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Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 2 Network Working Group J. Alakuijala 3 Internet-Draft Z. Szabadka 4 Intended Status: Informational Google, Inc 5 Expires: June 10, 2016 December 2015 7 Brotli Compressed Data Format 8 draft-alakuijala-brotli-08 10 Abstract 12 This specification defines a lossless compressed data format that 13 compresses data using a combination of the LZ77 algorithm and Huffman 14 coding, with efficiency comparable to the best currently available 15 general-purpose compression methods. 17 Status of this Memo 19 This Internet-Draft is submitted in full conformance with the 20 provisions of BCP 78 and BCP 79. 22 Internet-Drafts are working documents of the Internet Engineering 23 Task Force (IETF). Note that other groups may also distribute 24 working documents as Internet-Drafts. The list of current Internet- 25 Drafts is at http://datatracker.ietf.org/drafts/current/. 27 Internet-Drafts are draft documents valid for a maximum of six months 28 and may be updated, replaced, or obsoleted by other documents at any 29 time. It is inappropriate to use Internet-Drafts as reference 30 material or to cite them other than as "work in progress." 32 This Internet-Draft will expire on June 10, 2016. 34 Copyright Notice 36 Copyright (c) 2015 IETF Trust and the persons identified as the 37 document authors. All rights reserved. 39 This document is subject to BCP 78 and the IETF Trust's Legal 40 Provisions Relating to IETF Documents 41 (http://trustee.ietf.org/license-info) in effect on the date of 42 publication of this document. Please review these documents 43 carefully, as they describe your rights and restrictions with respect 44 to this document. Code Components extracted from this document must 45 include Simplified BSD License text as described in Section 4.e of 46 the Trust Legal Provisions and are provided without warranty as 47 described in the Simplified BSD License. 49 Table of Contents 51 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3 52 1.1. Purpose . . . . . . . . . . . . . . . . . . . . . . . . . 3 53 1.2. Intended audience . . . . . . . . . . . . . . . . . . . . 3 54 1.3. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . 3 55 1.4. Compliance . . . . . . . . . . . . . . . . . . . . . . . . 4 56 1.5. Definitions of terms and conventions used . . . . . . . . 4 57 1.5.1. Packing into bytes . . . . . . . . . . . . . . . . . 4 58 2. Compressed representation overview . . . . . . . . . . . . . . 5 59 3. Compressed representation of prefix codes . . . . . . . . . . . 9 60 3.1. Introduction to prefix coding . . . . . . . . . . . . . . 9 61 3.2. Use of prefix coding in the brotli format . . . . . . . . 10 62 3.3. Alphabet sizes . . . . . . . . . . . . . . . . . . . . . 12 63 3.4. Simple prefix codes . . . . . . . . . . . . . . . . . . . 13 64 3.5. Complex prefix codes . . . . . . . . . . . . . . . . . . 14 65 4. Encoding of distances . . . . . . . . . . . . . . . . . . . . 16 66 5. Encoding of literal insertion lengths and copy lengths . . . . 18 67 6. Encoding of block switch commands . . . . . . . . . . . . . . 20 68 7. Context modeling . . . . . . . . . . . . . . . . . . . . . . . 22 69 7.1. Context modes and context ID lookup for literals . . . . 22 70 7.2. Context ID for distances . . . . . . . . . . . . . . . . 24 71 7.3. Encoding of the context map . . . . . . . . . . . . . . . 24 72 8. Static dictionary . . . . . . . . . . . . . . . . . . . . . . 26 73 9. Compressed data format . . . . . . . . . . . . . . . . . . . . 28 74 9.1. Format of the stream header . . . . . . . . . . . . . . . 29 75 9.2. Format of the meta-block header . . . . . . . . . . . . . 29 76 9.3. Format of the meta-block data . . . . . . . . . . . . . . 32 77 10. Decoding algorithm . . . . . . . . . . . . . . . . . . . . . 33 78 11. Security Considerations . . . . . . . . . . . . . . . . . . . 36 79 12. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 36 80 13. Informative References . . . . . . . . . . . . . . . . . . . 36 81 14. Source code . . . . . . . . . . . . . . . . . . . . . . . . . 37 82 15. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 37 83 Appendix A. Static dictionary data . . . . . . . . . . . . . . . 37 84 Appendix B. List of word transformations . . . . . . . . . . . . 117 85 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 120 87 1. Introduction 89 1.1. Purpose 91 The purpose of this specification is to define a lossless compressed 92 data format that: 94 * Is independent of CPU type, operating system, file system, 95 and character set, and hence can be used for interchange; 96 * Can be produced or consumed, even for an arbitrarily long 97 sequentially presented input data stream, using only an a 98 priori bounded amount of intermediate storage, and hence 99 can be used in data communications or similar structures, 100 such as Unix filters; 101 * Compresses data with a compression ratio comparable to the 102 best currently available general-purpose compression methods, 103 and in particular, considerably better than the gzip program; 104 * Decompresses much faster than current LZMA implementations. 106 The data format defined by this specification does not attempt to: 108 * Allow random access to compressed data; 109 * Compress specialized data (e.g., raster graphics) as well 110 as the best currently available specialized algorithms. 112 1.2. Intended audience 114 This specification is intended for use by software implementers to 115 compress data into and/or decompress data from the brotli format. 117 The text of the specification assumes a basic background in 118 programming at the level of bits and other primitive data 119 representations. Familiarity with the technique of Huffman coding is 120 helpful but not required. 122 This specification uses heavily the notations and terminology 123 introduced in the DEFLATE format specification [RFC 1951]. For the 124 sake of completeness, we always include the whole text of the 125 relevant parts of RFC 1951, therefore familiarity with the DEFLATE 126 format is helpful but not required. 128 The compressed data format defined in this specification is an 129 integral part of the WOFF 2.0 web font file format [WOFF2], therefore 130 this specification is also intended for implementers of WOFF 2.0 131 compressors and decompressors. 133 1.3. Scope 134 The specification specifies a method for representing a sequence of 135 bytes as a (usually shorter) sequence of bits, and a method for 136 packing the latter bit sequence into bytes. 138 1.4. Compliance 140 Unless otherwise indicated below, a compliant decompressor must be 141 able to accept and decompress any data set that conforms to all the 142 specifications presented here. A compliant compressor must produce 143 data sets that conform to all the specifications presented here. 145 1.5. Definitions of terms and conventions used 147 Byte: 8 bits stored or transmitted as a unit (same as an octet). For 148 this specification, a byte is exactly 8 bits, even on machines that 149 store a character on a number of bits different from eight. See 150 below for the numbering of bits within a byte. 152 String: a sequence of arbitrary bytes. 154 Bytes stored within a computer do not have a "bit order", since they 155 are always treated as a unit. However, a byte considered as an 156 integer between 0 and 255 does have a most- and least-significant 157 bit, and since we write numbers with the most-significant digit on 158 the left, we also write bytes with the most-significant bit on the 159 left. In the diagrams below, we number the bits of a byte so that bit 160 0 is the least-significant bit, i.e., the bits are numbered: 162 +--------+ 163 |76543210| 164 +--------+ 166 Within a computer, a number may occupy multiple bytes. All multi-byte 167 numbers in the format described here are stored with the least- 168 significant byte first (at the lower memory address). For example, 169 the decimal number 520 is stored as: 171 0 1 172 +--------+--------+ 173 |00001000|00000010| 174 +--------+--------+ 175 ^ ^ 176 | | 177 | + more significant byte = 2 x 256 178 + less significant byte = 8 180 1.5.1. Packing into bytes 181 This document does not address the issue of the order in which bits 182 of a byte are transmitted on a bit-sequential medium, since the final 183 data format described here is byte- rather than bit-oriented. 184 However, we describe the compressed block format below as a sequence 185 of data elements of various bit lengths, not a sequence of bytes. We 186 must therefore specify how to pack these data elements into bytes to 187 form the final compressed byte sequence: 189 * Data elements are packed into bytes in order of 190 increasing bit number within the byte, i.e., starting 191 with the least-significant bit of the byte. 192 * Data elements other than prefix codes are packed 193 starting with the least-significant bit of the data 194 element. These are referred to here as integer values 195 and are considered unsigned. 196 * Prefix codes are packed starting with the most-significant 197 bit of the code. 199 In other words, if one were to print out the compressed data as a 200 sequence of bytes, starting with the first byte at the *right* margin 201 and proceeding to the *left*, with the most-significant bit of each 202 byte on the left as usual, one would be able to parse the result from 203 right to left, with fixed-width elements in the correct MSB-to-LSB 204 order and prefix codes in bit-reversed order (i.e., with the first 205 bit of the code in the relative LSB position). 207 2. Compressed representation overview 209 A compressed data set consists of a header and a series of meta- 210 blocks. Each meta-block decompresses to a sequence of 0 to 16,777,216 211 (16 MiB) uncompressed bytes. The final uncompressed data is the 212 concatenation of the uncompressed sequences from each meta-block. 214 The header contains the size of the sliding window that was used 215 during compression. The decompressor must retain at least that 216 amount of uncompressed data prior to the current position in the 217 stream, in order to be able to decompress what follows. The sliding 218 window size is a power of two, minus 16, where the power is in the 219 range of 10 to 24. The possible sliding window sizes range from 1 KiB 220 - 16 B to 16 MiB - 16 B. 222 Each meta-block is compressed using a combination of the LZ77 223 algorithm (Lempel-Ziv 1977, [LZ77]) and Huffman coding. The result of 224 Huffman coding is referred to here as a prefix code. The prefix 225 codes for each meta-block are independent of those for previous or 226 subsequent meta-blocks; the LZ77 algorithm may use a reference to a 227 duplicated string occurring in a previous meta-block, up to the 228 sliding window size of uncompressed bytes before. In addition, in 229 the brotli format, a string reference may instead refer to a static 230 dictionary entry. 232 Each meta-block consists of two parts: a meta-block header that 233 describes the representation of the compressed data part, and a 234 compressed data part. The compressed data consists of a series of 235 commands. Each command consists of two parts: a sequence of literal 236 bytes (of strings that have not been detected as duplicated within 237 the sliding window), and a pointer to a duplicated string, 238 represented as a pair . There can be zero 239 literal bytes in the command. The minimum length of the string to be 240 duplicated is two, but the last command in the meta-block is 241 permitted to have only literals and no pointer to a string to 242 duplicate. 244 Each command in the compressed data is represented using three 245 categories of prefix codes: 247 1) One set of prefix codes are for the literal sequence lengths 248 (also referred to as literal insertion lengths) and 249 backward copy lengths. That is, a single code word represents 250 two lengths, one of the literal sequence and one of the 251 backward copy. 253 2) One set of prefix codes are for literals. 255 3) One set of prefix codes are for distances. 257 The prefix code descriptions for each meta-block appear in a compact 258 form just before the compressed data in the meta-block header. The 259 insert-and-copy length and distance prefix codes may be followed by 260 extra bits that are added to the base values determined by the codes. 261 The number of extra bits is determined by the code. 263 One meta-block command then appears as a sequence of prefix codes: 265 Insert-and-copy length, literal, literal, ..., literal, distance 267 where the insert-and-copy defines an insertion length and a copy 268 length. The insertion length determines the number of literals that 269 immediately follow. The distance defines how far back to go for the 270 copy and the copy length determines the number of bytes to copy. The 271 resulting uncompressed data is the sequence of bytes: 273 literal, literal, ..., literal, copy, copy, ..., copy 275 where the number of literal bytes and copy bytes are determined by 276 the insert-and-copy length code. (The number of bytes copied for a 277 static dictionary entry can vary from the copy length.) 279 The last command in the meta-block may end with the last literal if 280 the total uncompressed length of the meta-block has been satisfied. 281 In that case there is no distance in the last command, and the copy 282 length is ignored. 284 There can be more than one prefix code for each category, where the 285 prefix code to use for the next element of that category is 286 determined by the context of the compressed stream that precedes that 287 element. Part of that context is three current block types, one for 288 each category. A block type is in the range of 0..255. For each 289 category there is a count of how many elements of that category 290 remain to be decoded using the current block type. Once that count is 291 expended, a new block type and block count is read from the stream 292 immediately preceding the next element of that category, which will 293 use the new block type. 295 The insert-and-copy block type directly determines which prefix code 296 to use for the next insert-and-copy element. For the literal and 297 distance elements, the respective block type is used in combination 298 with other context information to determine which prefix code to use 299 for the next element. 301 Consider the following example: 303 (IaC0, L0, L1, L2, D0)(IaC1, D1)(IaC2, L3, L4, D2)(IaC3, L5, D3) 305 The meta-block here has four commands, contained in parentheses for 306 clarity, where each of the three categories of symbols within these 307 commands can be interpreted using different block types. Here we 308 separate out each category as its own sequence to show an example of 309 block types assigned to those elements. Each square-bracketed group 310 is a block that uses the same block type: 312 [IaC0, IaC1][IaC2, IaC3] <-- insert-and-copy: block types 0 and 1 314 [L0, L1][L2, L3, L4][L5] <-- literals: block types 0, 1, and 0 316 [D0][D1, D2, D3] <-- distances: block types 0 and 1 318 The subsequent blocks within each block category must have different 319 block types, but we see that block types can be reused later in the 320 meta-block. The block types are numbered from 0 to the maximum block 321 type number of 255 and the first block of each block category is type 322 0. The block structure of a meta-block is represented by the sequence 323 of block-switch commands for each block category, where a block- 324 switch command is a pair . The block-switch 325 commands are represented in the compressed data before the start of 326 each new block using a prefix code for block types and a separate 327 prefix code for block counts for each block category. For the above 328 example the physical layout of the meta-block is then: 330 IaC0 L0 L1 LBlockSwitch(1, 3) L2 D0 IaC1 DBlockSwitch(1, 3) D1 331 IaCBlockSwitch(1, 2) IaC2 L3 L4 D2 IaC3 LBlockSwitch(0, 1) L5 D3 333 where xBlockSwitch(t, n) switches to block type t for a count of n 334 elements. Note that in this example DBlockSwitch(1, 3) immediately 335 precedes the next required distance D1. It does not follow the last 336 distance of the previous block, D0. Whenever an element of a category 337 is needed, and the block count for that category has reached zero, 338 then a new block type and count is read from the stream just before 339 reading that next element. 341 The block-switch commands for the first blocks of each category are 342 not part of the meta-block compressed data. Instead the first block 343 type is defined to be 0, and the first block count for each category 344 is encoded in the meta-block header. The prefix codes for the block 345 types and counts, a total of six prefix codes over the three 346 categories, are defined in a compact form in the meta-block header. 348 Each category of value (insert-and-copy lengths, literals, and 349 distances) can be encoded with any prefix code from a collection of 350 prefix codes belonging to the same category appearing in the meta- 351 block header. The particular prefix code used can depend on two 352 factors: the block type of the block the value appears in, and the 353 context of the value. In the case of the literals, the context is 354 the previous two bytes in the uncompressed data, and in the case of 355 distances, the context is the copy length from the same command. For 356 insert-and-copy lengths, no context is used and the prefix code 357 depends only on the block type. In the case of literals and 358 distances, the context is mapped to a context ID in the range 0..63 359 for literals and 0..3 for distances. The matrix of the prefix code 360 indexes for each block type and context ID, called the context map, 361 is encoded in a compact form in the meta-block header. 363 For example, the prefix code to use to decode L2 depends on the block 364 type (1), and the literal context ID determined by the two 365 uncompressed bytes that were decoded from L0 and L1. Similarly, the 366 prefix code to use to decode D0 depends on the block type (0), and 367 the distance context ID determined by the copy length decoded from 368 IaC0. The prefix code to use to decode IaC3 depends only on the block 369 type (1). 371 In addition to the parts listed above (prefix code for insert-and- 372 copy lengths, literals, distances, block types and block counts, and 373 the context map), the meta-block header contains the number of 374 uncompressed bytes coded in the meta-block and two additional 375 parameters used in the representation of match distances: the number 376 of postfix bits and the number of direct distance codes. 378 A compressed meta-block may be marked in the header as the last meta- 379 block, which terminates the compressed stream. 381 A meta-block may instead simply store the uncompressed data directly 382 as bytes on byte boundaries with no coding or matching strings. In 383 this case the meta-block header information only contains the number 384 of uncompressed bytes and the indication that the meta-block is 385 uncompressed. An uncompressed meta-block cannot be the last meta- 386 block. 388 A meta-block may also be empty, which generates no uncompressed data 389 at all. An empty meta-block may contain metadata information as 390 bytes starting on byte boundaries, which are not part of either the 391 sliding window or the uncompressed data. Thus, these metadata bytes 392 cannot be used to create matching strings in subsequent meta-blocks 393 and are not used as context bytes for literals. 395 3. Compressed representation of prefix codes 397 3.1. Introduction to prefix coding 399 Prefix coding represents symbols from an a priori known alphabet by 400 bit sequences (codes), one code for each symbol, in a manner such 401 that different symbols may be represented by bit sequences of 402 different lengths, but a parser can always parse an encoded string 403 unambiguously symbol-by-symbol. 405 We define a prefix code in terms of a binary tree in which the two 406 edges descending from each non-leaf node are labeled 0 and 1 and in 407 which the leaf nodes correspond one-for-one with (are labeled with) 408 the symbols of the alphabet; then the code for a symbol is the 409 sequence of 0's and 1's on the edges leading from the root to the 410 leaf labeled with that symbol. For example: 412 /\ Symbol Code 413 0 1 ------ ---- 414 / \ A 00 415 /\ B B 1 416 0 1 C 011 417 / \ D 010 418 A /\ 419 0 1 420 / \ 421 D C 423 A parser can decode the next symbol from the compressed stream by 424 walking down the tree from the root, at each step choosing the edge 425 corresponding to the next compressed data bit. 427 Given an alphabet with known symbol frequencies, the Huffman 428 algorithm allows the construction of an optimal prefix code (one 429 which represents strings with those symbol frequencies using the 430 fewest bits of any possible prefix codes for that alphabet). Such a 431 prefix code is called a Huffman code. (See [HUFFMAN] in Chapter 5, 432 references for additional information on Huffman codes.) 434 Note that in the brotli format, the prefix codes for the various 435 alphabets must not exceed certain maximum code lengths. This 436 constraint complicates the algorithm for computing code lengths from 437 symbol frequencies. Again, see Chapter 5, references for details. 439 3.2. Use of prefix coding in the brotli format 441 The prefix codes used for each alphabet in the brotli format are 442 canonical prefix codes, which have two additional rules: 444 * All codes of a given bit length have lexicographically 445 consecutive values, in the same order as the symbols they 446 represent; 448 * Shorter codes lexicographically precede longer codes. 450 We could recode the example above to follow this rule as follows, 451 assuming that the order of the alphabet is ABCD: 453 Symbol Code 454 ------ ---- 455 A 10 456 B 0 457 C 110 458 D 111 460 I.e., 0 precedes 10, which precedes 11x, and 110 and 111 are 461 lexicographically consecutive. 463 Given this rule, we can define the canonical prefix code for an 464 alphabet just by giving the bit lengths of the codes for each symbol 465 of the alphabet in order; this is sufficient to determine the actual 466 codes. In our example, the code is completely defined by the sequence 467 of bit lengths (2, 1, 3, 3). The following algorithm generates the 468 codes as integers, intended to be read from most- to least- 469 significant bit. The code lengths are initially in tree[I].Len; the 470 codes are produced in tree[I].Code. 472 1) Count the number of codes for each code length. Let 473 bl_count[N] be the number of codes of length N, N >= 1. 475 2) Find the numerical value of the smallest code for each 476 code length: 478 code = 0; 479 bl_count[0] = 0; 480 for (bits = 1; bits <= MAX_BITS; bits++) { 481 code = (code + bl_count[bits-1]) << 1; 482 next_code[bits] = code; 483 } 485 3) Assign numerical values to all codes, using consecutive 486 values for all codes of the same length with the base 487 values determined at step 2. Codes that are never used 488 (which have a bit length of zero) must not be assigned a 489 value. 491 for (n = 0; n <= max_code; n++) { 492 len = tree[n].Len; 493 if (len != 0) { 494 tree[n].Code = next_code[len]; 495 next_code[len]++; 496 } 497 } 499 Example: 501 Consider the alphabet ABCDEFGH, with bit lengths (3, 3, 3, 3, 3, 2, 502 4, 4). After step 1, we have: 504 N bl_count[N] 505 - ----------- 506 2 1 507 3 5 508 4 2 510 Step 2 computes the following next_code values: 512 N next_code[N] 513 - ------------ 514 1 0 515 2 0 516 3 2 517 4 14 519 Step 3 produces the following code values: 521 Symbol Length Code 522 ------ ------ ---- 523 A 3 010 524 B 3 011 525 C 3 100 526 D 3 101 527 E 3 110 528 F 2 00 529 G 4 1110 530 H 4 1111 532 3.3. Alphabet sizes 534 Prefix codes are used for different purposes in the brotli format, 535 and each purpose has a different alphabet size. For literal codes the 536 alphabet size is 256. For insert-and-copy length codes the alphabet 537 size is 704. For block count codes, the alphabet size is 26. For 538 distance codes, block type codes, and the prefix codes used in 539 compressing the context map, the alphabet size is dynamic and is 540 based on parameters defined in later sections. The following table 541 summarizes the alphabet sizes for the various prefix codes and the 542 sections where they are defined. 544 +-----------------+-------------------------+------------+ 545 | Prefix code | Alphabet size | Definition | 546 +-----------------+-------------------------+------------+ 547 | literal | 256 | | 548 +-----------------+-------------------------+------------+ 549 | distance | 16 + NDIRECT + | Section 4. | 550 | | (48 << NPOSTFIX) | | 551 +-----------------+-------------------------+------------+ 552 | insert-and-copy | 704 | Section 5. | 553 | length | | | 554 +-----------------+-------------------------+------------+ 555 | block count | 26 | Section 6. | 556 +-----------------+-------------------------+------------+ 557 | block type | NBLTYPESx + 2, | Section 6. | 558 | | (where x is I, L, or D) | | 559 +-----------------+-------------------------+------------+ 560 | context map | NTREESx + RLEMAXx | Section 7. | 561 | | (where x is L or D) | | 562 +-----------------+-------------------------+------------+ 564 3.4. Simple prefix codes 566 The first two bits of the compressed representation of each prefix 567 code distinguish between simple and complex prefix codes. If this 568 value is 1, then a simple prefix code follows as described in this 569 section. Otherwise, a complex prefix code follows as described in 570 Section 3.5. 572 A simple prefix code can have only up to four symbols with non-zero 573 code length. The format of the simple prefix code is as follows: 575 2 bits: value of 1 indicates a simple prefix code 576 2 bits: NSYM - 1, where NSYM = # of symbols coded 578 NSYM symbols, each encoded using ALPHABET_BITS bits 580 1 bit: tree-select, present only for NSYM = 4 582 The value of ALPHABET_BITS depends on the alphabet of the prefix 583 code: it is the smallest number of bits that can represent all 584 symbols in the alphabet. E.g. for the alphabet of literal bytes, 585 ALPHABET_BITS is 8. The value of each of the NSYM symbols above is 586 the value of the ALPHABETS_BITS width integer value. If the integer 587 value is greater than or equal to the alphabet size, or the value is 588 identical to a previous value, then the stream should be rejected as 589 invalid. 591 Note that the NSYM symbols may not be presented in sorted order. 593 Prefix codes of the same bit length must be assigned to the symbols 594 in sorted order. 596 The (non-zero) code lengths of the symbols can be reconstructed as 597 follows: 599 * if NSYM = 1, the code length for the one symbol is zero -- 600 when encoding this symbol in the 601 compressed data stream using this prefix code, no 602 actual bits are emitted. Similarly, when decoding a symbol 603 using this prefix code, no bits are read and the one symbol 604 is returned. 606 * if NSYM = 2, both symbols have code length 1. 608 * if NSYM = 3, the code lengths for the symbols are 1, 2, 2 in 609 the order they appear in the representation of the simple 610 prefix code. 612 * if NSYM = 4, the code lengths (in order of symbols decoded) 613 depend on the tree-select bit: 2, 2, 2, 2 (tree-select bit 0), 614 or 1, 2, 3, 3 (tree-select bit 1). 616 3.5. Complex prefix codes 618 A complex prefix code is a canonical prefix code, defined by the 619 sequence of code lengths, as discussed in Section 3.2., above. For 620 even greater compactness, the code length sequences themselves are 621 compressed using a prefix code. The alphabet for code lengths is as 622 follows: 624 0 - 15: Represent code lengths of 0 - 15 625 16: Copy the previous non-zero code length 3 - 6 times 626 The next 2 bits indicate repeat length 627 (0 = 3, ... , 3 = 6) 628 If this is the first code length, or all previous 629 code lengths are zero, a code length of 8 is 630 repeated 3 - 6 times 631 A repeated code length code of 16 modifies the 632 repeat count of the previous one as follows: 633 repeat count = (4 * (repeat count - 2)) + 634 (3 - 6 on the next 2 bits) 635 Example: Codes 7, 16 (+2 bits 11), 16 (+2 bits 10) 636 will expand to 22 code lengths of 7 637 (1 + 4 * (6 - 2) + 5) 638 17: Repeat a code length of 0 for 3 - 10 times. 639 (3 bits of length) 640 A repeated code length code of 17 modifies the 641 repeat count of the previous one as follows: 642 repeat count = (8 * (repeat count - 2)) + 643 (3 - 10 on the next 3 bits) 645 Note that a code of 16 that follows an immediately preceding 16 646 modifies the previous repeat count, which becomes the new repeat 647 count. The same is true for a 17 following a 17. A sequence of three 648 or more 16 codes in a row or three of more 17 codes in a row is 649 possible, modifying the count each time. Only the final repeat count 650 is used. The modification only applies if the same code follows. A 16 651 repeat does not modify an immediately preceding 17 count nor vice 652 versa. 654 A code length of 0 indicates that the corresponding symbol in the 655 alphabet will not occur in the compressed data, and should not 656 participate in the prefix code construction algorithm given earlier. 657 A complex prefix code must have at least two non-zero code lengths. 659 The bit lengths of the prefix code over the code length alphabet are 660 compressed with the following variable length code (as it appears in 661 the compressed data, where the bits are parsed from right to left): 663 Symbol Code 664 ------ ---- 665 0 00 666 1 0111 667 2 011 668 3 10 669 4 01 670 5 1111 672 We can now define the format of the complex prefix code as follows: 674 2 bits: HSKIP, values of 0, 2, or 3 represent the respective 675 number of skipped code lengths. The skipped lengths 676 are taken to be zero. (An HSKIP of 1 indicates a 677 Simple prefix code.) 679 Code lengths for symbols in the code length alphabet given 680 just above, in the order: 1, 2, 3, 4, 0, 5, 17, 6, 16, 7, 681 8, 9, 10, 11, 12, 13, 14, 15. If HSKIP is 2, then the 682 code lengths for symbols 1 and 2 are zero, and the first 683 code length is for symbol 3. If HSKIP is 3, then the code 684 length for symbol 3 is also zero, and the first code length 685 is for symbol 4. 687 The code lengths of code length symbols are between 0 and 688 5, and they are represented with 2 - 4 bits according to 689 the variable length code above. A code length of 0 means 690 the corresponding code length symbol is not used. 692 If HSKIP is 2 or 3, a respective number of leading code 693 lengths are implicit zeros and are not present in the 694 code lengths sequence above. 696 If there are at least two non-zero code lengths, any 697 trailing zero code lengths are omitted, i.e. the last 698 code length in the sequence must be non-zero. In this 699 case, the sum of (32 >> code length) over all the non-zero 700 code lengths must equal to 32. 702 If the lengths have been read for the entire code length 703 alphabet and there was only one non-zero code length, 704 then the prefix code has one symbol whose code has zero 705 length. In this case, that symbol results in no bits 706 being emitted by the compressor, and no bits consumed by 707 the decompressor. That single symbol is immediately 708 returned when this code is decoded. 709 An example of where this occurs is if the 710 entire code to be represented has symbols of length 8. 711 E.g. a literal code that represents all literal values 712 with equal probability. In this case the single symbol 713 is 16, which repeats the previous length. The previous 714 length is taken to be 8 before any code length code 715 lengths are read. 717 Sequence of at most alphabet size code lengths symbols, encoded 718 using the code length prefix code. Any trailing 0 or 17 must be 719 omitted, i.e. the last encoded code length symbol must be 720 between 1 and 16. The sum of (32768 >> code length) over 721 all the non-zero code lengths in the alphabet, including 722 those encoded using repeat code(s) of 16, must equal to 723 32768. If the number of times to repeat the previous length 724 or repeat a zero length would result in more lengths in 725 total than the number of symbols in the alphabet, then the 726 stream should be rejected as invalid. 728 4. Encoding of distances 730 As described in Section 2., one component of a compressed meta-block 731 is a sequence of backward distances. In this section we provide the 732 details to the encoding of distances. 734 Each distance in the compressed data part of a meta-block is 735 represented with a pair . The distance 736 code and the extra bits are encoded back-to-back, the distance code 737 is encoded using a prefix code over the distance alphabet, while the 738 extra bits value is encoded as a fixed-width integer value. The 739 number of extra bits can be 0 - 24, and it is dependent on the 740 distance code. 742 To convert a distance code and associated extra bits to a backward 743 distance, we need the sequence of past distances and two additional 744 parameters, the number of "postfix bits", denoted by NPOSTFIX (0..3), 745 and the number of direct distance codes, denoted by NDIRECT (0..120). 746 Both of these parameters are encoded in the meta-block header. We 747 will also use the following derived parameter: 749 POSTFIX_MASK = (1 << NPOSTFIX) - 1 751 The first 16 distance symbols are special symbols that reference past 752 distances as follows: 754 0: last distance 755 1: second-to-last distance 756 2: third-to-last distance 757 3: fourth-to-last distance 758 4: last distance - 1 759 5: last distance + 1 760 6: last distance - 2 761 7: last distance + 2 762 8: last distance - 3 763 9: last distance + 3 764 10: second-to-last distance - 1 765 11: second-to-last distance + 1 766 12: second-to-last distance - 2 767 13: second-to-last distance + 2 768 14: second-to-last distance - 3 769 15: second-to-last distance + 3 771 The ring buffer of four last distances is initialized by the values 772 16, 15, 11, and 4 (i.e. the fourth-to-last is set to 16, the third- 773 to-last to 15, the second-to-last to 11, and the last distance to 4) 774 at the beginning of the *stream* (as opposed to the beginning of the 775 meta-block) and it is not reset at meta-block boundaries. When a 776 distance symbol 0 appears, the distance it represents (i.e. the last 777 distance in the sequence of distances) is not pushed to the ring 778 buffer of last distances, in other words, the expression "(second, 779 third, fourth)-to-last distance" means the (second, third, 780 fourth)-to-last distance that was not represented by a 0 distance 781 symbol. Similarly, distances that represent static dictionary words 782 (see Section 8.) are not pushed to the ring buffer of last distances. 784 If a special distance symbol resolves to a zero or negative value, 785 the stream should be rejected as invalid. 787 If NDIRECT is greater than zero, then the next NDIRECT distance 788 symbols, from 16 to 15 + NDIRECT, represent distances from 1 to 789 NDIRECT. Neither the special distance symbols, nor the NDIRECT 790 direct distance symbols are followed by any extra bits. 792 Distance symbols 16 + NDIRECT and greater all have extra bits, where 793 the number of extra bits for a distance symbol "dcode" is given by 794 the following formula: 796 ndistbits = 1 + ((dcode - NDIRECT - 16) >> (NPOSTFIX + 1)) 798 The maximum number of extra bits is 24, therefore the size of the 799 distance symbol alphabet is (16 + NDIRECT + (48 << NPOSTFIX)). 801 Given a distance symbol "dcode" (>= 16 + NDIRECT), and extra bits 802 "dextra", the backward distance is given by the following formula: 804 hcode = (dcode - NDIRECT - 16) >> NPOSTFIX 805 lcode = (dcode - NDIRECT - 16) & POSTFIX_MASK 806 offset = ((2 + (hcode & 1)) << ndistbits) - 4 807 distance = ((offset + dextra) << NPOSTFIX) + lcode + NDIRECT + 1 809 5. Encoding of literal insertion lengths and copy lengths 811 As described in Section 2., the literal insertion lengths and 812 backward copy lengths are encoded using a single prefix code. This 813 section provides the details to this encoding. 815 Each pair in the compressed data part 816 of a meta-block is represented with the following triplet: 818 820 The insert-and-copy length code, the insert extra bits, and the copy 821 extra bits are encoded back-to-back, the insert-and-copy length code 822 is encoded using a prefix code over the insert-and-copy length code 823 alphabet, while the extra bits values are encoded as fixed-width 824 integer values. The number of insert and copy extra bits can be 0 - 825 24, and they are dependent on the insert-and-copy length code. 827 Some of the insert-and-copy length codes also express the fact that 828 the distance symbol of the distance in the same command is 0, i.e. 829 the distance component of the command is the same as that of the 830 previous command. In this case, the distance code and extra bits for 831 the distance are omitted from the compressed data stream. 833 We describe the insert-and-copy length code alphabet in terms of the 834 (not directly used) insert length code and copy length code 835 alphabets. The symbols of the insert length code alphabet, along with 836 the number of insert extra bits, and the range of the insert lengths 837 are as follows: 839 Extra Extra Extra 840 Code Bits Lengths Code Bits Lengths Code Bits Lengths 841 ---- ---- ------ ---- ---- ------- ---- ---- ------- 842 0 0 0 8 2 10-13 16 6 130-193 843 1 0 1 9 2 14-17 17 7 194-321 844 2 0 2 10 3 18-25 18 8 322-577 845 3 0 3 11 3 26-33 19 9 578-1089 846 4 0 4 12 4 34-49 20 10 1090-2113 847 5 0 5 13 4 50-65 21 12 2114-6209 848 6 1 6,7 14 5 66-97 22 14 6210-22593 849 7 1 8,9 15 5 98-129 23 24 22594-16799809 851 The symbols of the copy length code alphabet, along with the number 852 of copy extra bits, and the range of copy lengths are as follows: 854 Extra Extra Extra 855 Code Bits Lengths Code Bits Lengths Code Bits Lengths 856 ---- ---- ------ ---- ---- ------- ---- ---- ------- 857 0 0 2 8 1 10,11 16 5 70-101 858 1 0 3 9 1 12,13 17 5 102-133 859 2 0 4 10 2 14-17 18 6 134-197 860 3 0 5 11 2 18-21 19 7 198-325 861 4 0 6 12 3 22-29 20 8 326-581 862 5 0 7 13 3 30-37 21 9 582-1093 863 6 0 8 14 4 38-53 22 10 1094-2117 864 7 0 9 15 4 54-69 23 24 2118-16779333 866 To convert an insert-and-copy length code to an insert length code 867 and a copy length code, the following table can be used: 869 Insert 870 length Copy length code 871 code 0-7 8-15 16-23 872 +---------+---------+ 873 | | | 874 0-7 | 0-63 | 64-127 | <--- distance symbol 0 875 | | | 876 +---------+---------+---------+ 877 | | | | 878 0-7 | 128-191 | 192-255 | 384-447 | 879 | | | | 880 +---------+---------+---------+ 881 | | | | 882 8-15 | 256-319 | 320-383 | 512-575 | 883 | | | | 884 +---------+---------+---------+ 885 | | | | 886 16-23 | 448-511 | 576-639 | 640-703 | 887 | | | | 888 +---------+---------+---------+ 890 First, look up the cell with the 64 value range containing the 891 insert-and-copy length code, this gives the insert length code and 892 the copy length code ranges, both 8 values long. The copy length 893 code within its range is determined by bits 0-2 (counted from the 894 LSB) of the insert-and-copy length code. The insert length code 895 within its range is determined by bits 3-5 (counted from the LSB) of 896 the insert-and-copy length code. Given the insert length and copy 897 length codes, the actual insert and copy lengths can be obtained by 898 reading the number of extra bits given by the tables above. 900 If the insert-and-copy length code is between 0 and 127, the distance 901 code of the command is set to zero (the last distance reused). 903 6. Encoding of block switch commands 905 As described in Section 2., a block-switch command is a pair . These are encoded in the compressed data part of 907 the meta-block, right before the start of each new block of a 908 particular block category. 910 Each block type in the compressed data is represented with a block 911 type code, encoded using a prefix code over the block type code 912 alphabet. A block type symbol 0 means that the new block type is the 913 same as the type of the previous block from the same block category, 914 i.e. the block type that preceded the current type, while a block 915 type symbol 1 means that the new block type equals the current block 916 type plus one. If the current block type is the maximal possible, 917 then a block type symbol of 1 results in wrapping to a new block type 918 of 0. Block type symbols 2 - 257 represent block types 0 - 255 919 respectively. The previous and current block types are initialized to 920 1 and 0, respectively, at the end of the meta-block header. 922 Since the first block type of each block category is 0, the block 923 type of the first block-switch command is not encoded in the 924 compressed data. If a block category has only one block type, the 925 block count of the first block-switch command is also omitted from 926 the compressed data, otherwise it is encoded in the meta-block 927 header. 929 Since the end of the meta-block is detected by the number of 930 uncompressed bytes produced, the block counts for any of the three 931 categories need not count down to exactly zero at the end of the 932 meta-block. 934 The number of different block types in each block category, denoted 935 by NBLTYPESL, NBLTYPESI, and NBLTYPESD for literals, insert-and-copy 936 lengths, and distances, respectively, is encoded in the meta-block 937 header, and it must equal to the largest block type plus one in that 938 block category. In other words, the set of literal, insert-and-copy 939 length, and distance block types must be [0..NBLTYPESL-1], 940 [0..NBLTYPESI-1], and [0..NBLTYPESD-1], respectively. From this it 941 follows that the alphabet size of literal, insert-and-copy length, 942 and distance block type codes is NBLTYPESL + 2, NBLTYPESI + 2, and 943 NBLTYPESD + 2, respectively. 945 Each block count in the compressed data is represented with a pair 946 . The block count code and the extra 947 bits are encoded back-to-back, the block count code is encoded using 948 a prefix code over the block count code alphabet, while the extra 949 bits value is encoded as a fixed-width integer value. The number of 950 extra bits can be 0 - 24, and it is dependent on the block count 951 code. The symbols of the block count code alphabet, along with the 952 number of extra bits, and the range of block counts are as follows: 954 Extra Extra Extra 955 Code Bits Lengths Code Bits Lengths Code Bits Lengths 956 ---- ---- ------ ---- ---- ------- ---- ---- ------- 957 0 2 1-4 9 4 65-80 18 7 369-496 958 1 2 5-8 10 4 81-96 19 8 497-752 959 2 2 9-12 11 4 97-112 20 9 753-1264 960 3 2 13-16 12 5 113-144 21 10 1265-2288 961 4 3 17-24 13 5 145-176 22 11 2289-4336 962 5 3 25-32 14 5 177-208 23 12 4337-8432 963 6 3 33-40 15 5 209-240 24 13 8433-16624 964 7 3 41-48 16 6 241-304 25 24 16625-16793840 965 8 4 49-64 17 6 305-368 967 The first block-switch command of each block category is special in 968 the sense that it is encoded in the meta-block header, and as 969 described earlier, the block type code is omitted since it is an 970 implicit zero. 972 7. Context modeling 974 As described in Section 2., the prefix tree used to encode a literal 975 byte or a distance code depends on the block type and the context ID. 976 This section specifies how to compute the context ID for a particular 977 literal and distance code, and how to encode the context map that 978 maps a pair to the index of a prefix code in 979 the array of literal and distance prefix codes. 981 7.1. Context modes and context ID lookup for literals 983 The context for encoding the next literal is defined by the last two 984 bytes in the stream (p1, p2, where p1 is the most recent byte), 985 regardless of whether these bytes are produced by uncompressed meta- 986 blocks, backward references, static dictionary references, or by 987 literal insertions. At the start of the stream p1 and p2 are 988 initialized to zero. 990 There are four methods, called context modes, to compute the Context 991 ID: 993 * LSB6, where the Context ID is the value of six 994 least-significant bits of p1, 995 * MSB6, where the Context ID is the value of six 996 most-significant bits of p1, 997 * UTF8, where the Context ID is a complex function of p1, p2, 998 optimized for text compression, and 999 * Signed, where Context ID is a complex function of p1, p2, 1000 optimized for compressing sequences of signed integers. 1002 The Context ID for the UTF8 and Signed context modes is computed 1003 using the following lookup tables Lut0, Lut1, and Lut2. 1005 Lut0 := 1006 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 1007 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1008 8, 12, 16, 12, 12, 20, 12, 16, 24, 28, 12, 12, 32, 12, 36, 12, 1009 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 32, 32, 24, 40, 28, 12, 1010 12, 48, 52, 52, 52, 48, 52, 52, 52, 48, 52, 52, 52, 52, 52, 48, 1011 52, 52, 52, 52, 52, 48, 52, 52, 52, 52, 52, 24, 12, 28, 12, 12, 1012 12, 56, 60, 60, 60, 56, 60, 60, 60, 56, 60, 60, 60, 60, 60, 56, 1013 60, 60, 60, 60, 60, 56, 60, 60, 60, 60, 60, 24, 12, 28, 12, 0, 1014 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1015 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1016 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1017 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1018 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 1019 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 1020 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 1021 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 1023 Lut1 := 1024 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1025 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1026 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1027 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1028 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1029 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1030 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1031 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 0, 1032 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1033 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1034 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1035 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1036 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1037 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1038 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1039 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 1041 Lut2 := 1042 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1043 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1044 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1045 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1046 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1047 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1048 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1049 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1050 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1051 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1052 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1053 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1054 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1055 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1056 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1057 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7 1059 The lengths and the zlib CRC-32 (ITU-T Recommendation V.42) check 1060 values of each of these tables as a sequence of bytes are as follows: 1062 Table Length CRC-32 1063 ----- ------ ------ 1064 Lut0 256 0x8e91efb7 1065 Lut1 256 0xd01a32f4 1066 Lut2 256 0x0dd7a0d6 1068 Given p1 is the last uncompressed byte and p2 is the second-to-last 1069 uncompressed byte, the context IDs can be computed as follows: 1071 For LSB6: Context ID = p1 & 0x3f 1072 For MSB6: Context ID = p1 >> 2 1073 For UTF8: Context ID = Lut0[p1] | Lut1[p2] 1074 For Signed: Context ID = (Lut2[p1] << 3) | Lut2[p2] 1076 From the lookup tables defined above and the operations to compute 1077 the context IDs, we can see that context IDs for literals are in the 1078 range of 0..63. 1080 The context modes LSB6, MSB6, UTF8, and Signed are denoted by 1081 integers 0, 1, 2, 3. 1083 A context mode is defined for each literal block type and they are 1084 stored in a consecutive array of bits in the meta-block header, 1085 always two bits per block type. 1087 7.2. Context ID for distances 1089 The context for encoding a distance code is defined by the copy 1090 length corresponding to the distance. The context IDs are 0, 1, 2, 1091 and 3 for copy lengths 2, 3, 4, and more than 4, respectively. 1093 7.3. Encoding of the context map 1095 There are two context maps, one for literals and one for distances. 1096 The size of the context map is 64 * NBLTYPESL for literals, and 4 * 1097 NBLTYPESD for distances. Each value in the context map is an integer 1098 between 0 and 255, indicating the index of the prefix code to be used 1099 when encoding the next literal or distance. 1101 The context maps are two-dimensional matrices, encoded as one- 1102 dimensional arrays: 1104 CMAPL[0..(64 * NBLTYPESL - 1)] 1105 CMAPD[0..(4 * NBLTYPESD - 1)] 1107 The index of the prefix code for encoding a literal or distance code 1108 with block type, BTYPE_x, and context ID, CIDx, is: 1110 index of literal prefix code = CMAPL[64 * BTYPE_L + CIDL] 1111 index of distance prefix code = CMAPD[4 * BTYPE_D + CIDD] 1113 The values of the context map are encoded with the combination of run 1114 length encoding for zero values and prefix coding. Let RLEMAX denote 1115 the number of run length codes and NTREES denote the maximum value in 1116 the context map plus one. NTREES must equal the number of different 1117 values in the context map, in other words, the different values in 1118 the context map must be the [0..NTREES-1] interval. The alphabet of 1119 the prefix code has the following RLEMAX + NTREES symbols: 1121 0: value zero 1122 1: repeat a zero 2 to 3 times, read 1 bit for repeat length 1123 2: repeat a zero 4 to 7 times, read 2 bits for repeat length 1124 ... 1125 RLEMAX: repeat a zero (1 << RLEMAX) to (1 << (RLEMAX+1))-1 1126 times, read RLEMAX bits for repeat length 1127 RLEMAX + 1: value 1 1128 ... 1129 RLEMAX + NTREES - 1: value NTREES - 1 1131 If RLEMAX = 0, the run length coding is not used, and the symbols of 1132 the alphabet are directly the values in the context map. We can now 1133 define the format of the context map (the same format is used for 1134 literal and distance context maps): 1136 1-5 bits: RLEMAX, 0 is encoded with one 0 bit, and values 1137 1 - 16 are encoded with bit pattern xxxx1 (so 01001 1138 is 5) 1140 Prefix code with alphabet size NTREES + RLEMAX 1142 Context map size values encoded with the above prefix code 1143 and run length coding for zero values. If a run length 1144 would result in more lengths in total than the size of 1145 the context map, then the stream should be rejected as 1146 invalid. 1148 1 bit: IMTF bit, if set, we do an inverse move-to-front 1149 transform on the values in the context map to get 1150 the prefix code indexes 1152 Note that RLEMAX may be larger than the value necessary to represent 1153 the longest sequence of zero values. Also, the NTREES value is 1154 encoded right before the context map as described in Section 9.2. 1156 We define the inverse move-to-front transform used in this 1157 specification by the following C language function: 1159 void InverseMoveToFrontTransform(uint8_t* v, int v_len) { 1160 uint8_t mtf[256]; 1161 int i; 1162 for (i = 0; i < 256; ++i) { 1163 mtf[i] = (uint8_t)i; 1164 } 1165 for (i = 0; i < v_len; ++i) { 1166 uint8_t index = v[i]; 1167 uint8_t value = mtf[index]; 1168 v[i] = value; 1169 for (; index; --index) { 1170 mtf[index] = mtf[index - 1]; 1171 } 1172 mtf[0] = value; 1173 } 1174 } 1176 Note that the inverse move-to-front transform will not produce values 1177 outside the [0..NTREES-1] interval. 1179 8. Static dictionary 1181 At any given point during decoding the compressed data, a reference 1182 to a duplicated string in the uncompressed data produced so far has a 1183 maximum backward distance value, which is the minimum of the window 1184 size and the number of uncompressed bytes produced. However, decoding 1185 a distance from the compressed stream, as described in Section 4., 1186 can produce distances that are greater than this maximum allowed 1187 value. In this case, the distance is treated as a reference to a word 1188 in the static dictionary given in Appendix A. The copy length for a 1189 static dictionary reference must be between 4 and 24. The static 1190 dictionary has three parts: 1192 * DICT[0..DICTSIZE], an array of bytes 1193 * DOFFSET[0..24], an array of byte offset values for each length 1194 * NDBITS[0..24], an array of bit-depth values for each length 1196 The number of static dictionary words for a given length is: 1198 NWORDS[length] = 0 (if length < 4) 1199 NWORDS[length] = (1 << NDBITS[length]) (if length >= 4) 1201 DOFFSET and DICTSIZE are defined by the following recursion: 1203 DOFFSET[0] = 0 1204 DOFFSET[length + 1] = DOFFSET[length] + length * NWORDS[length] 1205 DICTSIZE = DOFFSET[24] + 24 * NWORDS[24] 1207 The offset of a word within the DICT array for a given length and 1208 index is: 1210 offset(length, index) = DOFFSET[length] + index * length 1212 Each static dictionary word has 121 different forms, given by 1213 applying a word transformation to a base word in the DICT array. The 1214 list of word transformations is given in Appendix B. The static 1215 dictionary word for a pair can be reconstructed as 1216 follows: 1218 word_id = distance - (max allowed distance + 1) 1219 index = word_id % NWORDS[length] 1220 base_word = DICT[offset(length, index)..offset(length, index+1)-1] 1221 transform_id = word_id >> NDBITS[length] 1223 The string copied to the uncompressed stream is computed by applying 1224 the transformation to the base dictionary word. If transform_id is 1225 greater than 120, or the length is smaller than 4 or greater than 24, 1226 then the compressed stream should be rejected as invalid. 1228 Each word transformation has the following form: 1230 transform_i(word) = prefix_i + T_i(word) + suffix_i 1232 where the _i subscript denotes the transform_id above. Each T_i is 1233 one of the following 21 elementary transforms: 1235 Identity, UppercaseFirst, UppercaseAll, 1236 OmitFirst1, ..., OmitFirst9, OmitLast1, ..., OmitLast9 1238 The form of these elementary transforms is as follows: 1240 Identity(word) = word 1241 UppercaseFirst(word) = first UTF-8 character of word upper-cased 1243 UppercaseAll(word) = all UTF-8 characters of word upper-cased 1245 OmitFirstk(word) = the last (length(word) - k) bytes of word, or 1246 empty string if length(word) < k 1248 OmitLastk(word) = the first (length(word) - k) bytes of word, or 1249 empty string if length(word) < k 1251 For the purposes of UppercaseAll, word is parsed into UTF-8 1252 characters and converted to upper-case by taking 1 - 3 bytes at a 1253 time, using the algorithm below: 1255 i = 0 1256 while i < length(word): 1257 if word[i] < 192: 1258 if word[i] >= 97 and word[i] <= 122: 1259 word[i] = word[i] ^ 32 1260 i = i + 1 1261 else if word[i] < 224: 1262 if i + 1 < length(word): 1263 word[i + 1] = word[i + 1] ^ 32 1264 i = i + 2 1265 else: 1266 if i + 2 < length(word): 1267 word[i + 2] = word[i + 2] ^ 5 1268 i = i + 3 1270 For UppercaseFirst, the same algorithm is used, but the loop is 1271 executed only once. 1273 Appendix B. contains the list of transformations by specifying the 1274 prefix, elementary transform and suffix components of each of them. 1275 Note that the OmitFirst8 elementary transform is not used in the list 1276 of transformations. The strings in Appendix B. are in C string format 1277 with respect to escape (backslash) characters. 1279 The maximum number of additional bytes that a transform may add to a 1280 base word is 13. Since the largest base word is 24 bytes long, a 1281 buffer of 38 bytes is sufficient to store any transformed words 1282 (counting a terminating zero byte). 1284 9. Compressed data format 1286 In this section we describe the format of the compressed data set in 1287 terms of the format of the individual data items described in the 1288 previous sections. 1290 9.1. Format of the stream header 1292 The stream header has only the following one field: 1294 1-7 bits: WBITS, a value in the range 10 - 24, encoded with 1295 the following variable length code (as it appears in 1296 the compressed data, where the bits are parsed from 1297 right to left): 1299 Value Bit Pattern 1300 ----- ----------- 1301 10 0100001 1302 11 0110001 1303 12 1000001 1304 13 1010001 1305 14 1100001 1306 15 1110001 1307 16 0 1308 17 0000001 1309 18 0011 1310 19 0101 1311 20 0111 1312 21 1001 1313 22 1011 1314 23 1101 1315 24 1111 1317 Note that bit pattern 0010001 is invalid and must not 1318 be used. 1320 The size of the sliding window, which is the maximum value of any 1321 non-dictionary reference backward distance, is given by the following 1322 formula: 1324 window size = (1 << WBITS) - 16 1326 9.2. Format of the meta-block header 1328 A compliant compressed data set has at least one meta-block. Each 1329 meta-block contains a header with information about the uncompressed 1330 length of the meta-block, and a bit signaling if the meta-block is 1331 the last one. The format of the meta-block header is the following: 1333 1 bit: ISLAST, set to 1 if this is the last meta-block 1334 1 bit: ISLASTEMPTY, if set to 1, the meta-block is empty; 1335 this field is only present if ISLAST bit is set -- if 1336 it is 1, then the meta-block and the brotli stream ends 1337 at that bit, with any remaining bits in the last byte 1338 of the compressed stream filled with zeros (if the 1339 fill bits are not zero, then the stream should be 1340 rejected as invalid) 1341 2 bits: MNIBBLES, # of nibbles to represent the uncompressed 1342 length, encoded with the following fixed-length code: 1344 Value Bit Pattern 1345 ----- ----------- 1346 0 11 1347 4 00 1348 5 01 1349 6 10 1351 If MNIBBLES is 0, the meta-block is empty, i.e. it does 1352 not generate any uncompressed data. In this case, the 1353 rest of the meta-block has the following format: 1355 1 bit: reserved, must be zero 1357 2 bits: MSKIPBYTES, # of bytes to represent metadata 1358 length 1360 MSKIPBYTES x 8 bits: MSKIPLEN - 1, where MSKIPLEN is 1361 the number of metadata bytes; this field is 1362 only present if MSKIPBYTES is positive, 1363 otherwise MSKIPLEN is 0 (if MSKIPBYTES is 1364 greater than 1, and the last byte is all 1365 zeros, then the stream should be rejected 1366 as invalid) 1368 0 - 7 bits: fill bits until the next byte boundary, 1369 must be all zeros 1371 MSKIPLEN bytes of metadata, not part of the 1372 uncompressed data or the sliding window 1374 MNIBBLES x 4 bits: MLEN - 1, where MLEN is the length 1375 of the meta-block uncompressed data in bytes (if 1376 MNIBBLES is greater than 4, and the last 1377 nibble is all zeros, then the stream should be 1378 rejected as invalid) 1380 1 bit: ISUNCOMPRESSED, if set to 1, any bits of compressed 1381 data up to the next byte boundary are ignored, and 1382 the rest of the meta-block contains MLEN bytes of 1383 literal data; this field is only present if the 1384 ISLAST bit is not set (if the ignored bits are not 1385 all zeros, the stream should be rejected as invalid) 1387 1-11 bits: NBLTYPESL, # of literal block types, encoded with 1388 the following variable length code (as it appears in 1389 the compressed data, where the bits are parsed from 1390 right to left, so 0110111 has the value 12): 1392 Value Bit Pattern 1393 ----- ----------- 1394 1 0 1395 2 0001 1396 3-4 x0011 1397 5-8 xx0101 1398 9-16 xxx0111 1399 17-32 xxxx1001 1400 33-64 xxxxx1011 1401 65-128 xxxxxx1101 1402 129-256 xxxxxxx1111 1404 Prefix code over the block type code alphabet for 1405 literal block types, appears only if NBLTYPESL >= 2 1407 Prefix code over the block count code alphabet for 1408 literal block counts, appears only if NBLTYPESL >= 2 1410 Block count code + extra bits for first literal 1411 block count, appears only if NBLTYPESL >= 2 1413 1-11 bits: NBLTYPESI, # of insert-and-copy block types, encoded 1414 with the same variable length code as above 1416 Prefix code over the block type code alphabet for 1417 insert-and-copy block types, appears only if NBLTYPESI >= 2 1419 Prefix code over the block count code alphabet for 1420 insert-and-copy block counts, appears only if NBLTYPESI >= 2 1422 Block count code + extra bits for first insert-and-copy 1423 block count, appears only if NBLTYPESI >= 2 1425 1-11 bits: NBLTYPESD, # of distance block types, encoded 1426 with the same variable length code as above 1428 Prefix code over the block type code alphabet for 1429 distance block types, appears only if NBLTYPESD >= 2 1431 Prefix code over the block count code alphabet for 1432 distance block counts, appears only if NBLTYPESD >= 2 1434 Block count code + extra bits for first distance 1435 block count, appears only if NBLTYPESD >= 2 1437 2 bits: NPOSTFIX, parameter used in the distance coding 1439 4 bits: four most-significant bits of NDIRECT, to get the 1440 actual value of the parameter NDIRECT, left-shift 1441 this four-bit number by NPOSTFIX bits 1443 NBLTYPESL x 2 bits: context mode for each literal block type 1445 1-11 bits: NTREESL, # of literal prefix trees, encoded 1446 with the same variable length code as NBLTYPESL 1448 Literal context map, encoded as described in Section 7.3., 1449 appears only if NTREESL >= 2, otherwise the context map 1450 has only zero values 1452 1-11 bits: NTREESD, # of distance prefix trees, encoded 1453 with the same variable length code as NBLTYPESD 1455 Distance context map, encoded as described in Section 7.3., 1456 appears only if NTREESD >= 2, otherwise the context map 1457 has only zero values 1459 NTREESL prefix codes for literals 1461 NBLTYPESI prefix codes for insert-and-copy lengths 1463 NTREESD prefix codes for distances 1465 9.3. Format of the meta-block data 1467 The compressed data part of a meta-block consists of a series of 1468 commands. Each command has the following format: 1470 Block type code for next insert-and-copy block type, appears 1471 only if NBLTYPESI >= 2 and the previous insert-and-copy 1472 block count is zero 1474 Block count code + extra bits for next insert-and-copy 1475 block count, appears only if NBLTYPESI >= 2 and the 1476 previous insert-and-copy block count is zero 1478 Insert-and-copy length, encoded as in Section 5., using the 1479 insert-and-copy length prefix code with the current 1480 insert-and-copy block type index 1482 Insert length number of literals, with the following format: 1484 Block type code for next literal block type, appears 1485 only if NBLTYPESL >= 2 and the previous literal 1486 block count is zero 1488 Block count code + extra bits for next literal 1489 block count, appears only if NBLTYPESL >= 2 and the 1490 previous literal block count is zero 1492 Next byte of the uncompressed data, encoded with the 1493 literal prefix code with the index determined by the 1494 previous two bytes of the uncompressed data, the 1495 current literal block type, and the context map, as 1496 described in Section 7.3. 1498 Block type code for next distance block type, appears 1499 only if NBLTYPESD >= 2 and the previous distance 1500 block count is zero 1502 Block count code + extra bits for next distance 1503 block count, appears only if NBLTYPESD >= 2 and the 1504 previous distance block count is zero 1506 Distance code, encoded as in Section 4., using the distance 1507 prefix code with the current distance block type index, 1508 appears only if the distance code is not an implicit 0, 1509 as indicated by the insert-and-copy length code 1511 The number of commands in the meta-block is such that the sum of the 1512 uncompressed bytes produced (i.e. the number of literals inserted 1513 plus the number of bytes copied from past data or generated from the 1514 static dictionary) over all the commands gives the uncompressed 1515 length, MLEN encoded in the meta-block header. 1517 If the total number of uncompressed bytes produced after the insert 1518 part of the last command equals MLEN, then the copy length of the 1519 last command is ignored and will not produce any uncompressed output. 1520 In this case the copy length of the last command can have any value. 1521 In any other case, if the number of literals to insert, the copy 1522 length, or the resulting dictionary word length would cause MLEN to 1523 be exceeded, then the stream should be rejected as invalid. 1525 If the last command of the last non-empty meta-block does not end on 1526 a byte boundary, the unused bits in the last byte must be zeros. 1528 10. Decoding algorithm 1530 The decoding algorithm that produces the uncompressed data is as 1531 follows: 1533 read window size 1534 do 1535 read ISLAST bit 1536 if ISLAST 1537 read ISLASTEMPTY bit 1538 if ISLASTEMPTY 1539 break from loop 1540 read MNIBBLES 1541 if MNIBBLES is zero 1542 verify reserved bit is zero 1543 read MSKIPLEN 1544 skip any bits up to the next byte boundary 1545 skip MSKIPLEN bytes 1546 continue to the next meta-block 1547 else 1548 read MLEN 1549 if not ISLAST 1550 read ISUNCOMPRESSED bit 1551 if ISUNCOMPRESSED 1552 skip any bits up to the next byte boundary 1553 copy MLEN bytes of compressed data as literals 1554 continue to the next meta-block 1555 loop for each three block categories (i = L, I, D) 1556 read NBLTYPESi 1557 if NBLTYPESi >= 2 1558 read prefix code for block types, HTREE_BTYPE_i 1559 read prefix code for block counts, HTREE_BLEN_i 1560 read block count, BLEN_i 1561 set block type, BTYPE_i to 0 1562 initialize second-to-last and last block types to 0 and 1 1563 else 1564 set block type, BTYPE_i to 0 1565 set block count, BLEN_i to 16777216 1566 read NPOSTFIX and NDIRECT 1567 read array of literal context modes, CMODE[] 1568 read NTREESL 1569 if NTREESL >= 2 1570 read literal context map, CMAPL[] 1571 else 1572 fill CMAPL[] with zeros 1573 read NTREESD 1574 if NTREESD >= 2 1575 read distance context map, CMAPD[] 1576 else 1577 fill CMAPD[] with zeros 1578 read array of literal prefix codes, HTREEL[] 1579 read array of insert-and-copy length prefix codes, HTREEI[] 1580 read array of distance prefix codes, HTREED[] 1581 do 1582 if BLEN_I is zero 1583 read block type using HTREE_BTYPE_I and set BTYPE_I 1584 save previous block type 1585 read block count using HTREE_BLEN_I and set BLEN_I 1586 decrement BLEN_I 1587 read insert-and-copy length symbol using HTREEI[BTYPE_I] 1588 compute insert length, ILEN, and copy length, CLEN 1589 loop for ILEN 1590 if BLEN_L is zero 1591 read block type using HTREE_BTYPE_L and set BTYPE_L 1592 save previous block type 1593 read block count using HTREE_BLEN_L and set BLEN_L 1594 decrement BLEN_L 1595 look up context mode CMODE[BTYPE_L] 1596 compute context ID, CIDL from last two uncompressed bytes 1597 read literal using HTREEL[CMAPL[64*BTYPE_L + CIDL]] 1598 write literal to uncompressed stream 1599 if number of uncompressed bytes produced in the loop for 1600 this meta-block is MLEN, then break from loop (in this 1601 case the copy length is ignored and can have any value) 1602 if distance code is implicit zero from insert-and-copy code 1603 set backward distance to the last distance 1604 else 1605 if BLEN_D is zero 1606 read block type using HTREE_BTYPE_D and set BTYPE_D 1607 save previous block type 1608 read block count using HTREE_BLEN_D and set BLEN_D 1609 decrement BLEN_D 1610 compute context ID, CIDD from CLEN 1611 read distance code using HTREED[CMAPD[4*BTYPE_D + CIDD]] 1612 compute distance by distance short code substitution 1613 if distance code is not zero, 1614 and distance is not a static dictionary reference, 1615 push distance to the ring buffer of last distances 1616 if distance is less than the max allowed distance plus one 1617 move backwards distance bytes in the uncompressed data, 1618 and copy CLEN bytes from this position to 1619 the uncompressed stream 1620 else 1621 look up the static dictionary word, transform the word as 1622 directed, and copy the result to the uncompressed stream 1623 while number of uncompressed bytes for this meta-block < MLEN 1624 while not ISLAST 1626 If the stream ends before the completion of the last meta-block, then 1627 the stream should be rejected as invalid. 1629 Note that a duplicated string reference may refer to a string in a 1630 previous meta-block, i.e. the backward distance may cross one or more 1631 meta-block boundaries. However a backward copy distance will not 1632 refer past the beginning of the uncompressed stream or the window 1633 size; any such distance is interpreted as a reference to a static 1634 dictionary word. Also note that the referenced string may overlap the 1635 current position, for example, if the last 2 bytes decoded have 1636 values X and Y, a string reference with 1637 adds X,Y,X,Y,X to the uncompressed stream. 1639 11. Security Considerations 1641 As with any compressed file formats, decompressor implementations 1642 should handle all compressed data byte sequences, not only those that 1643 conform to this specification, where non-conformant compressed data 1644 sequences should be discarded. A possible attack against a system 1645 containing a decompressor implementation (e.g. a web browser) is to 1646 exploit a buffer overflow caused by an invalid compressed data. 1647 Therefore decompressor implementations should perform bounds-checking 1648 for each memory access that result from values decoded from the 1649 compressed stream. 1651 12. IANA Considerations 1653 The "HTTP Content Coding Registry" has been updated with the 1654 registration below: 1656 +-------+-------------------------------------+------------+ 1657 | Name | Description | Reference | 1658 +-------+-------------------------------------+------------+ 1659 | br | Brotli Compressed Data Format | RFCXXXX | 1660 +-------+-------------------------------------+------------+ 1662 13. Informative References 1664 [HUFFMAN] Huffman, D. A., "A Method for the Construction of Minimum 1665 Redundancy Codes", Proceedings of the Institute of Radio 1666 Engineers, September 1952, Volume 40, Number 9, pp. 1667 1098-1101. 1669 [LZ77] Ziv J., Lempel A., "A Universal Algorithm for Sequential 1670 Data Compression", IEEE Transactions on Information 1671 Theory, Vol. 23, No. 3, pp. 337-343. 1673 [RFC1951] Deutsch, P., "DEFLATE Compressed Data Format Specification 1674 version 1.3", RFC 1951, Aladdin Enterprises, May 1996. 1675 http://www.ietf.org/rfc/rfc1951.txt 1677 [WOFF2] Levantovsky, V. (ed.), Levien, R. (ed.), "WOFF File Format 1678 2.0", W3C WebFonts Working Group, 1679 http://www.w3.org/TR/WOFF2/ 1681 14. Source code 1683 Source code for a C language implementation of a brotli compliant 1684 decompressor and a C++ language implementation of a compressor is 1685 available in the brotli open-source project: 1686 https://github.com/google/brotli 1688 15. Acknowledgments 1690 The authors would like to thank Mark Adler, Robert Obryk, Thomas 1691 Pickert, and Joe Tsai for providing helpful review comments, 1692 validating the specification by writing an independent decompressor, 1693 and suggesting improvements to the format and the text of the 1694 specification. 1696 Appendix A. Static dictionary data 1698 The hexadecimal form of the DICT array is the following, where the 1699 length is 122,784 bytes and the zlib CRC-32 of the byte sequence is 1700 0x5136cb04. 1702 74696d65646f776e6c6966656c6566746261636b636f64656461746173686f77 1703 6f6e6c7973697465636974796f70656e6a7573746c696b6566726565776f726b 1704 74657874796561726f766572626f64796c6f7665666f726d626f6f6b706c6179 1705 6c6976656c696e6568656c70686f6d65736964656d6f7265776f72646c6f6e67 1706 7468656d7669657766696e64706167656461797366756c6c686561647465726d 1707 656163686172656166726f6d747275656d61726b61626c6575706f6e68696768 1708 646174656c616e646e6577736576656e6e65787463617365626f7468706f7374 1709 757365646d61646568616e6468657265776861746e616d654c696e6b626c6f67 1710 73697a656261736568656c646d616b656d61696e757365722729202b686f6c64 1711 656e6473776974684e65777372656164776572657369676e74616b6568617665 1712 67616d657365656e63616c6c7061746877656c6c706c75736d656e7566696c6d 1713 706172746a6f696e746869736c697374676f6f646e6565647761797377657374 1714 6a6f62736d696e64616c736f6c6f676f72696368757365736c6173747465616d 1715 61726d79666f6f646b696e6777696c6c65617374776172646265737466697265 1716 506167656b6e6f77617761792e706e676d6f76657468616e6c6f616467697665 1717 73656c666e6f74656d756368666565646d616e79726f636b69636f6e6f6e6365 1718 6c6f6f6b6869646564696564486f6d6572756c65686f7374616a6178696e666f 1719 636c75626c6177736c65737368616c66736f6d65737563687a6f6e6531303025 1720 6f6e65736361726554696d6572616365626c7565666f75727765656b66616365 1721 686f706567617665686172646c6f73747768656e7061726b6b65707470617373 1722 73686970726f6f6d48544d4c706c616e54797065646f6e65736176656b656570 1723 666c61676c696e6b736f6c6466697665746f6f6b72617465746f776e6a756d70 1724 746875736461726b6361726466696c6566656172737461796b696c6c74686174 1725 66616c6c6175746f657665722e636f6d74616c6b73686f70766f746564656570 1726 6d6f6465726573747475726e626f726e62616e6466656c6c726f736575726c28 1727 736b696e726f6c65636f6d6561637473616765736d656574676f6c642e6a7067 1728 6974656d7661727966656c747468656e73656e6464726f7056696577636f7079 1729 312e30223c2f613e73746f70656c73656c696573746f75727061636b2e676966 1730 706173746373733f677261796d65616e2667743b7269646573686f746c617465 1731 73616964726f6164766172206665656c6a6f686e7269636b706f727466617374 1732 2755412d646561643c2f623e706f6f7262696c6c74797065552e532e776f6f64 1733 6d7573743270783b496e666f72616e6b7769646577616e7477616c6c6c656164 1734 5b305d3b7061756c776176657375726524282723776169746d61737361726d73 1735 676f65736761696e6c616e6770616964212d2d206c6f636b756e6974726f6f74 1736 77616c6b6669726d77696665786d6c22736f6e6774657374323070786b696e64 1737 726f7773746f6f6c666f6e746d61696c73616665737461726d617073636f7265 1738 7261696e666c6f77626162797370616e736179733470783b3670783b61727473 1739 666f6f747265616c77696b696865617473746570747269706f72672f6c616b65 1740 7765616b746f6c64466f726d6361737466616e7362616e6b7665727972756e73 1741 6a756c797461736b3170783b676f616c67726577736c6f776564676569643d22 1742 736574733570783b2e6a733f3430707869662028736f6f6e736561746e6f6e65 1743 747562657a65726f73656e747265656466616374696e746f676966746861726d 1744 3138707863616d6568696c6c626f6c647a6f6f6d766f69646561737972696e67 1745 66696c6c7065616b696e6974636f73743370783b6a61636b7461677362697473 1746 726f6c6c656469746b6e65776e6561723c212d2d67726f774a534f4e64757479 1747 4e616d6573616c65796f75206c6f74737061696e6a617a7a636f6c6465796573 1748 666973687777772e7269736b7461627370726576313070787269736532357078 1749 426c756564696e673330302c62616c6c666f72646561726e77696c64626f782e 1750 666169726c61636b76657273706169726a756e6574656368696628217069636b 1751 6576696c242822237761726d6c6f7264646f657370756c6c2c30303069646561 1752 647261776875676573706f7466756e646275726e6872656663656c6c6b657973 1753 7469636b686f75726c6f73736675656c31327078737569746465616c52535322 1754 6167656467726579474554226561736561696d736769726c616964733870783b 1755 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61727365743d227574662d38223e3a75726c2220636f6e74656e743d22687474 5452 703a2f2f2e637373222072656c3d227374796c657368656574227374796c6520 5453 747970653d22746578742f637373223e747970653d22746578742f6373732220 5454 687265663d2277332e6f72672f313939392f7868746d6c2220786d6c74797065 5455 3d22746578742f6a61766173637269707422206d6574686f643d226765742220 5456 616374696f6e3d226c696e6b2072656c3d227374796c6573686565742220203d 5457 20646f63756d656e742e676574456c656d656e74747970653d22696d6167652f 5458 782d69636f6e22202f3e63656c6c70616464696e673d2230222063656c6c7370 5459 2e6373732220747970653d22746578742f63737322203c2f613e3c2f6c693e3c 5460 6c693e3c6120687265663d22222077696474683d223122206865696768743d22 5461 3122223e3c6120687265663d22687474703a2f2f7777772e7374796c653d2264 5462 6973706c61793a6e6f6e653b223e616c7465726e6174652220747970653d2261 5463 70706c692d2f2f5733432f2f445444205848544d4c20312e3020656c6c737061 5464 63696e673d2230222063656c6c70616420747970653d2268696464656e222076 5465 616c75653d222f613e266e6273703b3c7370616e20726f6c653d22730a3c696e 5466 70757420747970653d2268696464656e22206c616e67756167653d224a617661 5467 536372697074222020646f63756d656e742e676574456c656d656e747342673d 5468 2230222063656c6c73706163696e673d223022207970653d22746578742f6373 5469 7322206d656469613d22747970653d27746578742f6a61766173637269707427 5470 776974682074686520657863657074696f6e206f66207970653d22746578742f 5471 637373222072656c3d227374206865696768743d2231222077696474683d2231 5472 22203d272b656e636f6465555249436f6d706f6e656e74283c6c696e6b207265 5473 6c3d22616c7465726e61746522200a626f64792c2074722c20696e7075742c20 5474 746578746d657461206e616d653d22726f626f74732220636f6e6d6574686f64 5475 3d22706f73742220616374696f6e3d223e0a3c6120687265663d22687474703a 5476 2f2f7777772e637373222072656c3d227374796c65736865657422203c2f6469 5477 763e3c2f6469763e3c64697620636c6173736c616e67756167653d226a617661 5478 736372697074223e617269612d68696464656e3d2274727565223ec2b73c7269 5479 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636f6e74656e743d22746578742f3c6d65746120687474702d65717569763d22 5494 436f6e746572616e736974696f6e616c2f2f454e222022687474703a3c68746d 5495 6c20786d6c6e733d22687474703a2f2f7777772d2f2f5733432f2f4454442058 5496 48544d4c20312e3020544454442f7868746d6c312d7472616e736974696f6e61 5497 6c2f2f7777772e77332e6f72672f54522f7868746d6c312f7065203d20277465 5498 78742f6a617661736372697074273b3c6d657461206e616d653d226465736372 5499 697074696f6e706172656e744e6f64652e696e736572744265666f72653c696e 5500 70757420747970653d2268696464656e22206e616a732220747970653d227465 5501 78742f6a6176617363726928646f63756d656e74292e72656164792866756e63 5502 746973637269707420747970653d22746578742f6a61766173696d6167652220 5503 636f6e74656e743d22687474703a2f2f55412d436f6d70617469626c65222063 5504 6f6e74656e743d746d6c3b20636861727365743d7574662d3822202f3e0a6c69 5505 6e6b2072656c3d2273686f72746375742069636f6e3c6c696e6b2072656c3d22 5506 7374796c65736865657422203c2f7363726970743e0a3c736372697074207479 5507 70653d3d20646f63756d656e742e637265617465456c656d656e3c6120746172 5508 6765743d225f626c616e6b2220687265663d20646f63756d656e742e67657445 5509 6c656d656e747342696e70757420747970653d227465787422206e616d653d61 5510 2e74797065203d2027746578742f6a617661736372696e70757420747970653d 5511 2268696464656e22206e616d6568746d6c3b20636861727365743d7574662d38 5512 22202f3e647464223e0a3c68746d6c20786d6c6e733d22687474702d2f2f5733 5513 432f2f4454442048544d4c20342e30312054656e747342795461674e616d6528 5514 277363726970742729696e70757420747970653d2268696464656e22206e616d 5515 3c73637269707420747970653d22746578742f6a6176617322207374796c653d 5516 22646973706c61793a6e6f6e653b223e646f63756d656e742e676574456c656d 5517 656e7442794964283d646f63756d656e742e637265617465456c656d656e7428 5518 2720747970653d27746578742f6a61766173637269707427696e707574207479 5519 70653d227465787422206e616d653d22642e676574456c656d656e7473427954 5520 61674e616d6528736e6963616c2220687265663d22687474703a2f2f7777772e 5521 432f2f4454442048544d4c20342e3031205472616e7369743c7374796c652074 5522 7970653d22746578742f637373223e0a0a3c7374796c6520747970653d227465 5523 78742f637373223e696f6e616c2e647464223e0a3c68746d6c20786d6c6e733d 5524 687474702d65717569763d22436f6e74656e742d5479706564696e673d223022 5525 2063656c6c73706163696e673d22302268746d6c3b20636861727365743d7574 5526 662d3822202f3e0a207374796c653d22646973706c61793a6e6f6e653b223e3c 5527 3c6c693e3c6120687265663d22687474703a2f2f7777772e20747970653d2774 5528 6578742f6a617661736372697074273ed0b4d0b5d18fd182d0b5d0bbd18cd0bd 5529 d0bed181d182d0b8d181d0bed0bed182d0b2d0b5d182d181d182d0b2d0b8d0b8 5530 d0bfd180d0bed0b8d0b7d0b2d0bed0b4d181d182d0b2d0b0d0b1d0b5d0b7d0be 5531 d0bfd0b0d181d0bdd0bed181d182d0b8e0a4aae0a581e0a4b8e0a58de0a4a4e0 5532 a4bfe0a495e0a4bee0a495e0a4bee0a482e0a497e0a58de0a4b0e0a587e0a4b8 5533 e0a489e0a4a8e0a58de0a4b9e0a58be0a482e0a4a8e0a587e0a4b5e0a4bfe0a4 5534 a7e0a4bee0a4a8e0a4b8e0a4ade0a4bee0a4abe0a4bfe0a495e0a58de0a4b8e0 5535 a4bfe0a482e0a497e0a4b8e0a581e0a4b0e0a495e0a58de0a4b7e0a4bfe0a4a4 5536 e0a495e0a589e0a4aae0a580e0a4b0e0a4bee0a487e0a49fe0a4b5e0a4bfe0a4 5537 9ce0a58de0a49ee0a4bee0a4aae0a4a8e0a495e0a4bee0a4b0e0a58de0a4b0e0 5538 a4b5e0a4bee0a488e0a4b8e0a495e0a58de0a4b0e0a4bfe0a4afe0a4a4e0a4be 5540 The number of words for each length is given by the following 5541 bit-depth array: 5543 NDBITS := 0, 0, 0, 0, 10, 10, 11, 11, 10, 10, 5544 10, 10, 10, 9, 9, 8, 7, 7, 8, 7, 5545 7, 6, 6, 5, 5 5547 Appendix B. List of word transformations 5549 The string literals are in C format, with respect to the use of 5550 backslash escape characters. 5552 In order to generate a length and check value, the transforms can be 5553 converted to a series of bytes, where each transform is the prefix 5554 sequence of bytes plus a terminating zero byte, a single byte value 5555 identifying the transform, and the suffix sequence of bytes plus a 5556 terminating zero. The value for the transforms are 0 for Identity, 1 for 5557 UppercaseFirst, 2 for UppercaseAll, 3 to 11 for OmitFirst1 to 5558 OmitFirst9, and 12 to 20 for OmitLast1 to OmitLast9. The byte sequences 5559 that represent the 121 transforms are then concatenated to a single 5560 sequence of bytes. The length of that sequence is 648 bytes, and the 5561 zlib CRC is 0x3d965f81. 5563 ID Prefix Transform Suffix 5564 -- ------ --------- ------ 5565 0 "" Identity "" 5566 1 "" Identity " " 5567 2 " " Identity " " 5568 3 "" OmitFirst1 "" 5569 4 "" UppercaseFirst " " 5570 5 "" Identity " the " 5571 6 " " Identity "" 5572 7 "s " Identity " " 5573 8 "" Identity " of " 5574 9 "" UppercaseFirst "" 5575 10 "" Identity " and " 5576 11 "" OmitFirst2 "" 5577 12 "" OmitLast1 "" 5578 13 ", " Identity " " 5579 14 "" Identity ", " 5580 15 " " UppercaseFirst " " 5581 16 "" Identity " in " 5582 17 "" Identity " to " 5583 18 "e " Identity " " 5584 19 "" Identity "\"" 5585 20 "" Identity "." 5586 21 "" Identity "\">" 5587 22 "" Identity "\n" 5588 23 "" OmitLast3 "" 5589 24 "" Identity "]" 5590 25 "" Identity " for " 5591 26 "" OmitFirst3 "" 5592 27 "" OmitLast2 "" 5593 28 "" Identity " a " 5594 29 "" Identity " that " 5595 30 " " UppercaseFirst "" 5596 31 "" Identity ". " 5597 32 "." Identity "" 5598 33 " " Identity ", " 5599 34 "" OmitFirst4 "" 5600 35 "" Identity " with " 5601 36 "" Identity "'" 5602 37 "" Identity " from " 5603 38 "" Identity " by " 5604 39 "" OmitFirst5 "" 5605 40 "" OmitFirst6 "" 5606 41 " the " Identity "" 5607 42 "" OmitLast4 "" 5608 43 "" Identity ". The " 5609 44 "" UppercaseAll "" 5610 45 "" Identity " on " 5611 46 "" Identity " as " 5612 47 "" Identity " is " 5613 48 "" OmitLast7 "" 5614 49 "" OmitLast1 "ing " 5615 50 "" Identity "\n\t" 5616 51 "" Identity ":" 5617 52 " " Identity ". " 5618 53 "" Identity "ed " 5619 54 "" OmitFirst9 "" 5620 55 "" OmitFirst7 "" 5621 56 "" OmitLast6 "" 5622 57 "" Identity "(" 5623 58 "" UppercaseFirst ", " 5624 59 "" OmitLast8 "" 5625 60 "" Identity " at " 5626 61 "" Identity "ly " 5627 62 " the " Identity " of " 5628 63 "" OmitLast5 "" 5629 64 "" OmitLast9 "" 5630 65 " " UppercaseFirst ", " 5631 66 "" UppercaseFirst "\"" 5632 67 "." Identity "(" 5633 68 "" UppercaseAll " " 5634 69 "" UppercaseFirst "\">" 5635 70 "" Identity "=\"" 5636 71 " " Identity "." 5637 72 ".com/" Identity "" 5638 73 " the " Identity " of the " 5639 74 "" UppercaseFirst "'" 5640 75 "" Identity ". This " 5641 76 "" Identity "," 5642 77 "." Identity " " 5643 78 "" UppercaseFirst "(" 5644 79 "" UppercaseFirst "." 5645 80 "" Identity " not " 5646 81 " " Identity "=\"" 5647 82 "" Identity "er " 5648 83 " " UppercaseAll " " 5649 84 "" Identity "al " 5650 85 " " UppercaseAll "" 5651 86 "" Identity "='" 5652 87 "" UppercaseAll "\"" 5653 88 "" UppercaseFirst ". " 5654 89 " " Identity "(" 5655 90 "" Identity "ful " 5656 91 " " UppercaseFirst ". " 5657 92 "" Identity "ive " 5658 93 "" Identity "less " 5659 94 "" UppercaseAll "'" 5660 95 "" Identity "est " 5661 96 " " UppercaseFirst "." 5662 97 "" UppercaseAll "\">" 5663 98 " " Identity "='" 5664 99 "" UppercaseFirst "," 5665 100 "" Identity "ize " 5666 101 "" UppercaseAll "." 5667 102 "\xc2\xa0" Identity "" 5668 103 " " Identity "," 5669 104 "" UppercaseFirst "=\"" 5670 105 "" UppercaseAll "=\"" 5671 106 "" Identity "ous " 5672 107 "" UppercaseAll ", " 5673 108 "" UppercaseFirst "='" 5674 109 " " UppercaseFirst "," 5675 110 " " UppercaseAll "=\"" 5676 111 " " UppercaseAll ", " 5677 112 "" UppercaseAll "," 5678 113 "" UppercaseAll "(" 5679 114 "" UppercaseAll ". " 5680 115 " " UppercaseAll "." 5681 116 "" UppercaseAll "='" 5682 117 " " UppercaseAll ". " 5683 118 " " UppercaseFirst "=\"" 5684 119 " " UppercaseAll "='" 5685 120 " " UppercaseFirst "='" 5687 Authors' Addresses 5689 Jyrki Alakuijala 5690 Google, Inc 5692 Email: jyrki@google.com 5694 Zoltan Szabadka 5695 Google, Inc 5697 Email: szabadka@google.com