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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: April 27, 2015 October 2014 7 Brotli Compressed Data Format 8 draft-alakuijala-brotli-02 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 April 27, 2015. 34 Copyright Notice 36 Copyright (c) 2014 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 Huffman codes . . . . . . . . . . 7 60 3.1. Introduction to prefix and Huffman coding . . . . . . . . 7 61 3.2. Use of Huffman coding in the "brotli" format . . . . . . . 8 62 3.3. Alphabet sizes . . . . . . . . . . . . . . . . . . . . . 10 63 3.4. Simple Huffman codes . . . . . . . . . . . . . . . . . . 10 64 3.5. Complex Huffman codes . . . . . . . . . . . . . . . . . . 11 65 4. Encoding of distances . . . . . . . . . . . . . . . . . . . . 13 66 5. Encoding of literal insertion lengths and copy lengths . . . . 14 67 6. Encoding of block switch commands . . . . . . . . . . . . . . 17 68 7. Context modeling . . . . . . . . . . . . . . . . . . . . . . . 18 69 7.1. Context modes and context ID lookup for literals . . . . 18 70 7.2. Context ID for distances . . . . . . . . . . . . . . . . 20 71 7.3. Encoding of the context map . . . . . . . . . . . . . . . 20 72 8. Static dictionary . . . . . . . . . . . . . . . . . . . . . . 21 73 9. Compressed data format . . . . . . . . . . . . . . . . . . . . 23 74 9.1. Format of the stream header . . . . . . . . . . . . . . . 23 75 9.2. Format of the meta-block header . . . . . . . . . . . . . 24 76 9.3. Format of the meta-block data . . . . . . . . . . . . . . 26 77 10. Decoding algorithm . . . . . . . . . . . . . . . . . . . . . 27 78 11. Security Considerations . . . . . . . . . . . . . . . . . . . 29 79 12. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 29 80 13. Informative References . . . . . . . . . . . . . . . . . . . 29 81 14. Source code . . . . . . . . . . . . . . . . . . . . . . . . . 29 82 Appendix A. Static dictionary data . . . . . . . . . . . . . . . 29 83 Appendix B. List of word transformations . . . . . . . . . . . . 110 84 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 112 86 1. Introduction 88 1.1. Purpose 90 The purpose of this specification is to define a lossless compressed 91 data format that: 92 * Is independent of CPU type, operating system, file system, 93 and character set, and hence can be used for interchange; 94 * Can be produced or consumed, even for an arbitrarily long 95 sequentially presented input data stream, using only an a 96 priori bounded amount of intermediate storage, and hence 97 can be used in data communications or similar structures, 98 such as Unix filters; 99 * Compresses data with a compression ratio comparable to the 100 best currently available general-purpose compression methods, 101 and in particular considerably better than the gzip program; 102 * Decompresses much faster than current LZMA implementations. 104 The data format defined by this specification does not attempt to: 105 * Allow random access to compressed data; 106 * Compress specialized data (e.g., raster graphics) as well 107 as the best currently available specialized algorithms. 109 1.2. Intended audience 111 This specification is intended for use by software implementers to 112 compress data into and/or decompress data from "brotli" format. 114 The text of the specification assumes a basic background in 115 programming at the level of bits and other primitive data 116 representations. Familiarity with the technique of Huffman coding is 117 helpful but not required. 119 This specification uses heavily the notations and terminology 120 introduced in the DEFLATE format specification [RFC 1951]. For the 121 sake of completeness, we always include the whole text of the 122 relevant parts of RFC 1951, therefore familiarity with the DEFLATE 123 format is helpful but not required. 125 The compressed data format defined in this specification is an 126 integral part of the WOFF 2.0 web font file format [WOFF2], therefore 127 this specification is also intended for implementers of WOFF 2.0 128 compressors and decompressors. 130 1.3. Scope 132 The specification specifies a method for representing a sequence of 133 bytes as a (usually shorter) sequence of bits, and a method for 134 packing the latter bit sequence into bytes. 136 1.4. Compliance 138 Unless otherwise indicated below, a compliant decompressor must be 139 able to accept and decompress any data set that conforms to all the 140 specifications presented here. A compliant compressor must produce 141 data sets that conform to all the specifications presented here. 143 1.5. Definitions of terms and conventions used 145 Byte: 8 bits stored or transmitted as a unit (same as an octet). For 146 this specification, a byte is exactly 8 bits, even on machines which 147 store a character on a number of bits different from eight. See 148 below for the numbering of bits within a byte. 150 String: a sequence of arbitrary bytes. 152 Bytes stored within a computer do not have a "bit order", since they 153 are always treated as a unit. However, a byte considered as an 154 integer between 0 and 255 does have a most- and least- significant 155 bit, and since we write numbers with the most- significant digit on 156 the left, we also write bytes with the most- significant bit on the 157 left. In the diagrams below, we number the bits of a byte so that 158 bit 0 is the least-significant bit, i.e., the bits are numbered: 160 +--------+ 161 |76543210| 162 +--------+ 164 Within a computer, a number may occupy multiple bytes. All multi- 165 byte numbers in the format described here are stored with the least- 166 significant byte first (at the lower memory address). For example, 167 the decimal number 520 is stored as: 169 0 1 170 +--------+--------+ 171 |00001000|00000010| 172 +--------+--------+ 173 ^ ^ 174 | | 175 | + more significant byte = 2 x 256 176 + less significant byte = 8 178 1.5.1. Packing into bytes 180 This document does not address the issue of the order in which bits 181 of a byte are transmitted on a bit-sequential medium, since the final 182 data format described here is byte- rather than bit-oriented. 183 However, we describe the compressed block format below as a sequence 184 of data elements of various bit lengths, not a sequence of bytes. We 185 must therefore specify how to pack these data elements into bytes to 186 form the final compressed byte sequence: 188 * Data elements are packed into bytes in order of 189 increasing bit number within the byte, i.e., starting 190 with the least-significant bit of the byte. 191 * Data elements other than Huffman codes are packed 192 starting with the least-significant bit of the data 193 element. 194 * Huffman codes are packed starting with the most- 195 significant bit of the code. 197 In other words, if one were to print out the compressed data as a 198 sequence of bytes, starting with the first byte at the *right* margin 199 and proceeding to the *left*, with the most- significant bit of each 200 byte on the left as usual, one would be able to parse the result from 201 right to left, with fixed-width elements in the correct MSB-to-LSB 202 order and Huffman codes in bit-reversed order (i.e., with the first 203 bit of the code in the relative LSB position). 205 2. Compressed representation overview 207 A compressed data set consists of a header and a series of meta- 208 blocks corresponding to successive meta-blocks of input data. The 209 meta-block sizes are limited to bytes and the maximum meta-block size 210 is 268,435,456 bytes. 212 The header contains the size of a sliding window on the input data 213 that is sufficient to keep on the intermediate storage at any given 214 point during decoding the stream. 216 Each meta-block is compressed using a combination of the LZ77 217 algorithm (Lempel-Ziv 1977, [LZ77]) and Huffman coding. The Huffman 218 trees for each block are independent of those for previous or 219 subsequent blocks; the LZ77 algorithm may use a reference to a 220 duplicated string occurring in a previous meta-block, up to sliding 221 window size input bytes before. 223 Each meta-block consists of two parts: a meta-block header that 224 describes the representation of the compressed data part, and a 225 compressed data part. The compressed data consists of a series of 226 commands. Each command consists of two parts: a sequence of literal 227 bytes (of strings that have not been detected as duplicated within 228 the sliding window), and a pointer to a duplicated string, 229 represented as a pair . 231 Each command in the compressed data is represented using three kinds 232 of Huffman codes: one kind of code tree for the literal sequence 233 lengths (also referred to as literal insertion lengths) and backward 234 copy lengths (that is, a single code word represents two lengths, one 235 of the literal sequence and one of the backward copy), a separate 236 kind of code tree for literals, and a third kind of code tree for 237 distances. The code trees for each meta-block appear in a compact 238 form just before the compressed data in the meta-block header. 240 The sequence of each type of value in the representation of a command 241 (insert-and-copy lengths, literals and distances) within a meta- 242 block is further divided into blocks. In the "brotli" format, blocks 243 are not contiguous chunks of compressed data, but rather the pieces 244 of compressed data belonging to a block are interleaved with pieces 245 of data belonging to other blocks. Each meta-block can be logically 246 decomposed into a series of insert-and-copy length blocks, a series 247 of literal blocks and a series of distance blocks. These are also 248 called the three block categories: a meta-block has a series of 249 blocks for each block category. Note that the physical structure of 250 the meta-block is a series of commands, while the three series of 251 blocks is the logical structure. Consider the following example: 253 (IaC0, L0, L1, L2, D0)(IaC1, D1)(IaC2, L3, L4, D2)(IaC3, L5, D3) 255 The meta-block here has 4 commands, and each three types of symbols 256 within these commands can be rearranged for example into the 257 following logical block structure: 259 [IaC0, IaC1][IaC2, IaC3] <-- block types 0 and 1 261 [L0, L1][L2, L3, L4][L5] <-- block types 0, 1, and 0 263 [D0][D1, D2, D3] <-- block types 0 and 1 265 The subsequent blocks within each block category must have different 266 block types, but blocks further away in the block sequence can have 267 the same types. The block types are numbered from 0 to the maximum 268 block type number of 255 and the first block of each block category 269 must have type 0. The block structure of a meta-block is represented 270 by the sequence of block-switch commands for each block category, 271 where a block-switch command is a pair . 272 The block-switch commands are represented in the compressed data 273 before the start of each new block using a Huffman code tree for 274 block types and a separate Huffman code tree for block lengths for 275 each block category. In the above example the physical layout of the 276 meta-block is the following: 278 IaC0 L0 L1 LBlockSwitch(1, 3) L2 D0 IaC1 DBlockSwitch(1, 1) D1 279 IaCBlockSwitch(1, 2) IaC2 L3 L4 D2 IaC3 LBlockSwitch(0, 1) D3 281 Note that the block switch commands for the first blocks are not part 282 of the meta-block compressed data part, they are encoded in the meta- 283 block header. The code trees for block types and lengths (total of 284 six Huffman code trees) appear in a compact form in the meta-block 285 header. 287 Each type of value (insert-and-copy lengths, literals and distances) 288 can be encoded with any Huffman tree from a collection of Huffman 289 trees of the same kind appearing in the meta-block header. The 290 particular Huffman tree used can depend on two factors: the block 291 type of the block the value appears in, and the context of the value. 292 In the case of the literals, the context is the previous two bytes in 293 the input data, and in the case of distances, the context is the copy 294 length from the same command. For insert-and-copy lengths, no context 295 is used and the Huffman tree depends only on the block type (in fact, 296 the index of the Huffman tree is the block type number). In the case 297 of literals and distances, the context is mapped to a context ID in 298 the rage [0, 63] for literals and [0, 3] for distances and the matrix 299 of the Huffman tree indices for each block type and context ID, 300 called the context map, is encoded in a compact form in the meta- 301 block header. 303 In addition to the parts listed above (Huffman code trees for insert- 304 and-copy lengths, literals, distances, block types and block lengths 305 and the context map), the meta-block header contains the number of 306 input bytes in the meta-block and two additional parameters used in 307 the representation of copy distances (number of "postfix bits" and 308 number of direct distance codes). 310 3. Compressed representation of Huffman codes 312 3.1. Introduction to prefix and Huffman coding 314 Prefix coding represents symbols from an a priori known alphabet by 315 bit sequences (codes), one code for each symbol, in a manner such 316 that different symbols may be represented by bit sequences of 317 different lengths, but a parser can always parse an encoded string 318 unambiguously symbol-by-symbol. 320 We define a prefix code in terms of a binary tree in which the two 321 edges descending from each non-leaf node are labeled 0 and 1 and in 322 which the leaf nodes correspond one-for-one with (are labeled with) 323 the symbols of the alphabet; then the code for a symbol is the 324 sequence of 0's and 1's on the edges leading from the root to the 325 leaf labeled with that symbol. For example: 327 /\ Symbol Code 328 0 1 ------ ---- 329 / \ A 00 330 /\ B B 1 331 0 1 C 011 332 / \ D 010 333 A /\ 334 0 1 335 / \ 336 D C 338 A parser can decode the next symbol from an encoded input stream by 339 walking down the tree from the root, at each step choosing the edge 340 corresponding to the next input bit. 342 Given an alphabet with known symbol frequencies, the Huffman 343 algorithm allows the construction of an optimal prefix code (one 344 which represents strings with those symbol frequencies using the 345 fewest bits of any possible prefix codes for that alphabet). Such a 346 code is called a Huffman code. (See [HUFFMAN] in Chapter 5, 347 references for additional information on Huffman codes.) 349 Note that in the "brotli" format, the Huffman codes for the various 350 alphabets must not exceed certain maximum code lengths. This 351 constraint complicates the algorithm for computing code lengths from 352 symbol frequencies. Again, see Chapter 5, references for details. 354 3.2. Use of Huffman coding in the "brotli" format 356 The Huffman codes used for each alphabet in the "brotli" format are 357 canonical Huffman codes, which have two additional rules: 359 * All codes of a given bit length have lexicographically 360 consecutive values, in the same order as the symbols they 361 represent; 363 * Shorter codes lexicographically precede longer codes. 365 We could recode the example above to follow this rule as follows, 366 assuming that the order of the alphabet is ABCD: 368 Symbol Code 369 ------ ---- 370 A 10 371 B 0 372 C 110 373 D 111 375 I.e., 0 precedes 10 which precedes 11x, and 110 and 111 are 376 lexicographically consecutive. 378 Given this rule, we can define the canonical Huffman code for an 379 alphabet just by giving the bit lengths of the codes for each symbol 380 of the alphabet in order; this is sufficient to determine the actual 381 codes. In our example, the code is completely defined by the sequence 382 of bit lengths (2, 1, 3, 3). The following algorithm generates the 383 codes as integers, intended to be read from most- to least- 384 significant bit. The code lengths are initially in tree[I].Len; the 385 codes are produced in tree[I].Code. 387 1) Count the number of codes for each code length. Let 388 bl_count[N] be the number of codes of length N, N >= 1. 390 2) Find the numerical value of the smallest code for each 391 code length: 393 code = 0; 394 bl_count[0] = 0; 395 for (bits = 1; bits <= MAX_BITS; bits++) { 396 code = (code + bl_count[bits-1]) << 1; 397 next_code[bits] = code; 398 } 400 3) Assign numerical values to all codes, using consecutive 401 values for all codes of the same length with the base 402 values determined at step 2. Codes that are never used 403 (which have a bit length of zero) must not be assigned a 404 value. 406 for (n = 0; n <= max_code; n++) { 407 len = tree[n].Len; 408 if (len != 0) { 409 tree[n].Code = next_code[len]; 410 next_code[len]++; 411 } 412 } 414 Example: 416 Consider the alphabet ABCDEFGH, with bit lengths (3, 3, 3, 3, 3, 2, 417 4, 4). After step 1, we have: 419 N bl_count[N] 420 - ----------- 421 2 1 422 3 5 423 4 2 425 Step 2 computes the following next_code values: 427 N next_code[N] 428 - ------------ 429 1 0 430 2 0 431 3 2 432 4 14 434 Step 3 produces the following code values: 436 Symbol Length Code 437 ------ ------ ---- 438 A 3 010 439 B 3 011 440 C 3 100 441 D 3 101 442 E 3 110 443 F 2 00 444 G 4 1110 445 H 4 1111 447 3.3. Alphabet sizes 449 Huffman codes are used for different purposes in the "brotli" format, 450 and each purpose has a different alphabet size. For literal codes the 451 alphabet size is 256. For insert-and-copy length codes the alphabet 452 size is 704. For block length codes, the alphabet size is 26. For 453 distance codes, block type codes and the Huffman codes used in 454 compressing the context map, the alphabet size is dynamic and is 455 based on other parameters. 457 3.4. Simple Huffman codes 459 The first two bits of the compressed representation of each Huffman 460 code distinguishes between simple and complex Huffman codes. If this 461 value is 1, then a simple Huffman code follows. Otherwise the value 462 indicates the number of leading zeros. 464 A simple Huffman code can have only up to four symbols with non- zero 465 code length. The format of the simple Huffman code is as follows: 467 2 bits: value of 1 indicates a simple Huffman code 468 2 bits: NSYM - 1, where NSYM = # of symbols with non-zero 469 code length 471 NSYM symbols, each encoded using ALPHABET_BITS bits 473 1 bit: tree-select, present only for NSYM = 4 475 The value of ALPHABET_BITS depends on the alphabet of the Huffman 476 code: it is the smallest number of bits that can represent all 477 symbols in the alphabet. E.g. for the alphabet of literal bytes, 478 ALPHABET_BITS is 8. The value of each of the NSYM symbols above is 479 the value of the ALPHABETS_BITS width machine integer representing 480 the symbol modulo the alphabet size of the Huffman code. 482 The (non-zero) code lengths of the symbols can be reconstructed as 483 follows: 485 * if NSYM = 1, the code length for the one symbol is one at 486 this stage, but only to distinguish it from the other zero 487 code length symbols, when encoding this symbol in the 488 compressed data stream using this Huffman code later, no 489 actual bits are emitted. Similarly, when decoding a symbol 490 using this Huffman code, no bits are read and the one symbol 491 is returned. 493 * if NSYM = 2, both symbols have code length 1. 495 * if NSYM = 3, the code lengths for the symbols are 1, 2, 2 in 496 the order they appear in the representation of the simple 497 Huffman code. 499 * if NSYM = 4, the code lengths (in order of symbols decoded) 500 depend on the tree-select bit: 2, 2, 2, 2, (tree-select bit 0) 501 or 1, 2, 3, 3 (tree-select bit 1). 503 3.5. Complex Huffman codes 505 A complex Huffman code is a canonical Huffman code, defined by the 506 sequence of code lengths, as discussed in Paragraph 3.2, above. For 507 even greater compactness, the code length sequences themselves are 508 compressed using a Huffman code. The alphabet for code lengths is as 509 follows: 511 0 - 15: Represent code lengths of 0 - 15 512 16: Copy the previous non-zero code length 3 - 6 times 513 The next 2 bits indicate repeat length 514 (0 = 3, ... , 3 = 6) 516 If this is the first code length, or all previous 517 code lengths are zero, a code length of 8 is 518 repeated 3 - 6 times 519 A repeated code length code of 16 modifies the 520 repeat count of the previous one as follows: 521 repeat count = (4 * (repeat count - 2)) + 522 (3 - 6 on the next 2 bits) 523 Example: Codes 7, 16 (+2 bits 11), 16 (+2 bits 10) 524 will expand to 22 code lengths of 7 525 (1 + 4 * (6 - 2) + 5) 526 17: Repeat a code length of 0 for 3 - 10 times. 527 (3 bits of length) 528 A repeated code length code of 17 modifies the 529 repeat count of the previous one as follows: 530 repeat count = (8 * (repeat count - 2)) + 531 (3 - 10 on the next 3 bits) 533 A code length of 0 indicates that the corresponding symbol in the 534 alphabet will not occur in the compressed data, and should not 535 participate in the Huffman code construction algorithm given earlier. 536 A complex Huffman code must have at least two non-zero code lengths. 538 The bit lengths of the Huffman code over the code length alphabet are 539 compressed with the following static Huffman code: 541 Symbol Code 542 ------ ---- 543 0 00 544 1 1110 545 2 110 546 3 01 547 4 10 548 5 1111 550 We can now define the format of the complex Huffman code as follows: 552 2 bits: HSKIP, values of 0, 2 or 3 represent the respective 553 number of leading zeros. (Value of 1 indicates the 554 Simple Huffman code.) 556 Code lengths for symbols in the code length alphabet given 557 just above, in the order: 1, 2, 3, 4, 0, 5, 17, 6, 16, 7, 558 8, 9, 10, 11, 12, 13, 14, 15 560 The code lengths of code length symbols are between 0 and 561 5 and they are represented with 2 - 5 bits according to 562 the static Huffman code above. A code length of 0 means 563 the corresponding code length symbol is not used. 565 If HSKIP is 2 or 3, a respective number of leading code 566 lengths are implicit zeros and are not present in the 567 code lengths sequence above. If there are at least two 568 non-zero code lengths, any trailing zero code lengths are 569 omitted, i.e. the last code length in the sequence must 570 be non-zero. In this case the sum of (32 >> code length) 571 over all the non-zero code lengths must equal to 32. 573 Sequence of code lengths symbols, encoded using the code 574 length Huffman code. Any trailing 0 or 17 must be 575 omitted, i.e. the last encoded code length symbol must be 576 between 1 and 16. The sum of (32768 >> code length) over 577 all the non-zero code lengths in the alphabet, including 578 those encoded using repeat code(s) of 16, must equal to 579 32768. 581 4. Encoding of distances 583 As described in Section 2, one component of a compressed meta-block 584 is a sequence of backward distances. In this section we provide the 585 details to the encoding of distances. 587 Each distance in the compressed data part of a meta-block is 588 represented with a pair . The distance 589 code and the extra bits are encoded back-to-back, the distance code 590 is encoded using a Huffman code over the distance code alphabet, 591 while the extra bits value is encoded as a fixed-width machine 592 integer. The number of extra bits can be 0 - 24, and it is dependent 593 on the distance code. 595 To convert a distance code and associated extra bits to a backward 596 distance, we need the sequence of past distances and two additional 597 parameters, the number of "postfix bits", denoted by NPOSTFIX, and 598 the number of direct distance codes, denoted by NDIRECT. Both of 599 these parameters are encoded in the meta-block header. We will also 600 use the following derived parameter: 602 POSTFIX_MASK = ((1 << NPOSTFIX) - 1) 604 The first 16 distance codes are special short codes that reference 605 past distances as follows: 607 0: last distance 608 1: second last distance 609 2: third last distance 610 3: fourth last distance 611 4: last distance - 1 612 5: last distance + 1 613 6: last distance - 2 614 7: last distance + 2 615 8: last distance - 3 616 9: last distance + 3 617 10: second last distance - 1 618 11: second last distance + 1 619 12: second last distance - 2 620 13: second last distance + 2 621 14: second last distance - 3 622 15: second last distance + 3 624 The ring-buffer of four last distances is initialized by the values 625 16, 15, 11 and 4 (i.e. the fourth last is set to 16, the third last 626 to 15, the second last to 11 and the last distance to 4) at the 627 beginning of the *stream* (as opposed to the beginning of the meta- 628 block) and it is not reset at meta-block boundaries. When a distance 629 code 0 appears, the distance it represents (i.e. the last distance in 630 the sequence of distances) is not pushed to the ring-buffer of last 631 distances, in other words, the expression "(second, third, fourth) 632 last distance" means the (second, third, fourth) last distance that 633 was not represented by a 0 distance code. Similarly, distances that 634 represent static dictionary words (see Section 8.) are not pushed to 635 the ringbuffer of last distances. 637 The next NDIRECT distance codes, from 16 to 15 + NDIRECT, represent 638 distances from 1 to NDIRECT. Neither the distance short codes, nor 639 the NDIRECT direct distance codes have any extra bits. 641 Distance codes 16 + NDIRECT and greater all have extra bits, the 642 number of extra bits for a distance code "dcode" is given by the 643 following formula: 645 ndistbits = 1 + ((dcode - NDIRECT - 16) >> (NPOSTFIX + 1)) 647 The maximum number of extra bits is 24, therefore the size of the 648 distance code alphabet is (16 + NDIRECT + (48 << NPOSTFIX)). 650 Given a distance code "dcode" (>= 16 + NDIRECT), and extra bits 651 "dextra", the backward distance is given by the following formula: 653 hcode = (dcode - NDIRECT - 16) >> NPOSTFIX 654 lcode = (dcode - NDIRECT - 16) & POSTFIX_MASK 655 offset = ((2 + (hcode & 1)) << ndistbits) - 4; 656 distance = ((offset + dextra) << NPOSTFIX) + lcode + NDIRECT + 1 658 5. Encoding of literal insertion lengths and copy lengths 660 As described in Section 2, the literal insertion lengths and backward 661 copy lengths are encoded using a single Huffman code. This section 662 provides the details to this encoding. 664 Each pair in the compressed data part 665 of a meta-block is represented with the following triplet: 667 669 The insert-and-copy length code, the insert extra bits and the copy 670 extra bits are encoded back-to-back, the insert-and-copy length code 671 is encoded using a Huffman code over the insert-and-copy length code 672 alphabet, while the extra bits values are encoded as fixed-width 673 machine integers. The number of insert and copy extra bits can be 0 - 674 24, and they are dependent on the insert-and-copy length code. 676 Some of the insert-and-copy length codes also express the fact that 677 the distance code of the distance in the same command is 0, i.e. the 678 distance component of the command is the same as that of the previous 679 command. In this case, the distance code and extra bits for the 680 distance are omitted from the compressed data stream. 682 We describe the insert-and-copy length code alphabet in terms of the 683 (not directly used) insert length code and copy length code 684 alphabets. The symbols of the insert length code alphabet, along with 685 the number of insert extra bits and the range of the insert lengths 686 are as follows: 688 Extra Extra Extra 689 Code Bits Lengths Code Bits Lengths Code Bits Lengths 690 ---- ---- ------ ---- ---- ------- ---- ---- ------- 691 0 0 0 8 2 10-13 16 6 130-193 692 1 0 1 9 2 14-17 17 7 194-321 693 2 0 2 10 3 18-25 18 8 322-577 694 3 0 3 11 3 26-33 19 9 578-1089 695 4 0 4 12 4 34-49 20 10 1090-2113 696 5 0 5 13 4 50-65 21 12 2114-6209 697 6 1 6,7 14 5 66-97 22 14 6210-22593 698 7 1 8,9 15 5 98-129 23 24 22594-16799809 700 The symbols of the copy length code alphabet, along with the number 701 of copy extra bits and the range of copy lengths are as follows: 703 Extra Extra Extra 704 Code Bits Lengths Code Bits Lengths Code Bits Lengths 705 ---- ---- ------ ---- ---- ------- ---- ---- ------- 706 0 0 2 8 1 10,11 16 5 70-101 707 1 0 3 9 1 12,13 17 5 102-133 708 2 0 4 10 2 14-17 18 6 134-197 709 3 0 5 11 2 18-21 19 7 198-325 710 4 0 6 12 3 22-29 20 8 326-581 711 5 0 7 13 3 30-37 21 9 582-1093 712 6 0 8 14 4 38-53 22 10 1094-2117 713 7 0 9 15 4 54-69 23 24 2118-16779333 715 To convert an insert-and-copy length code to an insert length code 716 and a copy length code, the following table can be used: 718 Insert 719 length Copy length code 720 code 0-7 8-15 16-23 721 +---------+---------+ 722 | | | 723 0-7 | 0-63 | 64-127 | <--- distance code 0 724 | | | 725 +---------+---------+---------+ 726 | | | | 727 0-7 | 128-191 | 192-255 | 384-447 | 728 | | | | 729 +---------+---------+---------+ 730 | | | | 731 8-15 | 256-319 | 320-383 | 512-575 | 732 | | | | 733 +---------+---------+---------+ 734 | | | | 735 16-23 | 448-511 | 576-639 | 640-703 | 736 | | | | 737 +---------+---------+---------+ 739 First, look up the cell with the 64 value range containing the 740 insert-and-copy length code, this gives the insert length code and 741 the copy length code ranges, both 8 values long. The copy length code 742 within its range is determined by the lowest 3 bits of the insert- 743 and-copy length code, and the insert length code within its range is 744 determined by bits 3-5 (counted from the LSB) of the insert- and-copy 745 length code. Given the insert length and copy length codes, the 746 actual insert and copy lengths can be obtained by reading the number 747 of extra bits given by the tables above. 749 If the insert-and-copy length code is between 0 and 127, the distance 750 code of the command is set to zero (the last distance reused). 752 6. Encoding of block switch commands 754 As described in Section 2, a block-switch command is a pair . These are encoded in the compressed data part of 756 the meta-block, right before the start of each new block of a 757 particular block category. 759 Each block type in the compressed data is represented with a block 760 type code, encoded using a Huffman code over the block type code 761 alphabet. A block type code 0 means that the block type is the same 762 as the type of the second last block from the same block category, 763 while a block type code 1 means that the block type equals the last 764 block type plus one. If the last block type is the maximal possible, 765 then a block type code 1 means block type 0. Block type codes 2 - 257 766 represent block types 0 - 255. The second last and last block types 767 are initialized with 0 and 1, respectively, at the beginning of each 768 meta-block. 770 The first block type of each block category must be 0 and the block 771 type of the first block switch command is therefore not encoded in 772 the compressed data. 774 The number of different block types in each block category, denoted 775 by NBLTYPESL, NBLTYPESI, and NBLTYPESD for literals, insert-and-copy 776 lengths and distances, respectively, is encoded in the meta-block 777 header, and it must equal to the largest block type plus one in that 778 block category. In other words, the set of literal, insert-and-copy 779 length and distance block types must be [0..NBLTYPESL-1], 780 [0..NBLTYPESI-1], and [0..NBLTYPESD-1], respectively. From this it 781 follows that the alphabet size of literal, insert-and-copy length and 782 distance block type codes is NBLTYPES + 2, NBLTYPESI + 2 and 783 NBLTYPESD + 2, respectively. 785 Each block length in the compressed data is represented with a pair 786 . The block length code and the extra 787 bits are encoded back-to-back, the block length code is encoded using 788 a Huffman code over the block length code alphabet, while the extra 789 bits value is encoded as a fixed-width machine integer. The number of 790 extra bits can be 0 - 24, and it is dependent on the block length 791 code. The symbols of the block length code alphabet, along with the 792 number of extra bits and the range of block lengths are as follows: 794 Extra Extra Extra 795 Code Bits Lengths Code Bits Lengths Code Bits Lengths 796 ---- ---- ------ ---- ---- ------- ---- ---- ------- 797 0 2 1-4 9 4 65-80 18 7 369-496 798 1 2 5-8 10 4 81-96 19 8 497-752 799 2 2 9-12 11 4 97-112 20 9 753-1264 800 3 2 13-16 12 5 113-144 21 10 1265-2288 801 4 3 17-24 13 5 145-176 22 11 2289-4336 802 5 3 25-32 14 5 177-208 23 12 4337-8432 803 6 3 33-40 15 5 209-240 24 13 8433-16624 804 7 3 41-48 16 6 241-304 25 24 16625-16793840 805 8 4 49-64 17 6 305-368 807 The first block switch command of each block category is special in 808 the sense that it is encoded in the meta-block header, and as 809 described earlier the block type code is omitted, since it is an 810 implicit zero. 812 7. Context modeling 814 As described in Section 2, the Huffman tree used to encode a literal 815 byte or a distance code depends on the context ID and the block type. 816 This section specifies how to compute the context ID for a particular 817 literal and distance code, and how to encode the context map that 818 maps a pair to the index of a Huffman tree 819 in the array of literal and distance Huffman trees. 821 7.1. Context modes and context ID lookup for literals 823 The context for encoding the next literal is defined by the last two 824 bytes in the stream (p1, p2, where p1 is the most recent byte), 825 regardless if these bytes are produced by backward references or by 826 literal insertions. 828 There are four methods, called context modes, to compute the Context 829 ID: 830 * MSB6, where the Context ID is the value of six most 831 significant bits of p1, 832 * LSB6, where the Context ID is the value of six least 833 significant bits of p1, 834 * UTF8, where the Context ID is a complex function of p1, p2, 835 optimized for text compression, and 836 * Signed, where Context ID is a complex function of p1, p2, 837 optimized for compressing sequences of signed integers. 839 The Context ID for the UTF8 and Signed context modes is computed 840 using the following lookup tables Lut0, Lut1, and Lut2. 842 Lut0 := 843 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 844 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 845 8, 12, 16, 12, 12, 20, 12, 16, 24, 28, 12, 12, 32, 12, 36, 12, 846 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 32, 32, 24, 40, 28, 12, 847 12, 48, 52, 52, 52, 48, 52, 52, 52, 48, 52, 52, 52, 52, 52, 48, 848 52, 52, 52, 52, 52, 48, 52, 52, 52, 52, 52, 24, 12, 28, 12, 12, 849 12, 56, 60, 60, 60, 56, 60, 60, 60, 56, 60, 60, 60, 60, 60, 56, 850 60, 60, 60, 60, 60, 56, 60, 60, 60, 60, 60, 24, 12, 28, 12, 0, 851 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 852 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 853 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 854 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 855 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 856 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 857 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 858 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 860 Lut1 := 861 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 862 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 863 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 864 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 865 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 866 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 867 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 868 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 0, 869 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 870 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 871 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 872 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 873 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 874 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 875 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 876 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 878 Lut2 := 879 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 880 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 881 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 882 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 883 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 884 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 885 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 886 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 887 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 888 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 889 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 890 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 891 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 892 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 893 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 894 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7 896 Given p1 is the last decoded byte and p2 is the second last decoded 897 byte the context IDs can be computed as follows: 899 For LSB6 : Context ID = p1 & 0x3f 900 For MSB6 : Context ID = p1 >> 2 901 For UTF8 : Context ID = Lut0[p1] | Lut1[p2] 902 For Signed: Context ID = (Lut2[p1] << 3) | Lut2[p2] 904 The context modes LSB6, MSB6, UTF8, and Signed are denoted by 905 integers 0, 1, 2, 3. 907 The context mode is defined for each literal block type and they are 908 stored in a consecutive array of bits in the meta-block header, 909 always two bits per block type. 911 7.2. Context ID for distances 913 The context for encoding a distance code is defined by the copy 914 length corresponding to the distance. The context IDs are 0, 1, 2, 915 and 3 for copy lengths 2, 3, 4, and more than 4, respectively. 917 7.3. Encoding of the context map 919 There are two kinds of context maps, for literals and for distances. 920 The size of the context map is 64 * NBLTYPESL for literals, and 4 * 921 NBLTYPESD for distances. Each value in the context map is an integer 922 between 0 and 255, indicating the index of the Huffman tree to be 923 used when encoding the next literal or distance. 925 The context map is encoded as a one-dimensional array, CMAPL[0..(64 * 926 NBLTYPESL - 1)] and CMAPD[0..(4 * NBLTYPESD - 1)]. 928 The index of the Huffman tree for encoding a literal or distance code 929 with context ID "cid" and block type "bltype" is 931 index of literal Huffman tree = CMAPL[bltype * 64 + cid] 933 index of distance Huffman tree = CMAPD[bltype * 4 + cid] 935 The values of the context map are encoded with the combination of run 936 length encoding for zero values and Huffman coding. Let RLEMAX denote 937 the number of run length codes and NTREES denote the maximum value in 938 the context map plus one. NTREES must equal the number of different 939 values in the context map, in other words, the different values in 940 the context map must be the [0..NTREES-1] interval. The alphabet of 941 the Huffman code has the following RLEMAX + NTREES symbols: 943 0: value zero 944 1: repeat a zero 2-3 times, read 1 bit for repeat length 945 2: repeat a zero 4-7 times, read 2 bits for repeat length 946 ... 947 RLEMAX: repeat a zero (2^RLEMAX)-(2^(RLEMAX+1) - 1) times, 948 read RLEMAX bits for repeat length 949 RLEMAX + 1: value 1 950 ... 951 RLEMAX + NTREES - 1: value NTREES - 1 953 If RLEMAX = 0, the run length coding is not used, and the symbols of 954 the alphabet are directly the values in the context map. We can now 955 define the format of the context map (the same format is used for 956 literal and distance context maps): 958 1-5 bits: RLEMAX, 0 is encoded with one 0 bit, and values 959 1 - 16 are encoded with bit pattern 1xxxx 961 Huffman code with alphabet size NTREES + RLEMAX 963 Context map size values encoded with the above Huffman code 964 and run length coding for zero values 966 1 bit: IMTF bit, if set, we do an inverse move-to-front 967 transform on the values in the context map to get 968 the Huffman code indexes 970 For the encoding of NTREES see Section 9.2. 972 8. Static dictionary 974 At any given point during decoding the compressed data, a reference 975 to a duplicated string in the output produced so far has a maximum 976 backward distance value, which is the minimum of the window size and 977 the number of output bytes produced. However, decoding a distance 978 from the input stream, as described in section 4, can produce 979 distances that are greater than this maximum allowed value. The 980 difference between these distances and the first invalid distance 981 value is treated as reference to a word in the static dictionary 982 given in Appendix A. The maximum valid copy length for a static 983 dictionary reference is 24. The static dictionary has three parts: 985 * DICT[0..DICTSIZE], an array of bytes 986 * DOFFSET[0..24], an array of byte offset values for each length 987 * NDBITS[0..24], an array of bit-depth values for each length 989 The number of static dictionary words for a given length is: 991 NWORDS[length] = 0 (if length < 4) 992 NWORDS[length] = (1 << NDBITS[lengths]) (if length >= 4) 994 DOFFSET and DICTSIZE are defined by the following recursion: 996 DOFFSET[0] = 0 997 DOFFSET[length + 1] = DOFFSET[length] + length * NWORDS[length] 998 DICTSIZE = DOFFSET[24] + 24 * NWORDS[24] 1000 The offset of a word within the DICT array for a given length and 1001 index is: 1003 offset(length, index) = DOFFSET[length] + index * length 1005 Each static dictionary word has NTRANSFORMS different forms, given by 1006 applying a word transformation to a base word in the DICT array. The 1007 list of word transformations is given in Appendix B. The static 1008 dictionary word for a pair can be reconstructed as 1009 follows: 1011 word_id = distance - (max allowed distance + 1) 1012 index = word_id % NWORDS[length] 1013 base_word = DICT[offset(length, index)..offset(length, index+1)) 1014 transform_id = word_id >> NDBITS[length] 1016 The string copied to the output stream is computed by applying the 1017 transformation to the base dictionary word. If transform_id is 1018 greater than NTRANSFORMS - 1 or length is greater than 24, the 1019 compressed data set is invalid. 1021 Each word transformation has the follwing form: 1023 transform_i(word) = prefix_i + T_i(word) + suffix_i 1025 where the _i subscript denotes the transform_id above. Each T_i is 1026 one of the following 20 elementary transforms: 1028 Identity, OmitLast1, ..., OmitLast9, UppercaseFirst, UppercaseAll, 1029 OmitFirst1, ..., OmitFirst9 1031 The form of these elementary transforms are as follows: 1033 Identity(word) = word 1034 OmitLastk(word) = the first (length(word) - k) bytes of word, or 1035 empty string if length(word) < k 1037 UppercaseFirst(word) = first UTF-8 character of word upper-cased 1039 UppercaseAll(word) = all UTF-8 characters of word upper-cased 1041 OmitFirstk(word) = the last (length(word) - k) bytes of word, or 1042 empty string if length(word) < k 1044 For the purposes of UppercaseAll, word is parsed into UTF-8 1045 characters an coverted to upper-case by taking 1 - 3 bytes at a time, 1046 using the algorithm below: 1048 i = 0 1049 while i < length(word): 1050 if word[i] < 192: 1051 if word[i] >= 97 and word[i] <= 122: 1052 word[i] = word[i] ^ 32 1053 i = i + 1 1054 else if word[i] < 224: 1055 if i + 1 < length(word): 1056 word[i + 1] = word[i + 1] ^ 32 1057 i = i + 2 1058 else: 1059 if i + 2 < length(word): 1060 word[i + 2] = word[i + 2] ^ 5 1061 i = i + 3 1063 For UppercaseFirst, the same algorithm is used, but the loop is 1064 executed only once. 1066 Appendix B. contains the list of transformations by specifying the 1067 prefix, elementary transform and suffix components of each of them. 1069 9. Compressed data format 1071 In this section we describe the format of the compressed data set in 1072 terms of the format of the individual data items described in the 1073 previous sections. 1075 9.1. Format of the stream header 1077 The stream header has only the following one field: 1079 1-4 bits: WBITS, a value in the range 16 - 24, value 16 is 1080 encoded with one 0 bit, and values 17 - 24 are 1081 encoded with bit pattern 1xxx 1083 The size of the sliding window, which is the maximum value of any 1084 non-dictionary reference backward distance, is given by the following 1085 formula: 1087 window size = (1 << WBITS) - 16 1089 9.2. Format of the meta-block header 1091 A compliant compressed data set has at least one meta-block. Each 1092 meta-block contains a header with information about the uncompressed 1093 length of the meta-block, and a bit signaling if the meta-block is 1094 the last one. The format of the meta-block header is the following: 1096 1 bit: ISLAST, set to 1 if this is the last meta-block 1097 1 bit: ISEMPTY, set to 1 if the meta-block is empty, this 1098 field is only present if ISLAST bit is set, since 1099 only the last meta-block can be empty 1100 2 bits: MNIBBLES - 4, where MNIBBLES is # of nibbles to 1101 represent the length 1103 MNIBBLES x 4 bits: MLEN - 1, where MLEN is the length 1104 of the meta-block in the input data in bytes 1106 1 bit: ISUNCOMPRESSED, if set to 1, any bits of input up to 1107 the next byte boundary are ignored, and the rest of 1108 the meta-block contains MLEN bytes of literal data; 1109 this field is only present if ISLAST bit is not set 1111 1-11 bits: NBLTYPESL, # of literal block types, encoded with 1112 the following variable length code: 1114 Value Bit Pattern 1115 ----- ----------- 1116 1 0 1117 2 1000 1118 3-4 1001x 1119 5-8 1010xx 1120 9-16 1011xxx 1121 17-32 1100xxxx 1122 33-64 1101xxxxx 1123 65-128 1110xxxxxx 1124 129-256 1111xxxxxxx 1126 Huffman code over the block type code alphabet for literal 1127 block types, appears only if NBLTYPESL >= 2 1129 Huffman code over the block length code alphabet for literal 1130 block lengths, appears only if NBLTYPESL >= 2 1132 Block length code + Extra bits for first literal block 1133 length, appears only if NBLTYPESL >= 2 1135 1-11 bits: NBLTYPESI, # of insert-and-copy block types, encoded 1136 with the same variable length code as above 1138 Huffman code over the block type code alphabet for insert- 1139 and-copy block types, only if NBLTYPESI >= 2 1141 Huffman code over the block length code alphabet for insert- 1142 and-copy block lengths, only if NBLTYPESI >= 2 1144 Block length code + Extra bits for first insert-and-copy 1145 block length, only if NBLTYPESI >= 2 1147 1-11 bits: NBLTYPESD, # of distance block types, encoded with 1148 the same variable length code as above 1150 Huffman code over the block type code alphabet for distance 1151 block types, appears only if NBLTYPESD >= 2 1153 Huffman code over the block length code alphabet for 1154 distance block lengths, only if NBLTYPESD >= 2 1156 Block length code + Extra bits for first distance block 1157 length, only if NBLTYPESD >= 2 1159 2 bits: NPOSTFIX, parameter used in the distance coding 1161 4 bits: four most significant bits of NDIRECT, to get the 1162 actual value of the parameter NDIRECT, left-shift 1163 this four bit number by NPOSTFIX bits 1165 NBLTYPESL x 2 bits: context mode for each literal block type 1167 1-11 bits: NTREESL, # of literal Huffman trees, encoded with 1168 the same variable length code as NBLTYPESL 1170 Literal context map, encoded as described in Paragraph 7.3, 1171 appears only if NTREESL >= 2, otherwise the context map 1172 has only zero values 1174 1-11 bits: NTREESD, # of distance Huffman trees, encoded with 1175 the same variable length code as NBLTYPESD 1177 Distance context map, encoded as described in Paragraph 7.3, 1178 appears only if NTREESD >= 2, otherwise the context map 1179 has only zero values 1181 NTREESL Huffman codes for literals 1183 NBLTYPESI Huffman codes for insert-and-copy lengths 1185 NTREESD Huffman codes for distances 1187 9.3. Format of the meta-block data 1189 The compressed data part of a meta-block consists of a series of 1190 commands. Each command has the following format: 1192 Block type code for next insert-and-copy block type, appears 1193 only if NBLTYPESI >= 2 and the previous insert-and-copy 1194 block has ended 1196 Block length code + Extra bits for next insert-and-copy 1197 block length, appears only if NBLTYPESI >= 2 and the 1198 previous insert and-copy block has ended 1200 Insert-and-copy length, encoded as in section 5, using the 1201 insert-and-copy length Huffman code with the current 1202 insert-and-copy block type index 1204 Insert length number of literals, with the following format: 1206 Block type code for next literal block type, appears 1207 only if NBLTYPESL >= 2 and the previous literal 1208 block has ended 1210 Block length code + Extra bits for next literal block 1211 length, appears only if NBLTYPESL >= 2 and the 1212 previous literal block has ended 1214 Next byte of the input data, encoded with the literal 1215 Huffman code with the index determined by the 1216 previuos two bytes of the input data, the current 1217 literal block type and the context map, as 1218 described in Paragraph 7.3. 1220 Block type code for next distance block type, appears only 1221 if NBLTYPESD >= 2 and the previous distance block has 1222 ended 1224 Block length code + Extra bits for next distance block 1225 length, appears only if NBLTYPESD >= 2 and the previous 1226 distance block has ended 1228 Distance code, encoded as in section 4, using the distance 1229 Huffman code with the current distance block type index, 1230 appears only if the distance code is not an implicit 0, 1231 as indicated by the insert-and-copy length code 1233 The number of commands in the meta-block is such that the sum of 1234 insert lengths and copy lengths over all the commands gives the 1235 uncompressed length, MLEN encoded in the meta-block header. 1237 10. Decoding algorithm 1239 The decoding algorithm that produces the output data is as follows: 1241 read window size 1242 do 1243 read ISLAST bit 1244 if ISLAST 1245 read ISEMPTY bit 1246 if ISEMPTY 1247 break from loop 1248 read MLEN 1249 if not ISLAST 1250 read ISUNCOMPRESSED bit 1251 if ISUNCOMPRESSED 1252 skip any bits up to the next byte boundary 1253 copy MLEN bytes of input to the output stream 1254 continue to the next meta-block 1255 loop for each three block categories (i = L, I, D) 1256 read NBLTYPESi 1257 if NBLTYPESi >= 2 1258 read Huffman code for block types, HTREE_BTYPE_i 1259 read Huffman code for block lengths, HTREE_BLEN_i 1260 read block length, BLEN_i 1261 set block type, BTYPE_i to 0 1262 initialize second last and last block types to 0 and 1 1263 else 1264 set block type, BTYPE_i to 0 1265 set block length, BLEN_i to 268435456 1266 read NPOSTFIX and NDIRECT 1267 read array of literal context modes, CMODE[] 1268 read NTREESL 1269 if NTREESL >= 2 1270 read literal context map, CMAPL[] 1271 else 1272 fill CMAPL[] with zeros 1273 read NTREESD 1274 if NTREESD >= 2 1275 read distance context map, CMAPD[] 1276 else 1277 fill CMAPD[] with zeros 1278 read array of Huffman codes for literals, HTREEL[] 1279 read array of Huffman codes for insert-and-copy, HTREEI[] 1280 read array of Huffman codes for distances, HTREED[] 1281 do 1282 if BLEN_I is zero 1283 read block type using HTREE_BTYPE_I and set BTYPE_I 1284 read block length using HTREE_BLEN_I and set BLEN_I 1285 decrement BLEN_I 1286 read insert and copy length, ILEN, CLEN with HTREEI[BTYPE_I] 1287 loop for ILEN 1288 if BLEN_L is zero 1289 read block type using HTREE_BTYPE_L and set BTYPE_L 1290 read block length using HTREE_BLEN_L and set BLEN_L 1291 decrement BLEN_L 1292 look up context mode CMODE[BTYPE_L] 1293 compute context ID, CIDL from last two bytes of output 1294 read literal using HTREEL[CMAPL[64 * BTYPE_L + CIDL]] 1295 copy literal to output stream 1296 if number of output bytes produced in the loop is MLEN 1297 break from loop 1298 if distance code is implicit zero from insert-and-copy code 1299 set backward distance to the last distance 1300 else 1301 if BLEN_D is zero 1302 read block type using HTREE_BTYPE_D and set BTYPE_D 1303 read block length using HTREE_BLEN_D and set BLEN_D 1304 decrement BLEN_D 1305 compute context ID, CIDD from CLEN 1306 read distance code with HTREED[CMAPD[4 * BTYPE_D + CIDD]] 1307 compute distance by distance short code substitution 1308 move backwards distance bytes in the output stream, and 1309 copy CLEN bytes from this position to the output stream, 1310 or look up the static dictionary word and copy it to the 1311 output stram 1312 while number of output bytes produced in the loop < MLEN 1313 while not ISLAST 1315 Note that a duplicated string reference may refer to a string in a 1316 previous meta-block, i.e. the backward distance may cross one or more 1317 meta-block boundaries. However a backward copy distance cannot refer 1318 past the beginning of the output stream and it can not be greater 1319 than the window size; any such distance must be interpreted as a 1320 reference to a static dictionary word. Also note that the referenced 1321 string may overlap the current position, for example, if the last 2 1322 bytes decoded have values X and Y, a string reference with adds X,Y,X,Y,X to the output stream. 1325 11. Security Considerations 1327 As with any compressed file formats, decompressor implementations 1328 should handle all input byte sequences, not only those that conform 1329 to this specification and non-conformant input sequences should be 1330 discarded. A possible attack against a system containing a 1331 decompressor implementation (e.g. a web browser) is to exploit a 1332 buffer overflow caused by an invalid input. Therefore decompressor 1333 implementations should perform bound-checking for each memory access 1334 that result from values decoded from the input stream. 1336 12. IANA Considerations 1338 This document has no actions for IANA. 1340 13. Informative References 1342 [HUFFMAN] Huffman, D. A., "A Method for the Construction of Minimum 1343 Redundancy Codes", Proceedings of the Institute of Radio 1344 Engineers, September 1952, Volume 40, Number 9, pp. 1345 1098-1101. 1347 [LZ77] Ziv J., Lempel A., "A Universal Algorithm for Sequential 1348 Data Compression", IEEE Transactions on Information 1349 Theory, Vol. 23, No. 3, pp. 337-343. 1351 [RFC1951] Deutsch, P., "DEFLATE Compressed Data Format Specification 1352 version 1.3", RFC 1951, Aladdin Enterprises, May 1996. 1353 http://www.ietf.org/rfc/rfc1951.txt 1355 [WOFF2] Levantovsky, V. (ed.), Levien, R. (ed.), "WOFF File Format 1356 2.0", W3C WebFonts Working Group, 1357 http://www.w3.org/TR/WOFF2/ 1359 14. Source code 1361 Source code for a C language implementation of a "brotli" compliant 1362 decompressor and a C++ language implementation of a compressor is 1363 available in the brotli open-source project: 1364 https://github.com/google/brotli 1366 Appendix A. Static dictionary data 1368 The hexadecimal form of the DICT array is the following: 1370 74696d65646f776e6c6966656c6566746261636b636f64656461746173686f77 1371 6f6e6c7973697465636974796f70656e6a7573746c696b6566726565776f726b 1372 74657874796561726f766572626f64796c6f7665666f726d626f6f6b706c6179 1373 6c6976656c696e6568656c70686f6d65736964656d6f7265776f72646c6f6e67 1374 7468656d7669657766696e64706167656461797366756c6c686561647465726d 1375 656163686172656166726f6d747275656d61726b61626c6575706f6e68696768 1376 646174656c616e646e6577736576656e6e65787463617365626f7468706f7374 1377 757365646d61646568616e6468657265776861746e616d654c696e6b626c6f67 1378 73697a656261736568656c646d616b656d61696e757365722729202b686f6c64 1379 656e6473776974684e65777372656164776572657369676e74616b6568617665 1380 67616d657365656e63616c6c7061746877656c6c706c75736d656e7566696c6d 1381 706172746a6f696e746869736c697374676f6f646e6565647761797377657374 1382 6a6f62736d696e64616c736f6c6f676f72696368757365736c6173747465616d 1383 61726d79666f6f646b696e6777696c6c65617374776172646265737466697265 1384 506167656b6e6f77617761792e706e676d6f76657468616e6c6f616467697665 1385 73656c666e6f74656d756368666565646d616e79726f636b69636f6e6f6e6365 1386 6c6f6f6b6869646564696564486f6d6572756c65686f7374616a6178696e666f 1387 636c75626c6177736c65737368616c66736f6d65737563687a6f6e6531303025 1388 6f6e65736361726554696d6572616365626c7565666f75727765656b66616365 1389 686f706567617665686172646c6f73747768656e7061726b6b65707470617373 1390 73686970726f6f6d48544d4c706c616e54797065646f6e65736176656b656570 1391 666c61676c696e6b736f6c6466697665746f6f6b72617465746f776e6a756d70 1392 746875736461726b6361726466696c6566656172737461796b696c6c74686174 1393 66616c6c6175746f657665722e636f6d74616c6b73686f70766f746564656570 1394 6d6f6465726573747475726e626f726e62616e6466656c6c726f736575726c28 1395 736b696e726f6c65636f6d6561637473616765736d656574676f6c642e6a7067 1396 6974656d7661727966656c747468656e73656e6464726f7056696577636f7079 1397 312e30223c2f613e73746f70656c73656c696573746f75727061636b2e676966 1398 706173746373733f677261796d65616e2667743b7269646573686f746c617465 1399 73616964726f6164766172206665656c6a6f686e7269636b706f727466617374 1400 2755412d646561643c2f623e706f6f7262696c6c74797065552e532e776f6f64 1401 6d7573743270783b496e666f72616e6b7769646577616e7477616c6c6c656164 1402 5b305d3b7061756c776176657375726524282723776169746d61737361726d73 1403 676f65736761696e6c616e6770616964212d2d206c6f636b756e6974726f6f74 1404 77616c6b6669726d77696665786d6c22736f6e6774657374323070786b696e64 1405 726f7773746f6f6c666f6e746d61696c73616665737461726d617073636f7265 1406 7261696e666c6f77626162797370616e736179733470783b3670783b61727473 1407 666f6f747265616c77696b696865617473746570747269706f72672f6c616b65 1408 7765616b746f6c64466f726d6361737466616e7362616e6b7665727972756e73 1409 6a756c797461736b3170783b676f616c67726577736c6f776564676569643d22 1410 736574733570783b2e6a733f3430707869662028736f6f6e736561746e6f6e65 1411 747562657a65726f73656e747265656466616374696e746f676966746861726d 1412 3138707863616d6568696c6c626f6c647a6f6f6d766f69646561737972696e67 1413 66696c6c7065616b696e6974636f73743370783b6a61636b7461677362697473 1414 726f6c6c656469746b6e65776e6561723c212d2d67726f774a534f4e64757479 1415 4e616d6573616c65796f75206c6f74737061696e6a617a7a636f6c6465796573 1416 666973687777772e7269736b7461627370726576313070787269736532357078 1417 426c756564696e673330302c62616c6c666f72646561726e77696c64626f782e 1418 666169726c61636b76657273706169726a756e6574656368696628217069636b 1419 6576696c242822237761726d6c6f7264646f657370756c6c2c30303069646561 1420 647261776875676573706f7466756e646275726e6872656663656c6c6b657973 1421 7469636b686f75726c6f73736675656c31327078737569746465616c52535322 1422 6167656467726579474554226561736561696d736769726c616964733870783b 1423 6e617679677269647469707323393939776172736c61647963617273293b207d 1424 7068703f68656c6c74616c6c77686f6d7a683ae52a2f0d0a2031303068616c6c 1425 2e0a0a413770783b70757368636861743070783b637265772a2f3c2f68617368 1426 37357078666c6174726172652026262074656c6c63616d706f6e746f6c616964 1427 6d697373736b697074656e7466696e656d616c6567657473706c6f743430302c 1428 0d0a0d0a636f6f6c666565742e7068703c62723e657269636d6f737467756964 1429 62656c6c64657363686169726d61746861746f6d2f696d67262338326c75636b 1430 63656e743030303b74696e79676f6e6568746d6c73656c6c6472756746524545 1431 6e6f64656e69636b3f69643d6c6f73656e756c6c7661737477696e6452535320 1432 7765617272656c796265656e73616d6564756b656e6173616361706577697368 1433 67756c665432333a68697473736c6f74676174656b69636b626c757274686579 1434 313570782727293b293b223e6d73696577696e7362697264736f727462657461 1435 7365656b5431383a6f726473747265656d616c6c363070786661726de2809973 1436 626f79735b305d2e27293b22504f5354626561726b696473293b7d7d6d617279 1437 74656e6428554b29717561647a683ae62d73697a2d2d2d2d70726f7027293b0d 1438 6c6966745431393a76696365616e6479646562743e525353706f6f6c6e65636b 1439 626c6f775431363a646f6f726576616c5431373a6c6574736661696c6f72616c 1440 706f6c6c6e6f7661636f6c7367656e6520e28094736f6674726f6d6574696c6c 1441 726f73733c68333e706f75726661646570696e6b3c74723e6d696e69297c2128 1442 6d696e657a683ae862617273686561723030293b6d696c6b202d2d3e69726f6e 1443 667265646469736b77656e74736f696c707574732f6a732f686f6c795432323a 1444 4953424e5432303a6164616d736565733c68323e6a736f6e272c2027636f6e74 1445 5432313a205253536c6f6f70617369616d6f6f6e3c2f703e736f756c4c494e45 1446 666f7274636172745431343a3c68313e38307078212d2d3c3970783b5430343a 1447 6d696b653a34365a6e696365696e6368596f726b726963657a683ae42729293b 1448 707572656d61676570617261746f6e65626f6e643a33375a5f6f665f275d293b 1449 3030302c7a683ae774616e6b79617264626f776c627573683a35365a4a617661 1450 333070780a7c7d0a254333253a33345a6a656666455850496361736876697361 1451 676f6c66736e6f777a683ae9717565722e6373737369636b6d6561746d696e2e 1452 62696e6464656c6c686972657069637372656e743a33365a485454502d323031 1453 666f746f776f6c66454e442078626f783a35345a424f44596469636b3b0a7d0a 1454 657869743a33355a7661727362656174277d293b646965743939393b616e6e65 1455 7d7d3c2f5b695d2e4c616e676b6dc2b277697265746f7973616464737365616c 1456 616c65783b0a097d6563686f6e696e652e6f726730303529746f6e796a657773 1457 73616e646c656773726f6f66303030292032303077696e6567656172646f6773 1458 626f6f74676172796375747374796c6574656d7074696f6e2e786d6c636f636b 1459 67616e672428272e3530707850682e446d697363616c616e6c6f616e6465736b 1460 6d696c657279616e756e697864697363293b7d0a64757374636c6970292e0a0a 1461 373070782d32303044564473375d3e3c7461706564656d6f692b2b2977616765 1462 6575726f7068696c6f707473686f6c65464151736173696e2d3236546c616273 1463 7065747355524c2062756c6b636f6f6b3b7d0d0a484541445b305d2961626272 1464 6a75616e283139386c6573687477696e3c2f693e736f6e79677579736675636b 1465 706970657c2d0a21303032296e646f775b315d3b5b5d3b0a4c6f672073616c74 1466 0d0a090962616e677472696d62617468297b0d0a303070780a7d293b6b6f3aec 1467 6665657361643e0d733a2f2f205b5d3b746f6c6c706c756728297b0a7b0d0a20 1468 2e6a7327323030706475616c626f61742e4a5047293b0a7d71756f74293b0a0a 1469 27293b0a0d0a7d0d323031343230313532303136323031373230313832303139 1470 3230323032303231323032323230323332303234323032353230323632303237 1471 3230323832303239323033303230333132303332323033333230333432303335 1472 3230333632303337323031333230313232303131323031303230303932303038 1473 3230303732303036323030353230303432303033323030323230303132303030 1474 3139393931393938313939373139393631393935313939343139393331393932 1475 3139393131393930313938393139383831393837313938363139383531393834 1476 3139383331393832313938313139383031393739313937383139373731393736 1477 3139373531393734313937333139373231393731313937303139363931393638 1478 3139363731393636313936353139363431393633313936323139363131393630 1479 3139353931393538313935373139353631393535313935343139353331393532 1480 31393531313935303130303031303234313339343030303039393939636f6d6f 1481 6dc3a17365737465657374617065726f746f646f686163656361646161c3b16f 1482 6269656e64c3ad616173c3ad766964616361736f6f74726f666f726f736f6c6f 1483 6f7472616375616c64696a6f7369646f6772616e7469706f74656d6164656265 1484 616c676f7175c3a96573746f6e61646174726573706f636f6361736162616a6f 1485 746f646173696e6f6167756170756573756e6f73616e7465646963656c756973 1486 656c6c616d61796f7a6f6e61616d6f727069736f6f627261636c6963656c6c6f 1487 64696f73686f726163617369d0b7d0b0d0bdd0b0d0bed0bcd180d0b0d180d183 1488 d182d0b0d0bdd0b5d0bfd0bed0bed182d0b8d0b7d0bdd0bed0b4d0bed182d0be 1489 d0b6d0b5d0bed0bdd0b8d185d09dd0b0d0b5d0b5d0b1d18bd0bcd18bd092d18b 1490 d181d0bed0b2d18bd0b2d0bed09dd0bed0bed0b1d09fd0bed0bbd0b8d0bdd0b8 1491 d0a0d0a4d09dd0b5d09cd18bd182d18bd09ed0bdd0b8d0bcd0b4d0b0d097d0b0 1492 d094d0b0d09dd183d09ed0b1d182d0b5d098d0b7d0b5d0b9d0bdd183d0bcd0bc 1493 d0a2d18bd183d0b6d981d98ad8a3d986d985d8a7d985d8b9d983d984d8a3d988 1494 d8b1d8afd98ad8a7d981d989d987d988d984d985d984d983d8a7d988d984d987 1495 d8a8d8b3d8a7d984d8a5d986d987d98ad8a3d98ad982d8afd987d984d8abd985 1496 d8a8d987d984d988d984d98ad8a8d984d8a7d98ad8a8d983d8b4d98ad8a7d985 1497 d8a3d985d986d8aad8a8d98ad984d986d8add8a8d987d985d985d8b4d988d8b4 1498 6669727374766964656f6c69676874776f726c646d656469617768697465636c 1499 6f7365626c61636b7269676874736d616c6c626f6f6b73706c6163656d757369 1500 636669656c646f72646572706f696e7476616c75656c6576656c7461626c6562 1501 6f617264686f75736567726f7570776f726b7379656172737374617465746f64 1502 6179776174657273746172747374796c656465617468706f77657270686f6e65 1503 6e696768746572726f72696e70757461626f75747465726d737469746c65746f 1504 6f6c736576656e746c6f63616c74696d65736c61726765776f72647367616d65 1505 7373686f72747370616365666f637573636c6561726d6f64656c626c6f636b67 1506 75696465726164696f7368617265776f6d656e616761696e6d6f6e6579696d61 1507 67656e616d6573796f756e676c696e65736c61746572636f6c6f72677265656e 1508 66726f6e7426616d703b7761746368666f726365707269636572756c65736265 1509 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2f613e3c2f6c693e3c6c693e3c6120687265663d226809093c6c693e3c612068 5150 7265663d22687474703a2f2f61746f722220617269612d68696464656e3d2274 5151 72753e203c6120687265663d22687474703a2f2f7777772e6c616e6775616765 5152 3d226a61766173637269707422202f6f7074696f6e3e0a3c6f7074696f6e2076 5153 616c75652f6469763e3c2f6469763e3c64697620636c6173733d7261746f7222 5154 20617269612d68696464656e3d227472653d286e65772044617465292e676574 5155 54696d652829706f7274756775c3aa732028646f2042726173696c29d0bed180 5156 d0b3d0b0d0bdd0b8d0b7d0b0d186d0b8d0b8d0b2d0bed0b7d0bcd0bed0b6d0bd 5157 d0bed181d182d18cd0bed0b1d180d0b0d0b7d0bed0b2d0b0d0bdd0b8d18fd180 5158 d0b5d0b3d0b8d181d182d180d0b0d186d0b8d0b8d0b2d0bed0b7d0bcd0bed0b6 5159 d0bdd0bed181d182d0b8d0bed0b1d18fd0b7d0b0d182d0b5d0bbd18cd0bdd0b0 5160 3c21444f43545950452068746d6c205055424c494320226e742d547970652220 5161 636f6e74656e743d22746578742f3c6d65746120687474702d65717569763d22 5162 436f6e746572616e736974696f6e616c2f2f454e222022687474703a3c68746d 5163 6c20786d6c6e733d22687474703a2f2f7777772d2f2f5733432f2f4454442058 5164 48544d4c20312e3020544454442f7868746d6c312d7472616e736974696f6e61 5165 6c2f2f7777772e77332e6f72672f54522f7868746d6c312f7065203d20277465 5166 78742f6a617661736372697074273b3c6d657461206e616d653d226465736372 5167 697074696f6e706172656e744e6f64652e696e736572744265666f72653c696e 5168 70757420747970653d2268696464656e22206e616a732220747970653d227465 5169 78742f6a6176617363726928646f63756d656e74292e72656164792866756e63 5170 746973637269707420747970653d22746578742f6a61766173696d6167652220 5171 636f6e74656e743d22687474703a2f2f55412d436f6d70617469626c65222063 5172 6f6e74656e743d746d6c3b20636861727365743d7574662d3822202f3e0a6c69 5173 6e6b2072656c3d2273686f72746375742069636f6e3c6c696e6b2072656c3d22 5174 7374796c65736865657422203c2f7363726970743e0a3c736372697074207479 5175 70653d3d20646f63756d656e742e637265617465456c656d656e3c6120746172 5176 6765743d225f626c616e6b2220687265663d20646f63756d656e742e67657445 5177 6c656d656e747342696e70757420747970653d227465787422206e616d653d61 5178 2e74797065203d2027746578742f6a617661736372696e70757420747970653d 5179 2268696464656e22206e616d6568746d6c3b20636861727365743d7574662d38 5180 22202f3e647464223e0a3c68746d6c20786d6c6e733d22687474702d2f2f5733 5181 432f2f4454442048544d4c20342e30312054656e747342795461674e616d6528 5182 277363726970742729696e70757420747970653d2268696464656e22206e616d 5183 3c73637269707420747970653d22746578742f6a6176617322207374796c653d 5184 22646973706c61793a6e6f6e653b223e646f63756d656e742e676574456c656d 5185 656e7442794964283d646f63756d656e742e637265617465456c656d656e7428 5186 2720747970653d27746578742f6a61766173637269707427696e707574207479 5187 70653d227465787422206e616d653d22642e676574456c656d656e7473427954 5188 61674e616d6528736e6963616c2220687265663d22687474703a2f2f7777772e 5189 432f2f4454442048544d4c20342e3031205472616e7369743c7374796c652074 5190 7970653d22746578742f637373223e0a0a3c7374796c6520747970653d227465 5191 78742f637373223e696f6e616c2e647464223e0a3c68746d6c20786d6c6e733d 5192 687474702d65717569763d22436f6e74656e742d5479706564696e673d223022 5193 2063656c6c73706163696e673d22302268746d6c3b20636861727365743d7574 5194 662d3822202f3e0a207374796c653d22646973706c61793a6e6f6e653b223e3c 5195 3c6c693e3c6120687265663d22687474703a2f2f7777772e20747970653d2774 5196 6578742f6a617661736372697074273ed0b4d0b5d18fd182d0b5d0bbd18cd0bd 5197 d0bed181d182d0b8d181d0bed0bed182d0b2d0b5d182d181d182d0b2d0b8d0b8 5198 d0bfd180d0bed0b8d0b7d0b2d0bed0b4d181d182d0b2d0b0d0b1d0b5d0b7d0be 5199 d0bfd0b0d181d0bdd0bed181d182d0b8e0a4aae0a581e0a4b8e0a58de0a4a4e0 5200 a4bfe0a495e0a4bee0a495e0a4bee0a482e0a497e0a58de0a4b0e0a587e0a4b8 5201 e0a489e0a4a8e0a58de0a4b9e0a58be0a482e0a4a8e0a587e0a4b5e0a4bfe0a4 5202 a7e0a4bee0a4a8e0a4b8e0a4ade0a4bee0a4abe0a4bfe0a495e0a58de0a4b8e0 5203 a4bfe0a482e0a497e0a4b8e0a581e0a4b0e0a495e0a58de0a4b7e0a4bfe0a4a4 5204 e0a495e0a589e0a4aae0a580e0a4b0e0a4bee0a487e0a49fe0a4b5e0a4bfe0a4 5205 9ce0a58de0a49ee0a4bee0a4aae0a4a8e0a495e0a4bee0a4b0e0a58de0a4b0e0 5206 a4b5e0a4bee0a488e0a4b8e0a495e0a58de0a4b0e0a4bfe0a4afe0a4a4e0a4be 5208 The number of words for each length is given by the following bit- 5209 depth array: 5211 NDBITS := 0, 0, 0, 0, 10, 10, 11, 11, 10, 10, 5212 10, 10, 10, 9, 9, 8, 7, 7, 8, 7, 5213 7, 6, 6, 5, 5, 5215 Appendix B. List of word transformations 5217 ID Prefix Transform Suffix 5218 -- ------ --------- ------ 5219 0 "" Identity "" 5220 1 "" Identity " " 5221 2 " " Identity " " 5222 3 "" OmitFirst1 "" 5223 4 "" UppercaseFirst " " 5224 5 "" Identity " the " 5225 6 " " Identity "" 5226 7 "s " Identity " " 5227 8 "" Identity " of " 5228 9 "" UppercaseFirst "" 5229 10 "" Identity " and " 5230 11 "" OmitFirst2 "" 5231 12 "" OmitLast1 "" 5232 13 ", " Identity " " 5233 14 "" Identity ", " 5234 15 " " UppercaseFirst " " 5235 16 "" Identity " in " 5236 17 "" Identity " to " 5237 18 "e " Identity " " 5238 19 "" Identity "\"" 5239 20 "" Identity "." 5240 21 "" Identity "\">" 5241 22 "" Identity "\n" 5242 23 "" OmitLast3 "" 5243 24 "" Identity "]" 5244 25 "" Identity " for " 5245 26 "" OmitFirst3 "" 5246 27 "" OmitLast2 "" 5247 28 "" Identity " a " 5248 29 "" Identity " that " 5249 30 " " UppercaseFirst "" 5250 31 "" Identity ". " 5251 32 "." Identity "" 5252 33 " " Identity ", " 5253 34 "" OmitFirst4 "" 5254 35 "" Identity " with " 5255 36 "" Identity "'" 5256 37 "" Identity " from " 5257 38 "" Identity " by " 5258 39 "" OmitFirst5 "" 5259 40 "" OmitFirst6 "" 5260 41 " the " Identity "" 5261 42 "" OmitLast4 "" 5262 43 "" Identity ". The " 5263 44 "" UppercaseAll "" 5264 45 "" Identity " on " 5265 46 "" Identity " as " 5266 47 "" Identity " is " 5267 48 "" OmitLast7 "" 5268 49 "" OmitLast1 "ing " 5269 50 "" Identity "\n\t" 5270 51 "" Identity ":" 5271 52 " " Identity ". " 5272 53 "" Identity "ed " 5273 54 "" OmitFirst9 "" 5274 55 "" OmitFirst7 "" 5275 56 "" OmitLast6 "" 5276 57 "" Identity "(" 5277 58 "" UppercaseFirst ", " 5278 59 "" OmitLast8 "" 5279 60 "" Identity " at " 5280 61 "" Identity "ly " 5281 62 " the " Identity " of " 5282 63 "" OmitLast5 "" 5283 64 "" OmitLast9 "" 5284 65 " " UppercaseFirst ", " 5285 66 "" UppercaseFirst "\"" 5286 67 "." Identity "(" 5287 68 "" UppercaseAll " " 5288 69 "" UppercaseFirst "\">" 5289 70 "" Identity "=\"" 5290 71 " " Identity "." 5291 72 ".com/" Identity "" 5292 73 " the " Identity " of the " 5293 74 "" UppercaseFirst "'" 5294 75 "" Identity ". This " 5295 76 "" Identity "," 5296 77 "." Identity " " 5297 78 "" UppercaseFirst "(" 5298 79 "" UppercaseFirst "." 5299 80 "" Identity " not " 5300 81 " " Identity "=\"" 5301 82 "" Identity "er " 5302 83 " " UppercaseAll " " 5303 84 "" Identity "al " 5304 85 " " UppercaseAll "" 5305 86 "" Identity "='" 5306 87 "" UppercaseAll "\"" 5307 88 "" UppercaseFirst ". " 5308 89 " " Identity "(" 5309 90 "" Identity "ful " 5310 91 " " UppercaseFirst ". " 5311 92 "" Identity "ive " 5312 93 "" Identity "less " 5313 94 "" UppercaseAll "'" 5314 95 "" Identity "est " 5315 96 " " UppercaseFirst "." 5316 97 "" UppercaseAll "\">" 5317 98 " " Identity "='" 5318 99 "" UppercaseFirst "," 5319 100 "" Identity "ize " 5320 101 "" UppercaseAll "." 5321 102 "\xc2\xa0" Identity "" 5322 103 " " Identity "," 5323 104 "" UppercaseFirst "=\"" 5324 105 "" UppercaseAll "=\"" 5325 106 "" Identity "ous " 5326 107 "" UppercaseAll ", " 5327 108 "" UppercaseFirst "='" 5328 109 " " UppercaseFirst "," 5329 110 " " UppercaseAll "=\"" 5330 111 " " UppercaseAll ", " 5331 112 "" UppercaseAll "," 5332 113 "" UppercaseAll "(" 5333 114 "" UppercaseAll ". " 5334 115 " " UppercaseAll "." 5335 116 "" UppercaseAll "='" 5336 117 " " UppercaseAll ". " 5337 118 " " UppercaseFirst "=\"" 5338 119 " " UppercaseAll "='" 5339 120 " " UppercaseFirst "='" 5341 Authors' Addresses 5343 Jyrki Alakuijala 5344 Google, Inc 5346 Email: jyrki@google.com 5348 Zoltan Szabadka 5349 Google, Inc 5351 Email: szabadka@google.com