2 "" Identity "\">"
3 "" UppercaseFirst ""
4 "" Identity "\""
5 "" Identity "."
6 "" Identity "=\""
7 "" UppercaseFirst " "
8 " " Identity "=\""
9 " " Identity " "
10 "" Identity ":"
11 " " Identity ""
12 "" Identity "\n"
13 "" Identity "("
14 "" UppercaseAll ""
15 "." Identity "("
16 "" Identity "'"
17 "" UppercaseFirst "\""
18 " " UppercaseFirst " "
19 "" Omit3 ""
20 "" Omit4 ""
21 "." Identity ""
22 "" Omit1 ""
23 "" Omit2 ""
24 "" UppercaseFirst "\">"
25 "" Omit5 ""
26 "" UppercaseAll " "
27 " " UppercaseFirst ""
28 "" Identity ", "
29 "" UppercaseFirst "("
30 "" Identity "\n\t"
31 "" UppercaseFirst "'"
32 "." Identity " "
33 " " UppercaseAll " "
34 "" Identity "='"
35 "" UppercaseFirst "."
36 " " Identity "."
37 " " Identity ", "
38 " " UppercaseAll ""
39 "" Omit6 ""
40 "" Omit9 ""
41 "" UppercaseAll "\""
42 "" Identity " the "
43 "" Identity " in "
44 "" Identity " of "
45 "" Identity " to "
46 "" Identity " and "
47 "" Identity " is "
48 "" Identity " on "
49 "" Identity " by "
50 "" Identity " for "
51 "" Identity " with "
52 "" Identity " from "
53 "" Identity " as "
54 "" Identity " at "
55 "" Identity "er "
56 " " Identity "='"
57 "" Identity " a "
58 "" Omit7 ""
59 "" Omit8 ""
60 " " Identity "("
61 " " Identity ". "
62 "" Identity ". "
63 "" Identity ","
64 "" Omit1 "ing "
65 "" Identity "ed "
66 "" UppercaseFirst ", "
67 "" UppercaseAll "."
68 "" UppercaseAll "=\""
69 "" UppercaseAll ", "
70 "" UppercaseAll "\">"
71 " " UppercaseFirst "."
72 " " UppercaseAll "=\""
73 " " UppercaseFirst ", "
74 "" UppercaseAll "'"
75 "" UppercaseFirst "=\""
76 " " Identity ","
77 "" Identity " that "
78 "" UppercaseFirst "='"
79 "" UppercaseFirst ". "
80 "" UppercaseFirst ","
81 "" Identity ". The "
82 "\xc2\xa0" Identity ""
83 " " UppercaseFirst ". "
84 "" UppercaseAll ","
85 "" UppercaseAll "("
86 " " UppercaseAll "='"
87 "" Identity "]"
88 "" UppercaseAll "='"
89 " " UppercaseAll "."
90 "" UppercaseAll ". "
91 " " UppercaseFirst "=\""
92 " " UppercaseAll ". "
93 " " UppercaseFirst ","
94 " " UppercaseAll ", "
95 "" Identity "ize "
96 " " UppercaseFirst "='"
97 "" Identity "est "
98 "" Identity ". This "