From 26cf47f3f03da1cb66e64d09c9201ac4e2b4217c Mon Sep 17 00:00:00 2001 From: Zoltan Szabadka Date: Wed, 20 Apr 2016 10:45:40 +0200 Subject: Create -09 version of the draft. --- docs/draft-alakuijala-brotli-08.nroff | 5891 ----------------------------- docs/draft-alakuijala-brotli-08.txt | 6723 --------------------------------- docs/draft-alakuijala-brotli-09.nroff | 5891 +++++++++++++++++++++++++++++ docs/draft-alakuijala-brotli-09.txt | 6723 +++++++++++++++++++++++++++++++++ 4 files changed, 12614 insertions(+), 12614 deletions(-) delete mode 100644 docs/draft-alakuijala-brotli-08.nroff delete mode 100644 docs/draft-alakuijala-brotli-08.txt create mode 100644 docs/draft-alakuijala-brotli-09.nroff create mode 100644 docs/draft-alakuijala-brotli-09.txt (limited to 'docs') diff --git a/docs/draft-alakuijala-brotli-08.nroff b/docs/draft-alakuijala-brotli-08.nroff deleted file mode 100644 index 5bbf373..0000000 --- a/docs/draft-alakuijala-brotli-08.nroff +++ /dev/null @@ -1,5891 +0,0 @@ -.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 December 2015 -.ds CH Brotli -.ds CF Expires June 10, 2016 -.hy 0 -.nh -.ad l -.in 0 -.nf -.tl 'Network Working Group''J. Alakuijala' -.tl 'Internet-Draft''Z. Szabadka' -.tl 'Intended Status: Informational''Google, Inc' -.tl 'Expires: June 10, 2016''December 2015' -.fi - - -.ce 2 -Brotli Compressed Data Format -draft-alakuijala-brotli-08 -.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 June 10, 2016. - -.ti 0 -Copyright Notice - -Copyright (c) 2015 IETF Trust and the persons identified as the document -authors. All rights reserved. - -This document is subject to BCP 78 and the IETF Trust's Legal -Provisions Relating to IETF Documents -(http://trustee.ietf.org/license-info) in effect on the date of -publication of this document. Please review these documents -carefully, as they describe your rights and restrictions with respect -to this document. Code Components extracted from this document must -include Simplified BSD License text as described in Section 4.e of -the Trust Legal Provisions and are provided without warranty as -described in the Simplified BSD License. - -.ti 0 -Table of Contents - -.in 0 -.nf -INSERT_TOC_HERE -.fi -.in 3 - -.bp -.ti 0 -1. Introduction - -.ti 0 -1.1. Purpose - -The purpose of this specification is to define a lossless -compressed data format that: - -.nf - * Is independent of CPU type, operating system, file system, - and character set, and hence can be used for interchange; - * Can be produced or consumed, even for an arbitrarily long - sequentially presented input data stream, using only an a - priori bounded amount of intermediate storage, and hence - can be used in data communications or similar structures, - such as Unix filters; - * Compresses data with a compression ratio comparable to the - best currently available general-purpose compression methods, - and in particular, considerably better than the gzip program; - * Decompresses much faster than current LZMA implementations. -.fi - -The data format defined by this specification does not attempt to: - -.nf - * Allow random access to compressed data; - * Compress specialized data (e.g., raster graphics) as well - as the best currently available specialized algorithms. -.fi - -.ti 0 -1.2. Intended audience - -This specification is intended for use by software implementers -to compress data into and/or decompress data from the brotli format. - -The text of the specification assumes a basic background in -programming at the level of bits and other primitive data -representations. Familiarity with the technique of Huffman coding -is helpful but not required. - -This specification uses heavily the notations and terminology -introduced in the DEFLATE format specification [RFC 1951]. -For the sake of completeness, we always -include the whole text of the relevant parts of RFC 1951, -therefore familiarity with the DEFLATE format is helpful but not -required. - -The compressed data format defined in this specification is -an integral part of the WOFF 2.0 web font file format [WOFF2], -therefore this specification is also intended for implementers of -WOFF 2.0 compressors and decompressors. - -.ti 0 -1.3. Scope - -The specification specifies a method for representing a sequence -of bytes as a (usually shorter) sequence of bits, and a method for -packing the latter bit sequence into bytes. - -.ti 0 -1.4. Compliance - -Unless otherwise indicated below, a compliant decompressor must be -able to accept and decompress any data set that conforms to all -the specifications presented here. A compliant compressor must -produce data sets that conform to all the specifications presented -here. - -.ti 0 -1.5. Definitions of terms and conventions used - -Byte: 8 bits stored or transmitted as a unit (same as an octet). -For this specification, a byte is exactly 8 bits, even on machines -that store a character on a number of bits different from eight. -See below for the numbering of bits within a byte. - -String: a sequence of arbitrary bytes. - -Bytes stored within a computer do not have a "bit order", since -they are always treated as a unit. However, a byte considered as -an integer between 0 and 255 does have a most- and -least-significant bit, and since we write numbers with the -most-significant digit on the left, we also write bytes with the -most-significant bit on the left. In the diagrams below, we number -the bits of a byte so that bit 0 is the least-significant bit, i.e., -the bits are numbered: - -.nf - +--------+ - |76543210| - +--------+ -.fi - -Within a computer, a number may occupy multiple bytes. All -multi-byte numbers in the format described here are stored with -the least-significant byte first (at the lower memory address). -For example, the decimal number 520 is stored as: - -.nf - 0 1 - +--------+--------+ - |00001000|00000010| - +--------+--------+ - ^ ^ - | | - | + more significant byte = 2 x 256 - + less significant byte = 8 -.fi - -.ti 0 -1.5.1. Packing into bytes - -This document does not address the issue of the order in which -bits of a byte are transmitted on a bit-sequential medium, -since the final data format described here is byte- rather than -bit-oriented. However, we describe the compressed block format -below as a sequence of data elements of various bit -lengths, not a sequence of bytes. We must therefore specify -how to pack these data elements into bytes to form the final -compressed byte sequence: - -.nf - * Data elements are packed into bytes in order of - increasing bit number within the byte, i.e., starting - with the least-significant bit of the byte. - * Data elements other than prefix codes are packed - starting with the least-significant bit of the data - element. These are referred to here as integer values - and are considered unsigned. - * Prefix codes are packed starting with the most-significant - bit of the code. -.fi - -In other words, if one were to print out the compressed data as -a sequence of bytes, starting with the first byte at the -*right* margin and proceeding to the *left*, with the -most-significant bit of each byte on the left as usual, one would -be able to parse the result from right to left, with fixed-width -elements in the correct MSB-to-LSB order and prefix codes in -bit-reversed order (i.e., with the first bit of the code in the -relative LSB position). - -.ti 0 -2. Compressed representation overview - -A compressed data set consists of a header and a series of -meta-blocks. Each meta-block decompresses to a sequence of 0 -to 16,777,216 (16 MiB) uncompressed bytes. The final uncompressed data is -the concatenation of the uncompressed sequences from each meta-block. - -The header contains the size of the sliding window that was used during compression. -The decompressor must retain at least that amount of uncompressed data prior to the -current position in the stream, in order to be able to decompress -what follows. The sliding window size is a power of two, minus 16, where -the power is in the range of 10 to 24. The possible sliding window -sizes range from 1 KiB - 16 B to 16 MiB - 16 B. - -Each meta-block is compressed using a combination of the LZ77 -algorithm (Lempel-Ziv 1977, [LZ77]) and Huffman coding. The -result of Huffman coding is referred to here as a prefix code. -The prefix codes for each meta-block are independent of -those for previous or subsequent meta-blocks; the LZ77 algorithm may -use a reference to a duplicated string occurring in a previous -meta-block, up to the sliding window size of uncompressed bytes before. -In addition, in the brotli format, a string reference may instead refer -to a static dictionary entry. - -Each meta-block consists of two parts: a meta-block header that -describes the representation of the compressed data part, and a -compressed data part. The compressed data consists of a series of -commands. Each command consists of two parts: a sequence of literal -bytes (of strings that have not been detected as duplicated within -the sliding window), and a pointer to a duplicated string, -represented as a pair . There can be -zero literal bytes in the command. The minimum length of the string to be -duplicated is two, but the last command in the meta-block is permitted to have -only literals and no pointer to a string to duplicate. - -Each command in the compressed data is represented using three categories -of prefix codes: - -.nf - 1) One set of prefix codes are for the literal sequence lengths - (also referred to as literal insertion lengths) and - backward copy lengths. That is, a single code word represents - two lengths, one of the literal sequence and one of the - backward copy. - - 2) One set of prefix codes are for literals. - - 3) One set of prefix codes are for distances. -.fi - -The prefix code descriptions for each meta-block appear in a compact -form just before the compressed data in the meta-block header. -The insert-and-copy length and distance prefix codes may be followed by -extra bits that are added to the base values determined by the codes. -The number of extra bits is determined by the code. - -One meta-block command then appears as a sequence of prefix codes: - -.nf - Insert-and-copy length, literal, literal, ..., literal, distance -.fi - -where the insert-and-copy defines an insertion length and a copy length. -The insertion length determines the number of literals that immediately -follow. The distance defines how far back to go for the copy and the -copy length determines the number of bytes to copy. The resulting -uncompressed data is the sequence of bytes: - -.nf - literal, literal, ..., literal, copy, copy, ..., copy -.fi - -where the number of literal bytes and copy bytes are determined by the -insert-and-copy length code. (The number of bytes copied for a static -dictionary entry can vary from the copy length.) - -The last command in the meta-block may end with the last literal if the -total uncompressed length of the meta-block has been satisfied. In -that case there is no distance in the last command, and the copy length is -ignored. - -There can be more than one prefix code for each category, where the -prefix code to use for the next element of that category is determined -by the context of the compressed stream that precedes that element. -Part of that context is three current block types, one for each -category. A block type is in the range of 0..255. For each category -there is a count of how many elements of that category remain to be -decoded using the current block type. Once that count is expended, -a new block type and block count is read from the stream immediately -preceding the next element of that category, which will use the new -block type. - -The insert-and-copy block type directly determines which prefix code to -use for the next insert-and-copy element. For the literal and distance -elements, the respective block type is used in combination with other -context information to determine which prefix code to use for the next -element. - -Consider the following example: - -.nf - (IaC0, L0, L1, L2, D0)(IaC1, D1)(IaC2, L3, L4, D2)(IaC3, L5, D3) -.fi - -The meta-block here has four commands, contained in parentheses for clarity, -where each of the three categories of -symbols within these commands can be interpreted using different block types. -Here we separate out each category as its own sequence to show an example of block -types assigned to those elements. Each square-bracketed group is a block that -uses the same block type: - -.nf - [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 -.fi - -The subsequent blocks within each block category must have different -block types, but we see that block types can be reused later in the meta-block. -The block types are numbered from 0 to the maximum -block type number of 255 and the first block of each block category -is type 0. The block structure of a meta-block is represented -by the sequence of block-switch commands for each block category, -where a block-switch command is a pair . -The block-switch commands are represented in the compressed data -before the start of each new block using a prefix code for -block types and a separate prefix code for block counts for -each block category. For the above example the physical layout of the -meta-block is then: - -.nf - IaC0 L0 L1 LBlockSwitch(1, 3) L2 D0 IaC1 DBlockSwitch(1, 3) D1 - IaCBlockSwitch(1, 2) IaC2 L3 L4 D2 IaC3 LBlockSwitch(0, 1) L5 D3 -.fi - -where xBlockSwitch(t, n) switches to block type t for a count of n elements. -Note that in this example DBlockSwitch(1, 3) immediately precedes the -next required distance D1. It does not follow the last distance of -the previous block, D0. Whenever an element of a category is needed, -and the block count for that category has reached zero, then a new -block type and count is read from the stream just before reading that next -element. - -The block-switch commands for the first blocks of each category are not part -of the meta-block compressed data. Instead the first block type -is defined to be 0, and the first block count for each category is -encoded in the meta-block header. The prefix codes for the block types and counts, a total of -six prefix codes over the three categories, are defined in a compact form in the meta-block -header. - -Each category of value (insert-and-copy lengths, literals, and distances) -can be encoded with any prefix code from a collection of prefix -codes belonging to the same category appearing in the meta-block header. The -particular prefix code used can depend on two factors: the block -type of the block the value appears in, and the context of the value. -In the case of the literals, the context is the previous two bytes in -the uncompressed data, and in the case of distances, the context is the copy -length from the same command. For insert-and-copy lengths, no context -is used and the prefix code depends only on the block type. In the case -of literals and distances, the context is mapped to a context ID in -the range 0..63 for literals and 0..3 for distances. The matrix -of the prefix code indexes for each block type and context ID, -called the context map, is encoded in a compact form in the meta-block header. - -For example, the prefix code to use to decode L2 depends on the -block type (1), and the literal context ID determined by the two uncompressed -bytes that were decoded from L0 and L1. -Similarly, the prefix code to use to decode D0 depends on the block -type (0), and the distance context ID determined by the copy length decoded -from IaC0. The prefix code to use to decode IaC3 depends only on the block -type (1). - -In addition to the parts listed above (prefix code for insert-and-copy -lengths, literals, distances, block types and block counts, -and the context map), the meta-block header contains the number of -uncompressed bytes coded in the meta-block and two additional parameters used in -the representation of match distances: the number of postfix bits and -the number of direct distance codes. - -A compressed meta-block may be marked in the header as the last meta-block, -which terminates the compressed stream. - -A meta-block may instead simply store the uncompressed data directly as -bytes on byte boundaries with no coding or matching strings. In this -case the meta-block header information only contains the number of -uncompressed bytes and the indication that the meta-block is uncompressed. -An uncompressed meta-block cannot be the last meta-block. - -A meta-block may also be empty, which generates no uncompressed data at all. -An empty meta-block may contain metadata information as bytes starting on byte -boundaries, which are not part of either the sliding window or the uncompressed -data. Thus, these metadata bytes cannot be used to create matching strings in -subsequent meta-blocks and are not used as context bytes for literals. - -.ti 0 -3. Compressed representation of prefix codes - -.ti 0 -3.1. Introduction to prefix coding - -Prefix coding represents symbols from an a priori known alphabet -by bit sequences (codes), one code for each symbol, in a manner -such that different symbols may be represented by bit sequences of -different lengths, but a parser can always parse an encoded string -unambiguously symbol-by-symbol. - -We define a prefix code in terms of a binary tree in which the two -edges descending from each non-leaf node are labeled 0 and 1 and -in which the leaf nodes correspond one-for-one with (are labeled -with) the symbols of the alphabet; then the code for a symbol is -the sequence of 0's and 1's on the edges leading from the root to -the leaf labeled with that symbol. For example: - -.nf -.KS - /\\ Symbol Code - 0 1 ------ ---- - / \\ A 00 - /\\ B B 1 - 0 1 C 011 - / \\ D 010 - A /\\ - 0 1 - / \\ - D C -.KE -.fi - -A parser can decode the next symbol from the compressed stream -by walking down the tree from the root, at each step choosing the -edge corresponding to the next compressed data bit. - -Given an alphabet with known symbol frequencies, the Huffman -algorithm allows the construction of an optimal prefix code (one -which represents strings with those symbol frequencies using the -fewest bits of any possible prefix codes for that alphabet). Such -a prefix code is called a Huffman code. (See [HUFFMAN] in Chapter 5, -references for additional information on Huffman codes.) - -Note that in the brotli format, the prefix codes for the -various alphabets must not exceed certain maximum code lengths. -This constraint complicates the algorithm for computing code -lengths from symbol frequencies. Again, see Chapter 5, references -for details. - -.ti 0 -3.2. Use of prefix coding in the brotli format - -The prefix codes used for each alphabet in the brotli format -are canonical prefix codes, which have two additional rules: - -.nf - * All codes of a given bit length have lexicographically - consecutive values, in the same order as the symbols they - represent; - - * Shorter codes lexicographically precede longer codes. -.fi - -We could recode the example above to follow this rule as follows, -assuming that the order of the alphabet is ABCD: - -.nf -.KS - Symbol Code - ------ ---- - A 10 - B 0 - C 110 - D 111 -.KE -.fi - -I.e., 0 precedes 10, which precedes 11x, and 110 and 111 are -lexicographically consecutive. - -Given this rule, we can define the canonical prefix code for an -alphabet just by giving the bit lengths of the codes for each -symbol of the alphabet in order; this is sufficient to determine -the actual codes. In our example, the code is completely defined -by the sequence of bit lengths (2, 1, 3, 3). The following -algorithm generates the codes as integers, intended to be read -from most- to least-significant bit. The code lengths are -initially in tree[I].Len; the codes are produced in tree[I].Code. - -.nf - 1) Count the number of codes for each code length. Let - bl_count[N] be the number of codes of length N, N >= 1. - - 2) Find the numerical value of the smallest code for each - code length: - -.KS - code = 0; - bl_count[0] = 0; - for (bits = 1; bits <= MAX_BITS; bits++) { - code = (code + bl_count[bits-1]) << 1; - next_code[bits] = code; - } -.KE - - 3) Assign numerical values to all codes, using consecutive - values for all codes of the same length with the base - values determined at step 2. Codes that are never used - (which have a bit length of zero) must not be assigned a - value. - -.KS - for (n = 0; n <= max_code; n++) { - len = tree[n].Len; - if (len != 0) { - tree[n].Code = next_code[len]; - next_code[len]++; - } - } -.KE -.fi - -Example: - -Consider the alphabet ABCDEFGH, with bit lengths (3, 3, 3, 3, 3, -2, 4, 4). After step 1, we have: - -.nf -.KS - N bl_count[N] - - ----------- - 2 1 - 3 5 - 4 2 -.KE -.fi - -Step 2 computes the following next_code values: - -.nf -.KS - N next_code[N] - - ------------ - 1 0 - 2 0 - 3 2 - 4 14 -.KE -.fi - -Step 3 produces the following code values: - -.nf -.KS - Symbol Length Code - ------ ------ ---- - A 3 010 - B 3 011 - C 3 100 - D 3 101 - E 3 110 - F 2 00 - G 4 1110 - H 4 1111 -.KE -.fi - -.ti 0 -3.3. Alphabet sizes - -Prefix codes are used for different purposes in the brotli -format, and each purpose has a different alphabet size. For -literal codes the alphabet size is 256. For insert-and-copy -length codes the alphabet size is 704. For block count codes, -the alphabet size is 26. For distance codes, block type codes, and -the prefix codes used in compressing the context map, the -alphabet size is dynamic and is based on parameters defined in -later sections. The following table summarizes the alphabet sizes -for the various prefix codes and the sections where they are defined. - -.nf -.KS - +-----------------+-------------------------+------------+ - | Prefix code | Alphabet size | Definition | - +-----------------+-------------------------+------------+ - | literal | 256 | | - +-----------------+-------------------------+------------+ - | distance | 16 + NDIRECT + | Section 4. | - | | (48 << NPOSTFIX) | | - +-----------------+-------------------------+------------+ - | insert-and-copy | 704 | Section 5. | - | length | | | - +-----------------+-------------------------+------------+ - | block count | 26 | Section 6. | - +-----------------+-------------------------+------------+ - | block type | NBLTYPESx + 2, | Section 6. | - | | (where x is I, L, or D) | | - +-----------------+-------------------------+------------+ - | context map | NTREESx + RLEMAXx | Section 7. | - | | (where x is L or D) | | - +-----------------+-------------------------+------------+ -.KE -.fi - -.ti 0 -3.4. Simple prefix codes - -The first two bits of the compressed representation of each -prefix code distinguish between simple and complex prefix -codes. If this value is 1, then a simple prefix code follows -as described in this section. Otherwise, a complex prefix code -follows as described in Section 3.5. - -A simple prefix code can have only up to four symbols with -non-zero code length. The format of the simple prefix code is as -follows: - -.nf - 2 bits: value of 1 indicates a simple prefix code - 2 bits: NSYM - 1, where NSYM = # of symbols coded - - NSYM symbols, each encoded using ALPHABET_BITS bits - - 1 bit: tree-select, present only for NSYM = 4 -.fi - -The value of ALPHABET_BITS depends on the alphabet of the prefix -code: it is the smallest number of bits that can represent all -symbols in the alphabet. E.g. for the alphabet of literal bytes, -ALPHABET_BITS is 8. The value of each of the NSYM symbols above is -the value of the ALPHABETS_BITS width integer value. If the integer -value is greater than or equal to the alphabet size, or the value -is identical to a previous value, then the stream should be rejected -as invalid. - -Note that the NSYM symbols may not be presented in sorted order. Prefix codes -of the same bit length must be assigned to the symbols in sorted order. - -The (non-zero) code lengths of the symbols can be reconstructed as -follows: - -.nf - * if NSYM = 1, the code length for the one symbol is zero -- - when encoding this symbol in the - compressed data stream using this prefix code, no - actual bits are emitted. Similarly, when decoding a symbol - using this prefix code, no bits are read and the one symbol - is returned. - - * if NSYM = 2, both symbols have code length 1. - - * if NSYM = 3, the code lengths for the symbols are 1, 2, 2 in - the order they appear in the representation of the simple - prefix code. - - * if NSYM = 4, the code lengths (in order of symbols decoded) - depend on the tree-select bit: 2, 2, 2, 2 (tree-select bit 0), - or 1, 2, 3, 3 (tree-select bit 1). -.fi - -.ti 0 -3.5. Complex prefix codes - -A complex prefix code is a canonical prefix code, defined by the -sequence of code lengths, as discussed in Section 3.2., above. -For even greater compactness, the code length sequences themselves -are compressed using a prefix code. The alphabet for code lengths -is as follows: - -.nf - 0 - 15: Represent code lengths of 0 - 15 - 16: Copy the previous non-zero code length 3 - 6 times - The next 2 bits indicate repeat length - (0 = 3, ... , 3 = 6) - If this is the first code length, or all previous - code lengths are zero, a code length of 8 is - repeated 3 - 6 times - A repeated code length code of 16 modifies the - repeat count of the previous one as follows: - repeat count = (4 * (repeat count - 2)) + - (3 - 6 on the next 2 bits) - Example: Codes 7, 16 (+2 bits 11), 16 (+2 bits 10) - will expand to 22 code lengths of 7 - (1 + 4 * (6 - 2) + 5) - 17: Repeat a code length of 0 for 3 - 10 times. - (3 bits of length) - A repeated code length code of 17 modifies the - repeat count of the previous one as follows: - repeat count = (8 * (repeat count - 2)) + - (3 - 10 on the next 3 bits) -.fi - -Note that a code of 16 that follows an immediately preceding 16 modifies the -previous repeat count, which becomes the new repeat count. The same is true for -a 17 following a 17. A sequence of three or more 16 codes in a row or three of -more 17 codes in a row is possible, modifying the count each time. Only the -final repeat count is used. The modification only applies if the same code -follows. A 16 repeat does not modify an immediately preceding 17 count nor -vice versa. - -A code length of 0 indicates that the corresponding symbol in the -alphabet will not occur in the compressed data, and should not -participate in the prefix code construction algorithm given -earlier. A complex prefix code must have at least two non-zero -code lengths. - -The bit lengths of the prefix code over the code length alphabet -are compressed with the following variable length code (as it appears -in the compressed data, where the bits are parsed from right to left): - -.nf -.KS - Symbol Code - ------ ---- - 0 00 - 1 0111 - 2 011 - 3 10 - 4 01 - 5 1111 -.KE -.fi - -We can now define the format of the complex prefix code as follows: - -.nf - 2 bits: HSKIP, values of 0, 2, or 3 represent the respective - number of skipped code lengths. The skipped lengths - are taken to be zero. (An HSKIP of 1 indicates a - Simple prefix code.) - - Code lengths for symbols in the code length alphabet given - just above, in the order: 1, 2, 3, 4, 0, 5, 17, 6, 16, 7, - 8, 9, 10, 11, 12, 13, 14, 15. If HSKIP is 2, then the - code lengths for symbols 1 and 2 are zero, and the first - code length is for symbol 3. If HSKIP is 3, then the code - length for symbol 3 is also zero, and the first code length - is for symbol 4. - - The code lengths of code length symbols are between 0 and - 5, and they are represented with 2 - 4 bits according to - the variable length code above. A code length of 0 means - the corresponding code length symbol is not used. - - If HSKIP is 2 or 3, a respective number of leading code - lengths are implicit zeros and are not present in the - code lengths sequence above. - - If there are at least two non-zero code lengths, any - trailing zero code lengths are omitted, i.e. the last - code length in the sequence must be non-zero. In this - case, the sum of (32 >> code length) over all the non-zero - code lengths must equal to 32. - - If the lengths have been read for the entire code length - alphabet and there was only one non-zero code length, - then the prefix code has one symbol whose code has zero - length. In this case, that symbol results in no bits - being emitted by the compressor, and no bits consumed by - the decompressor. That single symbol is immediately - returned when this code is decoded. - An example of where this occurs is if the - entire code to be represented has symbols of length 8. - E.g. a literal code that represents all literal values - with equal probability. In this case the single symbol - is 16, which repeats the previous length. The previous - length is taken to be 8 before any code length code - lengths are read. - - Sequence of at most alphabet size code lengths symbols, encoded - using the code length prefix code. Any trailing 0 or 17 must be - omitted, i.e. the last encoded code length symbol must be - between 1 and 16. The sum of (32768 >> code length) over - all the non-zero code lengths in the alphabet, including - those encoded using repeat code(s) of 16, must equal to - 32768. If the number of times to repeat the previous length - or repeat a zero length would result in more lengths in - total than the number of symbols in the alphabet, then the - stream should be rejected as invalid. -.fi - -.ti 0 -4. Encoding of distances - -As described in Section 2., one component of a compressed meta-block -is a sequence of backward distances. In this section we provide the -details to the encoding of distances. - -Each distance in the compressed data part of a meta-block is -represented with a pair . The distance -code and the extra bits are encoded back-to-back, the distance code -is encoded using a prefix code over the distance alphabet, -while the extra bits value is encoded as a fixed-width integer -value. The number of extra bits can be 0 - 24, and it is dependent -on the distance code. - -To convert a distance code and associated extra bits to a backward -distance, we need the sequence of past distances and two additional -parameters, the number of "postfix bits", denoted by NPOSTFIX (0..3), and -the number of direct distance codes, denoted by NDIRECT (0..120). Both of -these parameters are encoded in the meta-block header. We will also -use the following derived parameter: - -.nf - POSTFIX_MASK = (1 << NPOSTFIX) - 1 -.fi - -The first 16 distance symbols are special symbols that reference -past distances as follows: - -.nf - 0: last distance - 1: second-to-last distance - 2: third-to-last distance - 3: fourth-to-last distance - 4: last distance - 1 - 5: last distance + 1 - 6: last distance - 2 - 7: last distance + 2 - 8: last distance - 3 - 9: last distance + 3 - 10: second-to-last distance - 1 - 11: second-to-last distance + 1 - 12: second-to-last distance - 2 - 13: second-to-last distance + 2 - 14: second-to-last distance - 3 - 15: second-to-last distance + 3 -.fi - -The ring buffer of four last distances is initialized by the values -16, 15, 11, and 4 (i.e. the fourth-to-last is set to 16, the third-to-last -to 15, the second-to-last to 11, and the last distance to 4) at the -beginning of the *stream* (as opposed to the beginning of the meta-block) -and it is not reset at meta-block boundaries. When a distance -symbol 0 appears, the distance it represents (i.e. the last distance -in the sequence of distances) is not pushed to the ring buffer of -last distances, in other words, the expression "(second, third, -fourth)-to-last distance" means the (second, third, fourth)-to-last -distance that was not represented by a 0 distance symbol. Similarly, -distances that represent static dictionary words (see Section 8.) are -not pushed to the ring buffer of last distances. - -If a special distance symbol resolves to a zero or negative value, the -stream should be rejected as invalid. - -If NDIRECT is greater than zero, then the next NDIRECT distance symbols, -from 16 to 15 + NDIRECT, represent distances from 1 to NDIRECT. -Neither the special distance symbols, nor the NDIRECT direct distance -symbols are followed by any extra bits. - -Distance symbols 16 + NDIRECT and greater all have extra bits, where the -number of extra bits for a distance symbol "dcode" is given by the -following formula: - -.nf - ndistbits = 1 + ((dcode - NDIRECT - 16) >> (NPOSTFIX + 1)) -.fi - -The maximum number of extra bits is 24, therefore the size of the -distance symbol alphabet is (16 + NDIRECT + (48 << NPOSTFIX)). - -Given a distance symbol "dcode" (>= 16 + NDIRECT), and extra bits -"dextra", the backward distance is given by the following formula: - -.nf - hcode = (dcode - NDIRECT - 16) >> NPOSTFIX - lcode = (dcode - NDIRECT - 16) & POSTFIX_MASK - offset = ((2 + (hcode & 1)) << ndistbits) - 4 - distance = ((offset + dextra) << NPOSTFIX) + lcode + NDIRECT + 1 -.fi - -.ti 0 -5. Encoding of literal insertion lengths and copy lengths - -As described in Section 2., the literal insertion lengths and backward -copy lengths are encoded using a single prefix code. This section -provides the details to this encoding. - -Each pair in the compressed data part -of a meta-block is represented with the following triplet: - -.nf - -.fi - -The insert-and-copy length code, the insert extra bits, and the copy -extra bits are encoded back-to-back, the insert-and-copy length code -is encoded using a prefix code over the insert-and-copy length code -alphabet, while the extra bits values are encoded as fixed-width -integer values. The number of insert and copy extra bits can be -0 - 24, and they are dependent on the insert-and-copy length code. - -Some of the insert-and-copy length codes also express the fact that -the distance symbol of the distance in the same command is 0, i.e. the -distance component of the command is the same as that of the previous -command. In this case, the distance code and extra bits for the -distance are omitted from the compressed data stream. - -We describe the insert-and-copy length code alphabet in terms of the -(not directly used) insert length code and copy length code -alphabets. The symbols of the insert length code alphabet, along with -the number of insert extra bits, and the range of the insert lengths -are as follows: - -.nf -.KS - Extra Extra Extra - Code Bits Lengths Code Bits Lengths Code Bits Lengths - ---- ---- ------ ---- ---- ------- ---- ---- ------- - 0 0 0 8 2 10-13 16 6 130-193 - 1 0 1 9 2 14-17 17 7 194-321 - 2 0 2 10 3 18-25 18 8 322-577 - 3 0 3 11 3 26-33 19 9 578-1089 - 4 0 4 12 4 34-49 20 10 1090-2113 - 5 0 5 13 4 50-65 21 12 2114-6209 - 6 1 6,7 14 5 66-97 22 14 6210-22593 - 7 1 8,9 15 5 98-129 23 24 22594-16799809 -.KE -.fi - -The symbols of the copy length code alphabet, along with the number -of copy extra bits, and the range of copy lengths are as follows: - -.nf -.KS - Extra Extra Extra - Code Bits Lengths Code Bits Lengths Code Bits Lengths - ---- ---- ------ ---- ---- ------- ---- ---- ------- - 0 0 2 8 1 10,11 16 5 70-101 - 1 0 3 9 1 12,13 17 5 102-133 - 2 0 4 10 2 14-17 18 6 134-197 - 3 0 5 11 2 18-21 19 7 198-325 - 4 0 6 12 3 22-29 20 8 326-581 - 5 0 7 13 3 30-37 21 9 582-1093 - 6 0 8 14 4 38-53 22 10 1094-2117 - 7 0 9 15 4 54-69 23 24 2118-16779333 -.KE -.fi - -To convert an insert-and-copy length code to an insert length code -and a copy length code, the following table can be used: - -.nf -.KS - Insert - length Copy length code - code 0-7 8-15 16-23 - +---------+---------+ - | | | - 0-7 | 0-63 | 64-127 | <--- distance symbol 0 - | | | - +---------+---------+---------+ - | | | | - 0-7 | 128-191 | 192-255 | 384-447 | - | | | | - +---------+---------+---------+ - | | | | - 8-15 | 256-319 | 320-383 | 512-575 | - | | | | - +---------+---------+---------+ - | | | | - 16-23 | 448-511 | 576-639 | 640-703 | - | | | | - +---------+---------+---------+ -.KE -.fi - -First, look up the cell with the 64 value range containing the -insert-and-copy length code, this gives the insert length code and -the copy length code ranges, both 8 values long. -The copy length code within its range is determined by bits 0-2 -(counted from the LSB) of the insert-and-copy length code. -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 -. These are encoded in the compressed data -part of the meta-block, right before the start of each new block of a -particular block category. - -Each block type in the compressed data is represented with a block -type code, encoded using a prefix code over the block type code -alphabet. A block type symbol 0 means that the new block type is the same -as the type of the previous block from the same block category, i.e. -the block type that preceded the current type, -while a block type symbol 1 means that the new block type equals the current -block type plus one. If the current block type is the maximal possible, -then a block type symbol of 1 results in wrapping to a new block type of 0. -Block type symbols 2 - 257 -represent block types 0 - 255 respectively. The previous and current block types -are initialized to 1 and 0, respectively, at the end of the -meta-block header. - -Since the first block type of each block category is 0, the block -type of the first block-switch command is not encoded in -the compressed data. If a block category has only one block type, -the block count of the first block-switch command is also omitted from -the compressed data, otherwise it is encoded in the meta-block header. - -Since the end of the meta-block is detected by the number of uncompressed -bytes produced, the block counts for any of the three categories need not -count down to exactly zero at the end of the meta-block. - -The number of different block types in each block category, denoted -by NBLTYPESL, NBLTYPESI, and NBLTYPESD for literals, insert-and-copy -lengths, and distances, respectively, is encoded in the meta-block -header, and it must equal to the largest block type plus one in that -block category. In other words, the set of literal, insert-and-copy -length, and distance block types must be [0..NBLTYPESL-1], -[0..NBLTYPESI-1], and [0..NBLTYPESD-1], respectively. From this it -follows that the alphabet size of literal, insert-and-copy length, and -distance block type codes is NBLTYPESL + 2, NBLTYPESI + 2, and -NBLTYPESD + 2, respectively. - -Each block count in the compressed data is represented with a pair -. The block count code and the extra -bits are encoded back-to-back, the block count code is encoded using -a prefix code over the block count code alphabet, while the extra -bits value is encoded as a fixed-width integer value. The number of -extra bits can be 0 - 24, and it is dependent on the block count -code. The symbols of the block count code alphabet, along with the -number of extra bits, and the range of block counts are as follows: - -.nf -.KS - Extra Extra Extra - Code Bits Lengths Code Bits Lengths Code Bits Lengths - ---- ---- ------ ---- ---- ------- ---- ---- ------- - 0 2 1-4 9 4 65-80 18 7 369-496 - 1 2 5-8 10 4 81-96 19 8 497-752 - 2 2 9-12 11 4 97-112 20 9 753-1264 - 3 2 13-16 12 5 113-144 21 10 1265-2288 - 4 3 17-24 13 5 145-176 22 11 2289-4336 - 5 3 25-32 14 5 177-208 23 12 4337-8432 - 6 3 33-40 15 5 209-240 24 13 8433-16624 - 7 3 41-48 16 6 241-304 25 24 16625-16793840 - 8 4 49-64 17 6 305-368 -.KE -.fi - -The first block-switch command of each block category is special in -the sense that it is encoded in the meta-block header, and as -described earlier, the block type code is omitted since it is an -implicit zero. - -.ti 0 -7. Context modeling - -As described in Section 2., the prefix tree used to encode a literal -byte or a distance code depends on the block type and the context ID. -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 pair to the index of a prefix -code in the array of literal and distance prefix codes. - -.ti 0 -7.1. Context modes and context ID lookup for literals - -The context for encoding the next literal is defined by the last -two bytes in the stream (p1, p2, where p1 is the most recent -byte), regardless of whether these bytes are produced by -uncompressed meta-blocks, backward references, static dictionary -references, or by literal insertions. At the start of the stream -p1 and p2 are initialized to zero. - -There are four methods, called context modes, to compute the -Context ID: - -.nf - * LSB6, where the Context ID is the value of six - least-significant bits of p1, - * MSB6, where the Context ID is the value of six - most-significant bits of p1, - * UTF8, where the Context ID is a complex function of p1, p2, - optimized for text compression, and - * Signed, where Context ID is a complex function of p1, p2, - optimized for compressing sequences of signed integers. -.fi - -The Context ID for the UTF8 and Signed context modes is computed -using the following lookup tables Lut0, Lut1, and Lut2. - -.nf - Lut0 := - 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 8, 12, 16, 12, 12, 20, 12, 16, 24, 28, 12, 12, 32, 12, 36, 12, - 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 32, 32, 24, 40, 28, 12, - 12, 48, 52, 52, 52, 48, 52, 52, 52, 48, 52, 52, 52, 52, 52, 48, - 52, 52, 52, 52, 52, 48, 52, 52, 52, 52, 52, 24, 12, 28, 12, 12, - 12, 56, 60, 60, 60, 56, 60, 60, 60, 56, 60, 60, 60, 60, 60, 56, - 60, 60, 60, 60, 60, 56, 60, 60, 60, 60, 60, 24, 12, 28, 12, 0, - 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, - 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, - 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, - 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, - 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, - 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, - 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, - 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 - - Lut1 := - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, - 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, - 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, - 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 - - Lut2 := - 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, - 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, - 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, - 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, - 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, - 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, - 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, - 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, - 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, - 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, - 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, - 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, - 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7 -.fi - -The lengths and the zlib CRC-32 (ITU-T Recommendation V.42) check values -of each of these tables as a sequence of bytes are as follows: - -.nf - Table Length CRC-32 - ----- ------ ------ - Lut0 256 0x8e91efb7 - Lut1 256 0xd01a32f4 - Lut2 256 0x0dd7a0d6 -.fi - -Given p1 is the last uncompressed byte and p2 is the second-to-last -uncompressed byte, the context IDs can be computed as follows: - -.nf - For LSB6: Context ID = p1 & 0x3f - For MSB6: Context ID = p1 >> 2 - For UTF8: Context ID = Lut0[p1] | Lut1[p2] - For Signed: Context ID = (Lut2[p1] << 3) | Lut2[p2] -.fi - -From the lookup tables defined above and the operations to compute the -context IDs, we can see that context IDs for literals are in the range -of 0..63. - -The context modes LSB6, MSB6, UTF8, and Signed are denoted by -integers 0, 1, 2, 3. - -A context mode is defined for each literal block type and they -are stored in a consecutive array of bits in the meta-block -header, always two bits per block type. - -.ti 0 -7.2. Context ID for distances - -The context for encoding a distance code is defined by the copy -length corresponding to the distance. The context IDs are 0, 1, 2, -and 3 for copy lengths 2, 3, 4, and more than 4, respectively. - -.ti 0 -7.3. Encoding of the context map - -There are two context maps, one for literals and one for -distances. The size of the context map is 64 * NBLTYPESL for -literals, and 4 * NBLTYPESD for distances. Each value in the -context map is an integer between 0 and 255, indicating the index -of the prefix code to be used when encoding the next literal or -distance. - -The context maps are two-dimensional matrices, encoded as -one-dimensional arrays: - -.nf - CMAPL[0..(64 * NBLTYPESL - 1)] - CMAPD[0..(4 * NBLTYPESD - 1)] -.fi - -The index of the prefix code for encoding a literal or distance -code with block type, BTYPE_x, and context ID, CIDx, is: - -.nf - index of literal prefix code = CMAPL[64 * BTYPE_L + CIDL] - index of distance prefix code = CMAPD[4 * BTYPE_D + CIDD] -.fi - -The values of the context map are encoded with the combination -of run length encoding for zero values and prefix coding. Let -RLEMAX denote the number of run length codes and NTREES denote the -maximum value in the context map plus one. NTREES must equal the -number of different values in the context map, in other words, -the different values in the context map must be the [0..NTREES-1] -interval. The alphabet of the prefix code has the following -RLEMAX + NTREES symbols: - -.nf - 0: value zero - 1: repeat a zero 2 to 3 times, read 1 bit for repeat length - 2: repeat a zero 4 to 7 times, read 2 bits for repeat length - ... - RLEMAX: repeat a zero (1 << RLEMAX) to (1 << (RLEMAX+1))-1 - times, read RLEMAX bits for repeat length - RLEMAX + 1: value 1 - ... - RLEMAX + NTREES - 1: value NTREES - 1 -.fi - -If RLEMAX = 0, the run length coding is not used, and the symbols -of the alphabet are directly the values in the context map. We can -now define the format of the context map (the same format is used -for literal and distance context maps): - -.nf - 1-5 bits: RLEMAX, 0 is encoded with one 0 bit, and values - 1 - 16 are encoded with bit pattern xxxx1 (so 01001 - is 5) - - Prefix code with alphabet size NTREES + RLEMAX - - Context map size values encoded with the above prefix code - and run length coding for zero values. If a run length - would result in more lengths in total than the size of - the context map, then the stream should be rejected as - invalid. - - 1 bit: IMTF bit, if set, we do an inverse move-to-front - transform on the values in the context map to get - the prefix code indexes -.fi - -Note that RLEMAX may be larger than the value necessary to represent -the longest sequence of zero values. Also, the NTREES value is encoded -right before the context map as described in 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 - -Note that the inverse move-to-front transform will not produce values -outside the [0..NTREES-1] interval. - -.ti 0 -8. Static dictionary - -At any given point during decoding the compressed data, a reference -to a duplicated string in the uncompressed data produced so far has a maximum -backward distance value, which is the minimum of the window size and -the number of uncompressed bytes produced. However, decoding a distance -from the compressed stream, as described in Section 4., can produce -distances that are greater than this maximum allowed value. In this case, -the distance is treated as a reference to a word in the static dictionary -given in Appendix A. The copy length for a static dictionary reference -must be between 4 and 24. The static dictionary has three parts: - -.nf - * DICT[0..DICTSIZE], an array of bytes - * DOFFSET[0..24], an array of byte offset values for each length - * NDBITS[0..24], an array of bit-depth values for each length -.fi - -The number of static dictionary words for a given length is: - -.nf - NWORDS[length] = 0 (if length < 4) - NWORDS[length] = (1 << NDBITS[length]) (if length >= 4) -.fi - -DOFFSET and DICTSIZE are defined by the following recursion: - -.nf - DOFFSET[0] = 0 - DOFFSET[length + 1] = DOFFSET[length] + length * NWORDS[length] - DICTSIZE = DOFFSET[24] + 24 * NWORDS[24] -.fi - -The offset of a word within the DICT array for a given length and -index is: - -.nf - offset(length, index) = DOFFSET[length] + index * length -.fi - -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 pair can be reconstructed as -follows: - -.nf - word_id = distance - (max allowed distance + 1) - index = word_id % NWORDS[length] - base_word = DICT[offset(length, index)..offset(length, index+1)-1] - transform_id = word_id >> NDBITS[length] -.fi - -The string copied to the uncompressed stream is computed by applying the -transformation to the base dictionary word. If transform_id is -greater than 120, or the length is smaller than 4 or greater than 24, then -the compressed stream should be rejected as invalid. - -Each word transformation has the following form: - -.nf - transform_i(word) = prefix_i + T_i(word) + suffix_i -.fi - -where the _i subscript denotes the transform_id above. Each T_i -is one of the following 21 elementary transforms: - -.nf - Identity, UppercaseFirst, UppercaseAll, - OmitFirst1, ..., OmitFirst9, OmitLast1, ..., OmitLast9 -.fi - -The form of these elementary transforms is as follows: - -.nf - Identity(word) = word - - UppercaseFirst(word) = first UTF-8 character of word upper-cased - - UppercaseAll(word) = all UTF-8 characters of word upper-cased - - OmitFirstk(word) = the last (length(word) - k) bytes of word, or - empty string if length(word) < k - - OmitLastk(word) = the first (length(word) - k) bytes of word, or - empty string if length(word) < k -.fi - -For the purposes of UppercaseAll, word is parsed into UTF-8 -characters and converted to upper-case by taking 1 - 3 bytes at a time, -using the algorithm below: - -.nf -.KS - i = 0 - while i < length(word): - if word[i] < 192: - if word[i] >= 97 and word[i] <= 122: - word[i] = word[i] ^ 32 - i = i + 1 - else if word[i] < 224: - if i + 1 < length(word): - word[i + 1] = word[i + 1] ^ 32 - i = i + 2 - else: - if i + 2 < length(word): - word[i + 2] = word[i + 2] ^ 5 - i = i + 3 -.KE -.fi - -For UppercaseFirst, the same algorithm is used, but the loop is -executed only once. - -Appendix B. contains the list of transformations by specifying the -prefix, elementary transform and suffix components of each of them. -Note that the OmitFirst8 elementary transform is not used in the list -of transformations. The strings in Appendix B. are in C string format -with respect to escape (backslash) characters. - -The maximum number of additional bytes that a transform may add to a -base word is 13. Since the largest base word is 24 bytes long, a buffer -of 38 bytes is sufficient to store any transformed words -(counting a terminating zero byte). - -.ti 0 -9. Compressed data format - -In this section we describe the format of the compressed data set in -terms of the format of the individual data items described in the -previous sections. - -.ti 0 -9.1. Format of the stream header - -The stream header has only the following one field: - -.nf - 1-7 bits: WBITS, a value in the range 10 - 24, encoded with - the following variable length code (as it appears in - the compressed data, where the bits are parsed from - right to left): - - Value Bit Pattern - ----- ----------- - 10 0100001 - 11 0110001 - 12 1000001 - 13 1010001 - 14 1100001 - 15 1110001 - 16 0 - 17 0000001 - 18 0011 - 19 0101 - 20 0111 - 21 1001 - 22 1011 - 23 1101 - 24 1111 - - Note that bit pattern 0010001 is invalid and must not - be used. -.fi - -The size of the sliding window, which is the maximum value of any -non-dictionary reference backward distance, is given by the -following formula: - -.nf - window size = (1 << WBITS) - 16 -.fi - -.ti 0 -9.2. Format of the meta-block header - -A compliant compressed data set has at least one meta-block. Each -meta-block contains a header with information about the -uncompressed length of the meta-block, and a bit signaling if the -meta-block is the last one. The format of the meta-block header is -the following: - -.nf - 1 bit: ISLAST, set to 1 if this is the last meta-block - 1 bit: ISLASTEMPTY, if set to 1, the meta-block is empty; - this field is only present if ISLAST bit is set -- if - it is 1, then the meta-block and the brotli stream ends - at that bit, with any remaining bits in the last byte - of the compressed stream filled with zeros (if the - fill bits are not zero, then the stream should be - rejected as invalid) - 2 bits: MNIBBLES, # of nibbles to represent the uncompressed - length, encoded with the following fixed-length code: - - Value Bit Pattern - ----- ----------- - 0 11 - 4 00 - 5 01 - 6 10 - - If MNIBBLES is 0, the meta-block is empty, i.e. it does - not generate any uncompressed data. In this case, the - rest of the meta-block has the following format: - - 1 bit: reserved, must be zero - - 2 bits: MSKIPBYTES, # of bytes to represent metadata - length - - MSKIPBYTES x 8 bits: MSKIPLEN - 1, where MSKIPLEN is - the number of metadata bytes; this field is - only present if MSKIPBYTES is positive, - otherwise MSKIPLEN is 0 (if MSKIPBYTES is - greater than 1, and the last byte is all - zeros, then the stream should be rejected - as invalid) - - 0 - 7 bits: fill bits until the next byte boundary, - must be all zeros - - MSKIPLEN bytes of metadata, not part of the - uncompressed data or the sliding window - - MNIBBLES x 4 bits: MLEN - 1, where MLEN is the length - of the meta-block uncompressed data in bytes (if - MNIBBLES is greater than 4, and the last - nibble is all zeros, then the stream should be - rejected as invalid) - - 1 bit: ISUNCOMPRESSED, if set to 1, any bits of compressed - data up to the next byte boundary are ignored, and - the rest of the meta-block contains MLEN bytes of - literal data; this field is only present if the - ISLAST bit is not set (if the ignored bits are not - all zeros, the stream should be rejected as invalid) - - 1-11 bits: NBLTYPESL, # of literal block types, encoded with - the following variable length code (as it appears in - the compressed data, where the bits are parsed from - right to left, so 0110111 has the value 12): - - Value Bit Pattern - ----- ----------- - 1 0 - 2 0001 - 3-4 x0011 - 5-8 xx0101 - 9-16 xxx0111 - 17-32 xxxx1001 - 33-64 xxxxx1011 - 65-128 xxxxxx1101 - 129-256 xxxxxxx1111 - - Prefix code over the block type code alphabet for - literal block types, appears only if NBLTYPESL >= 2 - - Prefix code over the block count code alphabet for - literal block counts, appears only if NBLTYPESL >= 2 - - Block count code + extra bits for first literal - block count, appears only if NBLTYPESL >= 2 - - 1-11 bits: NBLTYPESI, # of insert-and-copy block types, encoded - with the same variable length code as above - - Prefix code over the block type code alphabet for - insert-and-copy block types, appears only if NBLTYPESI >= 2 - - Prefix code over the block count code alphabet for - insert-and-copy block counts, appears only if NBLTYPESI >= 2 - - Block count code + extra bits for first insert-and-copy - block count, appears only if NBLTYPESI >= 2 - - 1-11 bits: NBLTYPESD, # of distance block types, encoded - with the same variable length code as above - - Prefix code over the block type code alphabet for - distance block types, appears only if NBLTYPESD >= 2 - - Prefix code over the block count code alphabet for - distance block counts, appears only if NBLTYPESD >= 2 - - Block count code + extra bits for first distance - block count, appears only if NBLTYPESD >= 2 - - 2 bits: NPOSTFIX, parameter used in the distance coding - - 4 bits: four most-significant bits of NDIRECT, to get the - actual value of the parameter NDIRECT, left-shift - this four-bit number by NPOSTFIX bits - - NBLTYPESL x 2 bits: context mode for each literal block type - - 1-11 bits: NTREESL, # of literal prefix trees, encoded - with the same variable length code as NBLTYPESL - - Literal context map, encoded as described in Section 7.3., - appears only if NTREESL >= 2, otherwise the context map - has only zero values - - 1-11 bits: NTREESD, # of distance prefix trees, encoded - with the same variable length code as NBLTYPESD - - Distance context map, encoded as described in Section 7.3., - appears only if NTREESD >= 2, otherwise the context map - has only zero values - - NTREESL prefix codes for literals - - NBLTYPESI prefix codes for insert-and-copy lengths - - NTREESD prefix codes for distances -.fi - -.ti 0 -9.3. Format of the meta-block data - -The compressed data part of a meta-block consists of a series of -commands. Each command has the following format: - -.nf - Block type code for next insert-and-copy block type, appears - only if NBLTYPESI >= 2 and the previous insert-and-copy - block count is zero - - Block count code + extra bits for next insert-and-copy - block count, appears only if NBLTYPESI >= 2 and the - previous insert-and-copy block count is zero - - Insert-and-copy length, encoded as in Section 5., using the - insert-and-copy length prefix code with the current - insert-and-copy block type index - - Insert length number of literals, with the following format: - - Block type code for next literal block type, appears - only if NBLTYPESL >= 2 and the previous literal - block count is zero - - Block count code + extra bits for next literal - block count, appears only if NBLTYPESL >= 2 and the - previous literal block count is zero - - Next byte of the uncompressed data, encoded with the - literal prefix code with the index determined by the - previous two bytes of the uncompressed data, the - current literal block type, and the context map, as - described in Section 7.3. - - Block type code for next distance block type, appears - only if NBLTYPESD >= 2 and the previous distance - block count is zero - - Block count code + extra bits for next distance - block count, appears only if NBLTYPESD >= 2 and the - previous distance block count is zero - - Distance code, encoded as in Section 4., using the distance - prefix code with the current distance block type index, - appears only if the distance code is not an implicit 0, - as indicated by the insert-and-copy length code -.fi - -The number of commands in the meta-block is such that the sum of -the uncompressed bytes produced (i.e. the number of literals inserted -plus the number of bytes copied from past data or generated from the -static dictionary) over all the commands gives the uncompressed length, -MLEN encoded in the meta-block header. - -If the total number of uncompressed bytes produced after the insert part -of the last command equals MLEN, then the copy length of the last command -is ignored and will not produce any uncompressed output. In this case the -copy length of the last command can have any value. In any other case, if -the number of literals to insert, the copy length, or the resulting -dictionary word length would cause MLEN to be exceeded, then the stream -should be rejected as invalid. - -If the last command of the last non-empty meta-block does not end on -a byte boundary, the unused bits in the last byte must be zeros. - -.ti 0 -10. Decoding algorithm - -The decoding algorithm that produces the uncompressed data is as follows: - -.nf - read window size - do - read ISLAST bit - if ISLAST - read ISLASTEMPTY bit - if ISLASTEMPTY - break from loop - read MNIBBLES - if MNIBBLES is zero - verify reserved bit is zero - read MSKIPLEN - skip any bits up to the next byte boundary - skip MSKIPLEN bytes - continue to the next meta-block - else - read MLEN - if not ISLAST - read ISUNCOMPRESSED bit - if ISUNCOMPRESSED - skip any bits up to the next byte boundary - copy MLEN bytes of compressed data as literals - continue to the next meta-block - loop for each three block categories (i = L, I, D) - read NBLTYPESi - if NBLTYPESi >= 2 - read prefix code for block types, HTREE_BTYPE_i - read prefix code for block counts, HTREE_BLEN_i - read block count, BLEN_i - set block type, BTYPE_i to 0 - initialize second-to-last and last block types to 0 and 1 - else - set block type, BTYPE_i to 0 - set block count, BLEN_i to 16777216 - 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 literal prefix codes, HTREEL[] - read array of insert-and-copy length prefix codes, HTREEI[] - read array of distance prefix codes, HTREED[] - do - if BLEN_I is zero - read block type using HTREE_BTYPE_I and set BTYPE_I - save previous block type - read block count using HTREE_BLEN_I and set BLEN_I - decrement BLEN_I - read insert-and-copy length symbol using HTREEI[BTYPE_I] - compute insert length, ILEN, and copy length, CLEN - loop for ILEN - if BLEN_L is zero - read block type using HTREE_BTYPE_L and set BTYPE_L - save previous block type - read block count using HTREE_BLEN_L and set BLEN_L - decrement BLEN_L - look up context mode CMODE[BTYPE_L] - compute context ID, CIDL from last two uncompressed bytes - read literal using HTREEL[CMAPL[64*BTYPE_L + CIDL]] - write literal to uncompressed stream - if number of uncompressed bytes produced in the loop for - this meta-block is MLEN, then break from loop (in this - case the copy length is ignored and can have any value) - if distance code is implicit zero from insert-and-copy code - set backward distance to the last distance - else - if BLEN_D is zero - read block type using HTREE_BTYPE_D and set BTYPE_D - save previous block type - read block count using HTREE_BLEN_D and set BLEN_D - decrement BLEN_D - compute context ID, CIDD from CLEN - read distance code using HTREED[CMAPD[4*BTYPE_D + CIDD]] - compute distance by distance short code substitution - if distance code is not zero, - and distance is not a static dictionary reference, - push distance to the ring buffer of last distances - if distance is less than the max allowed distance plus one - move backwards distance bytes in the uncompressed data, - and copy CLEN bytes from this position to - the uncompressed stream - else - look up the static dictionary word, transform the word as - directed, and copy the result to the uncompressed stream - while number of uncompressed bytes for this meta-block < MLEN - while not ISLAST -.fi - -If the stream ends before the completion of the last meta-block, then -the stream should be rejected as invalid. - -Note that a duplicated string reference may refer to a string in a -previous meta-block, i.e. the backward distance may cross one or -more meta-block boundaries. However a backward copy distance -will not refer past the beginning of the uncompressed stream or the -window size; any such distance is -interpreted as a reference to a static dictionary word. Also note -that the referenced string may overlap the current position, for -example, if the last 2 bytes decoded have values X and Y, a string -reference with adds X,Y,X,Y,X to the -uncompressed stream. - -.ti 0 -11. Security Considerations - -As with any compressed file formats, decompressor implementations should -handle all compressed data byte sequences, not only those that conform to this -specification, where non-conformant compressed data sequences should be discarded. -A possible attack against a system containing a decompressor -implementation (e.g. a web browser) is to exploit a buffer -overflow caused by an invalid compressed data. Therefore decompressor -implementations should perform bounds-checking for each memory access -that result from values decoded from the compressed stream. - -.ti 0 -12. IANA Considerations - -The "HTTP Content Coding Registry" has been updated with the -registration below: - -.nf -.KS - +-------+-------------------------------------+------------+ - | Name | Description | Reference | - +-------+-------------------------------------+------------+ - | br | Brotli Compressed Data Format | RFCXXXX | - +-------+-------------------------------------+------------+ -.KE -.fi - -.ti 0 -13. Informative References -.in 14 - -.ti 3 -[HUFFMAN] Huffman, D. A., "A Method for the Construction of Minimum -Redundancy Codes", Proceedings of the Institute of Radio -Engineers, September 1952, Volume 40, Number 9, pp. 1098-1101. - -.ti 3 -[LZ77] Ziv J., Lempel A., "A Universal Algorithm for Sequential Data -Compression", IEEE Transactions on Information Theory, Vol. 23, -No. 3, pp. 337-343. - -.ti 3 -[RFC1951] Deutsch, P., "DEFLATE Compressed Data Format Specification -version 1.3", RFC 1951, Aladdin Enterprises, May 1996. -http://www.ietf.org/rfc/rfc1951.txt - -.ti 3 -[WOFF2] Levantovsky, V. (ed.), Levien, R. (ed.), "WOFF File Format -2.0", W3C WebFonts Working Group, http://www.w3.org/TR/WOFF2/ -.in 3 - -.ti 0 -14. Source code - -Source code for a C language implementation of a brotli compliant -decompressor and a C++ language implementation of a compressor is -available in the brotli open-source project: -https://github.com/google/brotli - -.ti 0 -15. Acknowledgments - -The authors would like to thank Mark Adler, Robert Obryk, Thomas -Pickert, and Joe Tsai for providing helpful review comments, -validating the specification by writing an independent decompressor, -and suggesting improvements to the format and the text of the -specification. - -.ti 0 -Appendix A. Static dictionary data - -The hexadecimal form of the DICT array is the following, where the -length is 122,784 bytes and the zlib CRC-32 of the byte sequence is -0x5136cb04. - -.in 0 -.nf - 74696d65646f776e6c6966656c6566746261636b636f64656461746173686f77 - 6f6e6c7973697465636974796f70656e6a7573746c696b6566726565776f726b - 74657874796561726f766572626f64796c6f7665666f726d626f6f6b706c6179 - 6c6976656c696e6568656c70686f6d65736964656d6f7265776f72646c6f6e67 - 7468656d7669657766696e64706167656461797366756c6c686561647465726d - 656163686172656166726f6d747275656d61726b61626c6575706f6e68696768 - 646174656c616e646e6577736576656e6e65787463617365626f7468706f7374 - 757365646d61646568616e6468657265776861746e616d654c696e6b626c6f67 - 73697a656261736568656c646d616b656d61696e757365722729202b686f6c64 - 656e6473776974684e65777372656164776572657369676e74616b6568617665 - 67616d657365656e63616c6c7061746877656c6c706c75736d656e7566696c6d - 706172746a6f696e746869736c697374676f6f646e6565647761797377657374 - 6a6f62736d696e64616c736f6c6f676f72696368757365736c6173747465616d - 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bit-depth array: - - NDBITS := 0, 0, 0, 0, 10, 10, 11, 11, 10, 10, - 10, 10, 10, 9, 9, 8, 7, 7, 8, 7, - 7, 6, 6, 5, 5 -.fi - -.ti 0 -Appendix B. List of word transformations - -The string literals are in C format, with respect to the use of -backslash escape characters. - -In order to generate a length and check value, the transforms can be converted -to a series of bytes, where each transform is the prefix sequence of bytes plus -a terminating zero byte, a single byte value identifying the transform, and the -suffix sequence of bytes plus a terminating zero. The value for the transforms -are 0 for Identity, 1 for UppercaseFirst, 2 for UppercaseAll, 3 to 11 for -OmitFirst1 to OmitFirst9, and 12 to 20 for OmitLast1 to OmitLast9. The byte -sequences that represent the 121 transforms are then concatenated to a single -sequence of bytes. The length of that sequence is 648 bytes, and the zlib CRC -is 0x3d965f81. - -.nf - ID Prefix Transform Suffix - -- ------ --------- ------ - 0 "" Identity "" - 1 "" Identity " " - 2 " " Identity " " - 3 "" OmitFirst1 "" - 4 "" UppercaseFirst " " - 5 "" Identity " the " - 6 " " Identity "" - 7 "s " Identity " " - 8 "" Identity " of " - 9 "" UppercaseFirst "" - 10 "" Identity " and " - 11 "" OmitFirst2 "" - 12 "" OmitLast1 "" - 13 ", " Identity " " - 14 "" Identity ", " - 15 " " UppercaseFirst " " - 16 "" Identity " in " - 17 "" Identity " to " - 18 "e " Identity " " - 19 "" Identity "\\"" - 20 "" Identity "." - 21 "" Identity "\\">" - 22 "" Identity "\\n" - 23 "" OmitLast3 "" - 24 "" Identity "]" - 25 "" Identity " for " - 26 "" OmitFirst3 "" - 27 "" OmitLast2 "" - 28 "" Identity " a " - 29 "" Identity " that " - 30 " " UppercaseFirst "" - 31 "" Identity ". " - 32 "." Identity "" - 33 " " Identity ", " - 34 "" OmitFirst4 "" - 35 "" Identity " with " - 36 "" Identity "'" - 37 "" Identity " from " - 38 "" Identity " by " - 39 "" OmitFirst5 "" - 40 "" OmitFirst6 "" - 41 " the " Identity "" - 42 "" OmitLast4 "" - 43 "" Identity ". The " - 44 "" UppercaseAll "" - 45 "" Identity " on " - 46 "" Identity " as " - 47 "" Identity " is " - 48 "" OmitLast7 "" - 49 "" OmitLast1 "ing " - 50 "" Identity "\\n\\t" - 51 "" Identity ":" - 52 " " Identity ". " - 53 "" Identity "ed " - 54 "" OmitFirst9 "" - 55 "" OmitFirst7 "" - 56 "" OmitLast6 "" - 57 "" Identity "(" - 58 "" UppercaseFirst ", " - 59 "" OmitLast8 "" - 60 "" Identity " at " - 61 "" Identity "ly " - 62 " the " Identity " of " - 63 "" OmitLast5 "" - 64 "" OmitLast9 "" - 65 " " UppercaseFirst ", " - 66 "" UppercaseFirst "\\"" - 67 "." Identity "(" - 68 "" UppercaseAll " " - 69 "" UppercaseFirst "\\">" - 70 "" Identity "=\\"" - 71 " " Identity "." - 72 ".com/" Identity "" - 73 " the " Identity " of the " - 74 "" UppercaseFirst "'" - 75 "" Identity ". This " - 76 "" Identity "," - 77 "." Identity " " - 78 "" UppercaseFirst "(" - 79 "" UppercaseFirst "." - 80 "" Identity " not " - 81 " " Identity "=\\"" - 82 "" Identity "er " - 83 " " UppercaseAll " " - 84 "" Identity "al " - 85 " " UppercaseAll "" - 86 "" Identity "='" - 87 "" UppercaseAll "\\"" - 88 "" UppercaseFirst ". " - 89 " " Identity "(" - 90 "" Identity "ful " - 91 " " UppercaseFirst ". " - 92 "" Identity "ive " - 93 "" Identity "less " - 94 "" UppercaseAll "'" - 95 "" Identity "est " - 96 " " UppercaseFirst "." - 97 "" UppercaseAll "\\">" - 98 " " Identity "='" - 99 "" UppercaseFirst "," - 100 "" Identity "ize " - 101 "" UppercaseAll "." - 102 "\\xc2\\xa0" Identity "" - 103 " " Identity "," - 104 "" UppercaseFirst "=\\"" - 105 "" UppercaseAll "=\\"" - 106 "" Identity "ous " - 107 "" UppercaseAll ", " - 108 "" UppercaseFirst "='" - 109 " " UppercaseFirst "," - 110 " " UppercaseAll "=\\"" - 111 " " UppercaseAll ", " - 112 "" UppercaseAll "," - 113 "" UppercaseAll "(" - 114 "" UppercaseAll ". " - 115 " " UppercaseAll "." - 116 "" UppercaseAll "='" - 117 " " UppercaseAll ". " - 118 " " UppercaseFirst "=\\"" - 119 " " UppercaseAll "='" - 120 " " UppercaseFirst "='" -.fi -.in 3 - - -.ti 0 -Authors' Addresses - -.nf -Jyrki Alakuijala -Google, Inc - -Email: jyrki@google.com - - -Zoltan Szabadka -Google, Inc - -Email: szabadka@google.com -.fi - diff --git a/docs/draft-alakuijala-brotli-08.txt b/docs/draft-alakuijala-brotli-08.txt deleted file mode 100644 index e119136..0000000 --- a/docs/draft-alakuijala-brotli-08.txt +++ /dev/null @@ -1,6723 +0,0 @@ - - - - - - -Network Working Group J. Alakuijala -Internet-Draft Z. Szabadka -Intended Status: Informational Google, Inc -Expires: June 10, 2016 December 2015 - - - Brotli Compressed Data Format - draft-alakuijala-brotli-08 - -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. - -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 June 10, 2016. - -Copyright Notice - - Copyright (c) 2015 IETF Trust and the persons identified as the - document authors. All rights reserved. - - This document is subject to BCP 78 and the IETF Trust's Legal - Provisions Relating to IETF Documents - (http://trustee.ietf.org/license-info) in effect on the date of - publication of this document. Please review these documents - carefully, as they describe your rights and restrictions with respect - to this document. Code Components extracted from this document must - include Simplified BSD License text as described in Section 4.e of - the Trust Legal Provisions and are provided without warranty as - described in the Simplified BSD License. - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 1] - -Internet-Draft Brotli December 2015 - - -Table of Contents - - 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 1.1. Purpose . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 1.2. Intended audience . . . . . . . . . . . . . . . . . . . . 3 - 1.3. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 1.4. Compliance . . . . . . . . . . . . . . . . . . . . . . . . 4 - 1.5. Definitions of terms and conventions used . . . . . . . . 4 - 1.5.1. Packing into bytes . . . . . . . . . . . . . . . . . 4 - 2. Compressed representation overview . . . . . . . . . . . . . . 5 - 3. Compressed representation of prefix codes . . . . . . . . . . . 9 - 3.1. Introduction to prefix coding . . . . . . . . . . . . . . 9 - 3.2. Use of prefix coding in the brotli format . . . . . . . . 10 - 3.3. Alphabet sizes . . . . . . . . . . . . . . . . . . . . . 12 - 3.4. Simple prefix codes . . . . . . . . . . . . . . . . . . . 13 - 3.5. Complex prefix codes . . . . . . . . . . . . . . . . . . 14 - 4. Encoding of distances . . . . . . . . . . . . . . . . . . . . 16 - 5. Encoding of literal insertion lengths and copy lengths . . . . 18 - 6. Encoding of block switch commands . . . . . . . . . . . . . . 20 - 7. Context modeling . . . . . . . . . . . . . . . . . . . . . . . 22 - 7.1. Context modes and context ID lookup for literals . . . . 22 - 7.2. Context ID for distances . . . . . . . . . . . . . . . . 24 - 7.3. Encoding of the context map . . . . . . . . . . . . . . . 24 - 8. Static dictionary . . . . . . . . . . . . . . . . . . . . . . 26 - 9. Compressed data format . . . . . . . . . . . . . . . . . . . . 28 - 9.1. Format of the stream header . . . . . . . . . . . . . . . 29 - 9.2. Format of the meta-block header . . . . . . . . . . . . . 29 - 9.3. Format of the meta-block data . . . . . . . . . . . . . . 32 - 10. Decoding algorithm . . . . . . . . . . . . . . . . . . . . . 33 - 11. Security Considerations . . . . . . . . . . . . . . . . . . . 36 - 12. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 36 - 13. Informative References . . . . . . . . . . . . . . . . . . . 36 - 14. Source code . . . . . . . . . . . . . . . . . . . . . . . . . 37 - 15. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 37 - Appendix A. Static dictionary data . . . . . . . . . . . . . . . 37 - Appendix B. List of word transformations . . . . . . . . . . . . 117 - Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 120 - - - - - - - - - - - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 2] - -Internet-Draft Brotli December 2015 - - -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 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. - - 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 the brotli format. - - The text of the specification assumes a basic background in - programming at the level of bits and other primitive data - representations. Familiarity with the technique of Huffman coding is - helpful but not required. - - This specification uses heavily the notations and terminology - introduced in the DEFLATE format specification [RFC 1951]. For the - sake of completeness, we always include the whole text of the - relevant parts of RFC 1951, therefore familiarity with the DEFLATE - format is helpful but not required. - - The compressed data format defined in this specification is an - integral part of the WOFF 2.0 web font file format [WOFF2], therefore - this specification is also intended for implementers of WOFF 2.0 - compressors and decompressors. - -1.3. Scope - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 3] - -Internet-Draft Brotli December 2015 - - - 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 that - 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 - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 4] - -Internet-Draft Brotli December 2015 - - - 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 prefix codes are packed - starting with the least-significant bit of the data - element. These are referred to here as integer values - and are considered unsigned. - * Prefix codes are packed starting with the most-significant - bit of the code. - - In other words, if one were to print out the compressed data as a - sequence of bytes, starting with the first byte at the *right* margin - and proceeding to the *left*, with the most-significant bit of each - byte on the left as usual, one would be able to parse the result from - right to left, with fixed-width elements in the correct MSB-to-LSB - order and prefix codes in bit-reversed order (i.e., with the first - bit of the code in the relative LSB position). - -2. Compressed representation overview - - A compressed data set consists of a header and a series of meta- - blocks. Each meta-block decompresses to a sequence of 0 to 16,777,216 - (16 MiB) uncompressed bytes. The final uncompressed data is the - concatenation of the uncompressed sequences from each meta-block. - - The header contains the size of the sliding window that was used - during compression. The decompressor must retain at least that - amount of uncompressed data prior to the current position in the - stream, in order to be able to decompress what follows. The sliding - window size is a power of two, minus 16, where the power is in the - range of 10 to 24. The possible sliding window sizes range from 1 KiB - - 16 B to 16 MiB - 16 B. - - Each meta-block is compressed using a combination of the LZ77 - algorithm (Lempel-Ziv 1977, [LZ77]) and Huffman coding. The result of - Huffman coding is referred to here as a prefix code. The prefix - codes for each meta-block are independent of those for previous or - subsequent meta-blocks; the LZ77 algorithm may use a reference to a - duplicated string occurring in a previous meta-block, up to the - sliding window size of uncompressed bytes before. In addition, in - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 5] - -Internet-Draft Brotli December 2015 - - - the brotli format, a string reference may instead refer to a static - dictionary entry. - - Each meta-block consists of two parts: a meta-block header that - describes the representation of the compressed data part, and a - compressed data part. The compressed data consists of a series of - commands. Each command consists of two parts: a sequence of literal - bytes (of strings that have not been detected as duplicated within - the sliding window), and a pointer to a duplicated string, - represented as a pair . There can be zero - literal bytes in the command. The minimum length of the string to be - duplicated is two, but the last command in the meta-block is - permitted to have only literals and no pointer to a string to - duplicate. - - Each command in the compressed data is represented using three - categories of prefix codes: - - 1) One set of prefix codes are for the literal sequence lengths - (also referred to as literal insertion lengths) and - backward copy lengths. That is, a single code word represents - two lengths, one of the literal sequence and one of the - backward copy. - - 2) One set of prefix codes are for literals. - - 3) One set of prefix codes are for distances. - - The prefix code descriptions for each meta-block appear in a compact - form just before the compressed data in the meta-block header. The - insert-and-copy length and distance prefix codes may be followed by - extra bits that are added to the base values determined by the codes. - The number of extra bits is determined by the code. - - One meta-block command then appears as a sequence of prefix codes: - - Insert-and-copy length, literal, literal, ..., literal, distance - - where the insert-and-copy defines an insertion length and a copy - length. The insertion length determines the number of literals that - immediately follow. The distance defines how far back to go for the - copy and the copy length determines the number of bytes to copy. The - resulting uncompressed data is the sequence of bytes: - - literal, literal, ..., literal, copy, copy, ..., copy - - where the number of literal bytes and copy bytes are determined by - the insert-and-copy length code. (The number of bytes copied for a - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 6] - -Internet-Draft Brotli December 2015 - - - static dictionary entry can vary from the copy length.) - - The last command in the meta-block may end with the last literal if - the total uncompressed length of the meta-block has been satisfied. - In that case there is no distance in the last command, and the copy - length is ignored. - - There can be more than one prefix code for each category, where the - prefix code to use for the next element of that category is - determined by the context of the compressed stream that precedes that - element. Part of that context is three current block types, one for - each category. A block type is in the range of 0..255. For each - category there is a count of how many elements of that category - remain to be decoded using the current block type. Once that count is - expended, a new block type and block count is read from the stream - immediately preceding the next element of that category, which will - use the new block type. - - The insert-and-copy block type directly determines which prefix code - to use for the next insert-and-copy element. For the literal and - distance elements, the respective block type is used in combination - with other context information to determine which prefix code to use - for the next element. - - Consider the following example: - - (IaC0, L0, L1, L2, D0)(IaC1, D1)(IaC2, L3, L4, D2)(IaC3, L5, D3) - - The meta-block here has four commands, contained in parentheses for - clarity, where each of the three categories of symbols within these - commands can be interpreted using different block types. Here we - separate out each category as its own sequence to show an example of - block types assigned to those elements. Each square-bracketed group - is a block that uses the same block type: - - [IaC0, IaC1][IaC2, IaC3] <-- insert-and-copy: block types 0 and 1 - - [L0, L1][L2, L3, L4][L5] <-- literals: block types 0, 1, and 0 - - [D0][D1, D2, D3] <-- distances: block types 0 and 1 - - The subsequent blocks within each block category must have different - block types, but we see that block types can be reused later in the - meta-block. The block types are numbered from 0 to the maximum block - type number of 255 and the first block of each block category is type - 0. The block structure of a meta-block is represented by the sequence - of block-switch commands for each block category, where a block- - switch command is a pair . The block-switch - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 7] - -Internet-Draft Brotli December 2015 - - - commands are represented in the compressed data before the start of - each new block using a prefix code for block types and a separate - prefix code for block counts for each block category. For the above - example the physical layout of the meta-block is then: - - IaC0 L0 L1 LBlockSwitch(1, 3) L2 D0 IaC1 DBlockSwitch(1, 3) D1 - IaCBlockSwitch(1, 2) IaC2 L3 L4 D2 IaC3 LBlockSwitch(0, 1) L5 D3 - - where xBlockSwitch(t, n) switches to block type t for a count of n - elements. Note that in this example DBlockSwitch(1, 3) immediately - precedes the next required distance D1. It does not follow the last - distance of the previous block, D0. Whenever an element of a category - is needed, and the block count for that category has reached zero, - then a new block type and count is read from the stream just before - reading that next element. - - The block-switch commands for the first blocks of each category are - not part of the meta-block compressed data. Instead the first block - type is defined to be 0, and the first block count for each category - is encoded in the meta-block header. The prefix codes for the block - types and counts, a total of six prefix codes over the three - categories, are defined in a compact form in the meta-block header. - - Each category of value (insert-and-copy lengths, literals, and - distances) can be encoded with any prefix code from a collection of - prefix codes belonging to the same category appearing in the meta- - block header. The particular prefix code used can depend on two - factors: the block type of the block the value appears in, and the - context of the value. In the case of the literals, the context is - the previous two bytes in the uncompressed data, and in the case of - distances, the context is the copy length from the same command. For - insert-and-copy lengths, no context is used and the prefix code - depends only on the block type. In the case of literals and - distances, the context is mapped to a context ID in the range 0..63 - for literals and 0..3 for distances. The matrix of the prefix code - indexes for each block type and context ID, called the context map, - is encoded in a compact form in the meta-block header. - - For example, the prefix code to use to decode L2 depends on the block - type (1), and the literal context ID determined by the two - uncompressed bytes that were decoded from L0 and L1. Similarly, the - prefix code to use to decode D0 depends on the block type (0), and - the distance context ID determined by the copy length decoded from - IaC0. The prefix code to use to decode IaC3 depends only on the block - type (1). - - In addition to the parts listed above (prefix code for insert-and- - copy lengths, literals, distances, block types and block counts, and - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 8] - -Internet-Draft Brotli December 2015 - - - the context map), the meta-block header contains the number of - uncompressed bytes coded in the meta-block and two additional - parameters used in the representation of match distances: the number - of postfix bits and the number of direct distance codes. - - A compressed meta-block may be marked in the header as the last meta- - block, which terminates the compressed stream. - - A meta-block may instead simply store the uncompressed data directly - as bytes on byte boundaries with no coding or matching strings. In - this case the meta-block header information only contains the number - of uncompressed bytes and the indication that the meta-block is - uncompressed. An uncompressed meta-block cannot be the last meta- - block. - - A meta-block may also be empty, which generates no uncompressed data - at all. An empty meta-block may contain metadata information as - bytes starting on byte boundaries, which are not part of either the - sliding window or the uncompressed data. Thus, these metadata bytes - cannot be used to create matching strings in subsequent meta-blocks - and are not used as context bytes for literals. - -3. Compressed representation of prefix codes - -3.1. Introduction to prefix coding - - Prefix coding represents symbols from an a priori known alphabet by - bit sequences (codes), one code for each symbol, in a manner such - that different symbols may be represented by bit sequences of - different lengths, but a parser can always parse an encoded string - unambiguously symbol-by-symbol. - - We define a prefix code in terms of a binary tree in which the two - edges descending from each non-leaf node are labeled 0 and 1 and in - which the leaf nodes correspond one-for-one with (are labeled with) - the symbols of the alphabet; then the code for a symbol is the - sequence of 0's and 1's on the edges leading from the root to the - leaf labeled with that symbol. For example: - - - - - - - - - - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 9] - -Internet-Draft Brotli December 2015 - - - /\ 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 the compressed stream by - walking down the tree from the root, at each step choosing the edge - corresponding to the next compressed data bit. - - Given an alphabet with known symbol frequencies, the Huffman - algorithm allows the construction of an optimal prefix code (one - which represents strings with those symbol frequencies using the - fewest bits of any possible prefix codes for that alphabet). Such a - prefix code is called a Huffman code. (See [HUFFMAN] in Chapter 5, - references for additional information on Huffman codes.) - - Note that in the brotli format, the prefix codes for the various - alphabets must not exceed certain maximum code lengths. This - constraint complicates the algorithm for computing code lengths from - symbol frequencies. Again, see Chapter 5, references for details. - -3.2. Use of prefix coding in the brotli format - - The prefix codes used for each alphabet in the brotli format are - canonical prefix codes, which have two additional rules: - - * 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 - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 10] - -Internet-Draft Brotli December 2015 - - - I.e., 0 precedes 10, which precedes 11x, and 110 and 111 are - lexicographically consecutive. - - Given this rule, we can define the canonical prefix code for an - alphabet just by giving the bit lengths of the codes for each symbol - of the alphabet in order; this is sufficient to determine the actual - codes. In our example, the code is completely defined by the sequence - of bit lengths (2, 1, 3, 3). The following algorithm generates the - codes as integers, intended to be read from most- to least- - significant bit. The code lengths are initially in tree[I].Len; the - codes are produced in tree[I].Code. - - 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: - - - - - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 11] - -Internet-Draft Brotli December 2015 - - - 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 - - Prefix codes are used for different purposes in the brotli format, - and each purpose has a different alphabet size. For literal codes the - alphabet size is 256. For insert-and-copy length codes the alphabet - size is 704. For block count codes, the alphabet size is 26. For - distance codes, block type codes, and the prefix codes used in - compressing the context map, the alphabet size is dynamic and is - based on parameters defined in later sections. The following table - summarizes the alphabet sizes for the various prefix codes and the - sections where they are defined. - - - - - - - - - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 12] - -Internet-Draft Brotli December 2015 - - - +-----------------+-------------------------+------------+ - | Prefix code | Alphabet size | Definition | - +-----------------+-------------------------+------------+ - | literal | 256 | | - +-----------------+-------------------------+------------+ - | distance | 16 + NDIRECT + | Section 4. | - | | (48 << NPOSTFIX) | | - +-----------------+-------------------------+------------+ - | insert-and-copy | 704 | Section 5. | - | length | | | - +-----------------+-------------------------+------------+ - | block count | 26 | Section 6. | - +-----------------+-------------------------+------------+ - | block type | NBLTYPESx + 2, | Section 6. | - | | (where x is I, L, or D) | | - +-----------------+-------------------------+------------+ - | context map | NTREESx + RLEMAXx | Section 7. | - | | (where x is L or D) | | - +-----------------+-------------------------+------------+ - -3.4. Simple prefix codes - - The first two bits of the compressed representation of each prefix - code distinguish between simple and complex prefix codes. If this - value is 1, then a simple prefix code follows as described in this - section. Otherwise, a complex prefix code follows as described in - Section 3.5. - - A simple prefix code can have only up to four symbols with non-zero - code length. The format of the simple prefix code is as follows: - - 2 bits: value of 1 indicates a simple prefix code - 2 bits: NSYM - 1, where NSYM = # of symbols coded - - NSYM symbols, each encoded using ALPHABET_BITS bits - - 1 bit: tree-select, present only for NSYM = 4 - - The value of ALPHABET_BITS depends on the alphabet of the prefix - code: it is the smallest number of bits that can represent all - symbols in the alphabet. E.g. for the alphabet of literal bytes, - ALPHABET_BITS is 8. The value of each of the NSYM symbols above is - the value of the ALPHABETS_BITS width integer value. If the integer - value is greater than or equal to the alphabet size, or the value is - identical to a previous value, then the stream should be rejected as - invalid. - - Note that the NSYM symbols may not be presented in sorted order. - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 13] - -Internet-Draft Brotli December 2015 - - - Prefix codes of the same bit length must be assigned to the symbols - in sorted order. - - The (non-zero) code lengths of the symbols can be reconstructed as - follows: - - * if NSYM = 1, the code length for the one symbol is zero -- - when encoding this symbol in the - compressed data stream using this prefix code, no - actual bits are emitted. Similarly, when decoding a symbol - using this prefix code, no bits are read and the one symbol - is returned. - - * if NSYM = 2, both symbols have code length 1. - - * if NSYM = 3, the code lengths for the symbols are 1, 2, 2 in - the order they appear in the representation of the simple - prefix code. - - * if NSYM = 4, the code lengths (in order of symbols decoded) - depend on the tree-select bit: 2, 2, 2, 2 (tree-select bit 0), - or 1, 2, 3, 3 (tree-select bit 1). - -3.5. Complex prefix codes - - A complex prefix code is a canonical prefix code, defined by the - sequence of code lengths, as discussed in Section 3.2., above. For - even greater compactness, the code length sequences themselves are - compressed using a prefix code. The alphabet for code lengths is as - follows: - - 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 - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 14] - -Internet-Draft Brotli December 2015 - - - repeat count of the previous one as follows: - repeat count = (8 * (repeat count - 2)) + - (3 - 10 on the next 3 bits) - - Note that a code of 16 that follows an immediately preceding 16 - modifies the previous repeat count, which becomes the new repeat - count. The same is true for a 17 following a 17. A sequence of three - or more 16 codes in a row or three of more 17 codes in a row is - possible, modifying the count each time. Only the final repeat count - is used. The modification only applies if the same code follows. A 16 - repeat does not modify an immediately preceding 17 count nor vice - versa. - - A code length of 0 indicates that the corresponding symbol in the - alphabet will not occur in the compressed data, and should not - participate in the prefix code construction algorithm given earlier. - A complex prefix code must have at least two non-zero code lengths. - - The bit lengths of the prefix code over the code length alphabet are - compressed with the following variable length code (as it appears in - the compressed data, where the bits are parsed from right to left): - - Symbol Code - ------ ---- - 0 00 - 1 0111 - 2 011 - 3 10 - 4 01 - 5 1111 - - We can now define the format of the complex prefix code as follows: - - 2 bits: HSKIP, values of 0, 2, or 3 represent the respective - number of skipped code lengths. The skipped lengths - are taken to be zero. (An HSKIP of 1 indicates a - Simple prefix code.) - - Code lengths for symbols in the code length alphabet given - just above, in the order: 1, 2, 3, 4, 0, 5, 17, 6, 16, 7, - 8, 9, 10, 11, 12, 13, 14, 15. If HSKIP is 2, then the - code lengths for symbols 1 and 2 are zero, and the first - code length is for symbol 3. If HSKIP is 3, then the code - length for symbol 3 is also zero, and the first code length - is for symbol 4. - - The code lengths of code length symbols are between 0 and - 5, and they are represented with 2 - 4 bits according to - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 15] - -Internet-Draft Brotli December 2015 - - - the variable length code above. A code length of 0 means - the corresponding code length symbol is not used. - - If HSKIP is 2 or 3, a respective number of leading code - lengths are implicit zeros and are not present in the - code lengths sequence above. - - If there are at least two non-zero code lengths, any - trailing zero code lengths are omitted, i.e. the last - code length in the sequence must be non-zero. In this - case, the sum of (32 >> code length) over all the non-zero - code lengths must equal to 32. - - If the lengths have been read for the entire code length - alphabet and there was only one non-zero code length, - then the prefix code has one symbol whose code has zero - length. In this case, that symbol results in no bits - being emitted by the compressor, and no bits consumed by - the decompressor. That single symbol is immediately - returned when this code is decoded. - An example of where this occurs is if the - entire code to be represented has symbols of length 8. - E.g. a literal code that represents all literal values - with equal probability. In this case the single symbol - is 16, which repeats the previous length. The previous - length is taken to be 8 before any code length code - lengths are read. - - Sequence of at most alphabet size code lengths symbols, encoded - using the code length prefix code. Any trailing 0 or 17 must be - omitted, i.e. the last encoded code length symbol must be - between 1 and 16. The sum of (32768 >> code length) over - all the non-zero code lengths in the alphabet, including - those encoded using repeat code(s) of 16, must equal to - 32768. If the number of times to repeat the previous length - or repeat a zero length would result in more lengths in - total than the number of symbols in the alphabet, then the - stream should be rejected as invalid. - -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 . The distance - code and the extra bits are encoded back-to-back, the distance code - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 16] - -Internet-Draft Brotli December 2015 - - - is encoded using a prefix code over the distance alphabet, while the - extra bits value is encoded as a fixed-width integer value. The - number of extra bits can be 0 - 24, and it is dependent on the - distance code. - - To convert a distance code and associated extra bits to a backward - distance, we need the sequence of past distances and two additional - parameters, the number of "postfix bits", denoted by NPOSTFIX (0..3), - and the number of direct distance codes, denoted by NDIRECT (0..120). - Both of these parameters are encoded in the meta-block header. We - will also use the following derived parameter: - - POSTFIX_MASK = (1 << NPOSTFIX) - 1 - - The first 16 distance symbols are special symbols that reference past - distances as follows: - - 0: last distance - 1: second-to-last distance - 2: third-to-last distance - 3: fourth-to-last distance - 4: last distance - 1 - 5: last distance + 1 - 6: last distance - 2 - 7: last distance + 2 - 8: last distance - 3 - 9: last distance + 3 - 10: second-to-last distance - 1 - 11: second-to-last distance + 1 - 12: second-to-last distance - 2 - 13: second-to-last distance + 2 - 14: second-to-last distance - 3 - 15: second-to-last distance + 3 - - The ring buffer of four last distances is initialized by the values - 16, 15, 11, and 4 (i.e. the fourth-to-last is set to 16, the third- - to-last to 15, the second-to-last to 11, and the last distance to 4) - at the beginning of the *stream* (as opposed to the beginning of the - meta-block) and it is not reset at meta-block boundaries. When a - distance symbol 0 appears, the distance it represents (i.e. the last - distance in the sequence of distances) is not pushed to the ring - buffer of last distances, in other words, the expression "(second, - third, fourth)-to-last distance" means the (second, third, - fourth)-to-last distance that was not represented by a 0 distance - symbol. Similarly, distances that represent static dictionary words - (see Section 8.) are not pushed to the ring buffer of last distances. - - If a special distance symbol resolves to a zero or negative value, - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 17] - -Internet-Draft Brotli December 2015 - - - the stream should be rejected as invalid. - - If NDIRECT is greater than zero, then the next NDIRECT distance - symbols, from 16 to 15 + NDIRECT, represent distances from 1 to - NDIRECT. Neither the special distance symbols, nor the NDIRECT - direct distance symbols are followed by any extra bits. - - Distance symbols 16 + NDIRECT and greater all have extra bits, where - the number of extra bits for a distance symbol "dcode" is given by - the following formula: - - ndistbits = 1 + ((dcode - NDIRECT - 16) >> (NPOSTFIX + 1)) - - The maximum number of extra bits is 24, therefore the size of the - distance symbol alphabet is (16 + NDIRECT + (48 << NPOSTFIX)). - - Given a distance symbol "dcode" (>= 16 + NDIRECT), and extra bits - "dextra", the backward distance is given by the following formula: - - 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 prefix code. This - section provides the details to this encoding. - - Each pair in the compressed data part - of a meta-block is represented with the following triplet: - - - - The insert-and-copy length code, the insert extra bits, and the copy - extra bits are encoded back-to-back, the insert-and-copy length code - is encoded using a prefix code over the insert-and-copy length code - alphabet, while the extra bits values are encoded as fixed-width - integer values. The number of insert and copy extra bits can be 0 - - 24, and they are dependent on the insert-and-copy length code. - - Some of the insert-and-copy length codes also express the fact that - the distance symbol of the distance in the same command is 0, i.e. - the distance component of the command is the same as that of the - previous command. In this case, the distance code and extra bits for - the distance are omitted from the compressed data stream. - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 18] - -Internet-Draft Brotli December 2015 - - - 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: - - - - - - - - - - - - - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 19] - -Internet-Draft Brotli December 2015 - - - Insert - length Copy length code - code 0-7 8-15 16-23 - +---------+---------+ - | | | - 0-7 | 0-63 | 64-127 | <--- distance symbol 0 - | | | - +---------+---------+---------+ - | | | | - 0-7 | 128-191 | 192-255 | 384-447 | - | | | | - +---------+---------+---------+ - | | | | - 8-15 | 256-319 | 320-383 | 512-575 | - | | | | - +---------+---------+---------+ - | | | | - 16-23 | 448-511 | 576-639 | 640-703 | - | | | | - +---------+---------+---------+ - - 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 bits 0-2 (counted from the - LSB) of the insert-and-copy length code. 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 . These are encoded in the compressed data part of - the meta-block, right before the start of each new block of a - particular block category. - - Each block type in the compressed data is represented with a block - type code, encoded using a prefix code over the block type code - alphabet. A block type symbol 0 means that the new block type is the - same as the type of the previous block from the same block category, - i.e. the block type that preceded the current type, while a block - type symbol 1 means that the new block type equals the current block - type plus one. If the current block type is the maximal possible, - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 20] - -Internet-Draft Brotli December 2015 - - - then a block type symbol of 1 results in wrapping to a new block type - of 0. Block type symbols 2 - 257 represent block types 0 - 255 - respectively. The previous and current block types are initialized to - 1 and 0, respectively, at the end of the meta-block header. - - Since the first block type of each block category is 0, the block - type of the first block-switch command is not encoded in the - compressed data. If a block category has only one block type, the - block count of the first block-switch command is also omitted from - the compressed data, otherwise it is encoded in the meta-block - header. - - Since the end of the meta-block is detected by the number of - uncompressed bytes produced, the block counts for any of the three - categories need not count down to exactly zero at the end of the - meta-block. - - The number of different block types in each block category, denoted - by NBLTYPESL, NBLTYPESI, and NBLTYPESD for literals, insert-and-copy - lengths, and distances, respectively, is encoded in the meta-block - header, and it must equal to the largest block type plus one in that - block category. In other words, the set of literal, insert-and-copy - length, and distance block types must be [0..NBLTYPESL-1], - [0..NBLTYPESI-1], and [0..NBLTYPESD-1], respectively. From this it - follows that the alphabet size of literal, insert-and-copy length, - and distance block type codes is NBLTYPESL + 2, NBLTYPESI + 2, and - NBLTYPESD + 2, respectively. - - Each block count in the compressed data is represented with a pair - . The block count code and the extra - bits are encoded back-to-back, the block count code is encoded using - a prefix code over the block count code alphabet, while the extra - bits value is encoded as a fixed-width integer value. The number of - extra bits can be 0 - 24, and it is dependent on the block count - code. The symbols of the block count code alphabet, along with the - number of extra bits, and the range of block counts are as follows: - - - - - - - - - - - - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 21] - -Internet-Draft Brotli December 2015 - - - 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 prefix tree used to encode a literal - byte or a distance code depends on the block type and the context ID. - 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 pair to the index of a prefix code in - the array of literal and distance prefix codes. - -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 of whether these bytes are produced by uncompressed meta- - blocks, backward references, static dictionary references, or by - literal insertions. At the start of the stream p1 and p2 are - initialized to zero. - - There are four methods, called context modes, to compute the Context - ID: - - * LSB6, where the Context ID is the value of six - least-significant bits of p1, - * MSB6, where the Context ID is the value of six - most-significant bits of p1, - * UTF8, where the Context ID is a complex function of p1, p2, - optimized for text compression, and - * Signed, where Context ID is a complex function of p1, p2, - optimized for compressing sequences of signed integers. - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 22] - -Internet-Draft Brotli December 2015 - - - 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, - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 23] - -Internet-Draft Brotli December 2015 - - - 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 - - The lengths and the zlib CRC-32 (ITU-T Recommendation V.42) check - values of each of these tables as a sequence of bytes are as follows: - - Table Length CRC-32 - ----- ------ ------ - Lut0 256 0x8e91efb7 - Lut1 256 0xd01a32f4 - Lut2 256 0x0dd7a0d6 - - Given p1 is the last uncompressed byte and p2 is the second-to-last - uncompressed 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] - - From the lookup tables defined above and the operations to compute - the context IDs, we can see that context IDs for literals are in the - range of 0..63. - - The context modes LSB6, MSB6, UTF8, and Signed are denoted by - integers 0, 1, 2, 3. - - A 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 context maps, one for literals and one for distances. - The size of the context map is 64 * NBLTYPESL for literals, and 4 * - NBLTYPESD for distances. Each value in the context map is an integer - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 24] - -Internet-Draft Brotli December 2015 - - - between 0 and 255, indicating the index of the prefix code to be used - when encoding the next literal or distance. - - The context maps are two-dimensional matrices, encoded as one- - dimensional arrays: - - CMAPL[0..(64 * NBLTYPESL - 1)] - CMAPD[0..(4 * NBLTYPESD - 1)] - - The index of the prefix code for encoding a literal or distance code - with block type, BTYPE_x, and context ID, CIDx, is: - - index of literal prefix code = CMAPL[64 * BTYPE_L + CIDL] - index of distance prefix code = CMAPD[4 * BTYPE_D + CIDD] - - The values of the context map are encoded with the combination of run - length encoding for zero values and prefix coding. Let RLEMAX denote - the number of run length codes and NTREES denote the maximum value in - the context map plus one. NTREES must equal the number of different - values in the context map, in other words, the different values in - the context map must be the [0..NTREES-1] interval. The alphabet of - the prefix code has the following RLEMAX + NTREES symbols: - - 0: value zero - 1: repeat a zero 2 to 3 times, read 1 bit for repeat length - 2: repeat a zero 4 to 7 times, read 2 bits for repeat length - ... - RLEMAX: repeat a zero (1 << RLEMAX) to (1 << (RLEMAX+1))-1 - times, read RLEMAX bits for repeat length - RLEMAX + 1: value 1 - ... - RLEMAX + NTREES - 1: value NTREES - 1 - - 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 xxxx1 (so 01001 - is 5) - - Prefix code with alphabet size NTREES + RLEMAX - - Context map size values encoded with the above prefix code - and run length coding for zero values. If a run length - would result in more lengths in total than the size of - the context map, then the stream should be rejected as - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 25] - -Internet-Draft Brotli December 2015 - - - invalid. - - 1 bit: IMTF bit, if set, we do an inverse move-to-front - transform on the values in the context map to get - the prefix code indexes - - Note that RLEMAX may be larger than the value necessary to represent - the longest sequence of zero values. Also, the NTREES value is - encoded right before the context map as described in Section 9.2. - - We define the inverse move-to-front transform used in this - specification by the following C language function: - - 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; - } - } - - Note that the inverse move-to-front transform will not produce values - outside the [0..NTREES-1] interval. - -8. Static dictionary - - At any given point during decoding the compressed data, a reference - to a duplicated string in the uncompressed data produced so far has a - maximum backward distance value, which is the minimum of the window - size and the number of uncompressed bytes produced. However, decoding - a distance from the compressed stream, as described in Section 4., - can produce distances that are greater than this maximum allowed - value. In this case, the distance is treated as a reference to a word - in the static dictionary given in Appendix A. The copy length for a - static dictionary reference must be between 4 and 24. The static - dictionary has three parts: - - * DICT[0..DICTSIZE], an array of bytes - * DOFFSET[0..24], an array of byte offset values for each length - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 26] - -Internet-Draft Brotli December 2015 - - - * 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 < 4) - NWORDS[length] = (1 << NDBITS[length]) (if length >= 4) - - 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 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 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)-1] - transform_id = word_id >> NDBITS[length] - - The string copied to the uncompressed stream is computed by applying - the transformation to the base dictionary word. If transform_id is - greater than 120, or the length is smaller than 4 or greater than 24, - then the compressed stream should be rejected as invalid. - - Each word transformation has the following form: - - transform_i(word) = prefix_i + T_i(word) + suffix_i - - where the _i subscript denotes the transform_id above. Each T_i is - one of the following 21 elementary transforms: - - Identity, UppercaseFirst, UppercaseAll, - OmitFirst1, ..., OmitFirst9, OmitLast1, ..., OmitLast9 - - The form of these elementary transforms is as follows: - - Identity(word) = word - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 27] - -Internet-Draft Brotli December 2015 - - - UppercaseFirst(word) = first UTF-8 character of word upper-cased - - UppercaseAll(word) = all UTF-8 characters of word upper-cased - - OmitFirstk(word) = the last (length(word) - k) bytes of word, or - empty string if length(word) < k - - OmitLastk(word) = the first (length(word) - k) bytes of word, or - empty string if length(word) < k - - 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: - - 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. - 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. - - The maximum number of additional bytes that a transform may add to a - base word is 13. Since the largest base word is 24 bytes long, a - buffer of 38 bytes is sufficient to store any transformed words - (counting a terminating zero byte). - -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. - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 28] - -Internet-Draft Brotli December 2015 - - -9.1. Format of the stream header - - The stream header has only the following one field: - - 1-7 bits: WBITS, a value in the range 10 - 24, encoded with - the following variable length code (as it appears in - the compressed data, where the bits are parsed from - right to left): - - Value Bit Pattern - ----- ----------- - 10 0100001 - 11 0110001 - 12 1000001 - 13 1010001 - 14 1100001 - 15 1110001 - 16 0 - 17 0000001 - 18 0011 - 19 0101 - 20 0111 - 21 1001 - 22 1011 - 23 1101 - 24 1111 - - Note that bit pattern 0010001 is invalid and must not - be used. - - 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: ISLASTEMPTY, if set to 1, the meta-block is empty; - this field is only present if ISLAST bit is set -- if - it is 1, then the meta-block and the brotli stream ends - at that bit, with any remaining bits in the last byte - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 29] - -Internet-Draft Brotli December 2015 - - - of the compressed stream filled with zeros (if the - fill bits are not zero, then the stream should be - rejected as invalid) - 2 bits: MNIBBLES, # of nibbles to represent the uncompressed - length, encoded with the following fixed-length code: - - Value Bit Pattern - ----- ----------- - 0 11 - 4 00 - 5 01 - 6 10 - - If MNIBBLES is 0, the meta-block is empty, i.e. it does - not generate any uncompressed data. In this case, the - rest of the meta-block has the following format: - - 1 bit: reserved, must be zero - - 2 bits: MSKIPBYTES, # of bytes to represent metadata - length - - MSKIPBYTES x 8 bits: MSKIPLEN - 1, where MSKIPLEN is - the number of metadata bytes; this field is - only present if MSKIPBYTES is positive, - otherwise MSKIPLEN is 0 (if MSKIPBYTES is - greater than 1, and the last byte is all - zeros, then the stream should be rejected - as invalid) - - 0 - 7 bits: fill bits until the next byte boundary, - must be all zeros - - MSKIPLEN bytes of metadata, not part of the - uncompressed data or the sliding window - - MNIBBLES x 4 bits: MLEN - 1, where MLEN is the length - of the meta-block uncompressed data in bytes (if - MNIBBLES is greater than 4, and the last - nibble is all zeros, then the stream should be - rejected as invalid) - - 1 bit: ISUNCOMPRESSED, if set to 1, any bits of compressed - data up to the next byte boundary are ignored, and - the rest of the meta-block contains MLEN bytes of - literal data; this field is only present if the - ISLAST bit is not set (if the ignored bits are not - all zeros, the stream should be rejected as invalid) - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 30] - -Internet-Draft Brotli December 2015 - - - 1-11 bits: NBLTYPESL, # of literal block types, encoded with - the following variable length code (as it appears in - the compressed data, where the bits are parsed from - right to left, so 0110111 has the value 12): - - Value Bit Pattern - ----- ----------- - 1 0 - 2 0001 - 3-4 x0011 - 5-8 xx0101 - 9-16 xxx0111 - 17-32 xxxx1001 - 33-64 xxxxx1011 - 65-128 xxxxxx1101 - 129-256 xxxxxxx1111 - - Prefix code over the block type code alphabet for - literal block types, appears only if NBLTYPESL >= 2 - - Prefix code over the block count code alphabet for - literal block counts, appears only if NBLTYPESL >= 2 - - Block count code + extra bits for first literal - block count, appears only if NBLTYPESL >= 2 - - 1-11 bits: NBLTYPESI, # of insert-and-copy block types, encoded - with the same variable length code as above - - Prefix code over the block type code alphabet for - insert-and-copy block types, appears only if NBLTYPESI >= 2 - - Prefix code over the block count code alphabet for - insert-and-copy block counts, appears only if NBLTYPESI >= 2 - - Block count code + extra bits for first insert-and-copy - block count, appears only if NBLTYPESI >= 2 - - 1-11 bits: NBLTYPESD, # of distance block types, encoded - with the same variable length code as above - - Prefix code over the block type code alphabet for - distance block types, appears only if NBLTYPESD >= 2 - - Prefix code over the block count code alphabet for - distance block counts, appears only if NBLTYPESD >= 2 - - Block count code + extra bits for first distance - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 31] - -Internet-Draft Brotli December 2015 - - - block count, appears only if NBLTYPESD >= 2 - - 2 bits: NPOSTFIX, parameter used in the distance coding - - 4 bits: four most-significant bits of NDIRECT, to get the - actual value of the parameter NDIRECT, left-shift - this four-bit number by NPOSTFIX bits - - NBLTYPESL x 2 bits: context mode for each literal block type - - 1-11 bits: NTREESL, # of literal prefix trees, encoded - with the same variable length code as NBLTYPESL - - Literal context map, encoded as described in Section 7.3., - appears only if NTREESL >= 2, otherwise the context map - has only zero values - - 1-11 bits: NTREESD, # of distance prefix trees, encoded - with the same variable length code as NBLTYPESD - - Distance context map, encoded as described in Section 7.3., - appears only if NTREESD >= 2, otherwise the context map - has only zero values - - NTREESL prefix codes for literals - - NBLTYPESI prefix codes for insert-and-copy lengths - - NTREESD prefix codes for distances - -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 count is zero - - Block count code + extra bits for next insert-and-copy - block count, appears only if NBLTYPESI >= 2 and the - previous insert-and-copy block count is zero - - Insert-and-copy length, encoded as in Section 5., using the - insert-and-copy length prefix code with the current - insert-and-copy block type index - - Insert length number of literals, with the following format: - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 32] - -Internet-Draft Brotli December 2015 - - - Block type code for next literal block type, appears - only if NBLTYPESL >= 2 and the previous literal - block count is zero - - Block count code + extra bits for next literal - block count, appears only if NBLTYPESL >= 2 and the - previous literal block count is zero - - Next byte of the uncompressed data, encoded with the - literal prefix code with the index determined by the - previous two bytes of the uncompressed data, the - current literal block type, and the context map, as - described in Section 7.3. - - Block type code for next distance block type, appears - only if NBLTYPESD >= 2 and the previous distance - block count is zero - - Block count code + extra bits for next distance - block count, appears only if NBLTYPESD >= 2 and the - previous distance block count is zero - - Distance code, encoded as in Section 4., using the distance - prefix code with the current distance block type index, - appears only if the distance code is not an implicit 0, - as indicated by the insert-and-copy length code - - The number of commands in the meta-block is such that the sum of the - uncompressed bytes produced (i.e. the number of literals inserted - plus the number of bytes copied from past data or generated from the - static dictionary) over all the commands gives the uncompressed - length, MLEN encoded in the meta-block header. - - If the total number of uncompressed bytes produced after the insert - part of the last command equals MLEN, then the copy length of the - last command is ignored and will not produce any uncompressed output. - In this case the copy length of the last command can have any value. - In any other case, if the number of literals to insert, the copy - length, or the resulting dictionary word length would cause MLEN to - be exceeded, then the stream should be rejected as invalid. - - If the last command of the last non-empty meta-block does not end on - a byte boundary, the unused bits in the last byte must be zeros. - -10. Decoding algorithm - - The decoding algorithm that produces the uncompressed data is as - follows: - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 33] - -Internet-Draft Brotli December 2015 - - - read window size - do - read ISLAST bit - if ISLAST - read ISLASTEMPTY bit - if ISLASTEMPTY - break from loop - read MNIBBLES - if MNIBBLES is zero - verify reserved bit is zero - read MSKIPLEN - skip any bits up to the next byte boundary - skip MSKIPLEN bytes - continue to the next meta-block - else - read MLEN - if not ISLAST - read ISUNCOMPRESSED bit - if ISUNCOMPRESSED - skip any bits up to the next byte boundary - copy MLEN bytes of compressed data as literals - continue to the next meta-block - loop for each three block categories (i = L, I, D) - read NBLTYPESi - if NBLTYPESi >= 2 - read prefix code for block types, HTREE_BTYPE_i - read prefix code for block counts, HTREE_BLEN_i - read block count, BLEN_i - set block type, BTYPE_i to 0 - initialize second-to-last and last block types to 0 and 1 - else - set block type, BTYPE_i to 0 - set block count, BLEN_i to 16777216 - 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 literal prefix codes, HTREEL[] - read array of insert-and-copy length prefix codes, HTREEI[] - read array of distance prefix codes, HTREED[] - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 34] - -Internet-Draft Brotli December 2015 - - - do - if BLEN_I is zero - read block type using HTREE_BTYPE_I and set BTYPE_I - save previous block type - read block count using HTREE_BLEN_I and set BLEN_I - decrement BLEN_I - read insert-and-copy length symbol using HTREEI[BTYPE_I] - compute insert length, ILEN, and copy length, CLEN - loop for ILEN - if BLEN_L is zero - read block type using HTREE_BTYPE_L and set BTYPE_L - save previous block type - read block count using HTREE_BLEN_L and set BLEN_L - decrement BLEN_L - look up context mode CMODE[BTYPE_L] - compute context ID, CIDL from last two uncompressed bytes - read literal using HTREEL[CMAPL[64*BTYPE_L + CIDL]] - write literal to uncompressed stream - if number of uncompressed bytes produced in the loop for - this meta-block is MLEN, then break from loop (in this - case the copy length is ignored and can have any value) - if distance code is implicit zero from insert-and-copy code - set backward distance to the last distance - else - if BLEN_D is zero - read block type using HTREE_BTYPE_D and set BTYPE_D - save previous block type - read block count using HTREE_BLEN_D and set BLEN_D - decrement BLEN_D - compute context ID, CIDD from CLEN - read distance code using HTREED[CMAPD[4*BTYPE_D + CIDD]] - compute distance by distance short code substitution - if distance code is not zero, - and distance is not a static dictionary reference, - push distance to the ring buffer of last distances - if distance is less than the max allowed distance plus one - move backwards distance bytes in the uncompressed data, - and copy CLEN bytes from this position to - the uncompressed stream - else - look up the static dictionary word, transform the word as - directed, and copy the result to the uncompressed stream - while number of uncompressed bytes for this meta-block < MLEN - while not ISLAST - - If the stream ends before the completion of the last meta-block, then - the stream should be rejected as invalid. - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 35] - -Internet-Draft Brotli December 2015 - - - Note that a duplicated string reference may refer to a string in a - previous meta-block, i.e. the backward distance may cross one or more - meta-block boundaries. However a backward copy distance will not - refer past the beginning of the uncompressed stream or the window - size; any such distance is interpreted as a reference to a static - dictionary word. Also note that the referenced string may overlap the - current position, for example, if the last 2 bytes decoded have - values X and Y, a string reference with - adds X,Y,X,Y,X to the uncompressed stream. - -11. Security Considerations - - As with any compressed file formats, decompressor implementations - should handle all compressed data byte sequences, not only those that - conform to this specification, where non-conformant compressed data - sequences should be discarded. A possible attack against a system - containing a decompressor implementation (e.g. a web browser) is to - exploit a buffer overflow caused by an invalid compressed data. - Therefore decompressor implementations should perform bounds-checking - for each memory access that result from values decoded from the - compressed stream. - -12. IANA Considerations - - The "HTTP Content Coding Registry" has been updated with the - registration below: - - +-------+-------------------------------------+------------+ - | Name | Description | Reference | - +-------+-------------------------------------+------------+ - | br | Brotli Compressed Data Format | RFCXXXX | - +-------+-------------------------------------+------------+ - -13. Informative References - - [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. - - [LZ77] Ziv J., Lempel A., "A Universal Algorithm for Sequential - Data Compression", IEEE Transactions on Information - Theory, Vol. 23, No. 3, pp. 337-343. - - [RFC1951] Deutsch, P., "DEFLATE Compressed Data Format Specification - version 1.3", RFC 1951, Aladdin Enterprises, May 1996. - http://www.ietf.org/rfc/rfc1951.txt - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 36] - -Internet-Draft Brotli December 2015 - - - [WOFF2] Levantovsky, V. (ed.), Levien, R. (ed.), "WOFF File Format - 2.0", W3C WebFonts Working Group, - http://www.w3.org/TR/WOFF2/ - -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 - -15. Acknowledgments - - The authors would like to thank Mark Adler, Robert Obryk, Thomas - Pickert, and Joe Tsai for providing helpful review comments, - validating the specification by writing an independent decompressor, - and suggesting improvements to the format and the text of the - specification. - -Appendix A. Static dictionary data - - The hexadecimal form of the DICT array is the following, where the - length is 122,784 bytes and the zlib CRC-32 of the byte sequence is - 0x5136cb04. - - 74696d65646f776e6c6966656c6566746261636b636f64656461746173686f77 - 6f6e6c7973697465636974796f70656e6a7573746c696b6566726565776f726b - 74657874796561726f766572626f64796c6f7665666f726d626f6f6b706c6179 - 6c6976656c696e6568656c70686f6d65736964656d6f7265776f72646c6f6e67 - 7468656d7669657766696e64706167656461797366756c6c686561647465726d - 656163686172656166726f6d747275656d61726b61626c6575706f6e68696768 - 646174656c616e646e6577736576656e6e65787463617365626f7468706f7374 - 757365646d61646568616e6468657265776861746e616d654c696e6b626c6f67 - 73697a656261736568656c646d616b656d61696e757365722729202b686f6c64 - 656e6473776974684e65777372656164776572657369676e74616b6568617665 - 67616d657365656e63616c6c7061746877656c6c706c75736d656e7566696c6d - 706172746a6f696e746869736c697374676f6f646e6565647761797377657374 - 6a6f62736d696e64616c736f6c6f676f72696368757365736c6173747465616d - 61726d79666f6f646b696e6777696c6c65617374776172646265737466697265 - 506167656b6e6f77617761792e706e676d6f76657468616e6c6f616467697665 - 73656c666e6f74656d756368666565646d616e79726f636b69636f6e6f6e6365 - 6c6f6f6b6869646564696564486f6d6572756c65686f7374616a6178696e666f - 636c75626c6177736c65737368616c66736f6d65737563687a6f6e6531303025 - 6f6e65736361726554696d6572616365626c7565666f75727765656b66616365 - 686f706567617665686172646c6f73747768656e7061726b6b65707470617373 - 73686970726f6f6d48544d4c706c616e54797065646f6e65736176656b656570 - 666c61676c696e6b736f6c6466697665746f6f6b72617465746f776e6a756d70 - 746875736461726b6361726466696c6566656172737461796b696c6c74686174 - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 37] - -Internet-Draft Brotli December 2015 - - - 66616c6c6175746f657665722e636f6d74616c6b73686f70766f746564656570 - 6d6f6465726573747475726e626f726e62616e6466656c6c726f736575726c28 - 736b696e726f6c65636f6d6561637473616765736d656574676f6c642e6a7067 - 6974656d7661727966656c747468656e73656e6464726f7056696577636f7079 - 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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 - -Appendix B. List of word transformations - -The string literals are in C format, with respect to the use of -backslash escape characters. - -In order to generate a length and check value, the transforms can be -converted to a series of bytes, where each transform is the prefix -sequence of bytes plus a terminating zero byte, a single byte value -identifying the transform, and the suffix sequence of bytes plus a -terminating zero. The value for the transforms are 0 for Identity, 1 for -UppercaseFirst, 2 for UppercaseAll, 3 to 11 for OmitFirst1 to -OmitFirst9, and 12 to 20 for OmitLast1 to OmitLast9. The byte sequences -that represent the 121 transforms are then concatenated to a single -sequence of bytes. The length of that sequence is 648 bytes, and the -zlib CRC is 0x3d965f81. - - ID Prefix Transform Suffix - -- ------ --------- ------ - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 117] - -Internet-Draft Brotli December 2015 - - - 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 " - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 118] - -Internet-Draft Brotli December 2015 - - - 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 " - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 119] - -Internet-Draft Brotli December 2015 - - - 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 "='" - - -Authors' Addresses - - Jyrki Alakuijala - Google, Inc - - Email: jyrki@google.com - - - Zoltan Szabadka - Google, Inc - - Email: szabadka@google.com - - - - - - - - - - - - -Alakuijala & Szabadka Expires June 10, 2016 [Page 120] - diff --git a/docs/draft-alakuijala-brotli-09.nroff b/docs/draft-alakuijala-brotli-09.nroff new file mode 100644 index 0000000..5bbf373 --- /dev/null +++ b/docs/draft-alakuijala-brotli-09.nroff @@ -0,0 +1,5891 @@ +.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 December 2015 +.ds CH Brotli +.ds CF Expires June 10, 2016 +.hy 0 +.nh +.ad l +.in 0 +.nf +.tl 'Network Working Group''J. Alakuijala' +.tl 'Internet-Draft''Z. Szabadka' +.tl 'Intended Status: Informational''Google, Inc' +.tl 'Expires: June 10, 2016''December 2015' +.fi + + +.ce 2 +Brotli Compressed Data Format +draft-alakuijala-brotli-08 +.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 June 10, 2016. + +.ti 0 +Copyright Notice + +Copyright (c) 2015 IETF Trust and the persons identified as the document +authors. All rights reserved. + +This document is subject to BCP 78 and the IETF Trust's Legal +Provisions Relating to IETF Documents +(http://trustee.ietf.org/license-info) in effect on the date of +publication of this document. Please review these documents +carefully, as they describe your rights and restrictions with respect +to this document. Code Components extracted from this document must +include Simplified BSD License text as described in Section 4.e of +the Trust Legal Provisions and are provided without warranty as +described in the Simplified BSD License. + +.ti 0 +Table of Contents + +.in 0 +.nf +INSERT_TOC_HERE +.fi +.in 3 + +.bp +.ti 0 +1. Introduction + +.ti 0 +1.1. Purpose + +The purpose of this specification is to define a lossless +compressed data format that: + +.nf + * Is independent of CPU type, operating system, file system, + and character set, and hence can be used for interchange; + * Can be produced or consumed, even for an arbitrarily long + sequentially presented input data stream, using only an a + priori bounded amount of intermediate storage, and hence + can be used in data communications or similar structures, + such as Unix filters; + * Compresses data with a compression ratio comparable to the + best currently available general-purpose compression methods, + and in particular, considerably better than the gzip program; + * Decompresses much faster than current LZMA implementations. +.fi + +The data format defined by this specification does not attempt to: + +.nf + * Allow random access to compressed data; + * Compress specialized data (e.g., raster graphics) as well + as the best currently available specialized algorithms. +.fi + +.ti 0 +1.2. Intended audience + +This specification is intended for use by software implementers +to compress data into and/or decompress data from the brotli format. + +The text of the specification assumes a basic background in +programming at the level of bits and other primitive data +representations. Familiarity with the technique of Huffman coding +is helpful but not required. + +This specification uses heavily the notations and terminology +introduced in the DEFLATE format specification [RFC 1951]. +For the sake of completeness, we always +include the whole text of the relevant parts of RFC 1951, +therefore familiarity with the DEFLATE format is helpful but not +required. + +The compressed data format defined in this specification is +an integral part of the WOFF 2.0 web font file format [WOFF2], +therefore this specification is also intended for implementers of +WOFF 2.0 compressors and decompressors. + +.ti 0 +1.3. Scope + +The specification specifies a method for representing a sequence +of bytes as a (usually shorter) sequence of bits, and a method for +packing the latter bit sequence into bytes. + +.ti 0 +1.4. Compliance + +Unless otherwise indicated below, a compliant decompressor must be +able to accept and decompress any data set that conforms to all +the specifications presented here. A compliant compressor must +produce data sets that conform to all the specifications presented +here. + +.ti 0 +1.5. Definitions of terms and conventions used + +Byte: 8 bits stored or transmitted as a unit (same as an octet). +For this specification, a byte is exactly 8 bits, even on machines +that store a character on a number of bits different from eight. +See below for the numbering of bits within a byte. + +String: a sequence of arbitrary bytes. + +Bytes stored within a computer do not have a "bit order", since +they are always treated as a unit. However, a byte considered as +an integer between 0 and 255 does have a most- and +least-significant bit, and since we write numbers with the +most-significant digit on the left, we also write bytes with the +most-significant bit on the left. In the diagrams below, we number +the bits of a byte so that bit 0 is the least-significant bit, i.e., +the bits are numbered: + +.nf + +--------+ + |76543210| + +--------+ +.fi + +Within a computer, a number may occupy multiple bytes. All +multi-byte numbers in the format described here are stored with +the least-significant byte first (at the lower memory address). +For example, the decimal number 520 is stored as: + +.nf + 0 1 + +--------+--------+ + |00001000|00000010| + +--------+--------+ + ^ ^ + | | + | + more significant byte = 2 x 256 + + less significant byte = 8 +.fi + +.ti 0 +1.5.1. Packing into bytes + +This document does not address the issue of the order in which +bits of a byte are transmitted on a bit-sequential medium, +since the final data format described here is byte- rather than +bit-oriented. However, we describe the compressed block format +below as a sequence of data elements of various bit +lengths, not a sequence of bytes. We must therefore specify +how to pack these data elements into bytes to form the final +compressed byte sequence: + +.nf + * Data elements are packed into bytes in order of + increasing bit number within the byte, i.e., starting + with the least-significant bit of the byte. + * Data elements other than prefix codes are packed + starting with the least-significant bit of the data + element. These are referred to here as integer values + and are considered unsigned. + * Prefix codes are packed starting with the most-significant + bit of the code. +.fi + +In other words, if one were to print out the compressed data as +a sequence of bytes, starting with the first byte at the +*right* margin and proceeding to the *left*, with the +most-significant bit of each byte on the left as usual, one would +be able to parse the result from right to left, with fixed-width +elements in the correct MSB-to-LSB order and prefix codes in +bit-reversed order (i.e., with the first bit of the code in the +relative LSB position). + +.ti 0 +2. Compressed representation overview + +A compressed data set consists of a header and a series of +meta-blocks. Each meta-block decompresses to a sequence of 0 +to 16,777,216 (16 MiB) uncompressed bytes. The final uncompressed data is +the concatenation of the uncompressed sequences from each meta-block. + +The header contains the size of the sliding window that was used during compression. +The decompressor must retain at least that amount of uncompressed data prior to the +current position in the stream, in order to be able to decompress +what follows. The sliding window size is a power of two, minus 16, where +the power is in the range of 10 to 24. The possible sliding window +sizes range from 1 KiB - 16 B to 16 MiB - 16 B. + +Each meta-block is compressed using a combination of the LZ77 +algorithm (Lempel-Ziv 1977, [LZ77]) and Huffman coding. The +result of Huffman coding is referred to here as a prefix code. +The prefix codes for each meta-block are independent of +those for previous or subsequent meta-blocks; the LZ77 algorithm may +use a reference to a duplicated string occurring in a previous +meta-block, up to the sliding window size of uncompressed bytes before. +In addition, in the brotli format, a string reference may instead refer +to a static dictionary entry. + +Each meta-block consists of two parts: a meta-block header that +describes the representation of the compressed data part, and a +compressed data part. The compressed data consists of a series of +commands. Each command consists of two parts: a sequence of literal +bytes (of strings that have not been detected as duplicated within +the sliding window), and a pointer to a duplicated string, +represented as a pair . There can be +zero literal bytes in the command. The minimum length of the string to be +duplicated is two, but the last command in the meta-block is permitted to have +only literals and no pointer to a string to duplicate. + +Each command in the compressed data is represented using three categories +of prefix codes: + +.nf + 1) One set of prefix codes are for the literal sequence lengths + (also referred to as literal insertion lengths) and + backward copy lengths. That is, a single code word represents + two lengths, one of the literal sequence and one of the + backward copy. + + 2) One set of prefix codes are for literals. + + 3) One set of prefix codes are for distances. +.fi + +The prefix code descriptions for each meta-block appear in a compact +form just before the compressed data in the meta-block header. +The insert-and-copy length and distance prefix codes may be followed by +extra bits that are added to the base values determined by the codes. +The number of extra bits is determined by the code. + +One meta-block command then appears as a sequence of prefix codes: + +.nf + Insert-and-copy length, literal, literal, ..., literal, distance +.fi + +where the insert-and-copy defines an insertion length and a copy length. +The insertion length determines the number of literals that immediately +follow. The distance defines how far back to go for the copy and the +copy length determines the number of bytes to copy. The resulting +uncompressed data is the sequence of bytes: + +.nf + literal, literal, ..., literal, copy, copy, ..., copy +.fi + +where the number of literal bytes and copy bytes are determined by the +insert-and-copy length code. (The number of bytes copied for a static +dictionary entry can vary from the copy length.) + +The last command in the meta-block may end with the last literal if the +total uncompressed length of the meta-block has been satisfied. In +that case there is no distance in the last command, and the copy length is +ignored. + +There can be more than one prefix code for each category, where the +prefix code to use for the next element of that category is determined +by the context of the compressed stream that precedes that element. +Part of that context is three current block types, one for each +category. A block type is in the range of 0..255. For each category +there is a count of how many elements of that category remain to be +decoded using the current block type. Once that count is expended, +a new block type and block count is read from the stream immediately +preceding the next element of that category, which will use the new +block type. + +The insert-and-copy block type directly determines which prefix code to +use for the next insert-and-copy element. For the literal and distance +elements, the respective block type is used in combination with other +context information to determine which prefix code to use for the next +element. + +Consider the following example: + +.nf + (IaC0, L0, L1, L2, D0)(IaC1, D1)(IaC2, L3, L4, D2)(IaC3, L5, D3) +.fi + +The meta-block here has four commands, contained in parentheses for clarity, +where each of the three categories of +symbols within these commands can be interpreted using different block types. +Here we separate out each category as its own sequence to show an example of block +types assigned to those elements. Each square-bracketed group is a block that +uses the same block type: + +.nf + [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 +.fi + +The subsequent blocks within each block category must have different +block types, but we see that block types can be reused later in the meta-block. +The block types are numbered from 0 to the maximum +block type number of 255 and the first block of each block category +is type 0. The block structure of a meta-block is represented +by the sequence of block-switch commands for each block category, +where a block-switch command is a pair . +The block-switch commands are represented in the compressed data +before the start of each new block using a prefix code for +block types and a separate prefix code for block counts for +each block category. For the above example the physical layout of the +meta-block is then: + +.nf + IaC0 L0 L1 LBlockSwitch(1, 3) L2 D0 IaC1 DBlockSwitch(1, 3) D1 + IaCBlockSwitch(1, 2) IaC2 L3 L4 D2 IaC3 LBlockSwitch(0, 1) L5 D3 +.fi + +where xBlockSwitch(t, n) switches to block type t for a count of n elements. +Note that in this example DBlockSwitch(1, 3) immediately precedes the +next required distance D1. It does not follow the last distance of +the previous block, D0. Whenever an element of a category is needed, +and the block count for that category has reached zero, then a new +block type and count is read from the stream just before reading that next +element. + +The block-switch commands for the first blocks of each category are not part +of the meta-block compressed data. Instead the first block type +is defined to be 0, and the first block count for each category is +encoded in the meta-block header. The prefix codes for the block types and counts, a total of +six prefix codes over the three categories, are defined in a compact form in the meta-block +header. + +Each category of value (insert-and-copy lengths, literals, and distances) +can be encoded with any prefix code from a collection of prefix +codes belonging to the same category appearing in the meta-block header. The +particular prefix code used can depend on two factors: the block +type of the block the value appears in, and the context of the value. +In the case of the literals, the context is the previous two bytes in +the uncompressed data, and in the case of distances, the context is the copy +length from the same command. For insert-and-copy lengths, no context +is used and the prefix code depends only on the block type. In the case +of literals and distances, the context is mapped to a context ID in +the range 0..63 for literals and 0..3 for distances. The matrix +of the prefix code indexes for each block type and context ID, +called the context map, is encoded in a compact form in the meta-block header. + +For example, the prefix code to use to decode L2 depends on the +block type (1), and the literal context ID determined by the two uncompressed +bytes that were decoded from L0 and L1. +Similarly, the prefix code to use to decode D0 depends on the block +type (0), and the distance context ID determined by the copy length decoded +from IaC0. The prefix code to use to decode IaC3 depends only on the block +type (1). + +In addition to the parts listed above (prefix code for insert-and-copy +lengths, literals, distances, block types and block counts, +and the context map), the meta-block header contains the number of +uncompressed bytes coded in the meta-block and two additional parameters used in +the representation of match distances: the number of postfix bits and +the number of direct distance codes. + +A compressed meta-block may be marked in the header as the last meta-block, +which terminates the compressed stream. + +A meta-block may instead simply store the uncompressed data directly as +bytes on byte boundaries with no coding or matching strings. In this +case the meta-block header information only contains the number of +uncompressed bytes and the indication that the meta-block is uncompressed. +An uncompressed meta-block cannot be the last meta-block. + +A meta-block may also be empty, which generates no uncompressed data at all. +An empty meta-block may contain metadata information as bytes starting on byte +boundaries, which are not part of either the sliding window or the uncompressed +data. Thus, these metadata bytes cannot be used to create matching strings in +subsequent meta-blocks and are not used as context bytes for literals. + +.ti 0 +3. Compressed representation of prefix codes + +.ti 0 +3.1. Introduction to prefix coding + +Prefix coding represents symbols from an a priori known alphabet +by bit sequences (codes), one code for each symbol, in a manner +such that different symbols may be represented by bit sequences of +different lengths, but a parser can always parse an encoded string +unambiguously symbol-by-symbol. + +We define a prefix code in terms of a binary tree in which the two +edges descending from each non-leaf node are labeled 0 and 1 and +in which the leaf nodes correspond one-for-one with (are labeled +with) the symbols of the alphabet; then the code for a symbol is +the sequence of 0's and 1's on the edges leading from the root to +the leaf labeled with that symbol. For example: + +.nf +.KS + /\\ Symbol Code + 0 1 ------ ---- + / \\ A 00 + /\\ B B 1 + 0 1 C 011 + / \\ D 010 + A /\\ + 0 1 + / \\ + D C +.KE +.fi + +A parser can decode the next symbol from the compressed stream +by walking down the tree from the root, at each step choosing the +edge corresponding to the next compressed data bit. + +Given an alphabet with known symbol frequencies, the Huffman +algorithm allows the construction of an optimal prefix code (one +which represents strings with those symbol frequencies using the +fewest bits of any possible prefix codes for that alphabet). Such +a prefix code is called a Huffman code. (See [HUFFMAN] in Chapter 5, +references for additional information on Huffman codes.) + +Note that in the brotli format, the prefix codes for the +various alphabets must not exceed certain maximum code lengths. +This constraint complicates the algorithm for computing code +lengths from symbol frequencies. Again, see Chapter 5, references +for details. + +.ti 0 +3.2. Use of prefix coding in the brotli format + +The prefix codes used for each alphabet in the brotli format +are canonical prefix codes, which have two additional rules: + +.nf + * All codes of a given bit length have lexicographically + consecutive values, in the same order as the symbols they + represent; + + * Shorter codes lexicographically precede longer codes. +.fi + +We could recode the example above to follow this rule as follows, +assuming that the order of the alphabet is ABCD: + +.nf +.KS + Symbol Code + ------ ---- + A 10 + B 0 + C 110 + D 111 +.KE +.fi + +I.e., 0 precedes 10, which precedes 11x, and 110 and 111 are +lexicographically consecutive. + +Given this rule, we can define the canonical prefix code for an +alphabet just by giving the bit lengths of the codes for each +symbol of the alphabet in order; this is sufficient to determine +the actual codes. In our example, the code is completely defined +by the sequence of bit lengths (2, 1, 3, 3). The following +algorithm generates the codes as integers, intended to be read +from most- to least-significant bit. The code lengths are +initially in tree[I].Len; the codes are produced in tree[I].Code. + +.nf + 1) Count the number of codes for each code length. Let + bl_count[N] be the number of codes of length N, N >= 1. + + 2) Find the numerical value of the smallest code for each + code length: + +.KS + code = 0; + bl_count[0] = 0; + for (bits = 1; bits <= MAX_BITS; bits++) { + code = (code + bl_count[bits-1]) << 1; + next_code[bits] = code; + } +.KE + + 3) Assign numerical values to all codes, using consecutive + values for all codes of the same length with the base + values determined at step 2. Codes that are never used + (which have a bit length of zero) must not be assigned a + value. + +.KS + for (n = 0; n <= max_code; n++) { + len = tree[n].Len; + if (len != 0) { + tree[n].Code = next_code[len]; + next_code[len]++; + } + } +.KE +.fi + +Example: + +Consider the alphabet ABCDEFGH, with bit lengths (3, 3, 3, 3, 3, +2, 4, 4). After step 1, we have: + +.nf +.KS + N bl_count[N] + - ----------- + 2 1 + 3 5 + 4 2 +.KE +.fi + +Step 2 computes the following next_code values: + +.nf +.KS + N next_code[N] + - ------------ + 1 0 + 2 0 + 3 2 + 4 14 +.KE +.fi + +Step 3 produces the following code values: + +.nf +.KS + Symbol Length Code + ------ ------ ---- + A 3 010 + B 3 011 + C 3 100 + D 3 101 + E 3 110 + F 2 00 + G 4 1110 + H 4 1111 +.KE +.fi + +.ti 0 +3.3. Alphabet sizes + +Prefix codes are used for different purposes in the brotli +format, and each purpose has a different alphabet size. For +literal codes the alphabet size is 256. For insert-and-copy +length codes the alphabet size is 704. For block count codes, +the alphabet size is 26. For distance codes, block type codes, and +the prefix codes used in compressing the context map, the +alphabet size is dynamic and is based on parameters defined in +later sections. The following table summarizes the alphabet sizes +for the various prefix codes and the sections where they are defined. + +.nf +.KS + +-----------------+-------------------------+------------+ + | Prefix code | Alphabet size | Definition | + +-----------------+-------------------------+------------+ + | literal | 256 | | + +-----------------+-------------------------+------------+ + | distance | 16 + NDIRECT + | Section 4. | + | | (48 << NPOSTFIX) | | + +-----------------+-------------------------+------------+ + | insert-and-copy | 704 | Section 5. | + | length | | | + +-----------------+-------------------------+------------+ + | block count | 26 | Section 6. | + +-----------------+-------------------------+------------+ + | block type | NBLTYPESx + 2, | Section 6. | + | | (where x is I, L, or D) | | + +-----------------+-------------------------+------------+ + | context map | NTREESx + RLEMAXx | Section 7. | + | | (where x is L or D) | | + +-----------------+-------------------------+------------+ +.KE +.fi + +.ti 0 +3.4. Simple prefix codes + +The first two bits of the compressed representation of each +prefix code distinguish between simple and complex prefix +codes. If this value is 1, then a simple prefix code follows +as described in this section. Otherwise, a complex prefix code +follows as described in Section 3.5. + +A simple prefix code can have only up to four symbols with +non-zero code length. The format of the simple prefix code is as +follows: + +.nf + 2 bits: value of 1 indicates a simple prefix code + 2 bits: NSYM - 1, where NSYM = # of symbols coded + + NSYM symbols, each encoded using ALPHABET_BITS bits + + 1 bit: tree-select, present only for NSYM = 4 +.fi + +The value of ALPHABET_BITS depends on the alphabet of the prefix +code: it is the smallest number of bits that can represent all +symbols in the alphabet. E.g. for the alphabet of literal bytes, +ALPHABET_BITS is 8. The value of each of the NSYM symbols above is +the value of the ALPHABETS_BITS width integer value. If the integer +value is greater than or equal to the alphabet size, or the value +is identical to a previous value, then the stream should be rejected +as invalid. + +Note that the NSYM symbols may not be presented in sorted order. Prefix codes +of the same bit length must be assigned to the symbols in sorted order. + +The (non-zero) code lengths of the symbols can be reconstructed as +follows: + +.nf + * if NSYM = 1, the code length for the one symbol is zero -- + when encoding this symbol in the + compressed data stream using this prefix code, no + actual bits are emitted. Similarly, when decoding a symbol + using this prefix code, no bits are read and the one symbol + is returned. + + * if NSYM = 2, both symbols have code length 1. + + * if NSYM = 3, the code lengths for the symbols are 1, 2, 2 in + the order they appear in the representation of the simple + prefix code. + + * if NSYM = 4, the code lengths (in order of symbols decoded) + depend on the tree-select bit: 2, 2, 2, 2 (tree-select bit 0), + or 1, 2, 3, 3 (tree-select bit 1). +.fi + +.ti 0 +3.5. Complex prefix codes + +A complex prefix code is a canonical prefix code, defined by the +sequence of code lengths, as discussed in Section 3.2., above. +For even greater compactness, the code length sequences themselves +are compressed using a prefix code. The alphabet for code lengths +is as follows: + +.nf + 0 - 15: Represent code lengths of 0 - 15 + 16: Copy the previous non-zero code length 3 - 6 times + The next 2 bits indicate repeat length + (0 = 3, ... , 3 = 6) + If this is the first code length, or all previous + code lengths are zero, a code length of 8 is + repeated 3 - 6 times + A repeated code length code of 16 modifies the + repeat count of the previous one as follows: + repeat count = (4 * (repeat count - 2)) + + (3 - 6 on the next 2 bits) + Example: Codes 7, 16 (+2 bits 11), 16 (+2 bits 10) + will expand to 22 code lengths of 7 + (1 + 4 * (6 - 2) + 5) + 17: Repeat a code length of 0 for 3 - 10 times. + (3 bits of length) + A repeated code length code of 17 modifies the + repeat count of the previous one as follows: + repeat count = (8 * (repeat count - 2)) + + (3 - 10 on the next 3 bits) +.fi + +Note that a code of 16 that follows an immediately preceding 16 modifies the +previous repeat count, which becomes the new repeat count. The same is true for +a 17 following a 17. A sequence of three or more 16 codes in a row or three of +more 17 codes in a row is possible, modifying the count each time. Only the +final repeat count is used. The modification only applies if the same code +follows. A 16 repeat does not modify an immediately preceding 17 count nor +vice versa. + +A code length of 0 indicates that the corresponding symbol in the +alphabet will not occur in the compressed data, and should not +participate in the prefix code construction algorithm given +earlier. A complex prefix code must have at least two non-zero +code lengths. + +The bit lengths of the prefix code over the code length alphabet +are compressed with the following variable length code (as it appears +in the compressed data, where the bits are parsed from right to left): + +.nf +.KS + Symbol Code + ------ ---- + 0 00 + 1 0111 + 2 011 + 3 10 + 4 01 + 5 1111 +.KE +.fi + +We can now define the format of the complex prefix code as follows: + +.nf + 2 bits: HSKIP, values of 0, 2, or 3 represent the respective + number of skipped code lengths. The skipped lengths + are taken to be zero. (An HSKIP of 1 indicates a + Simple prefix code.) + + Code lengths for symbols in the code length alphabet given + just above, in the order: 1, 2, 3, 4, 0, 5, 17, 6, 16, 7, + 8, 9, 10, 11, 12, 13, 14, 15. If HSKIP is 2, then the + code lengths for symbols 1 and 2 are zero, and the first + code length is for symbol 3. If HSKIP is 3, then the code + length for symbol 3 is also zero, and the first code length + is for symbol 4. + + The code lengths of code length symbols are between 0 and + 5, and they are represented with 2 - 4 bits according to + the variable length code above. A code length of 0 means + the corresponding code length symbol is not used. + + If HSKIP is 2 or 3, a respective number of leading code + lengths are implicit zeros and are not present in the + code lengths sequence above. + + If there are at least two non-zero code lengths, any + trailing zero code lengths are omitted, i.e. the last + code length in the sequence must be non-zero. In this + case, the sum of (32 >> code length) over all the non-zero + code lengths must equal to 32. + + If the lengths have been read for the entire code length + alphabet and there was only one non-zero code length, + then the prefix code has one symbol whose code has zero + length. In this case, that symbol results in no bits + being emitted by the compressor, and no bits consumed by + the decompressor. That single symbol is immediately + returned when this code is decoded. + An example of where this occurs is if the + entire code to be represented has symbols of length 8. + E.g. a literal code that represents all literal values + with equal probability. In this case the single symbol + is 16, which repeats the previous length. The previous + length is taken to be 8 before any code length code + lengths are read. + + Sequence of at most alphabet size code lengths symbols, encoded + using the code length prefix code. Any trailing 0 or 17 must be + omitted, i.e. the last encoded code length symbol must be + between 1 and 16. The sum of (32768 >> code length) over + all the non-zero code lengths in the alphabet, including + those encoded using repeat code(s) of 16, must equal to + 32768. If the number of times to repeat the previous length + or repeat a zero length would result in more lengths in + total than the number of symbols in the alphabet, then the + stream should be rejected as invalid. +.fi + +.ti 0 +4. Encoding of distances + +As described in Section 2., one component of a compressed meta-block +is a sequence of backward distances. In this section we provide the +details to the encoding of distances. + +Each distance in the compressed data part of a meta-block is +represented with a pair . The distance +code and the extra bits are encoded back-to-back, the distance code +is encoded using a prefix code over the distance alphabet, +while the extra bits value is encoded as a fixed-width integer +value. The number of extra bits can be 0 - 24, and it is dependent +on the distance code. + +To convert a distance code and associated extra bits to a backward +distance, we need the sequence of past distances and two additional +parameters, the number of "postfix bits", denoted by NPOSTFIX (0..3), and +the number of direct distance codes, denoted by NDIRECT (0..120). Both of +these parameters are encoded in the meta-block header. We will also +use the following derived parameter: + +.nf + POSTFIX_MASK = (1 << NPOSTFIX) - 1 +.fi + +The first 16 distance symbols are special symbols that reference +past distances as follows: + +.nf + 0: last distance + 1: second-to-last distance + 2: third-to-last distance + 3: fourth-to-last distance + 4: last distance - 1 + 5: last distance + 1 + 6: last distance - 2 + 7: last distance + 2 + 8: last distance - 3 + 9: last distance + 3 + 10: second-to-last distance - 1 + 11: second-to-last distance + 1 + 12: second-to-last distance - 2 + 13: second-to-last distance + 2 + 14: second-to-last distance - 3 + 15: second-to-last distance + 3 +.fi + +The ring buffer of four last distances is initialized by the values +16, 15, 11, and 4 (i.e. the fourth-to-last is set to 16, the third-to-last +to 15, the second-to-last to 11, and the last distance to 4) at the +beginning of the *stream* (as opposed to the beginning of the meta-block) +and it is not reset at meta-block boundaries. When a distance +symbol 0 appears, the distance it represents (i.e. the last distance +in the sequence of distances) is not pushed to the ring buffer of +last distances, in other words, the expression "(second, third, +fourth)-to-last distance" means the (second, third, fourth)-to-last +distance that was not represented by a 0 distance symbol. Similarly, +distances that represent static dictionary words (see Section 8.) are +not pushed to the ring buffer of last distances. + +If a special distance symbol resolves to a zero or negative value, the +stream should be rejected as invalid. + +If NDIRECT is greater than zero, then the next NDIRECT distance symbols, +from 16 to 15 + NDIRECT, represent distances from 1 to NDIRECT. +Neither the special distance symbols, nor the NDIRECT direct distance +symbols are followed by any extra bits. + +Distance symbols 16 + NDIRECT and greater all have extra bits, where the +number of extra bits for a distance symbol "dcode" is given by the +following formula: + +.nf + ndistbits = 1 + ((dcode - NDIRECT - 16) >> (NPOSTFIX + 1)) +.fi + +The maximum number of extra bits is 24, therefore the size of the +distance symbol alphabet is (16 + NDIRECT + (48 << NPOSTFIX)). + +Given a distance symbol "dcode" (>= 16 + NDIRECT), and extra bits +"dextra", the backward distance is given by the following formula: + +.nf + hcode = (dcode - NDIRECT - 16) >> NPOSTFIX + lcode = (dcode - NDIRECT - 16) & POSTFIX_MASK + offset = ((2 + (hcode & 1)) << ndistbits) - 4 + distance = ((offset + dextra) << NPOSTFIX) + lcode + NDIRECT + 1 +.fi + +.ti 0 +5. Encoding of literal insertion lengths and copy lengths + +As described in Section 2., the literal insertion lengths and backward +copy lengths are encoded using a single prefix code. This section +provides the details to this encoding. + +Each pair in the compressed data part +of a meta-block is represented with the following triplet: + +.nf + +.fi + +The insert-and-copy length code, the insert extra bits, and the copy +extra bits are encoded back-to-back, the insert-and-copy length code +is encoded using a prefix code over the insert-and-copy length code +alphabet, while the extra bits values are encoded as fixed-width +integer values. The number of insert and copy extra bits can be +0 - 24, and they are dependent on the insert-and-copy length code. + +Some of the insert-and-copy length codes also express the fact that +the distance symbol of the distance in the same command is 0, i.e. the +distance component of the command is the same as that of the previous +command. In this case, the distance code and extra bits for the +distance are omitted from the compressed data stream. + +We describe the insert-and-copy length code alphabet in terms of the +(not directly used) insert length code and copy length code +alphabets. The symbols of the insert length code alphabet, along with +the number of insert extra bits, and the range of the insert lengths +are as follows: + +.nf +.KS + Extra Extra Extra + Code Bits Lengths Code Bits Lengths Code Bits Lengths + ---- ---- ------ ---- ---- ------- ---- ---- ------- + 0 0 0 8 2 10-13 16 6 130-193 + 1 0 1 9 2 14-17 17 7 194-321 + 2 0 2 10 3 18-25 18 8 322-577 + 3 0 3 11 3 26-33 19 9 578-1089 + 4 0 4 12 4 34-49 20 10 1090-2113 + 5 0 5 13 4 50-65 21 12 2114-6209 + 6 1 6,7 14 5 66-97 22 14 6210-22593 + 7 1 8,9 15 5 98-129 23 24 22594-16799809 +.KE +.fi + +The symbols of the copy length code alphabet, along with the number +of copy extra bits, and the range of copy lengths are as follows: + +.nf +.KS + Extra Extra Extra + Code Bits Lengths Code Bits Lengths Code Bits Lengths + ---- ---- ------ ---- ---- ------- ---- ---- ------- + 0 0 2 8 1 10,11 16 5 70-101 + 1 0 3 9 1 12,13 17 5 102-133 + 2 0 4 10 2 14-17 18 6 134-197 + 3 0 5 11 2 18-21 19 7 198-325 + 4 0 6 12 3 22-29 20 8 326-581 + 5 0 7 13 3 30-37 21 9 582-1093 + 6 0 8 14 4 38-53 22 10 1094-2117 + 7 0 9 15 4 54-69 23 24 2118-16779333 +.KE +.fi + +To convert an insert-and-copy length code to an insert length code +and a copy length code, the following table can be used: + +.nf +.KS + Insert + length Copy length code + code 0-7 8-15 16-23 + +---------+---------+ + | | | + 0-7 | 0-63 | 64-127 | <--- distance symbol 0 + | | | + +---------+---------+---------+ + | | | | + 0-7 | 128-191 | 192-255 | 384-447 | + | | | | + +---------+---------+---------+ + | | | | + 8-15 | 256-319 | 320-383 | 512-575 | + | | | | + +---------+---------+---------+ + | | | | + 16-23 | 448-511 | 576-639 | 640-703 | + | | | | + +---------+---------+---------+ +.KE +.fi + +First, look up the cell with the 64 value range containing the +insert-and-copy length code, this gives the insert length code and +the copy length code ranges, both 8 values long. +The copy length code within its range is determined by bits 0-2 +(counted from the LSB) of the insert-and-copy length code. +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 +. These are encoded in the compressed data +part of the meta-block, right before the start of each new block of a +particular block category. + +Each block type in the compressed data is represented with a block +type code, encoded using a prefix code over the block type code +alphabet. A block type symbol 0 means that the new block type is the same +as the type of the previous block from the same block category, i.e. +the block type that preceded the current type, +while a block type symbol 1 means that the new block type equals the current +block type plus one. If the current block type is the maximal possible, +then a block type symbol of 1 results in wrapping to a new block type of 0. +Block type symbols 2 - 257 +represent block types 0 - 255 respectively. The previous and current block types +are initialized to 1 and 0, respectively, at the end of the +meta-block header. + +Since the first block type of each block category is 0, the block +type of the first block-switch command is not encoded in +the compressed data. If a block category has only one block type, +the block count of the first block-switch command is also omitted from +the compressed data, otherwise it is encoded in the meta-block header. + +Since the end of the meta-block is detected by the number of uncompressed +bytes produced, the block counts for any of the three categories need not +count down to exactly zero at the end of the meta-block. + +The number of different block types in each block category, denoted +by NBLTYPESL, NBLTYPESI, and NBLTYPESD for literals, insert-and-copy +lengths, and distances, respectively, is encoded in the meta-block +header, and it must equal to the largest block type plus one in that +block category. In other words, the set of literal, insert-and-copy +length, and distance block types must be [0..NBLTYPESL-1], +[0..NBLTYPESI-1], and [0..NBLTYPESD-1], respectively. From this it +follows that the alphabet size of literal, insert-and-copy length, and +distance block type codes is NBLTYPESL + 2, NBLTYPESI + 2, and +NBLTYPESD + 2, respectively. + +Each block count in the compressed data is represented with a pair +. The block count code and the extra +bits are encoded back-to-back, the block count code is encoded using +a prefix code over the block count code alphabet, while the extra +bits value is encoded as a fixed-width integer value. The number of +extra bits can be 0 - 24, and it is dependent on the block count +code. The symbols of the block count code alphabet, along with the +number of extra bits, and the range of block counts are as follows: + +.nf +.KS + Extra Extra Extra + Code Bits Lengths Code Bits Lengths Code Bits Lengths + ---- ---- ------ ---- ---- ------- ---- ---- ------- + 0 2 1-4 9 4 65-80 18 7 369-496 + 1 2 5-8 10 4 81-96 19 8 497-752 + 2 2 9-12 11 4 97-112 20 9 753-1264 + 3 2 13-16 12 5 113-144 21 10 1265-2288 + 4 3 17-24 13 5 145-176 22 11 2289-4336 + 5 3 25-32 14 5 177-208 23 12 4337-8432 + 6 3 33-40 15 5 209-240 24 13 8433-16624 + 7 3 41-48 16 6 241-304 25 24 16625-16793840 + 8 4 49-64 17 6 305-368 +.KE +.fi + +The first block-switch command of each block category is special in +the sense that it is encoded in the meta-block header, and as +described earlier, the block type code is omitted since it is an +implicit zero. + +.ti 0 +7. Context modeling + +As described in Section 2., the prefix tree used to encode a literal +byte or a distance code depends on the block type and the context ID. +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 pair to the index of a prefix +code in the array of literal and distance prefix codes. + +.ti 0 +7.1. Context modes and context ID lookup for literals + +The context for encoding the next literal is defined by the last +two bytes in the stream (p1, p2, where p1 is the most recent +byte), regardless of whether these bytes are produced by +uncompressed meta-blocks, backward references, static dictionary +references, or by literal insertions. At the start of the stream +p1 and p2 are initialized to zero. + +There are four methods, called context modes, to compute the +Context ID: + +.nf + * LSB6, where the Context ID is the value of six + least-significant bits of p1, + * MSB6, where the Context ID is the value of six + most-significant bits of p1, + * UTF8, where the Context ID is a complex function of p1, p2, + optimized for text compression, and + * Signed, where Context ID is a complex function of p1, p2, + optimized for compressing sequences of signed integers. +.fi + +The Context ID for the UTF8 and Signed context modes is computed +using the following lookup tables Lut0, Lut1, and Lut2. + +.nf + Lut0 := + 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 8, 12, 16, 12, 12, 20, 12, 16, 24, 28, 12, 12, 32, 12, 36, 12, + 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 32, 32, 24, 40, 28, 12, + 12, 48, 52, 52, 52, 48, 52, 52, 52, 48, 52, 52, 52, 52, 52, 48, + 52, 52, 52, 52, 52, 48, 52, 52, 52, 52, 52, 24, 12, 28, 12, 12, + 12, 56, 60, 60, 60, 56, 60, 60, 60, 56, 60, 60, 60, 60, 60, 56, + 60, 60, 60, 60, 60, 56, 60, 60, 60, 60, 60, 24, 12, 28, 12, 0, + 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, + 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, + 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, + 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, + 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, + 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, + 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, + 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 + + Lut1 := + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, + 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, + 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, + 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 + + Lut2 := + 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, + 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, + 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, + 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, + 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, + 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, + 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, + 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, + 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, + 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, + 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, + 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7 +.fi + +The lengths and the zlib CRC-32 (ITU-T Recommendation V.42) check values +of each of these tables as a sequence of bytes are as follows: + +.nf + Table Length CRC-32 + ----- ------ ------ + Lut0 256 0x8e91efb7 + Lut1 256 0xd01a32f4 + Lut2 256 0x0dd7a0d6 +.fi + +Given p1 is the last uncompressed byte and p2 is the second-to-last +uncompressed byte, the context IDs can be computed as follows: + +.nf + For LSB6: Context ID = p1 & 0x3f + For MSB6: Context ID = p1 >> 2 + For UTF8: Context ID = Lut0[p1] | Lut1[p2] + For Signed: Context ID = (Lut2[p1] << 3) | Lut2[p2] +.fi + +From the lookup tables defined above and the operations to compute the +context IDs, we can see that context IDs for literals are in the range +of 0..63. + +The context modes LSB6, MSB6, UTF8, and Signed are denoted by +integers 0, 1, 2, 3. + +A context mode is defined for each literal block type and they +are stored in a consecutive array of bits in the meta-block +header, always two bits per block type. + +.ti 0 +7.2. Context ID for distances + +The context for encoding a distance code is defined by the copy +length corresponding to the distance. The context IDs are 0, 1, 2, +and 3 for copy lengths 2, 3, 4, and more than 4, respectively. + +.ti 0 +7.3. Encoding of the context map + +There are two context maps, one for literals and one for +distances. The size of the context map is 64 * NBLTYPESL for +literals, and 4 * NBLTYPESD for distances. Each value in the +context map is an integer between 0 and 255, indicating the index +of the prefix code to be used when encoding the next literal or +distance. + +The context maps are two-dimensional matrices, encoded as +one-dimensional arrays: + +.nf + CMAPL[0..(64 * NBLTYPESL - 1)] + CMAPD[0..(4 * NBLTYPESD - 1)] +.fi + +The index of the prefix code for encoding a literal or distance +code with block type, BTYPE_x, and context ID, CIDx, is: + +.nf + index of literal prefix code = CMAPL[64 * BTYPE_L + CIDL] + index of distance prefix code = CMAPD[4 * BTYPE_D + CIDD] +.fi + +The values of the context map are encoded with the combination +of run length encoding for zero values and prefix coding. Let +RLEMAX denote the number of run length codes and NTREES denote the +maximum value in the context map plus one. NTREES must equal the +number of different values in the context map, in other words, +the different values in the context map must be the [0..NTREES-1] +interval. The alphabet of the prefix code has the following +RLEMAX + NTREES symbols: + +.nf + 0: value zero + 1: repeat a zero 2 to 3 times, read 1 bit for repeat length + 2: repeat a zero 4 to 7 times, read 2 bits for repeat length + ... + RLEMAX: repeat a zero (1 << RLEMAX) to (1 << (RLEMAX+1))-1 + times, read RLEMAX bits for repeat length + RLEMAX + 1: value 1 + ... + RLEMAX + NTREES - 1: value NTREES - 1 +.fi + +If RLEMAX = 0, the run length coding is not used, and the symbols +of the alphabet are directly the values in the context map. We can +now define the format of the context map (the same format is used +for literal and distance context maps): + +.nf + 1-5 bits: RLEMAX, 0 is encoded with one 0 bit, and values + 1 - 16 are encoded with bit pattern xxxx1 (so 01001 + is 5) + + Prefix code with alphabet size NTREES + RLEMAX + + Context map size values encoded with the above prefix code + and run length coding for zero values. If a run length + would result in more lengths in total than the size of + the context map, then the stream should be rejected as + invalid. + + 1 bit: IMTF bit, if set, we do an inverse move-to-front + transform on the values in the context map to get + the prefix code indexes +.fi + +Note that RLEMAX may be larger than the value necessary to represent +the longest sequence of zero values. Also, the NTREES value is encoded +right before the context map as described in 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 + +Note that the inverse move-to-front transform will not produce values +outside the [0..NTREES-1] interval. + +.ti 0 +8. Static dictionary + +At any given point during decoding the compressed data, a reference +to a duplicated string in the uncompressed data produced so far has a maximum +backward distance value, which is the minimum of the window size and +the number of uncompressed bytes produced. However, decoding a distance +from the compressed stream, as described in Section 4., can produce +distances that are greater than this maximum allowed value. In this case, +the distance is treated as a reference to a word in the static dictionary +given in Appendix A. The copy length for a static dictionary reference +must be between 4 and 24. The static dictionary has three parts: + +.nf + * DICT[0..DICTSIZE], an array of bytes + * DOFFSET[0..24], an array of byte offset values for each length + * NDBITS[0..24], an array of bit-depth values for each length +.fi + +The number of static dictionary words for a given length is: + +.nf + NWORDS[length] = 0 (if length < 4) + NWORDS[length] = (1 << NDBITS[length]) (if length >= 4) +.fi + +DOFFSET and DICTSIZE are defined by the following recursion: + +.nf + DOFFSET[0] = 0 + DOFFSET[length + 1] = DOFFSET[length] + length * NWORDS[length] + DICTSIZE = DOFFSET[24] + 24 * NWORDS[24] +.fi + +The offset of a word within the DICT array for a given length and +index is: + +.nf + offset(length, index) = DOFFSET[length] + index * length +.fi + +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 pair can be reconstructed as +follows: + +.nf + word_id = distance - (max allowed distance + 1) + index = word_id % NWORDS[length] + base_word = DICT[offset(length, index)..offset(length, index+1)-1] + transform_id = word_id >> NDBITS[length] +.fi + +The string copied to the uncompressed stream is computed by applying the +transformation to the base dictionary word. If transform_id is +greater than 120, or the length is smaller than 4 or greater than 24, then +the compressed stream should be rejected as invalid. + +Each word transformation has the following form: + +.nf + transform_i(word) = prefix_i + T_i(word) + suffix_i +.fi + +where the _i subscript denotes the transform_id above. Each T_i +is one of the following 21 elementary transforms: + +.nf + Identity, UppercaseFirst, UppercaseAll, + OmitFirst1, ..., OmitFirst9, OmitLast1, ..., OmitLast9 +.fi + +The form of these elementary transforms is as follows: + +.nf + Identity(word) = word + + UppercaseFirst(word) = first UTF-8 character of word upper-cased + + UppercaseAll(word) = all UTF-8 characters of word upper-cased + + OmitFirstk(word) = the last (length(word) - k) bytes of word, or + empty string if length(word) < k + + OmitLastk(word) = the first (length(word) - k) bytes of word, or + empty string if length(word) < k +.fi + +For the purposes of UppercaseAll, word is parsed into UTF-8 +characters and converted to upper-case by taking 1 - 3 bytes at a time, +using the algorithm below: + +.nf +.KS + i = 0 + while i < length(word): + if word[i] < 192: + if word[i] >= 97 and word[i] <= 122: + word[i] = word[i] ^ 32 + i = i + 1 + else if word[i] < 224: + if i + 1 < length(word): + word[i + 1] = word[i + 1] ^ 32 + i = i + 2 + else: + if i + 2 < length(word): + word[i + 2] = word[i + 2] ^ 5 + i = i + 3 +.KE +.fi + +For UppercaseFirst, the same algorithm is used, but the loop is +executed only once. + +Appendix B. contains the list of transformations by specifying the +prefix, elementary transform and suffix components of each of them. +Note that the OmitFirst8 elementary transform is not used in the list +of transformations. The strings in Appendix B. are in C string format +with respect to escape (backslash) characters. + +The maximum number of additional bytes that a transform may add to a +base word is 13. Since the largest base word is 24 bytes long, a buffer +of 38 bytes is sufficient to store any transformed words +(counting a terminating zero byte). + +.ti 0 +9. Compressed data format + +In this section we describe the format of the compressed data set in +terms of the format of the individual data items described in the +previous sections. + +.ti 0 +9.1. Format of the stream header + +The stream header has only the following one field: + +.nf + 1-7 bits: WBITS, a value in the range 10 - 24, encoded with + the following variable length code (as it appears in + the compressed data, where the bits are parsed from + right to left): + + Value Bit Pattern + ----- ----------- + 10 0100001 + 11 0110001 + 12 1000001 + 13 1010001 + 14 1100001 + 15 1110001 + 16 0 + 17 0000001 + 18 0011 + 19 0101 + 20 0111 + 21 1001 + 22 1011 + 23 1101 + 24 1111 + + Note that bit pattern 0010001 is invalid and must not + be used. +.fi + +The size of the sliding window, which is the maximum value of any +non-dictionary reference backward distance, is given by the +following formula: + +.nf + window size = (1 << WBITS) - 16 +.fi + +.ti 0 +9.2. Format of the meta-block header + +A compliant compressed data set has at least one meta-block. Each +meta-block contains a header with information about the +uncompressed length of the meta-block, and a bit signaling if the +meta-block is the last one. The format of the meta-block header is +the following: + +.nf + 1 bit: ISLAST, set to 1 if this is the last meta-block + 1 bit: ISLASTEMPTY, if set to 1, the meta-block is empty; + this field is only present if ISLAST bit is set -- if + it is 1, then the meta-block and the brotli stream ends + at that bit, with any remaining bits in the last byte + of the compressed stream filled with zeros (if the + fill bits are not zero, then the stream should be + rejected as invalid) + 2 bits: MNIBBLES, # of nibbles to represent the uncompressed + length, encoded with the following fixed-length code: + + Value Bit Pattern + ----- ----------- + 0 11 + 4 00 + 5 01 + 6 10 + + If MNIBBLES is 0, the meta-block is empty, i.e. it does + not generate any uncompressed data. In this case, the + rest of the meta-block has the following format: + + 1 bit: reserved, must be zero + + 2 bits: MSKIPBYTES, # of bytes to represent metadata + length + + MSKIPBYTES x 8 bits: MSKIPLEN - 1, where MSKIPLEN is + the number of metadata bytes; this field is + only present if MSKIPBYTES is positive, + otherwise MSKIPLEN is 0 (if MSKIPBYTES is + greater than 1, and the last byte is all + zeros, then the stream should be rejected + as invalid) + + 0 - 7 bits: fill bits until the next byte boundary, + must be all zeros + + MSKIPLEN bytes of metadata, not part of the + uncompressed data or the sliding window + + MNIBBLES x 4 bits: MLEN - 1, where MLEN is the length + of the meta-block uncompressed data in bytes (if + MNIBBLES is greater than 4, and the last + nibble is all zeros, then the stream should be + rejected as invalid) + + 1 bit: ISUNCOMPRESSED, if set to 1, any bits of compressed + data up to the next byte boundary are ignored, and + the rest of the meta-block contains MLEN bytes of + literal data; this field is only present if the + ISLAST bit is not set (if the ignored bits are not + all zeros, the stream should be rejected as invalid) + + 1-11 bits: NBLTYPESL, # of literal block types, encoded with + the following variable length code (as it appears in + the compressed data, where the bits are parsed from + right to left, so 0110111 has the value 12): + + Value Bit Pattern + ----- ----------- + 1 0 + 2 0001 + 3-4 x0011 + 5-8 xx0101 + 9-16 xxx0111 + 17-32 xxxx1001 + 33-64 xxxxx1011 + 65-128 xxxxxx1101 + 129-256 xxxxxxx1111 + + Prefix code over the block type code alphabet for + literal block types, appears only if NBLTYPESL >= 2 + + Prefix code over the block count code alphabet for + literal block counts, appears only if NBLTYPESL >= 2 + + Block count code + extra bits for first literal + block count, appears only if NBLTYPESL >= 2 + + 1-11 bits: NBLTYPESI, # of insert-and-copy block types, encoded + with the same variable length code as above + + Prefix code over the block type code alphabet for + insert-and-copy block types, appears only if NBLTYPESI >= 2 + + Prefix code over the block count code alphabet for + insert-and-copy block counts, appears only if NBLTYPESI >= 2 + + Block count code + extra bits for first insert-and-copy + block count, appears only if NBLTYPESI >= 2 + + 1-11 bits: NBLTYPESD, # of distance block types, encoded + with the same variable length code as above + + Prefix code over the block type code alphabet for + distance block types, appears only if NBLTYPESD >= 2 + + Prefix code over the block count code alphabet for + distance block counts, appears only if NBLTYPESD >= 2 + + Block count code + extra bits for first distance + block count, appears only if NBLTYPESD >= 2 + + 2 bits: NPOSTFIX, parameter used in the distance coding + + 4 bits: four most-significant bits of NDIRECT, to get the + actual value of the parameter NDIRECT, left-shift + this four-bit number by NPOSTFIX bits + + NBLTYPESL x 2 bits: context mode for each literal block type + + 1-11 bits: NTREESL, # of literal prefix trees, encoded + with the same variable length code as NBLTYPESL + + Literal context map, encoded as described in Section 7.3., + appears only if NTREESL >= 2, otherwise the context map + has only zero values + + 1-11 bits: NTREESD, # of distance prefix trees, encoded + with the same variable length code as NBLTYPESD + + Distance context map, encoded as described in Section 7.3., + appears only if NTREESD >= 2, otherwise the context map + has only zero values + + NTREESL prefix codes for literals + + NBLTYPESI prefix codes for insert-and-copy lengths + + NTREESD prefix codes for distances +.fi + +.ti 0 +9.3. Format of the meta-block data + +The compressed data part of a meta-block consists of a series of +commands. Each command has the following format: + +.nf + Block type code for next insert-and-copy block type, appears + only if NBLTYPESI >= 2 and the previous insert-and-copy + block count is zero + + Block count code + extra bits for next insert-and-copy + block count, appears only if NBLTYPESI >= 2 and the + previous insert-and-copy block count is zero + + Insert-and-copy length, encoded as in Section 5., using the + insert-and-copy length prefix code with the current + insert-and-copy block type index + + Insert length number of literals, with the following format: + + Block type code for next literal block type, appears + only if NBLTYPESL >= 2 and the previous literal + block count is zero + + Block count code + extra bits for next literal + block count, appears only if NBLTYPESL >= 2 and the + previous literal block count is zero + + Next byte of the uncompressed data, encoded with the + literal prefix code with the index determined by the + previous two bytes of the uncompressed data, the + current literal block type, and the context map, as + described in Section 7.3. + + Block type code for next distance block type, appears + only if NBLTYPESD >= 2 and the previous distance + block count is zero + + Block count code + extra bits for next distance + block count, appears only if NBLTYPESD >= 2 and the + previous distance block count is zero + + Distance code, encoded as in Section 4., using the distance + prefix code with the current distance block type index, + appears only if the distance code is not an implicit 0, + as indicated by the insert-and-copy length code +.fi + +The number of commands in the meta-block is such that the sum of +the uncompressed bytes produced (i.e. the number of literals inserted +plus the number of bytes copied from past data or generated from the +static dictionary) over all the commands gives the uncompressed length, +MLEN encoded in the meta-block header. + +If the total number of uncompressed bytes produced after the insert part +of the last command equals MLEN, then the copy length of the last command +is ignored and will not produce any uncompressed output. In this case the +copy length of the last command can have any value. In any other case, if +the number of literals to insert, the copy length, or the resulting +dictionary word length would cause MLEN to be exceeded, then the stream +should be rejected as invalid. + +If the last command of the last non-empty meta-block does not end on +a byte boundary, the unused bits in the last byte must be zeros. + +.ti 0 +10. Decoding algorithm + +The decoding algorithm that produces the uncompressed data is as follows: + +.nf + read window size + do + read ISLAST bit + if ISLAST + read ISLASTEMPTY bit + if ISLASTEMPTY + break from loop + read MNIBBLES + if MNIBBLES is zero + verify reserved bit is zero + read MSKIPLEN + skip any bits up to the next byte boundary + skip MSKIPLEN bytes + continue to the next meta-block + else + read MLEN + if not ISLAST + read ISUNCOMPRESSED bit + if ISUNCOMPRESSED + skip any bits up to the next byte boundary + copy MLEN bytes of compressed data as literals + continue to the next meta-block + loop for each three block categories (i = L, I, D) + read NBLTYPESi + if NBLTYPESi >= 2 + read prefix code for block types, HTREE_BTYPE_i + read prefix code for block counts, HTREE_BLEN_i + read block count, BLEN_i + set block type, BTYPE_i to 0 + initialize second-to-last and last block types to 0 and 1 + else + set block type, BTYPE_i to 0 + set block count, BLEN_i to 16777216 + 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 literal prefix codes, HTREEL[] + read array of insert-and-copy length prefix codes, HTREEI[] + read array of distance prefix codes, HTREED[] + do + if BLEN_I is zero + read block type using HTREE_BTYPE_I and set BTYPE_I + save previous block type + read block count using HTREE_BLEN_I and set BLEN_I + decrement BLEN_I + read insert-and-copy length symbol using HTREEI[BTYPE_I] + compute insert length, ILEN, and copy length, CLEN + loop for ILEN + if BLEN_L is zero + read block type using HTREE_BTYPE_L and set BTYPE_L + save previous block type + read block count using HTREE_BLEN_L and set BLEN_L + decrement BLEN_L + look up context mode CMODE[BTYPE_L] + compute context ID, CIDL from last two uncompressed bytes + read literal using HTREEL[CMAPL[64*BTYPE_L + CIDL]] + write literal to uncompressed stream + if number of uncompressed bytes produced in the loop for + this meta-block is MLEN, then break from loop (in this + case the copy length is ignored and can have any value) + if distance code is implicit zero from insert-and-copy code + set backward distance to the last distance + else + if BLEN_D is zero + read block type using HTREE_BTYPE_D and set BTYPE_D + save previous block type + read block count using HTREE_BLEN_D and set BLEN_D + decrement BLEN_D + compute context ID, CIDD from CLEN + read distance code using HTREED[CMAPD[4*BTYPE_D + CIDD]] + compute distance by distance short code substitution + if distance code is not zero, + and distance is not a static dictionary reference, + push distance to the ring buffer of last distances + if distance is less than the max allowed distance plus one + move backwards distance bytes in the uncompressed data, + and copy CLEN bytes from this position to + the uncompressed stream + else + look up the static dictionary word, transform the word as + directed, and copy the result to the uncompressed stream + while number of uncompressed bytes for this meta-block < MLEN + while not ISLAST +.fi + +If the stream ends before the completion of the last meta-block, then +the stream should be rejected as invalid. + +Note that a duplicated string reference may refer to a string in a +previous meta-block, i.e. the backward distance may cross one or +more meta-block boundaries. However a backward copy distance +will not refer past the beginning of the uncompressed stream or the +window size; any such distance is +interpreted as a reference to a static dictionary word. Also note +that the referenced string may overlap the current position, for +example, if the last 2 bytes decoded have values X and Y, a string +reference with adds X,Y,X,Y,X to the +uncompressed stream. + +.ti 0 +11. Security Considerations + +As with any compressed file formats, decompressor implementations should +handle all compressed data byte sequences, not only those that conform to this +specification, where non-conformant compressed data sequences should be discarded. +A possible attack against a system containing a decompressor +implementation (e.g. a web browser) is to exploit a buffer +overflow caused by an invalid compressed data. Therefore decompressor +implementations should perform bounds-checking for each memory access +that result from values decoded from the compressed stream. + +.ti 0 +12. IANA Considerations + +The "HTTP Content Coding Registry" has been updated with the +registration below: + +.nf +.KS + +-------+-------------------------------------+------------+ + | Name | Description | Reference | + +-------+-------------------------------------+------------+ + | br | Brotli Compressed Data Format | RFCXXXX | + +-------+-------------------------------------+------------+ +.KE +.fi + +.ti 0 +13. Informative References +.in 14 + +.ti 3 +[HUFFMAN] Huffman, D. A., "A Method for the Construction of Minimum +Redundancy Codes", Proceedings of the Institute of Radio +Engineers, September 1952, Volume 40, Number 9, pp. 1098-1101. + +.ti 3 +[LZ77] Ziv J., Lempel A., "A Universal Algorithm for Sequential Data +Compression", IEEE Transactions on Information Theory, Vol. 23, +No. 3, pp. 337-343. + +.ti 3 +[RFC1951] Deutsch, P., "DEFLATE Compressed Data Format Specification +version 1.3", RFC 1951, Aladdin Enterprises, May 1996. +http://www.ietf.org/rfc/rfc1951.txt + +.ti 3 +[WOFF2] Levantovsky, V. (ed.), Levien, R. (ed.), "WOFF File Format +2.0", W3C WebFonts Working Group, http://www.w3.org/TR/WOFF2/ +.in 3 + +.ti 0 +14. Source code + +Source code for a C language implementation of a brotli compliant +decompressor and a C++ language implementation of a compressor is +available in the brotli open-source project: +https://github.com/google/brotli + +.ti 0 +15. Acknowledgments + +The authors would like to thank Mark Adler, Robert Obryk, Thomas +Pickert, and Joe Tsai for providing helpful review comments, +validating the specification by writing an independent decompressor, +and suggesting improvements to the format and the text of the +specification. + +.ti 0 +Appendix A. Static dictionary data + +The hexadecimal form of the DICT array is the following, where the +length is 122,784 bytes and the zlib CRC-32 of the byte sequence is +0x5136cb04. + +.in 0 +.nf + 74696d65646f776e6c6966656c6566746261636b636f64656461746173686f77 + 6f6e6c7973697465636974796f70656e6a7573746c696b6566726565776f726b + 74657874796561726f766572626f64796c6f7665666f726d626f6f6b706c6179 + 6c6976656c696e6568656c70686f6d65736964656d6f7265776f72646c6f6e67 + 7468656d7669657766696e64706167656461797366756c6c686561647465726d + 656163686172656166726f6d747275656d61726b61626c6575706f6e68696768 + 646174656c616e646e6577736576656e6e65787463617365626f7468706f7374 + 757365646d61646568616e6468657265776861746e616d654c696e6b626c6f67 + 73697a656261736568656c646d616b656d61696e757365722729202b686f6c64 + 656e6473776974684e65777372656164776572657369676e74616b6568617665 + 67616d657365656e63616c6c7061746877656c6c706c75736d656e7566696c6d + 706172746a6f696e746869736c697374676f6f646e6565647761797377657374 + 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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 + +The string literals are in C format, with respect to the use of +backslash escape characters. + +In order to generate a length and check value, the transforms can be converted +to a series of bytes, where each transform is the prefix sequence of bytes plus +a terminating zero byte, a single byte value identifying the transform, and the +suffix sequence of bytes plus a terminating zero. The value for the transforms +are 0 for Identity, 1 for UppercaseFirst, 2 for UppercaseAll, 3 to 11 for +OmitFirst1 to OmitFirst9, and 12 to 20 for OmitLast1 to OmitLast9. The byte +sequences that represent the 121 transforms are then concatenated to a single +sequence of bytes. The length of that sequence is 648 bytes, and the zlib CRC +is 0x3d965f81. + +.nf + ID Prefix Transform Suffix + -- ------ --------- ------ + 0 "" Identity "" + 1 "" Identity " " + 2 " " Identity " " + 3 "" OmitFirst1 "" + 4 "" UppercaseFirst " " + 5 "" Identity " the " + 6 " " Identity "" + 7 "s " Identity " " + 8 "" Identity " of " + 9 "" UppercaseFirst "" + 10 "" Identity " and " + 11 "" OmitFirst2 "" + 12 "" OmitLast1 "" + 13 ", " Identity " " + 14 "" Identity ", " + 15 " " UppercaseFirst " " + 16 "" Identity " in " + 17 "" Identity " to " + 18 "e " Identity " " + 19 "" Identity "\\"" + 20 "" Identity "." + 21 "" Identity "\\">" + 22 "" Identity "\\n" + 23 "" OmitLast3 "" + 24 "" Identity "]" + 25 "" Identity " for " + 26 "" OmitFirst3 "" + 27 "" OmitLast2 "" + 28 "" Identity " a " + 29 "" Identity " that " + 30 " " UppercaseFirst "" + 31 "" Identity ". " + 32 "." Identity "" + 33 " " Identity ", " + 34 "" OmitFirst4 "" + 35 "" Identity " with " + 36 "" Identity "'" + 37 "" Identity " from " + 38 "" Identity " by " + 39 "" OmitFirst5 "" + 40 "" OmitFirst6 "" + 41 " the " Identity "" + 42 "" OmitLast4 "" + 43 "" Identity ". The " + 44 "" UppercaseAll "" + 45 "" Identity " on " + 46 "" Identity " as " + 47 "" Identity " is " + 48 "" OmitLast7 "" + 49 "" OmitLast1 "ing " + 50 "" Identity "\\n\\t" + 51 "" Identity ":" + 52 " " Identity ". " + 53 "" Identity "ed " + 54 "" OmitFirst9 "" + 55 "" OmitFirst7 "" + 56 "" OmitLast6 "" + 57 "" Identity "(" + 58 "" UppercaseFirst ", " + 59 "" OmitLast8 "" + 60 "" Identity " at " + 61 "" Identity "ly " + 62 " the " Identity " of " + 63 "" OmitLast5 "" + 64 "" OmitLast9 "" + 65 " " UppercaseFirst ", " + 66 "" UppercaseFirst "\\"" + 67 "." Identity "(" + 68 "" UppercaseAll " " + 69 "" UppercaseFirst "\\">" + 70 "" Identity "=\\"" + 71 " " Identity "." + 72 ".com/" Identity "" + 73 " the " Identity " of the " + 74 "" UppercaseFirst "'" + 75 "" Identity ". This " + 76 "" Identity "," + 77 "." Identity " " + 78 "" UppercaseFirst "(" + 79 "" UppercaseFirst "." + 80 "" Identity " not " + 81 " " Identity "=\\"" + 82 "" Identity "er " + 83 " " UppercaseAll " " + 84 "" Identity "al " + 85 " " UppercaseAll "" + 86 "" Identity "='" + 87 "" UppercaseAll "\\"" + 88 "" UppercaseFirst ". " + 89 " " Identity "(" + 90 "" Identity "ful " + 91 " " UppercaseFirst ". " + 92 "" Identity "ive " + 93 "" Identity "less " + 94 "" UppercaseAll "'" + 95 "" Identity "est " + 96 " " UppercaseFirst "." + 97 "" UppercaseAll "\\">" + 98 " " Identity "='" + 99 "" UppercaseFirst "," + 100 "" Identity "ize " + 101 "" UppercaseAll "." + 102 "\\xc2\\xa0" Identity "" + 103 " " Identity "," + 104 "" UppercaseFirst "=\\"" + 105 "" UppercaseAll "=\\"" + 106 "" Identity "ous " + 107 "" UppercaseAll ", " + 108 "" UppercaseFirst "='" + 109 " " UppercaseFirst "," + 110 " " UppercaseAll "=\\"" + 111 " " UppercaseAll ", " + 112 "" UppercaseAll "," + 113 "" UppercaseAll "(" + 114 "" UppercaseAll ". " + 115 " " UppercaseAll "." + 116 "" UppercaseAll "='" + 117 " " UppercaseAll ". " + 118 " " UppercaseFirst "=\\"" + 119 " " UppercaseAll "='" + 120 " " UppercaseFirst "='" +.fi +.in 3 + + +.ti 0 +Authors' Addresses + +.nf +Jyrki Alakuijala +Google, Inc + +Email: jyrki@google.com + + +Zoltan Szabadka +Google, Inc + +Email: szabadka@google.com +.fi + diff --git a/docs/draft-alakuijala-brotli-09.txt b/docs/draft-alakuijala-brotli-09.txt new file mode 100644 index 0000000..e119136 --- /dev/null +++ b/docs/draft-alakuijala-brotli-09.txt @@ -0,0 +1,6723 @@ + + + + + + +Network Working Group J. Alakuijala +Internet-Draft Z. Szabadka +Intended Status: Informational Google, Inc +Expires: June 10, 2016 December 2015 + + + Brotli Compressed Data Format + draft-alakuijala-brotli-08 + +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. + +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 June 10, 2016. + +Copyright Notice + + Copyright (c) 2015 IETF Trust and the persons identified as the + document authors. All rights reserved. + + This document is subject to BCP 78 and the IETF Trust's Legal + Provisions Relating to IETF Documents + (http://trustee.ietf.org/license-info) in effect on the date of + publication of this document. Please review these documents + carefully, as they describe your rights and restrictions with respect + to this document. Code Components extracted from this document must + include Simplified BSD License text as described in Section 4.e of + the Trust Legal Provisions and are provided without warranty as + described in the Simplified BSD License. + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 1] + +Internet-Draft Brotli December 2015 + + +Table of Contents + + 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3 + 1.1. Purpose . . . . . . . . . . . . . . . . . . . . . . . . . 3 + 1.2. Intended audience . . . . . . . . . . . . . . . . . . . . 3 + 1.3. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . 3 + 1.4. Compliance . . . . . . . . . . . . . . . . . . . . . . . . 4 + 1.5. Definitions of terms and conventions used . . . . . . . . 4 + 1.5.1. Packing into bytes . . . . . . . . . . . . . . . . . 4 + 2. Compressed representation overview . . . . . . . . . . . . . . 5 + 3. Compressed representation of prefix codes . . . . . . . . . . . 9 + 3.1. Introduction to prefix coding . . . . . . . . . . . . . . 9 + 3.2. Use of prefix coding in the brotli format . . . . . . . . 10 + 3.3. Alphabet sizes . . . . . . . . . . . . . . . . . . . . . 12 + 3.4. Simple prefix codes . . . . . . . . . . . . . . . . . . . 13 + 3.5. Complex prefix codes . . . . . . . . . . . . . . . . . . 14 + 4. Encoding of distances . . . . . . . . . . . . . . . . . . . . 16 + 5. Encoding of literal insertion lengths and copy lengths . . . . 18 + 6. Encoding of block switch commands . . . . . . . . . . . . . . 20 + 7. Context modeling . . . . . . . . . . . . . . . . . . . . . . . 22 + 7.1. Context modes and context ID lookup for literals . . . . 22 + 7.2. Context ID for distances . . . . . . . . . . . . . . . . 24 + 7.3. Encoding of the context map . . . . . . . . . . . . . . . 24 + 8. Static dictionary . . . . . . . . . . . . . . . . . . . . . . 26 + 9. Compressed data format . . . . . . . . . . . . . . . . . . . . 28 + 9.1. Format of the stream header . . . . . . . . . . . . . . . 29 + 9.2. Format of the meta-block header . . . . . . . . . . . . . 29 + 9.3. Format of the meta-block data . . . . . . . . . . . . . . 32 + 10. Decoding algorithm . . . . . . . . . . . . . . . . . . . . . 33 + 11. Security Considerations . . . . . . . . . . . . . . . . . . . 36 + 12. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 36 + 13. Informative References . . . . . . . . . . . . . . . . . . . 36 + 14. Source code . . . . . . . . . . . . . . . . . . . . . . . . . 37 + 15. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 37 + Appendix A. Static dictionary data . . . . . . . . . . . . . . . 37 + Appendix B. List of word transformations . . . . . . . . . . . . 117 + Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 120 + + + + + + + + + + + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 2] + +Internet-Draft Brotli December 2015 + + +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 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. + + 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 the brotli format. + + The text of the specification assumes a basic background in + programming at the level of bits and other primitive data + representations. Familiarity with the technique of Huffman coding is + helpful but not required. + + This specification uses heavily the notations and terminology + introduced in the DEFLATE format specification [RFC 1951]. For the + sake of completeness, we always include the whole text of the + relevant parts of RFC 1951, therefore familiarity with the DEFLATE + format is helpful but not required. + + The compressed data format defined in this specification is an + integral part of the WOFF 2.0 web font file format [WOFF2], therefore + this specification is also intended for implementers of WOFF 2.0 + compressors and decompressors. + +1.3. Scope + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 3] + +Internet-Draft Brotli December 2015 + + + 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 that + 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 + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 4] + +Internet-Draft Brotli December 2015 + + + 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 prefix codes are packed + starting with the least-significant bit of the data + element. These are referred to here as integer values + and are considered unsigned. + * Prefix codes are packed starting with the most-significant + bit of the code. + + In other words, if one were to print out the compressed data as a + sequence of bytes, starting with the first byte at the *right* margin + and proceeding to the *left*, with the most-significant bit of each + byte on the left as usual, one would be able to parse the result from + right to left, with fixed-width elements in the correct MSB-to-LSB + order and prefix codes in bit-reversed order (i.e., with the first + bit of the code in the relative LSB position). + +2. Compressed representation overview + + A compressed data set consists of a header and a series of meta- + blocks. Each meta-block decompresses to a sequence of 0 to 16,777,216 + (16 MiB) uncompressed bytes. The final uncompressed data is the + concatenation of the uncompressed sequences from each meta-block. + + The header contains the size of the sliding window that was used + during compression. The decompressor must retain at least that + amount of uncompressed data prior to the current position in the + stream, in order to be able to decompress what follows. The sliding + window size is a power of two, minus 16, where the power is in the + range of 10 to 24. The possible sliding window sizes range from 1 KiB + - 16 B to 16 MiB - 16 B. + + Each meta-block is compressed using a combination of the LZ77 + algorithm (Lempel-Ziv 1977, [LZ77]) and Huffman coding. The result of + Huffman coding is referred to here as a prefix code. The prefix + codes for each meta-block are independent of those for previous or + subsequent meta-blocks; the LZ77 algorithm may use a reference to a + duplicated string occurring in a previous meta-block, up to the + sliding window size of uncompressed bytes before. In addition, in + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 5] + +Internet-Draft Brotli December 2015 + + + the brotli format, a string reference may instead refer to a static + dictionary entry. + + Each meta-block consists of two parts: a meta-block header that + describes the representation of the compressed data part, and a + compressed data part. The compressed data consists of a series of + commands. Each command consists of two parts: a sequence of literal + bytes (of strings that have not been detected as duplicated within + the sliding window), and a pointer to a duplicated string, + represented as a pair . There can be zero + literal bytes in the command. The minimum length of the string to be + duplicated is two, but the last command in the meta-block is + permitted to have only literals and no pointer to a string to + duplicate. + + Each command in the compressed data is represented using three + categories of prefix codes: + + 1) One set of prefix codes are for the literal sequence lengths + (also referred to as literal insertion lengths) and + backward copy lengths. That is, a single code word represents + two lengths, one of the literal sequence and one of the + backward copy. + + 2) One set of prefix codes are for literals. + + 3) One set of prefix codes are for distances. + + The prefix code descriptions for each meta-block appear in a compact + form just before the compressed data in the meta-block header. The + insert-and-copy length and distance prefix codes may be followed by + extra bits that are added to the base values determined by the codes. + The number of extra bits is determined by the code. + + One meta-block command then appears as a sequence of prefix codes: + + Insert-and-copy length, literal, literal, ..., literal, distance + + where the insert-and-copy defines an insertion length and a copy + length. The insertion length determines the number of literals that + immediately follow. The distance defines how far back to go for the + copy and the copy length determines the number of bytes to copy. The + resulting uncompressed data is the sequence of bytes: + + literal, literal, ..., literal, copy, copy, ..., copy + + where the number of literal bytes and copy bytes are determined by + the insert-and-copy length code. (The number of bytes copied for a + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 6] + +Internet-Draft Brotli December 2015 + + + static dictionary entry can vary from the copy length.) + + The last command in the meta-block may end with the last literal if + the total uncompressed length of the meta-block has been satisfied. + In that case there is no distance in the last command, and the copy + length is ignored. + + There can be more than one prefix code for each category, where the + prefix code to use for the next element of that category is + determined by the context of the compressed stream that precedes that + element. Part of that context is three current block types, one for + each category. A block type is in the range of 0..255. For each + category there is a count of how many elements of that category + remain to be decoded using the current block type. Once that count is + expended, a new block type and block count is read from the stream + immediately preceding the next element of that category, which will + use the new block type. + + The insert-and-copy block type directly determines which prefix code + to use for the next insert-and-copy element. For the literal and + distance elements, the respective block type is used in combination + with other context information to determine which prefix code to use + for the next element. + + Consider the following example: + + (IaC0, L0, L1, L2, D0)(IaC1, D1)(IaC2, L3, L4, D2)(IaC3, L5, D3) + + The meta-block here has four commands, contained in parentheses for + clarity, where each of the three categories of symbols within these + commands can be interpreted using different block types. Here we + separate out each category as its own sequence to show an example of + block types assigned to those elements. Each square-bracketed group + is a block that uses the same block type: + + [IaC0, IaC1][IaC2, IaC3] <-- insert-and-copy: block types 0 and 1 + + [L0, L1][L2, L3, L4][L5] <-- literals: block types 0, 1, and 0 + + [D0][D1, D2, D3] <-- distances: block types 0 and 1 + + The subsequent blocks within each block category must have different + block types, but we see that block types can be reused later in the + meta-block. The block types are numbered from 0 to the maximum block + type number of 255 and the first block of each block category is type + 0. The block structure of a meta-block is represented by the sequence + of block-switch commands for each block category, where a block- + switch command is a pair . The block-switch + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 7] + +Internet-Draft Brotli December 2015 + + + commands are represented in the compressed data before the start of + each new block using a prefix code for block types and a separate + prefix code for block counts for each block category. For the above + example the physical layout of the meta-block is then: + + IaC0 L0 L1 LBlockSwitch(1, 3) L2 D0 IaC1 DBlockSwitch(1, 3) D1 + IaCBlockSwitch(1, 2) IaC2 L3 L4 D2 IaC3 LBlockSwitch(0, 1) L5 D3 + + where xBlockSwitch(t, n) switches to block type t for a count of n + elements. Note that in this example DBlockSwitch(1, 3) immediately + precedes the next required distance D1. It does not follow the last + distance of the previous block, D0. Whenever an element of a category + is needed, and the block count for that category has reached zero, + then a new block type and count is read from the stream just before + reading that next element. + + The block-switch commands for the first blocks of each category are + not part of the meta-block compressed data. Instead the first block + type is defined to be 0, and the first block count for each category + is encoded in the meta-block header. The prefix codes for the block + types and counts, a total of six prefix codes over the three + categories, are defined in a compact form in the meta-block header. + + Each category of value (insert-and-copy lengths, literals, and + distances) can be encoded with any prefix code from a collection of + prefix codes belonging to the same category appearing in the meta- + block header. The particular prefix code used can depend on two + factors: the block type of the block the value appears in, and the + context of the value. In the case of the literals, the context is + the previous two bytes in the uncompressed data, and in the case of + distances, the context is the copy length from the same command. For + insert-and-copy lengths, no context is used and the prefix code + depends only on the block type. In the case of literals and + distances, the context is mapped to a context ID in the range 0..63 + for literals and 0..3 for distances. The matrix of the prefix code + indexes for each block type and context ID, called the context map, + is encoded in a compact form in the meta-block header. + + For example, the prefix code to use to decode L2 depends on the block + type (1), and the literal context ID determined by the two + uncompressed bytes that were decoded from L0 and L1. Similarly, the + prefix code to use to decode D0 depends on the block type (0), and + the distance context ID determined by the copy length decoded from + IaC0. The prefix code to use to decode IaC3 depends only on the block + type (1). + + In addition to the parts listed above (prefix code for insert-and- + copy lengths, literals, distances, block types and block counts, and + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 8] + +Internet-Draft Brotli December 2015 + + + the context map), the meta-block header contains the number of + uncompressed bytes coded in the meta-block and two additional + parameters used in the representation of match distances: the number + of postfix bits and the number of direct distance codes. + + A compressed meta-block may be marked in the header as the last meta- + block, which terminates the compressed stream. + + A meta-block may instead simply store the uncompressed data directly + as bytes on byte boundaries with no coding or matching strings. In + this case the meta-block header information only contains the number + of uncompressed bytes and the indication that the meta-block is + uncompressed. An uncompressed meta-block cannot be the last meta- + block. + + A meta-block may also be empty, which generates no uncompressed data + at all. An empty meta-block may contain metadata information as + bytes starting on byte boundaries, which are not part of either the + sliding window or the uncompressed data. Thus, these metadata bytes + cannot be used to create matching strings in subsequent meta-blocks + and are not used as context bytes for literals. + +3. Compressed representation of prefix codes + +3.1. Introduction to prefix coding + + Prefix coding represents symbols from an a priori known alphabet by + bit sequences (codes), one code for each symbol, in a manner such + that different symbols may be represented by bit sequences of + different lengths, but a parser can always parse an encoded string + unambiguously symbol-by-symbol. + + We define a prefix code in terms of a binary tree in which the two + edges descending from each non-leaf node are labeled 0 and 1 and in + which the leaf nodes correspond one-for-one with (are labeled with) + the symbols of the alphabet; then the code for a symbol is the + sequence of 0's and 1's on the edges leading from the root to the + leaf labeled with that symbol. For example: + + + + + + + + + + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 9] + +Internet-Draft Brotli December 2015 + + + /\ 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 the compressed stream by + walking down the tree from the root, at each step choosing the edge + corresponding to the next compressed data bit. + + Given an alphabet with known symbol frequencies, the Huffman + algorithm allows the construction of an optimal prefix code (one + which represents strings with those symbol frequencies using the + fewest bits of any possible prefix codes for that alphabet). Such a + prefix code is called a Huffman code. (See [HUFFMAN] in Chapter 5, + references for additional information on Huffman codes.) + + Note that in the brotli format, the prefix codes for the various + alphabets must not exceed certain maximum code lengths. This + constraint complicates the algorithm for computing code lengths from + symbol frequencies. Again, see Chapter 5, references for details. + +3.2. Use of prefix coding in the brotli format + + The prefix codes used for each alphabet in the brotli format are + canonical prefix codes, which have two additional rules: + + * 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 + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 10] + +Internet-Draft Brotli December 2015 + + + I.e., 0 precedes 10, which precedes 11x, and 110 and 111 are + lexicographically consecutive. + + Given this rule, we can define the canonical prefix code for an + alphabet just by giving the bit lengths of the codes for each symbol + of the alphabet in order; this is sufficient to determine the actual + codes. In our example, the code is completely defined by the sequence + of bit lengths (2, 1, 3, 3). The following algorithm generates the + codes as integers, intended to be read from most- to least- + significant bit. The code lengths are initially in tree[I].Len; the + codes are produced in tree[I].Code. + + 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: + + + + + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 11] + +Internet-Draft Brotli December 2015 + + + 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 + + Prefix codes are used for different purposes in the brotli format, + and each purpose has a different alphabet size. For literal codes the + alphabet size is 256. For insert-and-copy length codes the alphabet + size is 704. For block count codes, the alphabet size is 26. For + distance codes, block type codes, and the prefix codes used in + compressing the context map, the alphabet size is dynamic and is + based on parameters defined in later sections. The following table + summarizes the alphabet sizes for the various prefix codes and the + sections where they are defined. + + + + + + + + + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 12] + +Internet-Draft Brotli December 2015 + + + +-----------------+-------------------------+------------+ + | Prefix code | Alphabet size | Definition | + +-----------------+-------------------------+------------+ + | literal | 256 | | + +-----------------+-------------------------+------------+ + | distance | 16 + NDIRECT + | Section 4. | + | | (48 << NPOSTFIX) | | + +-----------------+-------------------------+------------+ + | insert-and-copy | 704 | Section 5. | + | length | | | + +-----------------+-------------------------+------------+ + | block count | 26 | Section 6. | + +-----------------+-------------------------+------------+ + | block type | NBLTYPESx + 2, | Section 6. | + | | (where x is I, L, or D) | | + +-----------------+-------------------------+------------+ + | context map | NTREESx + RLEMAXx | Section 7. | + | | (where x is L or D) | | + +-----------------+-------------------------+------------+ + +3.4. Simple prefix codes + + The first two bits of the compressed representation of each prefix + code distinguish between simple and complex prefix codes. If this + value is 1, then a simple prefix code follows as described in this + section. Otherwise, a complex prefix code follows as described in + Section 3.5. + + A simple prefix code can have only up to four symbols with non-zero + code length. The format of the simple prefix code is as follows: + + 2 bits: value of 1 indicates a simple prefix code + 2 bits: NSYM - 1, where NSYM = # of symbols coded + + NSYM symbols, each encoded using ALPHABET_BITS bits + + 1 bit: tree-select, present only for NSYM = 4 + + The value of ALPHABET_BITS depends on the alphabet of the prefix + code: it is the smallest number of bits that can represent all + symbols in the alphabet. E.g. for the alphabet of literal bytes, + ALPHABET_BITS is 8. The value of each of the NSYM symbols above is + the value of the ALPHABETS_BITS width integer value. If the integer + value is greater than or equal to the alphabet size, or the value is + identical to a previous value, then the stream should be rejected as + invalid. + + Note that the NSYM symbols may not be presented in sorted order. + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 13] + +Internet-Draft Brotli December 2015 + + + Prefix codes of the same bit length must be assigned to the symbols + in sorted order. + + The (non-zero) code lengths of the symbols can be reconstructed as + follows: + + * if NSYM = 1, the code length for the one symbol is zero -- + when encoding this symbol in the + compressed data stream using this prefix code, no + actual bits are emitted. Similarly, when decoding a symbol + using this prefix code, no bits are read and the one symbol + is returned. + + * if NSYM = 2, both symbols have code length 1. + + * if NSYM = 3, the code lengths for the symbols are 1, 2, 2 in + the order they appear in the representation of the simple + prefix code. + + * if NSYM = 4, the code lengths (in order of symbols decoded) + depend on the tree-select bit: 2, 2, 2, 2 (tree-select bit 0), + or 1, 2, 3, 3 (tree-select bit 1). + +3.5. Complex prefix codes + + A complex prefix code is a canonical prefix code, defined by the + sequence of code lengths, as discussed in Section 3.2., above. For + even greater compactness, the code length sequences themselves are + compressed using a prefix code. The alphabet for code lengths is as + follows: + + 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 + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 14] + +Internet-Draft Brotli December 2015 + + + repeat count of the previous one as follows: + repeat count = (8 * (repeat count - 2)) + + (3 - 10 on the next 3 bits) + + Note that a code of 16 that follows an immediately preceding 16 + modifies the previous repeat count, which becomes the new repeat + count. The same is true for a 17 following a 17. A sequence of three + or more 16 codes in a row or three of more 17 codes in a row is + possible, modifying the count each time. Only the final repeat count + is used. The modification only applies if the same code follows. A 16 + repeat does not modify an immediately preceding 17 count nor vice + versa. + + A code length of 0 indicates that the corresponding symbol in the + alphabet will not occur in the compressed data, and should not + participate in the prefix code construction algorithm given earlier. + A complex prefix code must have at least two non-zero code lengths. + + The bit lengths of the prefix code over the code length alphabet are + compressed with the following variable length code (as it appears in + the compressed data, where the bits are parsed from right to left): + + Symbol Code + ------ ---- + 0 00 + 1 0111 + 2 011 + 3 10 + 4 01 + 5 1111 + + We can now define the format of the complex prefix code as follows: + + 2 bits: HSKIP, values of 0, 2, or 3 represent the respective + number of skipped code lengths. The skipped lengths + are taken to be zero. (An HSKIP of 1 indicates a + Simple prefix code.) + + Code lengths for symbols in the code length alphabet given + just above, in the order: 1, 2, 3, 4, 0, 5, 17, 6, 16, 7, + 8, 9, 10, 11, 12, 13, 14, 15. If HSKIP is 2, then the + code lengths for symbols 1 and 2 are zero, and the first + code length is for symbol 3. If HSKIP is 3, then the code + length for symbol 3 is also zero, and the first code length + is for symbol 4. + + The code lengths of code length symbols are between 0 and + 5, and they are represented with 2 - 4 bits according to + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 15] + +Internet-Draft Brotli December 2015 + + + the variable length code above. A code length of 0 means + the corresponding code length symbol is not used. + + If HSKIP is 2 or 3, a respective number of leading code + lengths are implicit zeros and are not present in the + code lengths sequence above. + + If there are at least two non-zero code lengths, any + trailing zero code lengths are omitted, i.e. the last + code length in the sequence must be non-zero. In this + case, the sum of (32 >> code length) over all the non-zero + code lengths must equal to 32. + + If the lengths have been read for the entire code length + alphabet and there was only one non-zero code length, + then the prefix code has one symbol whose code has zero + length. In this case, that symbol results in no bits + being emitted by the compressor, and no bits consumed by + the decompressor. That single symbol is immediately + returned when this code is decoded. + An example of where this occurs is if the + entire code to be represented has symbols of length 8. + E.g. a literal code that represents all literal values + with equal probability. In this case the single symbol + is 16, which repeats the previous length. The previous + length is taken to be 8 before any code length code + lengths are read. + + Sequence of at most alphabet size code lengths symbols, encoded + using the code length prefix code. Any trailing 0 or 17 must be + omitted, i.e. the last encoded code length symbol must be + between 1 and 16. The sum of (32768 >> code length) over + all the non-zero code lengths in the alphabet, including + those encoded using repeat code(s) of 16, must equal to + 32768. If the number of times to repeat the previous length + or repeat a zero length would result in more lengths in + total than the number of symbols in the alphabet, then the + stream should be rejected as invalid. + +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 . The distance + code and the extra bits are encoded back-to-back, the distance code + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 16] + +Internet-Draft Brotli December 2015 + + + is encoded using a prefix code over the distance alphabet, while the + extra bits value is encoded as a fixed-width integer value. The + number of extra bits can be 0 - 24, and it is dependent on the + distance code. + + To convert a distance code and associated extra bits to a backward + distance, we need the sequence of past distances and two additional + parameters, the number of "postfix bits", denoted by NPOSTFIX (0..3), + and the number of direct distance codes, denoted by NDIRECT (0..120). + Both of these parameters are encoded in the meta-block header. We + will also use the following derived parameter: + + POSTFIX_MASK = (1 << NPOSTFIX) - 1 + + The first 16 distance symbols are special symbols that reference past + distances as follows: + + 0: last distance + 1: second-to-last distance + 2: third-to-last distance + 3: fourth-to-last distance + 4: last distance - 1 + 5: last distance + 1 + 6: last distance - 2 + 7: last distance + 2 + 8: last distance - 3 + 9: last distance + 3 + 10: second-to-last distance - 1 + 11: second-to-last distance + 1 + 12: second-to-last distance - 2 + 13: second-to-last distance + 2 + 14: second-to-last distance - 3 + 15: second-to-last distance + 3 + + The ring buffer of four last distances is initialized by the values + 16, 15, 11, and 4 (i.e. the fourth-to-last is set to 16, the third- + to-last to 15, the second-to-last to 11, and the last distance to 4) + at the beginning of the *stream* (as opposed to the beginning of the + meta-block) and it is not reset at meta-block boundaries. When a + distance symbol 0 appears, the distance it represents (i.e. the last + distance in the sequence of distances) is not pushed to the ring + buffer of last distances, in other words, the expression "(second, + third, fourth)-to-last distance" means the (second, third, + fourth)-to-last distance that was not represented by a 0 distance + symbol. Similarly, distances that represent static dictionary words + (see Section 8.) are not pushed to the ring buffer of last distances. + + If a special distance symbol resolves to a zero or negative value, + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 17] + +Internet-Draft Brotli December 2015 + + + the stream should be rejected as invalid. + + If NDIRECT is greater than zero, then the next NDIRECT distance + symbols, from 16 to 15 + NDIRECT, represent distances from 1 to + NDIRECT. Neither the special distance symbols, nor the NDIRECT + direct distance symbols are followed by any extra bits. + + Distance symbols 16 + NDIRECT and greater all have extra bits, where + the number of extra bits for a distance symbol "dcode" is given by + the following formula: + + ndistbits = 1 + ((dcode - NDIRECT - 16) >> (NPOSTFIX + 1)) + + The maximum number of extra bits is 24, therefore the size of the + distance symbol alphabet is (16 + NDIRECT + (48 << NPOSTFIX)). + + Given a distance symbol "dcode" (>= 16 + NDIRECT), and extra bits + "dextra", the backward distance is given by the following formula: + + 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 prefix code. This + section provides the details to this encoding. + + Each pair in the compressed data part + of a meta-block is represented with the following triplet: + + + + The insert-and-copy length code, the insert extra bits, and the copy + extra bits are encoded back-to-back, the insert-and-copy length code + is encoded using a prefix code over the insert-and-copy length code + alphabet, while the extra bits values are encoded as fixed-width + integer values. The number of insert and copy extra bits can be 0 - + 24, and they are dependent on the insert-and-copy length code. + + Some of the insert-and-copy length codes also express the fact that + the distance symbol of the distance in the same command is 0, i.e. + the distance component of the command is the same as that of the + previous command. In this case, the distance code and extra bits for + the distance are omitted from the compressed data stream. + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 18] + +Internet-Draft Brotli December 2015 + + + 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: + + + + + + + + + + + + + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 19] + +Internet-Draft Brotli December 2015 + + + Insert + length Copy length code + code 0-7 8-15 16-23 + +---------+---------+ + | | | + 0-7 | 0-63 | 64-127 | <--- distance symbol 0 + | | | + +---------+---------+---------+ + | | | | + 0-7 | 128-191 | 192-255 | 384-447 | + | | | | + +---------+---------+---------+ + | | | | + 8-15 | 256-319 | 320-383 | 512-575 | + | | | | + +---------+---------+---------+ + | | | | + 16-23 | 448-511 | 576-639 | 640-703 | + | | | | + +---------+---------+---------+ + + 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 bits 0-2 (counted from the + LSB) of the insert-and-copy length code. 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 . These are encoded in the compressed data part of + the meta-block, right before the start of each new block of a + particular block category. + + Each block type in the compressed data is represented with a block + type code, encoded using a prefix code over the block type code + alphabet. A block type symbol 0 means that the new block type is the + same as the type of the previous block from the same block category, + i.e. the block type that preceded the current type, while a block + type symbol 1 means that the new block type equals the current block + type plus one. If the current block type is the maximal possible, + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 20] + +Internet-Draft Brotli December 2015 + + + then a block type symbol of 1 results in wrapping to a new block type + of 0. Block type symbols 2 - 257 represent block types 0 - 255 + respectively. The previous and current block types are initialized to + 1 and 0, respectively, at the end of the meta-block header. + + Since the first block type of each block category is 0, the block + type of the first block-switch command is not encoded in the + compressed data. If a block category has only one block type, the + block count of the first block-switch command is also omitted from + the compressed data, otherwise it is encoded in the meta-block + header. + + Since the end of the meta-block is detected by the number of + uncompressed bytes produced, the block counts for any of the three + categories need not count down to exactly zero at the end of the + meta-block. + + The number of different block types in each block category, denoted + by NBLTYPESL, NBLTYPESI, and NBLTYPESD for literals, insert-and-copy + lengths, and distances, respectively, is encoded in the meta-block + header, and it must equal to the largest block type plus one in that + block category. In other words, the set of literal, insert-and-copy + length, and distance block types must be [0..NBLTYPESL-1], + [0..NBLTYPESI-1], and [0..NBLTYPESD-1], respectively. From this it + follows that the alphabet size of literal, insert-and-copy length, + and distance block type codes is NBLTYPESL + 2, NBLTYPESI + 2, and + NBLTYPESD + 2, respectively. + + Each block count in the compressed data is represented with a pair + . The block count code and the extra + bits are encoded back-to-back, the block count code is encoded using + a prefix code over the block count code alphabet, while the extra + bits value is encoded as a fixed-width integer value. The number of + extra bits can be 0 - 24, and it is dependent on the block count + code. The symbols of the block count code alphabet, along with the + number of extra bits, and the range of block counts are as follows: + + + + + + + + + + + + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 21] + +Internet-Draft Brotli December 2015 + + + 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 prefix tree used to encode a literal + byte or a distance code depends on the block type and the context ID. + 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 pair to the index of a prefix code in + the array of literal and distance prefix codes. + +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 of whether these bytes are produced by uncompressed meta- + blocks, backward references, static dictionary references, or by + literal insertions. At the start of the stream p1 and p2 are + initialized to zero. + + There are four methods, called context modes, to compute the Context + ID: + + * LSB6, where the Context ID is the value of six + least-significant bits of p1, + * MSB6, where the Context ID is the value of six + most-significant bits of p1, + * UTF8, where the Context ID is a complex function of p1, p2, + optimized for text compression, and + * Signed, where Context ID is a complex function of p1, p2, + optimized for compressing sequences of signed integers. + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 22] + +Internet-Draft Brotli December 2015 + + + 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, + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 23] + +Internet-Draft Brotli December 2015 + + + 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 + + The lengths and the zlib CRC-32 (ITU-T Recommendation V.42) check + values of each of these tables as a sequence of bytes are as follows: + + Table Length CRC-32 + ----- ------ ------ + Lut0 256 0x8e91efb7 + Lut1 256 0xd01a32f4 + Lut2 256 0x0dd7a0d6 + + Given p1 is the last uncompressed byte and p2 is the second-to-last + uncompressed 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] + + From the lookup tables defined above and the operations to compute + the context IDs, we can see that context IDs for literals are in the + range of 0..63. + + The context modes LSB6, MSB6, UTF8, and Signed are denoted by + integers 0, 1, 2, 3. + + A 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 context maps, one for literals and one for distances. + The size of the context map is 64 * NBLTYPESL for literals, and 4 * + NBLTYPESD for distances. Each value in the context map is an integer + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 24] + +Internet-Draft Brotli December 2015 + + + between 0 and 255, indicating the index of the prefix code to be used + when encoding the next literal or distance. + + The context maps are two-dimensional matrices, encoded as one- + dimensional arrays: + + CMAPL[0..(64 * NBLTYPESL - 1)] + CMAPD[0..(4 * NBLTYPESD - 1)] + + The index of the prefix code for encoding a literal or distance code + with block type, BTYPE_x, and context ID, CIDx, is: + + index of literal prefix code = CMAPL[64 * BTYPE_L + CIDL] + index of distance prefix code = CMAPD[4 * BTYPE_D + CIDD] + + The values of the context map are encoded with the combination of run + length encoding for zero values and prefix coding. Let RLEMAX denote + the number of run length codes and NTREES denote the maximum value in + the context map plus one. NTREES must equal the number of different + values in the context map, in other words, the different values in + the context map must be the [0..NTREES-1] interval. The alphabet of + the prefix code has the following RLEMAX + NTREES symbols: + + 0: value zero + 1: repeat a zero 2 to 3 times, read 1 bit for repeat length + 2: repeat a zero 4 to 7 times, read 2 bits for repeat length + ... + RLEMAX: repeat a zero (1 << RLEMAX) to (1 << (RLEMAX+1))-1 + times, read RLEMAX bits for repeat length + RLEMAX + 1: value 1 + ... + RLEMAX + NTREES - 1: value NTREES - 1 + + 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 xxxx1 (so 01001 + is 5) + + Prefix code with alphabet size NTREES + RLEMAX + + Context map size values encoded with the above prefix code + and run length coding for zero values. If a run length + would result in more lengths in total than the size of + the context map, then the stream should be rejected as + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 25] + +Internet-Draft Brotli December 2015 + + + invalid. + + 1 bit: IMTF bit, if set, we do an inverse move-to-front + transform on the values in the context map to get + the prefix code indexes + + Note that RLEMAX may be larger than the value necessary to represent + the longest sequence of zero values. Also, the NTREES value is + encoded right before the context map as described in Section 9.2. + + We define the inverse move-to-front transform used in this + specification by the following C language function: + + 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; + } + } + + Note that the inverse move-to-front transform will not produce values + outside the [0..NTREES-1] interval. + +8. Static dictionary + + At any given point during decoding the compressed data, a reference + to a duplicated string in the uncompressed data produced so far has a + maximum backward distance value, which is the minimum of the window + size and the number of uncompressed bytes produced. However, decoding + a distance from the compressed stream, as described in Section 4., + can produce distances that are greater than this maximum allowed + value. In this case, the distance is treated as a reference to a word + in the static dictionary given in Appendix A. The copy length for a + static dictionary reference must be between 4 and 24. The static + dictionary has three parts: + + * DICT[0..DICTSIZE], an array of bytes + * DOFFSET[0..24], an array of byte offset values for each length + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 26] + +Internet-Draft Brotli December 2015 + + + * 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 < 4) + NWORDS[length] = (1 << NDBITS[length]) (if length >= 4) + + 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 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 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)-1] + transform_id = word_id >> NDBITS[length] + + The string copied to the uncompressed stream is computed by applying + the transformation to the base dictionary word. If transform_id is + greater than 120, or the length is smaller than 4 or greater than 24, + then the compressed stream should be rejected as invalid. + + Each word transformation has the following form: + + transform_i(word) = prefix_i + T_i(word) + suffix_i + + where the _i subscript denotes the transform_id above. Each T_i is + one of the following 21 elementary transforms: + + Identity, UppercaseFirst, UppercaseAll, + OmitFirst1, ..., OmitFirst9, OmitLast1, ..., OmitLast9 + + The form of these elementary transforms is as follows: + + Identity(word) = word + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 27] + +Internet-Draft Brotli December 2015 + + + UppercaseFirst(word) = first UTF-8 character of word upper-cased + + UppercaseAll(word) = all UTF-8 characters of word upper-cased + + OmitFirstk(word) = the last (length(word) - k) bytes of word, or + empty string if length(word) < k + + OmitLastk(word) = the first (length(word) - k) bytes of word, or + empty string if length(word) < k + + 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: + + 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. + 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. + + The maximum number of additional bytes that a transform may add to a + base word is 13. Since the largest base word is 24 bytes long, a + buffer of 38 bytes is sufficient to store any transformed words + (counting a terminating zero byte). + +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. + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 28] + +Internet-Draft Brotli December 2015 + + +9.1. Format of the stream header + + The stream header has only the following one field: + + 1-7 bits: WBITS, a value in the range 10 - 24, encoded with + the following variable length code (as it appears in + the compressed data, where the bits are parsed from + right to left): + + Value Bit Pattern + ----- ----------- + 10 0100001 + 11 0110001 + 12 1000001 + 13 1010001 + 14 1100001 + 15 1110001 + 16 0 + 17 0000001 + 18 0011 + 19 0101 + 20 0111 + 21 1001 + 22 1011 + 23 1101 + 24 1111 + + Note that bit pattern 0010001 is invalid and must not + be used. + + 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: ISLASTEMPTY, if set to 1, the meta-block is empty; + this field is only present if ISLAST bit is set -- if + it is 1, then the meta-block and the brotli stream ends + at that bit, with any remaining bits in the last byte + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 29] + +Internet-Draft Brotli December 2015 + + + of the compressed stream filled with zeros (if the + fill bits are not zero, then the stream should be + rejected as invalid) + 2 bits: MNIBBLES, # of nibbles to represent the uncompressed + length, encoded with the following fixed-length code: + + Value Bit Pattern + ----- ----------- + 0 11 + 4 00 + 5 01 + 6 10 + + If MNIBBLES is 0, the meta-block is empty, i.e. it does + not generate any uncompressed data. In this case, the + rest of the meta-block has the following format: + + 1 bit: reserved, must be zero + + 2 bits: MSKIPBYTES, # of bytes to represent metadata + length + + MSKIPBYTES x 8 bits: MSKIPLEN - 1, where MSKIPLEN is + the number of metadata bytes; this field is + only present if MSKIPBYTES is positive, + otherwise MSKIPLEN is 0 (if MSKIPBYTES is + greater than 1, and the last byte is all + zeros, then the stream should be rejected + as invalid) + + 0 - 7 bits: fill bits until the next byte boundary, + must be all zeros + + MSKIPLEN bytes of metadata, not part of the + uncompressed data or the sliding window + + MNIBBLES x 4 bits: MLEN - 1, where MLEN is the length + of the meta-block uncompressed data in bytes (if + MNIBBLES is greater than 4, and the last + nibble is all zeros, then the stream should be + rejected as invalid) + + 1 bit: ISUNCOMPRESSED, if set to 1, any bits of compressed + data up to the next byte boundary are ignored, and + the rest of the meta-block contains MLEN bytes of + literal data; this field is only present if the + ISLAST bit is not set (if the ignored bits are not + all zeros, the stream should be rejected as invalid) + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 30] + +Internet-Draft Brotli December 2015 + + + 1-11 bits: NBLTYPESL, # of literal block types, encoded with + the following variable length code (as it appears in + the compressed data, where the bits are parsed from + right to left, so 0110111 has the value 12): + + Value Bit Pattern + ----- ----------- + 1 0 + 2 0001 + 3-4 x0011 + 5-8 xx0101 + 9-16 xxx0111 + 17-32 xxxx1001 + 33-64 xxxxx1011 + 65-128 xxxxxx1101 + 129-256 xxxxxxx1111 + + Prefix code over the block type code alphabet for + literal block types, appears only if NBLTYPESL >= 2 + + Prefix code over the block count code alphabet for + literal block counts, appears only if NBLTYPESL >= 2 + + Block count code + extra bits for first literal + block count, appears only if NBLTYPESL >= 2 + + 1-11 bits: NBLTYPESI, # of insert-and-copy block types, encoded + with the same variable length code as above + + Prefix code over the block type code alphabet for + insert-and-copy block types, appears only if NBLTYPESI >= 2 + + Prefix code over the block count code alphabet for + insert-and-copy block counts, appears only if NBLTYPESI >= 2 + + Block count code + extra bits for first insert-and-copy + block count, appears only if NBLTYPESI >= 2 + + 1-11 bits: NBLTYPESD, # of distance block types, encoded + with the same variable length code as above + + Prefix code over the block type code alphabet for + distance block types, appears only if NBLTYPESD >= 2 + + Prefix code over the block count code alphabet for + distance block counts, appears only if NBLTYPESD >= 2 + + Block count code + extra bits for first distance + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 31] + +Internet-Draft Brotli December 2015 + + + block count, appears only if NBLTYPESD >= 2 + + 2 bits: NPOSTFIX, parameter used in the distance coding + + 4 bits: four most-significant bits of NDIRECT, to get the + actual value of the parameter NDIRECT, left-shift + this four-bit number by NPOSTFIX bits + + NBLTYPESL x 2 bits: context mode for each literal block type + + 1-11 bits: NTREESL, # of literal prefix trees, encoded + with the same variable length code as NBLTYPESL + + Literal context map, encoded as described in Section 7.3., + appears only if NTREESL >= 2, otherwise the context map + has only zero values + + 1-11 bits: NTREESD, # of distance prefix trees, encoded + with the same variable length code as NBLTYPESD + + Distance context map, encoded as described in Section 7.3., + appears only if NTREESD >= 2, otherwise the context map + has only zero values + + NTREESL prefix codes for literals + + NBLTYPESI prefix codes for insert-and-copy lengths + + NTREESD prefix codes for distances + +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 count is zero + + Block count code + extra bits for next insert-and-copy + block count, appears only if NBLTYPESI >= 2 and the + previous insert-and-copy block count is zero + + Insert-and-copy length, encoded as in Section 5., using the + insert-and-copy length prefix code with the current + insert-and-copy block type index + + Insert length number of literals, with the following format: + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 32] + +Internet-Draft Brotli December 2015 + + + Block type code for next literal block type, appears + only if NBLTYPESL >= 2 and the previous literal + block count is zero + + Block count code + extra bits for next literal + block count, appears only if NBLTYPESL >= 2 and the + previous literal block count is zero + + Next byte of the uncompressed data, encoded with the + literal prefix code with the index determined by the + previous two bytes of the uncompressed data, the + current literal block type, and the context map, as + described in Section 7.3. + + Block type code for next distance block type, appears + only if NBLTYPESD >= 2 and the previous distance + block count is zero + + Block count code + extra bits for next distance + block count, appears only if NBLTYPESD >= 2 and the + previous distance block count is zero + + Distance code, encoded as in Section 4., using the distance + prefix code with the current distance block type index, + appears only if the distance code is not an implicit 0, + as indicated by the insert-and-copy length code + + The number of commands in the meta-block is such that the sum of the + uncompressed bytes produced (i.e. the number of literals inserted + plus the number of bytes copied from past data or generated from the + static dictionary) over all the commands gives the uncompressed + length, MLEN encoded in the meta-block header. + + If the total number of uncompressed bytes produced after the insert + part of the last command equals MLEN, then the copy length of the + last command is ignored and will not produce any uncompressed output. + In this case the copy length of the last command can have any value. + In any other case, if the number of literals to insert, the copy + length, or the resulting dictionary word length would cause MLEN to + be exceeded, then the stream should be rejected as invalid. + + If the last command of the last non-empty meta-block does not end on + a byte boundary, the unused bits in the last byte must be zeros. + +10. Decoding algorithm + + The decoding algorithm that produces the uncompressed data is as + follows: + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 33] + +Internet-Draft Brotli December 2015 + + + read window size + do + read ISLAST bit + if ISLAST + read ISLASTEMPTY bit + if ISLASTEMPTY + break from loop + read MNIBBLES + if MNIBBLES is zero + verify reserved bit is zero + read MSKIPLEN + skip any bits up to the next byte boundary + skip MSKIPLEN bytes + continue to the next meta-block + else + read MLEN + if not ISLAST + read ISUNCOMPRESSED bit + if ISUNCOMPRESSED + skip any bits up to the next byte boundary + copy MLEN bytes of compressed data as literals + continue to the next meta-block + loop for each three block categories (i = L, I, D) + read NBLTYPESi + if NBLTYPESi >= 2 + read prefix code for block types, HTREE_BTYPE_i + read prefix code for block counts, HTREE_BLEN_i + read block count, BLEN_i + set block type, BTYPE_i to 0 + initialize second-to-last and last block types to 0 and 1 + else + set block type, BTYPE_i to 0 + set block count, BLEN_i to 16777216 + 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 literal prefix codes, HTREEL[] + read array of insert-and-copy length prefix codes, HTREEI[] + read array of distance prefix codes, HTREED[] + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 34] + +Internet-Draft Brotli December 2015 + + + do + if BLEN_I is zero + read block type using HTREE_BTYPE_I and set BTYPE_I + save previous block type + read block count using HTREE_BLEN_I and set BLEN_I + decrement BLEN_I + read insert-and-copy length symbol using HTREEI[BTYPE_I] + compute insert length, ILEN, and copy length, CLEN + loop for ILEN + if BLEN_L is zero + read block type using HTREE_BTYPE_L and set BTYPE_L + save previous block type + read block count using HTREE_BLEN_L and set BLEN_L + decrement BLEN_L + look up context mode CMODE[BTYPE_L] + compute context ID, CIDL from last two uncompressed bytes + read literal using HTREEL[CMAPL[64*BTYPE_L + CIDL]] + write literal to uncompressed stream + if number of uncompressed bytes produced in the loop for + this meta-block is MLEN, then break from loop (in this + case the copy length is ignored and can have any value) + if distance code is implicit zero from insert-and-copy code + set backward distance to the last distance + else + if BLEN_D is zero + read block type using HTREE_BTYPE_D and set BTYPE_D + save previous block type + read block count using HTREE_BLEN_D and set BLEN_D + decrement BLEN_D + compute context ID, CIDD from CLEN + read distance code using HTREED[CMAPD[4*BTYPE_D + CIDD]] + compute distance by distance short code substitution + if distance code is not zero, + and distance is not a static dictionary reference, + push distance to the ring buffer of last distances + if distance is less than the max allowed distance plus one + move backwards distance bytes in the uncompressed data, + and copy CLEN bytes from this position to + the uncompressed stream + else + look up the static dictionary word, transform the word as + directed, and copy the result to the uncompressed stream + while number of uncompressed bytes for this meta-block < MLEN + while not ISLAST + + If the stream ends before the completion of the last meta-block, then + the stream should be rejected as invalid. + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 35] + +Internet-Draft Brotli December 2015 + + + Note that a duplicated string reference may refer to a string in a + previous meta-block, i.e. the backward distance may cross one or more + meta-block boundaries. However a backward copy distance will not + refer past the beginning of the uncompressed stream or the window + size; any such distance is interpreted as a reference to a static + dictionary word. Also note that the referenced string may overlap the + current position, for example, if the last 2 bytes decoded have + values X and Y, a string reference with + adds X,Y,X,Y,X to the uncompressed stream. + +11. Security Considerations + + As with any compressed file formats, decompressor implementations + should handle all compressed data byte sequences, not only those that + conform to this specification, where non-conformant compressed data + sequences should be discarded. A possible attack against a system + containing a decompressor implementation (e.g. a web browser) is to + exploit a buffer overflow caused by an invalid compressed data. + Therefore decompressor implementations should perform bounds-checking + for each memory access that result from values decoded from the + compressed stream. + +12. IANA Considerations + + The "HTTP Content Coding Registry" has been updated with the + registration below: + + +-------+-------------------------------------+------------+ + | Name | Description | Reference | + +-------+-------------------------------------+------------+ + | br | Brotli Compressed Data Format | RFCXXXX | + +-------+-------------------------------------+------------+ + +13. Informative References + + [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. + + [LZ77] Ziv J., Lempel A., "A Universal Algorithm for Sequential + Data Compression", IEEE Transactions on Information + Theory, Vol. 23, No. 3, pp. 337-343. + + [RFC1951] Deutsch, P., "DEFLATE Compressed Data Format Specification + version 1.3", RFC 1951, Aladdin Enterprises, May 1996. + http://www.ietf.org/rfc/rfc1951.txt + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 36] + +Internet-Draft Brotli December 2015 + + + [WOFF2] Levantovsky, V. (ed.), Levien, R. (ed.), "WOFF File Format + 2.0", W3C WebFonts Working Group, + http://www.w3.org/TR/WOFF2/ + +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 + +15. Acknowledgments + + The authors would like to thank Mark Adler, Robert Obryk, Thomas + Pickert, and Joe Tsai for providing helpful review comments, + validating the specification by writing an independent decompressor, + and suggesting improvements to the format and the text of the + specification. + +Appendix A. Static dictionary data + + The hexadecimal form of the DICT array is the following, where the + length is 122,784 bytes and the zlib CRC-32 of the byte sequence is + 0x5136cb04. + + 74696d65646f776e6c6966656c6566746261636b636f64656461746173686f77 + 6f6e6c7973697465636974796f70656e6a7573746c696b6566726565776f726b + 74657874796561726f766572626f64796c6f7665666f726d626f6f6b706c6179 + 6c6976656c696e6568656c70686f6d65736964656d6f7265776f72646c6f6e67 + 7468656d7669657766696e64706167656461797366756c6c686561647465726d + 656163686172656166726f6d747275656d61726b61626c6575706f6e68696768 + 646174656c616e646e6577736576656e6e65787463617365626f7468706f7374 + 757365646d61646568616e6468657265776861746e616d654c696e6b626c6f67 + 73697a656261736568656c646d616b656d61696e757365722729202b686f6c64 + 656e6473776974684e65777372656164776572657369676e74616b6568617665 + 67616d657365656e63616c6c7061746877656c6c706c75736d656e7566696c6d + 706172746a6f696e746869736c697374676f6f646e6565647761797377657374 + 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10, + 10, 10, 10, 9, 9, 8, 7, 7, 8, 7, + 7, 6, 6, 5, 5 + +Appendix B. List of word transformations + +The string literals are in C format, with respect to the use of +backslash escape characters. + +In order to generate a length and check value, the transforms can be +converted to a series of bytes, where each transform is the prefix +sequence of bytes plus a terminating zero byte, a single byte value +identifying the transform, and the suffix sequence of bytes plus a +terminating zero. The value for the transforms are 0 for Identity, 1 for +UppercaseFirst, 2 for UppercaseAll, 3 to 11 for OmitFirst1 to +OmitFirst9, and 12 to 20 for OmitLast1 to OmitLast9. The byte sequences +that represent the 121 transforms are then concatenated to a single +sequence of bytes. The length of that sequence is 648 bytes, and the +zlib CRC is 0x3d965f81. + + ID Prefix Transform Suffix + -- ------ --------- ------ + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 117] + +Internet-Draft Brotli December 2015 + + + 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 " + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 118] + +Internet-Draft Brotli December 2015 + + + 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 " + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 119] + +Internet-Draft Brotli December 2015 + + + 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 "='" + + +Authors' Addresses + + Jyrki Alakuijala + Google, Inc + + Email: jyrki@google.com + + + Zoltan Szabadka + Google, Inc + + Email: szabadka@google.com + + + + + + + + + + + + +Alakuijala & Szabadka Expires June 10, 2016 [Page 120] + -- cgit v1.1