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author | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-03-09 13:19:48 +0000 |
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committer | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-03-09 13:20:02 +0000 |
commit | 58daab21cd043e1dc37024a7f99b396788372918 (patch) | |
tree | 96771e43bb69f7c1c2b0b4f7374cb74d7866d0cb /web/server/h2o/libh2o/deps/brotli/docs/draft-alakuijala-brotli-08.nroff | |
parent | Releasing debian version 1.43.2-1. (diff) | |
download | netdata-58daab21cd043e1dc37024a7f99b396788372918.tar.xz netdata-58daab21cd043e1dc37024a7f99b396788372918.zip |
Merging upstream version 1.44.3.
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
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diff --git a/web/server/h2o/libh2o/deps/brotli/docs/draft-alakuijala-brotli-08.nroff b/web/server/h2o/libh2o/deps/brotli/docs/draft-alakuijala-brotli-08.nroff new file mode 100644 index 000000000..5bbf37394 --- /dev/null +++ b/web/server/h2o/libh2o/deps/brotli/docs/draft-alakuijala-brotli-08.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 <length, backward distance>. There can be +zero literal bytes in the command. The minimum length of the string to be +duplicated is two, but the last command in the meta-block is permitted to have +only literals and no pointer to a string to duplicate. + +Each command in the compressed data is represented using three categories +of prefix codes: + +.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 <block type, block count>. +The block-switch commands are represented in the compressed data +before the start of each new block using a prefix code for +block types and a separate prefix code for block counts for +each block category. For the above example the physical layout of the +meta-block is then: + +.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 <distance code, extra bits>. The distance +code and the extra bits are encoded back-to-back, the distance code +is encoded using a prefix code over the distance alphabet, +while the extra bits value is encoded as a fixed-width integer +value. The number of extra bits can be 0 - 24, and it is dependent +on the distance code. + +To convert a distance code and associated extra bits to a backward +distance, we need the sequence of past distances and two additional +parameters, the number of "postfix bits", denoted by NPOSTFIX (0..3), and +the number of direct distance codes, denoted by NDIRECT (0..120). Both of +these parameters are encoded in the meta-block header. We will also +use the following derived parameter: + +.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 <insertion length, copy length> pair in the compressed data part +of a meta-block is represented with the following triplet: + +.nf + <insert-and-copy length code, insert extra bits, copy extra bits> +.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 +<block type, block count>. These are encoded in the compressed data +part of the meta-block, right before the start of each new block of a +particular block category. + +Each block type in the compressed data is represented with a block +type code, encoded using a prefix code over the block type code +alphabet. A block type symbol 0 means that the new block type is the same +as the type of the previous block from the same block category, i.e. +the block type that preceded the current type, +while a block type symbol 1 means that the new block type equals the current +block type plus one. If the current block type is the maximal possible, +then a block type symbol of 1 results in wrapping to a new block type of 0. +Block type symbols 2 - 257 +represent block types 0 - 255 respectively. The previous and current block types +are initialized to 1 and 0, respectively, at the end of the +meta-block header. + +Since the first block type of each block category is 0, the block +type of the first block-switch command is not encoded in +the compressed data. 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 +<block count code, extra bits>. The block count code and the extra +bits are encoded back-to-back, the block count code is encoded using +a prefix code over the block count code alphabet, while the extra +bits value is encoded as a fixed-width integer value. The number of +extra bits can be 0 - 24, and it is dependent on the block count +code. The symbols of the block count code alphabet, along with the +number of extra bits, and the range of block counts are as follows: + +.nf +.KS + Extra Extra Extra + Code Bits Lengths Code Bits Lengths Code Bits Lengths + ---- ---- ------ ---- ---- ------- ---- ---- ------- + 0 2 1-4 9 4 65-80 18 7 369-496 + 1 2 5-8 10 4 81-96 19 8 497-752 + 2 2 9-12 11 4 97-112 20 9 753-1264 + 3 2 13-16 12 5 113-144 21 10 1265-2288 + 4 3 17-24 13 5 145-176 22 11 2289-4336 + 5 3 25-32 14 5 177-208 23 12 4337-8432 + 6 3 33-40 15 5 209-240 24 13 8433-16624 + 7 3 41-48 16 6 241-304 25 24 16625-16793840 + 8 4 49-64 17 6 305-368 +.KE +.fi + +The first block-switch command of each block category is special in +the sense that it is encoded in the meta-block header, and as +described earlier, the block type code is omitted since it is an +implicit zero. + +.ti 0 +7. Context modeling + +As described in Section 2., the prefix tree used to encode a literal +byte or a distance code depends on the 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 <block type, context ID> 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 <length, distance> pair can be reconstructed as +follows: + +.nf + word_id = distance - (max allowed distance + 1) + index = word_id % NWORDS[length] + base_word = DICT[offset(length, index)..offset(length, index+1)-1] + transform_id = word_id >> NDBITS[length] +.fi + +The string copied to the uncompressed stream is computed by applying the +transformation to the base dictionary word. If transform_id is +greater than 120, or 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 <length = 5, distance = 2> adds X,Y,X,Y,X to the +uncompressed stream. + +.ti 0 +11. Security Considerations + +As with any compressed file formats, decompressor implementations should +handle all compressed data byte sequences, not only those that conform to this +specification, where non-conformant compressed data sequences should be discarded. +A possible attack against a system containing a decompressor +implementation (e.g. a web browser) is to exploit a buffer +overflow caused by an invalid compressed data. Therefore decompressor +implementations should perform 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 + |