draft-alakuijala-brotli-02.nroff

.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 2014
.ds CH Brotli
.ds CF Expires April 27, 2015
.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 27, 2015''October 2014'
.fi


.ce 2
Brotli Compressed Data Format 
draft-alakuijala-brotli-02
.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 27, 2015.

.ti 0
Copyright Notice

Copyright (c) 2014 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 "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 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.
.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 Huffman 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 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, [LZ77]) and Huffman
coding. The Huffman trees 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 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 category 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.

A block is defined by a type (0-255) and a length. The length is the
amount of huffman symbols of its category, the type dictates which
huffman code is used for these symbols. 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 of the three categories of
symbols within these commands are part of a logical block structure,
for example the following:

   [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 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).

.ti 0
3. Compressed representation of Huffman codes

.ti 0
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:

.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 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 [HUFFMAN] 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.

.ti 0
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:

.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 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.

.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

.ti 0
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.

.ti 0
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:

.nf
   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
.fi

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:

.nf
   * 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).
.fi

.ti 0
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:

.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

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:

.nf
.KS
   Symbol   Code
   ------   ----
   0          00
   1        1110
   2         110
   3          01
   4          10
   5        1111
.KE
.fi

We can now define the format of the complex Huffman code as
follows:

.nf
   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.
.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 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:

.nf
   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
.fi 

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:

.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 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:

.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 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 |
              |         |         |         |
              +---------+---------+---------+
.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 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:

.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 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.

.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 initizalized to zero.

There are four methods, called context modes, to compute the
Context ID:
.nf
   * 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.
.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 CRC32 checksums of these tables are as follows:

.nf
   Table    Length    CRC32
   -----    ------    -----
   Lut0     256       0x09a6512a
   Lut1     256       0x572d8c69
   Lut2     256       0x8ae01e4b
.fi

Given p1 is the last decoded byte and p2 is the second last
decoded 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 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:

.nf
   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 (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 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
.fi

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 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:

.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 output stream is computed by applying the
transformation to the base dictionary word. If transform_id is
greater than 120 or length is greater than 24, the
compressed data set is 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, OmitLast1, ..., OmitLast9, UppercaseFirst, UppercaseAll,
   OmitFirst1, ..., OmitFirst9
.fi

The form of these elementary transforms are as follows:

.nf
   Identity(word) = word

   OmitLastk(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

   OmitFirstk(word) = the last (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
   1-4 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
.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:  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
.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 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
.fi

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.

.ti 0
10. Decoding algorithm

The decoding algorithm that produces the output data is as follows:

.nf
   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
.fi

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.

.ti 0
11. Security Considerations

As with any compressed file formats, decompressor implementations should
handle all input byte sequences, not only those that conform to this
specification and non-conformant input 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 input. Therefore decompressor
implementations should perform bound-checking for each memory access
that result from values decoded from the input stream.

.ti 0
12. IANA Considerations

This document has no actions for IANA. 

.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
Appendix A. Static dictionary data

The hexadecimal form of the DICT array is the following:

.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
      d182d0b0d0bdd0b5d0bfd0bed0bed182d0b8d0b7d0bdd0bed0b4d0bed182d0be
      d0b6d0b5d0bed0bdd0b8d185d09dd0b0d0b5d0b5d0b1d18bd0bcd18bd092d18b
      d181d0bed0b2d18bd0b2d0bed09dd0bed0bed0b1d09fd0bed0bbd0b8d0bdd0b8
      d0a0d0a4d09dd0b5d09cd18bd182d18bd09ed0bdd0b8d0bcd0b4d0b0d097d0b0
      d094d0b0d09dd183d09ed0b1d182d0b5d098d0b7d0b5d0b9d0bdd183d0bcd0bc
      d0a2d18bd183d0b6d981d98ad8a3d986d985d8a7d985d8b9d983d984d8a3d988
      d8b1d8afd98ad8a7d981d989d987d988d984d985d984d983d8a7d988d984d987
      d8a8d8b3d8a7d984d8a5d986d987d98ad8a3d98ad982d8afd987d984d8abd985
      d8a8d987d984d988d984d98ad8a8d984d8a7d98ad8a8d983d8b4d98ad8a7d985
      d8a3d985d986d8aad8a8d98ad984d986d8add8a8d987d985d985d8b4d988d8b4
      6669727374766964656f6c69676874776f726c646d656469617768697465636c
      6f7365626c61636b7269676874736d616c6c626f6f6b73706c6163656d757369
      636669656c646f72646572706f696e7476616c75656c6576656c7461626c6562
      6f617264686f75736567726f7570776f726b7379656172737374617465746f64
      6179776174657273746172747374796c656465617468706f77657270686f6e65
      6e696768746572726f72696e70757461626f75747465726d737469746c65746f
      6f6c736576656e746c6f63616c74696d65736c61726765776f72647367616d65
      7373686f72747370616365666f637573636c6561726d6f64656c626c6f636b67
      75696465726164696f7368617265776f6d656e616761696e6d6f6e6579696d61
      67656e616d6573796f756e676c696e65736c61746572636f6c6f72677265656e
      66726f6e7426616d703b7761746368666f726365707269636572756c65736265
      67696e616674657276697369746973737565617265617362656c6f77696e6465
      78746f74616c686f7572736c6162656c7072696e7470726573736275696c746c
      696e6b73737065656473747564797472616465666f756e6473656e7365756e64
      657273686f776e666f726d7372616e676561646465647374696c6c6d6f766564
      74616b656e61626f7665666c61736866697865646f6674656e6f746865727669
      657773636865636b6c6567616c72697665726974656d73717569636b73686170
      6568756d616e6578697374676f696e676d6f7669657468697264626173696370
      65616365737461676577696474686c6f67696e696465617377726f7465706167
      65737573657273647269766573746f7265627265616b736f757468766f696365
      73697465736d6f6e746877686572656275696c6477686963686561727468666f
      72756d746872656573706f72747061727479436c69636b6c6f7765726c697665
      73636c6173736c61796572656e74727973746f72797573616765736f756e6463
      6f757274796f7572206269727468706f70757074797065736170706c79496d61
      67656265696e6775707065726e6f746573657665727973686f77736d65616e73
      65787472616d61746368747261636b6b6e6f776e6561726c79626567616e7375
      70657270617065726e6f7274686c6561726e676976656e6e616d6564656e6465
      645465726d73706172747347726f75706272616e647573696e67776f6d616e66
      616c73657265616479617564696f74616b65737768696c652e636f6d2f6c6976
      656463617365736461696c796368696c6467726561746a7564676574686f7365
      756e6974736e6576657262726f6164636f617374636f7665726170706c656669
      6c65736379636c657363656e65706c616e73636c69636b777269746571756565
      6e7069656365656d61696c6672616d656f6c64657270686f746f6c696d697463
      61636865636976696c7363616c65656e7465727468656d657468657265746f75
      6368626f756e64726f79616c61736b656477686f6c6573696e636573746f636b
      206e616d6566616974686865617274656d7074796f6666657273636f70656f77
      6e65646d69676874616c62756d7468696e6b626c6f6f6461727261796d616a6f
      72747275737463616e6f6e756e696f6e636f756e7476616c696473746f6e6553
      74796c654c6f67696e68617070796f636375726c6566743a6672657368717569
      746566696c6d7367726164656e65656473757262616e66696768746261736973
      686f7665726175746f3b726f7574652e68746d6c6d6978656466696e616c596f
      757220736c696465746f70696362726f776e616c6f6e65647261776e73706c69
      747265616368526967687464617465736d6172636871756f7465676f6f64734c
      696e6b73646f7562746173796e637468756d62616c6c6f776368696566796f75
      74686e6f76656c313070783b7365727665756e74696c68616e6473436865636b
      537061636571756572796a616d6573657175616c7477696365302c3030305374
      61727470616e656c736f6e6773726f756e6465696768747368696674776f7274
      68706f7374736c656164737765656b7361766f696474686573656d696c657370
      6c616e65736d617274616c706861706c616e746d61726b737261746573706c61
      7973636c61696d73616c65737465787473737461727377726f6e673c2f68333e
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      7269707420747970653d22746578742f206f6e636c69636b3d226a6176617363
      726970743a286e65772044617465292e67657454696d6528297d686569676874
      3d2231222077696474683d2231222050656f706c6527732052657075626c6963
      206f6620203c6120687265663d22687474703a2f2f7777772e746578742d6465
      636f726174696f6e3a756e64657274686520626567696e6e696e67206f662074
      6865203c2f6469763e0a3c2f6469763e0a3c2f6469763e0a65737461626c6973
      686d656e74206f6620746865203c2f6469763e3c2f6469763e3c2f6469763e3c
      2f642376696577706f72747b6d696e2d6865696768743a0a3c73637269707420
      7372633d22687474703a2f2f6f7074696f6e3e3c6f7074696f6e2076616c7565
      3d6f6674656e20726566657272656420746f206173202f6f7074696f6e3e0a3c
      6f7074696f6e2076616c753c21444f43545950452068746d6c3e0a3c212d2d5b
      496e7465726e6174696f6e616c20416972706f72743e0a3c6120687265663d22
      687474703a2f2f7777773c2f613e3c6120687265663d22687474703a2f2f77e0
      b8a0e0b8b2e0b8a9e0b8b2e0b984e0b897e0b8a2e183a5e18390e183a0e18397
      e183a3e1839ae18398e6ada3e9ab94e4b8ade696872028e7b981e9ab9429e0a4
      a8e0a4bfe0a4b0e0a58de0a4a6e0a587e0a4b6e0a4a1e0a4bee0a489e0a4a8e0
      a4b2e0a58be0a4a1e0a495e0a58de0a4b7e0a587e0a4a4e0a58de0a4b0e0a49c
      e0a4bee0a4a8e0a495e0a4bee0a4b0e0a580e0a4b8e0a482e0a4ace0a482e0a4
      a7e0a4bfe0a4a4e0a4b8e0a58de0a4a5e0a4bee0a4aae0a4a8e0a4bee0a4b8e0
      a58de0a4b5e0a580e0a495e0a4bee0a4b0e0a4b8e0a482e0a4b8e0a58de0a495
      e0a4b0e0a4a3e0a4b8e0a4bee0a4aee0a497e0a58de0a4b0e0a580e0a49ae0a4
      bfe0a49fe0a58de0a4a0e0a58be0a482e0a4b5e0a4bfe0a49ce0a58de0a49ee0
      a4bee0a4a8e0a485e0a4aee0a587e0a4b0e0a4bfe0a495e0a4bee0a4b5e0a4bf
      e0a4ade0a4bfe0a4a8e0a58de0a4a8e0a497e0a4bee0a4a1e0a4bfe0a4afe0a4
      bee0a481e0a495e0a58de0a4afe0a58be0a482e0a495e0a4bfe0a4b8e0a581e0
      a4b0e0a495e0a58de0a4b7e0a4bee0a4aae0a4b9e0a581e0a481e0a49ae0a4a4
      e0a580e0a4aae0a58de0a4b0e0a4ace0a482e0a4a7e0a4a8e0a49fe0a4bfe0a4
      aae0a58de0a4aae0a4a3e0a580e0a495e0a58de0a4b0e0a4bfe0a495e0a587e0
      a49fe0a4aae0a58de0a4b0e0a4bee0a4b0e0a482e0a4ade0a4aae0a58de0a4b0
      e0a4bee0a4aae0a58de0a4a4e0a4aee0a4bee0a4b2e0a4bfe0a495e0a58be0a4
      82e0a4b0e0a4abe0a4bce0a58de0a4a4e0a4bee0a4b0e0a4a8e0a4bfe0a4b0e0
      a58de0a4aee0a4bee0a4a3e0a4b2e0a4bfe0a4aee0a4bfe0a49fe0a587e0a4a1
      6465736372697074696f6e2220636f6e74656e743d22646f63756d656e742e6c
      6f636174696f6e2e70726f742e676574456c656d656e747342795461674e616d
      65283c21444f43545950452068746d6c3e0a3c68746d6c203c6d657461206368
      61727365743d227574662d38223e3a75726c2220636f6e74656e743d22687474
      703a2f2f2e637373222072656c3d227374796c657368656574227374796c6520
      747970653d22746578742f637373223e747970653d22746578742f6373732220
      687265663d2277332e6f72672f313939392f7868746d6c2220786d6c74797065
      3d22746578742f6a61766173637269707422206d6574686f643d226765742220
      616374696f6e3d226c696e6b2072656c3d227374796c6573686565742220203d
      20646f63756d656e742e676574456c656d656e74747970653d22696d6167652f
      782d69636f6e22202f3e63656c6c70616464696e673d2230222063656c6c7370
      2e6373732220747970653d22746578742f63737322203c2f613e3c2f6c693e3c
      6c693e3c6120687265663d22222077696474683d223122206865696768743d22
      3122223e3c6120687265663d22687474703a2f2f7777772e7374796c653d2264
      6973706c61793a6e6f6e653b223e616c7465726e6174652220747970653d2261
      70706c692d2f2f5733432f2f445444205848544d4c20312e3020656c6c737061
      63696e673d2230222063656c6c70616420747970653d2268696464656e222076
      616c75653d222f613e266e6273703b3c7370616e20726f6c653d22730a3c696e
      70757420747970653d2268696464656e22206c616e67756167653d224a617661
      536372697074222020646f63756d656e742e676574456c656d656e747342673d
      2230222063656c6c73706163696e673d223022207970653d22746578742f6373
      7322206d656469613d22747970653d27746578742f6a61766173637269707427
      776974682074686520657863657074696f6e206f66207970653d22746578742f
      637373222072656c3d227374206865696768743d2231222077696474683d2231
      22203d272b656e636f6465555249436f6d706f6e656e74283c6c696e6b207265
      6c3d22616c7465726e61746522200a626f64792c2074722c20696e7075742c20
      746578746d657461206e616d653d22726f626f74732220636f6e6d6574686f64
      3d22706f73742220616374696f6e3d223e0a3c6120687265663d22687474703a
      2f2f7777772e637373222072656c3d227374796c65736865657422203c2f6469
      763e3c2f6469763e3c64697620636c6173736c616e67756167653d226a617661
      736372697074223e617269612d68696464656e3d2274727565223ec2b73c7269
      70742220747970653d22746578742f6a617661736c3d303b7d2928293b0a2866
      756e6374696f6e28297b6261636b67726f756e642d696d6167653a2075726c28
      2f613e3c2f6c693e3c6c693e3c6120687265663d226809093c6c693e3c612068
      7265663d22687474703a2f2f61746f722220617269612d68696464656e3d2274
      72753e203c6120687265663d22687474703a2f2f7777772e6c616e6775616765
      3d226a61766173637269707422202f6f7074696f6e3e0a3c6f7074696f6e2076
      616c75652f6469763e3c2f6469763e3c64697620636c6173733d7261746f7222
      20617269612d68696464656e3d227472653d286e65772044617465292e676574
      54696d652829706f7274756775c3aa732028646f2042726173696c29d0bed180
      d0b3d0b0d0bdd0b8d0b7d0b0d186d0b8d0b8d0b2d0bed0b7d0bcd0bed0b6d0bd
      d0bed181d182d18cd0bed0b1d180d0b0d0b7d0bed0b2d0b0d0bdd0b8d18fd180
      d0b5d0b3d0b8d181d182d180d0b0d186d0b8d0b8d0b2d0bed0b7d0bcd0bed0b6
      d0bdd0bed181d182d0b8d0bed0b1d18fd0b7d0b0d182d0b5d0bbd18cd0bdd0b0
      3c21444f43545950452068746d6c205055424c494320226e742d547970652220
      636f6e74656e743d22746578742f3c6d65746120687474702d65717569763d22
      436f6e746572616e736974696f6e616c2f2f454e222022687474703a3c68746d
      6c20786d6c6e733d22687474703a2f2f7777772d2f2f5733432f2f4454442058
      48544d4c20312e3020544454442f7868746d6c312d7472616e736974696f6e61
      6c2f2f7777772e77332e6f72672f54522f7868746d6c312f7065203d20277465
      78742f6a617661736372697074273b3c6d657461206e616d653d226465736372
      697074696f6e706172656e744e6f64652e696e736572744265666f72653c696e
      70757420747970653d2268696464656e22206e616a732220747970653d227465
      78742f6a6176617363726928646f63756d656e74292e72656164792866756e63
      746973637269707420747970653d22746578742f6a61766173696d6167652220
      636f6e74656e743d22687474703a2f2f55412d436f6d70617469626c65222063
      6f6e74656e743d746d6c3b20636861727365743d7574662d3822202f3e0a6c69
      6e6b2072656c3d2273686f72746375742069636f6e3c6c696e6b2072656c3d22
      7374796c65736865657422203c2f7363726970743e0a3c736372697074207479
      70653d3d20646f63756d656e742e637265617465456c656d656e3c6120746172
      6765743d225f626c616e6b2220687265663d20646f63756d656e742e67657445
      6c656d656e747342696e70757420747970653d227465787422206e616d653d61
      2e74797065203d2027746578742f6a617661736372696e70757420747970653d
      2268696464656e22206e616d6568746d6c3b20636861727365743d7574662d38
      22202f3e647464223e0a3c68746d6c20786d6c6e733d22687474702d2f2f5733
      432f2f4454442048544d4c20342e30312054656e747342795461674e616d6528
      277363726970742729696e70757420747970653d2268696464656e22206e616d
      3c73637269707420747970653d22746578742f6a6176617322207374796c653d
      22646973706c61793a6e6f6e653b223e646f63756d656e742e676574456c656d
      656e7442794964283d646f63756d656e742e637265617465456c656d656e7428
      2720747970653d27746578742f6a61766173637269707427696e707574207479
      70653d227465787422206e616d653d22642e676574456c656d656e7473427954
      61674e616d6528736e6963616c2220687265663d22687474703a2f2f7777772e
      432f2f4454442048544d4c20342e3031205472616e7369743c7374796c652074
      7970653d22746578742f637373223e0a0a3c7374796c6520747970653d227465
      78742f637373223e696f6e616c2e647464223e0a3c68746d6c20786d6c6e733d
      687474702d65717569763d22436f6e74656e742d5479706564696e673d223022
      2063656c6c73706163696e673d22302268746d6c3b20636861727365743d7574
      662d3822202f3e0a207374796c653d22646973706c61793a6e6f6e653b223e3c
      3c6c693e3c6120687265663d22687474703a2f2f7777772e20747970653d2774
      6578742f6a617661736372697074273ed0b4d0b5d18fd182d0b5d0bbd18cd0bd
      d0bed181d182d0b8d181d0bed0bed182d0b2d0b5d182d181d182d0b2d0b8d0b8
      d0bfd180d0bed0b8d0b7d0b2d0bed0b4d181d182d0b2d0b0d0b1d0b5d0b7d0be
      d0bfd0b0d181d0bdd0bed181d182d0b8e0a4aae0a581e0a4b8e0a58de0a4a4e0
      a4bfe0a495e0a4bee0a495e0a4bee0a482e0a497e0a58de0a4b0e0a587e0a4b8
      e0a489e0a4a8e0a58de0a4b9e0a58be0a482e0a4a8e0a587e0a4b5e0a4bfe0a4
      a7e0a4bee0a4a8e0a4b8e0a4ade0a4bee0a4abe0a4bfe0a495e0a58de0a4b8e0
      a4bfe0a482e0a497e0a4b8e0a581e0a4b0e0a495e0a58de0a4b7e0a4bfe0a4a4
      e0a495e0a589e0a4aae0a580e0a4b0e0a4bee0a487e0a49fe0a4b5e0a4bfe0a4
      9ce0a58de0a49ee0a4bee0a4aae0a4a8e0a495e0a4bee0a4b0e0a58de0a4b0e0
      a4b5e0a4bee0a488e0a4b8e0a495e0a58de0a4b0e0a4bfe0a4afe0a4a4e0a4be

   The 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

.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