| 1 | LZMA specification (DRAFT version)\r |
| 2 | ----------------------------------\r |
| 3 | \r |
| 4 | Author: Igor Pavlov\r |
| 5 | Date: 2015-06-14\r |
| 6 | \r |
| 7 | This specification defines the format of LZMA compressed data and lzma file format.\r |
| 8 | \r |
| 9 | Notation \r |
| 10 | --------\r |
| 11 | \r |
| 12 | We use the syntax of C++ programming language.\r |
| 13 | We use the following types in C++ code:\r |
| 14 | unsigned - unsigned integer, at least 16 bits in size\r |
| 15 | int - signed integer, at least 16 bits in size\r |
| 16 | UInt64 - 64-bit unsigned integer\r |
| 17 | UInt32 - 32-bit unsigned integer\r |
| 18 | UInt16 - 16-bit unsigned integer\r |
| 19 | Byte - 8-bit unsigned integer\r |
| 20 | bool - boolean type with two possible values: false, true\r |
| 21 | \r |
| 22 | \r |
| 23 | lzma file format\r |
| 24 | ================\r |
| 25 | \r |
| 26 | The lzma file contains the raw LZMA stream and the header with related properties.\r |
| 27 | \r |
| 28 | The files in that format use ".lzma" extension.\r |
| 29 | \r |
| 30 | The lzma file format layout:\r |
| 31 | \r |
| 32 | Offset Size Description\r |
| 33 | \r |
| 34 | 0 1 LZMA model properties (lc, lp, pb) in encoded form\r |
| 35 | 1 4 Dictionary size (32-bit unsigned integer, little-endian)\r |
| 36 | 5 8 Uncompressed size (64-bit unsigned integer, little-endian)\r |
| 37 | 13 Compressed data (LZMA stream)\r |
| 38 | \r |
| 39 | LZMA properties:\r |
| 40 | \r |
| 41 | name Range Description\r |
| 42 | \r |
| 43 | lc [0, 8] the number of "literal context" bits\r |
| 44 | lp [0, 4] the number of "literal pos" bits\r |
| 45 | pb [0, 4] the number of "pos" bits\r |
| 46 | dictSize [0, 2^32 - 1] the dictionary size \r |
| 47 | \r |
| 48 | The following code encodes LZMA properties:\r |
| 49 | \r |
| 50 | void EncodeProperties(Byte *properties)\r |
| 51 | {\r |
| 52 | properties[0] = (Byte)((pb * 5 + lp) * 9 + lc);\r |
| 53 | Set_UInt32_LittleEndian(properties + 1, dictSize);\r |
| 54 | }\r |
| 55 | \r |
| 56 | If the value of dictionary size in properties is smaller than (1 << 12),\r |
| 57 | the LZMA decoder must set the dictionary size variable to (1 << 12).\r |
| 58 | \r |
| 59 | #define LZMA_DIC_MIN (1 << 12)\r |
| 60 | \r |
| 61 | unsigned lc, pb, lp;\r |
| 62 | UInt32 dictSize;\r |
| 63 | UInt32 dictSizeInProperties;\r |
| 64 | \r |
| 65 | void DecodeProperties(const Byte *properties)\r |
| 66 | {\r |
| 67 | unsigned d = properties[0];\r |
| 68 | if (d >= (9 * 5 * 5))\r |
| 69 | throw "Incorrect LZMA properties";\r |
| 70 | lc = d % 9;\r |
| 71 | d /= 9;\r |
| 72 | pb = d / 5;\r |
| 73 | lp = d % 5;\r |
| 74 | dictSizeInProperties = 0;\r |
| 75 | for (int i = 0; i < 4; i++)\r |
| 76 | dictSizeInProperties |= (UInt32)properties[i + 1] << (8 * i);\r |
| 77 | dictSize = dictSizeInProperties;\r |
| 78 | if (dictSize < LZMA_DIC_MIN)\r |
| 79 | dictSize = LZMA_DIC_MIN;\r |
| 80 | }\r |
| 81 | \r |
| 82 | If "Uncompressed size" field contains ones in all 64 bits, it means that\r |
| 83 | uncompressed size is unknown and there is the "end marker" in stream,\r |
| 84 | that indicates the end of decoding point.\r |
| 85 | In opposite case, if the value from "Uncompressed size" field is not\r |
| 86 | equal to ((2^64) - 1), the LZMA stream decoding must be finished after\r |
| 87 | specified number of bytes (Uncompressed size) is decoded. And if there \r |
| 88 | is the "end marker", the LZMA decoder must read that marker also.\r |
| 89 | \r |
| 90 | \r |
| 91 | The new scheme to encode LZMA properties\r |
| 92 | ----------------------------------------\r |
| 93 | \r |
| 94 | If LZMA compression is used for some another format, it's recommended to\r |
| 95 | use a new improved scheme to encode LZMA properties. That new scheme was\r |
| 96 | used in xz format that uses the LZMA2 compression algorithm.\r |
| 97 | The LZMA2 is a new compression algorithm that is based on the LZMA algorithm.\r |
| 98 | \r |
| 99 | The dictionary size in LZMA2 is encoded with just one byte and LZMA2 supports\r |
| 100 | only reduced set of dictionary sizes:\r |
| 101 | (2 << 11), (3 << 11),\r |
| 102 | (2 << 12), (3 << 12),\r |
| 103 | ...\r |
| 104 | (2 << 30), (3 << 30),\r |
| 105 | (2 << 31) - 1\r |
| 106 | \r |
| 107 | The dictionary size can be extracted from encoded value with the following code:\r |
| 108 | \r |
| 109 | dictSize = (p == 40) ? 0xFFFFFFFF : (((UInt32)2 | ((p) & 1)) << ((p) / 2 + 11));\r |
| 110 | \r |
| 111 | Also there is additional limitation (lc + lp <= 4) in LZMA2 for values of \r |
| 112 | "lc" and "lp" properties:\r |
| 113 | \r |
| 114 | if (lc + lp > 4)\r |
| 115 | throw "Unsupported properties: (lc + lp) > 4";\r |
| 116 | \r |
| 117 | There are some advantages for LZMA decoder with such (lc + lp) value\r |
| 118 | limitation. It reduces the maximum size of tables allocated by decoder.\r |
| 119 | And it reduces the complexity of initialization procedure, that can be \r |
| 120 | important to keep high speed of decoding of big number of small LZMA streams.\r |
| 121 | \r |
| 122 | It's recommended to use that limitation (lc + lp <= 4) for any new format\r |
| 123 | that uses LZMA compression. Note that the combinations of "lc" and "lp" \r |
| 124 | parameters, where (lc + lp > 4), can provide significant improvement in \r |
| 125 | compression ratio only in some rare cases.\r |
| 126 | \r |
| 127 | The LZMA properties can be encoded into two bytes in new scheme:\r |
| 128 | \r |
| 129 | Offset Size Description\r |
| 130 | \r |
| 131 | 0 1 The dictionary size encoded with LZMA2 scheme\r |
| 132 | 1 1 LZMA model properties (lc, lp, pb) in encoded form\r |
| 133 | \r |
| 134 | \r |
| 135 | The RAM usage \r |
| 136 | =============\r |
| 137 | \r |
| 138 | The RAM usage for LZMA decoder is determined by the following parts:\r |
| 139 | \r |
| 140 | 1) The Sliding Window (from 4 KiB to 4 GiB).\r |
| 141 | 2) The probability model counter arrays (arrays of 16-bit variables).\r |
| 142 | 3) Some additional state variables (about 10 variables of 32-bit integers).\r |
| 143 | \r |
| 144 | \r |
| 145 | The RAM usage for Sliding Window\r |
| 146 | --------------------------------\r |
| 147 | \r |
| 148 | There are two main scenarios of decoding:\r |
| 149 | \r |
| 150 | 1) The decoding of full stream to one RAM buffer.\r |
| 151 | \r |
| 152 | If we decode full LZMA stream to one output buffer in RAM, the decoder \r |
| 153 | can use that output buffer as sliding window. So the decoder doesn't \r |
| 154 | need additional buffer allocated for sliding window.\r |
| 155 | \r |
| 156 | 2) The decoding to some external storage.\r |
| 157 | \r |
| 158 | If we decode LZMA stream to external storage, the decoder must allocate\r |
| 159 | the buffer for sliding window. The size of that buffer must be equal \r |
| 160 | or larger than the value of dictionary size from properties of LZMA stream.\r |
| 161 | \r |
| 162 | In this specification we describe the code for decoding to some external\r |
| 163 | storage. The optimized version of code for decoding of full stream to one\r |
| 164 | output RAM buffer can require some minor changes in code.\r |
| 165 | \r |
| 166 | \r |
| 167 | The RAM usage for the probability model counters\r |
| 168 | ------------------------------------------------\r |
| 169 | \r |
| 170 | The size of the probability model counter arrays is calculated with the \r |
| 171 | following formula:\r |
| 172 | \r |
| 173 | size_of_prob_arrays = 1846 + 768 * (1 << (lp + lc))\r |
| 174 | \r |
| 175 | Each probability model counter is 11-bit unsigned integer.\r |
| 176 | If we use 16-bit integer variables (2-byte integers) for these probability \r |
| 177 | model counters, the RAM usage required by probability model counter arrays \r |
| 178 | can be estimated with the following formula:\r |
| 179 | \r |
| 180 | RAM = 4 KiB + 1.5 KiB * (1 << (lp + lc))\r |
| 181 | \r |
| 182 | For example, for default LZMA parameters (lp = 0 and lc = 3), the RAM usage is\r |
| 183 | \r |
| 184 | RAM_lc3_lp0 = 4 KiB + 1.5 KiB * 8 = 16 KiB\r |
| 185 | \r |
| 186 | The maximum RAM state usage is required for decoding the stream with lp = 4 \r |
| 187 | and lc = 8:\r |
| 188 | \r |
| 189 | RAM_lc8_lp4 = 4 KiB + 1.5 KiB * 4096 = 6148 KiB\r |
| 190 | \r |
| 191 | If the decoder uses LZMA2's limited property condition \r |
| 192 | (lc + lp <= 4), the RAM usage will be not larger than\r |
| 193 | \r |
| 194 | RAM_lc_lp_4 = 4 KiB + 1.5 KiB * 16 = 28 KiB\r |
| 195 | \r |
| 196 | \r |
| 197 | The RAM usage for encoder\r |
| 198 | -------------------------\r |
| 199 | \r |
| 200 | There are many variants for LZMA encoding code.\r |
| 201 | These variants have different values for memory consumption.\r |
| 202 | Note that memory consumption for LZMA Encoder can not be \r |
| 203 | smaller than memory consumption of LZMA Decoder for same stream.\r |
| 204 | \r |
| 205 | The RAM usage required by modern effective implementation of \r |
| 206 | LZMA Encoder can be estimated with the following formula:\r |
| 207 | \r |
| 208 | Encoder_RAM_Usage = 4 MiB + 11 * dictionarySize.\r |
| 209 | \r |
| 210 | But there are some modes of the encoder that require less memory.\r |
| 211 | \r |
| 212 | \r |
| 213 | LZMA Decoding\r |
| 214 | =============\r |
| 215 | \r |
| 216 | The LZMA compression algorithm uses LZ-based compression with Sliding Window\r |
| 217 | and Range Encoding as entropy coding method.\r |
| 218 | \r |
| 219 | \r |
| 220 | Sliding Window\r |
| 221 | --------------\r |
| 222 | \r |
| 223 | LZMA uses Sliding Window compression similar to LZ77 algorithm.\r |
| 224 | \r |
| 225 | LZMA stream must be decoded to the sequence that consists\r |
| 226 | of MATCHES and LITERALS:\r |
| 227 | \r |
| 228 | - a LITERAL is a 8-bit character (one byte).\r |
| 229 | The decoder just puts that LITERAL to the uncompressed stream.\r |
| 230 | \r |
| 231 | - a MATCH is a pair of two numbers (DISTANCE-LENGTH pair).\r |
| 232 | The decoder takes one byte exactly "DISTANCE" characters behind\r |
| 233 | current position in the uncompressed stream and puts it to \r |
| 234 | uncompressed stream. The decoder must repeat it "LENGTH" times.\r |
| 235 | \r |
| 236 | The "DISTANCE" can not be larger than dictionary size.\r |
| 237 | And the "DISTANCE" can not be larger than the number of bytes in\r |
| 238 | the uncompressed stream that were decoded before that match.\r |
| 239 | \r |
| 240 | In this specification we use cyclic buffer to implement Sliding Window\r |
| 241 | for LZMA decoder:\r |
| 242 | \r |
| 243 | class COutWindow\r |
| 244 | {\r |
| 245 | Byte *Buf;\r |
| 246 | UInt32 Pos;\r |
| 247 | UInt32 Size;\r |
| 248 | bool IsFull;\r |
| 249 | \r |
| 250 | public:\r |
| 251 | unsigned TotalPos;\r |
| 252 | COutStream OutStream;\r |
| 253 | \r |
| 254 | COutWindow(): Buf(NULL) {}\r |
| 255 | ~COutWindow() { delete []Buf; }\r |
| 256 | \r |
| 257 | void Create(UInt32 dictSize)\r |
| 258 | {\r |
| 259 | Buf = new Byte[dictSize];\r |
| 260 | Pos = 0;\r |
| 261 | Size = dictSize;\r |
| 262 | IsFull = false;\r |
| 263 | TotalPos = 0;\r |
| 264 | }\r |
| 265 | \r |
| 266 | void PutByte(Byte b)\r |
| 267 | {\r |
| 268 | TotalPos++;\r |
| 269 | Buf[Pos++] = b;\r |
| 270 | if (Pos == Size)\r |
| 271 | {\r |
| 272 | Pos = 0;\r |
| 273 | IsFull = true;\r |
| 274 | }\r |
| 275 | OutStream.WriteByte(b);\r |
| 276 | }\r |
| 277 | \r |
| 278 | Byte GetByte(UInt32 dist) const\r |
| 279 | {\r |
| 280 | return Buf[dist <= Pos ? Pos - dist : Size - dist + Pos];\r |
| 281 | }\r |
| 282 | \r |
| 283 | void CopyMatch(UInt32 dist, unsigned len)\r |
| 284 | {\r |
| 285 | for (; len > 0; len--)\r |
| 286 | PutByte(GetByte(dist));\r |
| 287 | }\r |
| 288 | \r |
| 289 | bool CheckDistance(UInt32 dist) const\r |
| 290 | {\r |
| 291 | return dist <= Pos || IsFull;\r |
| 292 | }\r |
| 293 | \r |
| 294 | bool IsEmpty() const\r |
| 295 | {\r |
| 296 | return Pos == 0 && !IsFull;\r |
| 297 | }\r |
| 298 | };\r |
| 299 | \r |
| 300 | \r |
| 301 | In another implementation it's possible to use one buffer that contains \r |
| 302 | Sliding Window and the whole data stream after uncompressing.\r |
| 303 | \r |
| 304 | \r |
| 305 | Range Decoder\r |
| 306 | -------------\r |
| 307 | \r |
| 308 | LZMA algorithm uses Range Encoding (1) as entropy coding method.\r |
| 309 | \r |
| 310 | LZMA stream contains just one very big number in big-endian encoding.\r |
| 311 | LZMA decoder uses the Range Decoder to extract a sequence of binary\r |
| 312 | symbols from that big number.\r |
| 313 | \r |
| 314 | The state of the Range Decoder:\r |
| 315 | \r |
| 316 | struct CRangeDecoder\r |
| 317 | {\r |
| 318 | UInt32 Range; \r |
| 319 | UInt32 Code;\r |
| 320 | InputStream *InStream;\r |
| 321 | \r |
| 322 | bool Corrupted;\r |
| 323 | }\r |
| 324 | \r |
| 325 | The notes about UInt32 type for the "Range" and "Code" variables:\r |
| 326 | \r |
| 327 | It's possible to use 64-bit (unsigned or signed) integer type\r |
| 328 | for the "Range" and the "Code" variables instead of 32-bit unsigned,\r |
| 329 | but some additional code must be used to truncate the values to \r |
| 330 | low 32-bits after some operations.\r |
| 331 | \r |
| 332 | If the programming language does not support 32-bit unsigned integer type \r |
| 333 | (like in case of JAVA language), it's possible to use 32-bit signed integer, \r |
| 334 | but some code must be changed. For example, it's required to change the code\r |
| 335 | that uses comparison operations for UInt32 variables in this specification.\r |
| 336 | \r |
| 337 | The Range Decoder can be in some states that can be treated as \r |
| 338 | "Corruption" in LZMA stream. The Range Decoder uses the variable "Corrupted":\r |
| 339 | \r |
| 340 | (Corrupted == false), if the Range Decoder has not detected any corruption.\r |
| 341 | (Corrupted == true), if the Range Decoder has detected some corruption.\r |
| 342 | \r |
| 343 | The reference LZMA Decoder ignores the value of the "Corrupted" variable.\r |
| 344 | So it continues to decode the stream, even if the corruption can be detected\r |
| 345 | in the Range Decoder. To provide the full compatibility with output of the \r |
| 346 | reference LZMA Decoder, another LZMA Decoder implementations must also \r |
| 347 | ignore the value of the "Corrupted" variable.\r |
| 348 | \r |
| 349 | The LZMA Encoder is required to create only such LZMA streams, that will not \r |
| 350 | lead the Range Decoder to states, where the "Corrupted" variable is set to true.\r |
| 351 | \r |
| 352 | The Range Decoder reads first 5 bytes from input stream to initialize\r |
| 353 | the state:\r |
| 354 | \r |
| 355 | bool CRangeDecoder::Init()\r |
| 356 | {\r |
| 357 | Corrupted = false;\r |
| 358 | Range = 0xFFFFFFFF;\r |
| 359 | Code = 0;\r |
| 360 | \r |
| 361 | Byte b = InStream->ReadByte();\r |
| 362 | \r |
| 363 | for (int i = 0; i < 4; i++)\r |
| 364 | Code = (Code << 8) | InStream->ReadByte();\r |
| 365 | \r |
| 366 | if (b != 0 || Code == Range)\r |
| 367 | Corrupted = true;\r |
| 368 | return b == 0;\r |
| 369 | }\r |
| 370 | \r |
| 371 | The LZMA Encoder always writes ZERO in initial byte of compressed stream.\r |
| 372 | That scheme allows to simplify the code of the Range Encoder in the \r |
| 373 | LZMA Encoder. If initial byte is not equal to ZERO, the LZMA Decoder must\r |
| 374 | stop decoding and report error.\r |
| 375 | \r |
| 376 | After the last bit of data was decoded by Range Decoder, the value of the\r |
| 377 | "Code" variable must be equal to 0. The LZMA Decoder must check it by \r |
| 378 | calling the IsFinishedOK() function:\r |
| 379 | \r |
| 380 | bool IsFinishedOK() const { return Code == 0; }\r |
| 381 | \r |
| 382 | If there is corruption in data stream, there is big probability that\r |
| 383 | the "Code" value will be not equal to 0 in the Finish() function. So that\r |
| 384 | check in the IsFinishedOK() function provides very good feature for \r |
| 385 | corruption detection.\r |
| 386 | \r |
| 387 | The value of the "Range" variable before each bit decoding can not be smaller \r |
| 388 | than ((UInt32)1 << 24). The Normalize() function keeps the "Range" value in \r |
| 389 | described range.\r |
| 390 | \r |
| 391 | #define kTopValue ((UInt32)1 << 24)\r |
| 392 | \r |
| 393 | void CRangeDecoder::Normalize()\r |
| 394 | {\r |
| 395 | if (Range < kTopValue)\r |
| 396 | {\r |
| 397 | Range <<= 8;\r |
| 398 | Code = (Code << 8) | InStream->ReadByte();\r |
| 399 | }\r |
| 400 | }\r |
| 401 | \r |
| 402 | Notes: if the size of the "Code" variable is larger than 32 bits, it's\r |
| 403 | required to keep only low 32 bits of the "Code" variable after the change\r |
| 404 | in Normalize() function.\r |
| 405 | \r |
| 406 | If the LZMA Stream is not corrupted, the value of the "Code" variable is\r |
| 407 | always smaller than value of the "Range" variable.\r |
| 408 | But the Range Decoder ignores some types of corruptions, so the value of\r |
| 409 | the "Code" variable can be equal or larger than value of the "Range" variable\r |
| 410 | for some "Corrupted" archives.\r |
| 411 | \r |
| 412 | \r |
| 413 | LZMA uses Range Encoding only with binary symbols of two types:\r |
| 414 | 1) binary symbols with fixed and equal probabilities (direct bits)\r |
| 415 | 2) binary symbols with predicted probabilities\r |
| 416 | \r |
| 417 | The DecodeDirectBits() function decodes the sequence of direct bits:\r |
| 418 | \r |
| 419 | UInt32 CRangeDecoder::DecodeDirectBits(unsigned numBits)\r |
| 420 | {\r |
| 421 | UInt32 res = 0;\r |
| 422 | do\r |
| 423 | {\r |
| 424 | Range >>= 1;\r |
| 425 | Code -= Range;\r |
| 426 | UInt32 t = 0 - ((UInt32)Code >> 31);\r |
| 427 | Code += Range & t;\r |
| 428 | \r |
| 429 | if (Code == Range)\r |
| 430 | Corrupted = true;\r |
| 431 | \r |
| 432 | Normalize();\r |
| 433 | res <<= 1;\r |
| 434 | res += t + 1;\r |
| 435 | }\r |
| 436 | while (--numBits);\r |
| 437 | return res;\r |
| 438 | }\r |
| 439 | \r |
| 440 | \r |
| 441 | The Bit Decoding with Probability Model\r |
| 442 | ---------------------------------------\r |
| 443 | \r |
| 444 | The task of Bit Probability Model is to estimate probabilities of binary\r |
| 445 | symbols. And then it provides the Range Decoder with that information.\r |
| 446 | The better prediction provides better compression ratio.\r |
| 447 | The Bit Probability Model uses statistical data of previous decoded\r |
| 448 | symbols.\r |
| 449 | \r |
| 450 | That estimated probability is presented as 11-bit unsigned integer value\r |
| 451 | that represents the probability of symbol "0".\r |
| 452 | \r |
| 453 | #define kNumBitModelTotalBits 11\r |
| 454 | \r |
| 455 | Mathematical probabilities can be presented with the following formulas:\r |
| 456 | probability(symbol_0) = prob / 2048.\r |
| 457 | probability(symbol_1) = 1 - Probability(symbol_0) = \r |
| 458 | = 1 - prob / 2048 = \r |
| 459 | = (2048 - prob) / 2048\r |
| 460 | where the "prob" variable contains 11-bit integer probability counter.\r |
| 461 | \r |
| 462 | It's recommended to use 16-bit unsigned integer type, to store these 11-bit\r |
| 463 | probability values:\r |
| 464 | \r |
| 465 | typedef UInt16 CProb;\r |
| 466 | \r |
| 467 | Each probability value must be initialized with value ((1 << 11) / 2),\r |
| 468 | that represents the state, where probabilities of symbols 0 and 1 \r |
| 469 | are equal to 0.5:\r |
| 470 | \r |
| 471 | #define PROB_INIT_VAL ((1 << kNumBitModelTotalBits) / 2)\r |
| 472 | \r |
| 473 | The INIT_PROBS macro is used to initialize the array of CProb variables:\r |
| 474 | \r |
| 475 | #define INIT_PROBS(p) \\r |
| 476 | { for (unsigned i = 0; i < sizeof(p) / sizeof(p[0]); i++) p[i] = PROB_INIT_VAL; }\r |
| 477 | \r |
| 478 | \r |
| 479 | The DecodeBit() function decodes one bit.\r |
| 480 | The LZMA decoder provides the pointer to CProb variable that contains \r |
| 481 | information about estimated probability for symbol 0 and the Range Decoder \r |
| 482 | updates that CProb variable after decoding. The Range Decoder increases \r |
| 483 | estimated probability of the symbol that was decoded:\r |
| 484 | \r |
| 485 | #define kNumMoveBits 5\r |
| 486 | \r |
| 487 | unsigned CRangeDecoder::DecodeBit(CProb *prob)\r |
| 488 | {\r |
| 489 | unsigned v = *prob;\r |
| 490 | UInt32 bound = (Range >> kNumBitModelTotalBits) * v;\r |
| 491 | unsigned symbol;\r |
| 492 | if (Code < bound)\r |
| 493 | {\r |
| 494 | v += ((1 << kNumBitModelTotalBits) - v) >> kNumMoveBits;\r |
| 495 | Range = bound;\r |
| 496 | symbol = 0;\r |
| 497 | }\r |
| 498 | else\r |
| 499 | {\r |
| 500 | v -= v >> kNumMoveBits;\r |
| 501 | Code -= bound;\r |
| 502 | Range -= bound;\r |
| 503 | symbol = 1;\r |
| 504 | }\r |
| 505 | *prob = (CProb)v;\r |
| 506 | Normalize();\r |
| 507 | return symbol;\r |
| 508 | }\r |
| 509 | \r |
| 510 | \r |
| 511 | The Binary Tree of bit model counters\r |
| 512 | -------------------------------------\r |
| 513 | \r |
| 514 | LZMA uses a tree of Bit model variables to decode symbol that needs\r |
| 515 | several bits for storing. There are two versions of such trees in LZMA:\r |
| 516 | 1) the tree that decodes bits from high bit to low bit (the normal scheme).\r |
| 517 | 2) the tree that decodes bits from low bit to high bit (the reverse scheme).\r |
| 518 | \r |
| 519 | Each binary tree structure supports different size of decoded symbol\r |
| 520 | (the size of binary sequence that contains value of symbol).\r |
| 521 | If that size of decoded symbol is "NumBits" bits, the tree structure \r |
| 522 | uses the array of (2 << NumBits) counters of CProb type. \r |
| 523 | But only ((2 << NumBits) - 1) items are used by encoder and decoder.\r |
| 524 | The first item (the item with index equal to 0) in array is unused.\r |
| 525 | That scheme with unused array's item allows to simplify the code.\r |
| 526 | \r |
| 527 | unsigned BitTreeReverseDecode(CProb *probs, unsigned numBits, CRangeDecoder *rc)\r |
| 528 | {\r |
| 529 | unsigned m = 1;\r |
| 530 | unsigned symbol = 0;\r |
| 531 | for (unsigned i = 0; i < numBits; i++)\r |
| 532 | {\r |
| 533 | unsigned bit = rc->DecodeBit(&probs[m]);\r |
| 534 | m <<= 1;\r |
| 535 | m += bit;\r |
| 536 | symbol |= (bit << i);\r |
| 537 | }\r |
| 538 | return symbol;\r |
| 539 | }\r |
| 540 | \r |
| 541 | template <unsigned NumBits>\r |
| 542 | class CBitTreeDecoder\r |
| 543 | {\r |
| 544 | CProb Probs[(unsigned)1 << NumBits];\r |
| 545 | \r |
| 546 | public:\r |
| 547 | \r |
| 548 | void Init()\r |
| 549 | {\r |
| 550 | INIT_PROBS(Probs);\r |
| 551 | }\r |
| 552 | \r |
| 553 | unsigned Decode(CRangeDecoder *rc)\r |
| 554 | {\r |
| 555 | unsigned m = 1;\r |
| 556 | for (unsigned i = 0; i < NumBits; i++)\r |
| 557 | m = (m << 1) + rc->DecodeBit(&Probs[m]);\r |
| 558 | return m - ((unsigned)1 << NumBits);\r |
| 559 | }\r |
| 560 | \r |
| 561 | unsigned ReverseDecode(CRangeDecoder *rc)\r |
| 562 | {\r |
| 563 | return BitTreeReverseDecode(Probs, NumBits, rc);\r |
| 564 | }\r |
| 565 | };\r |
| 566 | \r |
| 567 | \r |
| 568 | LZ part of LZMA \r |
| 569 | ---------------\r |
| 570 | \r |
| 571 | LZ part of LZMA describes details about the decoding of MATCHES and LITERALS.\r |
| 572 | \r |
| 573 | \r |
| 574 | The Literal Decoding\r |
| 575 | --------------------\r |
| 576 | \r |
| 577 | The LZMA Decoder uses (1 << (lc + lp)) tables with CProb values, where \r |
| 578 | each table contains 0x300 CProb values:\r |
| 579 | \r |
| 580 | CProb *LitProbs;\r |
| 581 | \r |
| 582 | void CreateLiterals()\r |
| 583 | {\r |
| 584 | LitProbs = new CProb[(UInt32)0x300 << (lc + lp)];\r |
| 585 | }\r |
| 586 | \r |
| 587 | void InitLiterals()\r |
| 588 | {\r |
| 589 | UInt32 num = (UInt32)0x300 << (lc + lp);\r |
| 590 | for (UInt32 i = 0; i < num; i++)\r |
| 591 | LitProbs[i] = PROB_INIT_VAL;\r |
| 592 | }\r |
| 593 | \r |
| 594 | To select the table for decoding it uses the context that consists of\r |
| 595 | (lc) high bits from previous literal and (lp) low bits from value that\r |
| 596 | represents current position in outputStream.\r |
| 597 | \r |
| 598 | If (State > 7), the Literal Decoder also uses "matchByte" that represents \r |
| 599 | the byte in OutputStream at position the is the DISTANCE bytes before \r |
| 600 | current position, where the DISTANCE is the distance in DISTANCE-LENGTH pair\r |
| 601 | of latest decoded match.\r |
| 602 | \r |
| 603 | The following code decodes one literal and puts it to Sliding Window buffer:\r |
| 604 | \r |
| 605 | void DecodeLiteral(unsigned state, UInt32 rep0)\r |
| 606 | {\r |
| 607 | unsigned prevByte = 0;\r |
| 608 | if (!OutWindow.IsEmpty())\r |
| 609 | prevByte = OutWindow.GetByte(1);\r |
| 610 | \r |
| 611 | unsigned symbol = 1;\r |
| 612 | unsigned litState = ((OutWindow.TotalPos & ((1 << lp) - 1)) << lc) + (prevByte >> (8 - lc));\r |
| 613 | CProb *probs = &LitProbs[(UInt32)0x300 * litState];\r |
| 614 | \r |
| 615 | if (state >= 7)\r |
| 616 | {\r |
| 617 | unsigned matchByte = OutWindow.GetByte(rep0 + 1);\r |
| 618 | do\r |
| 619 | {\r |
| 620 | unsigned matchBit = (matchByte >> 7) & 1;\r |
| 621 | matchByte <<= 1;\r |
| 622 | unsigned bit = RangeDec.DecodeBit(&probs[((1 + matchBit) << 8) + symbol]);\r |
| 623 | symbol = (symbol << 1) | bit;\r |
| 624 | if (matchBit != bit)\r |
| 625 | break;\r |
| 626 | }\r |
| 627 | while (symbol < 0x100);\r |
| 628 | }\r |
| 629 | while (symbol < 0x100)\r |
| 630 | symbol = (symbol << 1) | RangeDec.DecodeBit(&probs[symbol]);\r |
| 631 | OutWindow.PutByte((Byte)(symbol - 0x100));\r |
| 632 | }\r |
| 633 | \r |
| 634 | \r |
| 635 | The match length decoding\r |
| 636 | -------------------------\r |
| 637 | \r |
| 638 | The match length decoder returns normalized (zero-based value) \r |
| 639 | length of match. That value can be converted to real length of the match \r |
| 640 | with the following code:\r |
| 641 | \r |
| 642 | #define kMatchMinLen 2\r |
| 643 | \r |
| 644 | matchLen = len + kMatchMinLen;\r |
| 645 | \r |
| 646 | The match length decoder can return the values from 0 to 271.\r |
| 647 | And the corresponded real match length values can be in the range \r |
| 648 | from 2 to 273.\r |
| 649 | \r |
| 650 | The following scheme is used for the match length encoding:\r |
| 651 | \r |
| 652 | Binary encoding Binary Tree structure Zero-based match length \r |
| 653 | sequence (binary + decimal):\r |
| 654 | \r |
| 655 | 0 xxx LowCoder[posState] xxx\r |
| 656 | 1 0 yyy MidCoder[posState] yyy + 8\r |
| 657 | 1 1 zzzzzzzz HighCoder zzzzzzzz + 16\r |
| 658 | \r |
| 659 | LZMA uses bit model variable "Choice" to decode the first selection bit.\r |
| 660 | \r |
| 661 | If the first selection bit is equal to 0, the decoder uses binary tree \r |
| 662 | LowCoder[posState] to decode 3-bit zero-based match length (xxx).\r |
| 663 | \r |
| 664 | If the first selection bit is equal to 1, the decoder uses bit model \r |
| 665 | variable "Choice2" to decode the second selection bit.\r |
| 666 | \r |
| 667 | If the second selection bit is equal to 0, the decoder uses binary tree \r |
| 668 | MidCoder[posState] to decode 3-bit "yyy" value, and zero-based match\r |
| 669 | length is equal to (yyy + 8).\r |
| 670 | \r |
| 671 | If the second selection bit is equal to 1, the decoder uses binary tree \r |
| 672 | HighCoder to decode 8-bit "zzzzzzzz" value, and zero-based \r |
| 673 | match length is equal to (zzzzzzzz + 16).\r |
| 674 | \r |
| 675 | LZMA uses "posState" value as context to select the binary tree \r |
| 676 | from LowCoder and MidCoder binary tree arrays:\r |
| 677 | \r |
| 678 | unsigned posState = OutWindow.TotalPos & ((1 << pb) - 1);\r |
| 679 | \r |
| 680 | The full code of the length decoder:\r |
| 681 | \r |
| 682 | class CLenDecoder\r |
| 683 | {\r |
| 684 | CProb Choice;\r |
| 685 | CProb Choice2;\r |
| 686 | CBitTreeDecoder<3> LowCoder[1 << kNumPosBitsMax];\r |
| 687 | CBitTreeDecoder<3> MidCoder[1 << kNumPosBitsMax];\r |
| 688 | CBitTreeDecoder<8> HighCoder;\r |
| 689 | \r |
| 690 | public:\r |
| 691 | \r |
| 692 | void Init()\r |
| 693 | {\r |
| 694 | Choice = PROB_INIT_VAL;\r |
| 695 | Choice2 = PROB_INIT_VAL;\r |
| 696 | HighCoder.Init();\r |
| 697 | for (unsigned i = 0; i < (1 << kNumPosBitsMax); i++)\r |
| 698 | {\r |
| 699 | LowCoder[i].Init();\r |
| 700 | MidCoder[i].Init();\r |
| 701 | }\r |
| 702 | }\r |
| 703 | \r |
| 704 | unsigned Decode(CRangeDecoder *rc, unsigned posState)\r |
| 705 | {\r |
| 706 | if (rc->DecodeBit(&Choice) == 0)\r |
| 707 | return LowCoder[posState].Decode(rc);\r |
| 708 | if (rc->DecodeBit(&Choice2) == 0)\r |
| 709 | return 8 + MidCoder[posState].Decode(rc);\r |
| 710 | return 16 + HighCoder.Decode(rc);\r |
| 711 | }\r |
| 712 | };\r |
| 713 | \r |
| 714 | The LZMA decoder uses two instances of CLenDecoder class.\r |
| 715 | The first instance is for the matches of "Simple Match" type,\r |
| 716 | and the second instance is for the matches of "Rep Match" type:\r |
| 717 | \r |
| 718 | CLenDecoder LenDecoder;\r |
| 719 | CLenDecoder RepLenDecoder;\r |
| 720 | \r |
| 721 | \r |
| 722 | The match distance decoding\r |
| 723 | ---------------------------\r |
| 724 | \r |
| 725 | LZMA supports dictionary sizes up to 4 GiB minus 1.\r |
| 726 | The value of match distance (decoded by distance decoder) can be \r |
| 727 | from 1 to 2^32. But the distance value that is equal to 2^32 is used to\r |
| 728 | indicate the "End of stream" marker. So real largest match distance \r |
| 729 | that is used for LZ-window match is (2^32 - 1).\r |
| 730 | \r |
| 731 | LZMA uses normalized match length (zero-based length) \r |
| 732 | to calculate the context state "lenState" do decode the distance value:\r |
| 733 | \r |
| 734 | #define kNumLenToPosStates 4\r |
| 735 | \r |
| 736 | unsigned lenState = len;\r |
| 737 | if (lenState > kNumLenToPosStates - 1)\r |
| 738 | lenState = kNumLenToPosStates - 1;\r |
| 739 | \r |
| 740 | The distance decoder returns the "dist" value that is zero-based value \r |
| 741 | of match distance. The real match distance can be calculated with the\r |
| 742 | following code:\r |
| 743 | \r |
| 744 | matchDistance = dist + 1; \r |
| 745 | \r |
| 746 | The state of the distance decoder and the initialization code: \r |
| 747 | \r |
| 748 | #define kEndPosModelIndex 14\r |
| 749 | #define kNumFullDistances (1 << (kEndPosModelIndex >> 1))\r |
| 750 | #define kNumAlignBits 4\r |
| 751 | \r |
| 752 | CBitTreeDecoder<6> PosSlotDecoder[kNumLenToPosStates];\r |
| 753 | CProb PosDecoders[1 + kNumFullDistances - kEndPosModelIndex];\r |
| 754 | CBitTreeDecoder<kNumAlignBits> AlignDecoder;\r |
| 755 | \r |
| 756 | void InitDist()\r |
| 757 | {\r |
| 758 | for (unsigned i = 0; i < kNumLenToPosStates; i++)\r |
| 759 | PosSlotDecoder[i].Init();\r |
| 760 | AlignDecoder.Init();\r |
| 761 | INIT_PROBS(PosDecoders);\r |
| 762 | }\r |
| 763 | \r |
| 764 | At first stage the distance decoder decodes 6-bit "posSlot" value with bit\r |
| 765 | tree decoder from PosSlotDecoder array. It's possible to get 2^6=64 different \r |
| 766 | "posSlot" values.\r |
| 767 | \r |
| 768 | unsigned posSlot = PosSlotDecoder[lenState].Decode(&RangeDec);\r |
| 769 | \r |
| 770 | The encoding scheme for distance value is shown in the following table:\r |
| 771 | \r |
| 772 | posSlot (decimal) /\r |
| 773 | zero-based distance (binary)\r |
| 774 | 0 0\r |
| 775 | 1 1\r |
| 776 | 2 10\r |
| 777 | 3 11\r |
| 778 | \r |
| 779 | 4 10 x\r |
| 780 | 5 11 x\r |
| 781 | 6 10 xx\r |
| 782 | 7 11 xx\r |
| 783 | 8 10 xxx\r |
| 784 | 9 11 xxx\r |
| 785 | 10 10 xxxx\r |
| 786 | 11 11 xxxx\r |
| 787 | 12 10 xxxxx\r |
| 788 | 13 11 xxxxx\r |
| 789 | \r |
| 790 | 14 10 yy zzzz\r |
| 791 | 15 11 yy zzzz\r |
| 792 | 16 10 yyy zzzz\r |
| 793 | 17 11 yyy zzzz\r |
| 794 | ...\r |
| 795 | 62 10 yyyyyyyyyyyyyyyyyyyyyyyyyy zzzz\r |
| 796 | 63 11 yyyyyyyyyyyyyyyyyyyyyyyyyy zzzz\r |
| 797 | \r |
| 798 | where \r |
| 799 | "x ... x" means the sequence of binary symbols encoded with binary tree and \r |
| 800 | "Reverse" scheme. It uses separated binary tree for each posSlot from 4 to 13.\r |
| 801 | "y" means direct bit encoded with range coder.\r |
| 802 | "zzzz" means the sequence of four binary symbols encoded with binary\r |
| 803 | tree with "Reverse" scheme, where one common binary tree "AlignDecoder"\r |
| 804 | is used for all posSlot values.\r |
| 805 | \r |
| 806 | If (posSlot < 4), the "dist" value is equal to posSlot value.\r |
| 807 | \r |
| 808 | If (posSlot >= 4), the decoder uses "posSlot" value to calculate the value of\r |
| 809 | the high bits of "dist" value and the number of the low bits.\r |
| 810 | \r |
| 811 | If (4 <= posSlot < kEndPosModelIndex), the decoder uses bit tree decoders.\r |
| 812 | (one separated bit tree decoder per one posSlot value) and "Reverse" scheme.\r |
| 813 | In this implementation we use one CProb array "PosDecoders" that contains \r |
| 814 | all CProb variables for all these bit decoders.\r |
| 815 | \r |
| 816 | if (posSlot >= kEndPosModelIndex), the middle bits are decoded as direct \r |
| 817 | bits from RangeDecoder and the low 4 bits are decoded with a bit tree \r |
| 818 | decoder "AlignDecoder" with "Reverse" scheme.\r |
| 819 | \r |
| 820 | The code to decode zero-based match distance:\r |
| 821 | \r |
| 822 | unsigned DecodeDistance(unsigned len)\r |
| 823 | {\r |
| 824 | unsigned lenState = len;\r |
| 825 | if (lenState > kNumLenToPosStates - 1)\r |
| 826 | lenState = kNumLenToPosStates - 1;\r |
| 827 | \r |
| 828 | unsigned posSlot = PosSlotDecoder[lenState].Decode(&RangeDec);\r |
| 829 | if (posSlot < 4)\r |
| 830 | return posSlot;\r |
| 831 | \r |
| 832 | unsigned numDirectBits = (unsigned)((posSlot >> 1) - 1);\r |
| 833 | UInt32 dist = ((2 | (posSlot & 1)) << numDirectBits);\r |
| 834 | if (posSlot < kEndPosModelIndex)\r |
| 835 | dist += BitTreeReverseDecode(PosDecoders + dist - posSlot, numDirectBits, &RangeDec);\r |
| 836 | else\r |
| 837 | {\r |
| 838 | dist += RangeDec.DecodeDirectBits(numDirectBits - kNumAlignBits) << kNumAlignBits;\r |
| 839 | dist += AlignDecoder.ReverseDecode(&RangeDec);\r |
| 840 | }\r |
| 841 | return dist;\r |
| 842 | }\r |
| 843 | \r |
| 844 | \r |
| 845 | \r |
| 846 | LZMA Decoding modes\r |
| 847 | -------------------\r |
| 848 | \r |
| 849 | There are 2 types of LZMA streams:\r |
| 850 | \r |
| 851 | 1) The stream with "End of stream" marker.\r |
| 852 | 2) The stream without "End of stream" marker.\r |
| 853 | \r |
| 854 | And the LZMA Decoder supports 3 modes of decoding:\r |
| 855 | \r |
| 856 | 1) The unpack size is undefined. The LZMA decoder stops decoding after \r |
| 857 | getting "End of stream" marker. \r |
| 858 | The input variables for that case:\r |
| 859 | \r |
| 860 | markerIsMandatory = true\r |
| 861 | unpackSizeDefined = false\r |
| 862 | unpackSize contains any value\r |
| 863 | \r |
| 864 | 2) The unpack size is defined and LZMA decoder supports both variants, \r |
| 865 | where the stream can contain "End of stream" marker or the stream is\r |
| 866 | finished without "End of stream" marker. The LZMA decoder must detect \r |
| 867 | any of these situations.\r |
| 868 | The input variables for that case:\r |
| 869 | \r |
| 870 | markerIsMandatory = false\r |
| 871 | unpackSizeDefined = true\r |
| 872 | unpackSize contains unpack size\r |
| 873 | \r |
| 874 | 3) The unpack size is defined and the LZMA stream must contain \r |
| 875 | "End of stream" marker\r |
| 876 | The input variables for that case:\r |
| 877 | \r |
| 878 | markerIsMandatory = true\r |
| 879 | unpackSizeDefined = true\r |
| 880 | unpackSize contains unpack size\r |
| 881 | \r |
| 882 | \r |
| 883 | The main loop of decoder\r |
| 884 | ------------------------\r |
| 885 | \r |
| 886 | The main loop of LZMA decoder:\r |
| 887 | \r |
| 888 | Initialize the LZMA state.\r |
| 889 | loop\r |
| 890 | {\r |
| 891 | // begin of loop\r |
| 892 | Check "end of stream" conditions.\r |
| 893 | Decode Type of MATCH / LITERAL. \r |
| 894 | If it's LITERAL, decode LITERAL value and put the LITERAL to Window.\r |
| 895 | If it's MATCH, decode the length of match and the match distance. \r |
| 896 | Check error conditions, check end of stream conditions and copy\r |
| 897 | the sequence of match bytes from sliding window to current position\r |
| 898 | in window.\r |
| 899 | Go to begin of loop\r |
| 900 | }\r |
| 901 | \r |
| 902 | The reference implementation of LZMA decoder uses "unpackSize" variable\r |
| 903 | to keep the number of remaining bytes in output stream. So it reduces \r |
| 904 | "unpackSize" value after each decoded LITERAL or MATCH.\r |
| 905 | \r |
| 906 | The following code contains the "end of stream" condition check at the start\r |
| 907 | of the loop:\r |
| 908 | \r |
| 909 | if (unpackSizeDefined && unpackSize == 0 && !markerIsMandatory)\r |
| 910 | if (RangeDec.IsFinishedOK())\r |
| 911 | return LZMA_RES_FINISHED_WITHOUT_MARKER;\r |
| 912 | \r |
| 913 | LZMA uses three types of matches:\r |
| 914 | \r |
| 915 | 1) "Simple Match" - the match with distance value encoded with bit models.\r |
| 916 | \r |
| 917 | 2) "Rep Match" - the match that uses the distance from distance\r |
| 918 | history table.\r |
| 919 | \r |
| 920 | 3) "Short Rep Match" - the match of single byte length, that uses the latest \r |
| 921 | distance from distance history table.\r |
| 922 | \r |
| 923 | The LZMA decoder keeps the history of latest 4 match distances that were used \r |
| 924 | by decoder. That set of 4 variables contains zero-based match distances and \r |
| 925 | these variables are initialized with zero values:\r |
| 926 | \r |
| 927 | UInt32 rep0 = 0, rep1 = 0, rep2 = 0, rep3 = 0;\r |
| 928 | \r |
| 929 | The LZMA decoder uses binary model variables to select type of MATCH or LITERAL:\r |
| 930 | \r |
| 931 | #define kNumStates 12\r |
| 932 | #define kNumPosBitsMax 4\r |
| 933 | \r |
| 934 | CProb IsMatch[kNumStates << kNumPosBitsMax];\r |
| 935 | CProb IsRep[kNumStates];\r |
| 936 | CProb IsRepG0[kNumStates];\r |
| 937 | CProb IsRepG1[kNumStates];\r |
| 938 | CProb IsRepG2[kNumStates];\r |
| 939 | CProb IsRep0Long[kNumStates << kNumPosBitsMax];\r |
| 940 | \r |
| 941 | The decoder uses "state" variable value to select exact variable \r |
| 942 | from "IsRep", "IsRepG0", "IsRepG1" and "IsRepG2" arrays.\r |
| 943 | The "state" variable can get the value from 0 to 11.\r |
| 944 | Initial value for "state" variable is zero:\r |
| 945 | \r |
| 946 | unsigned state = 0;\r |
| 947 | \r |
| 948 | The "state" variable is updated after each LITERAL or MATCH with one of the\r |
| 949 | following functions:\r |
| 950 | \r |
| 951 | unsigned UpdateState_Literal(unsigned state)\r |
| 952 | {\r |
| 953 | if (state < 4) return 0;\r |
| 954 | else if (state < 10) return state - 3;\r |
| 955 | else return state - 6;\r |
| 956 | }\r |
| 957 | unsigned UpdateState_Match (unsigned state) { return state < 7 ? 7 : 10; }\r |
| 958 | unsigned UpdateState_Rep (unsigned state) { return state < 7 ? 8 : 11; }\r |
| 959 | unsigned UpdateState_ShortRep(unsigned state) { return state < 7 ? 9 : 11; }\r |
| 960 | \r |
| 961 | The decoder calculates "state2" variable value to select exact variable from \r |
| 962 | "IsMatch" and "IsRep0Long" arrays:\r |
| 963 | \r |
| 964 | unsigned posState = OutWindow.TotalPos & ((1 << pb) - 1);\r |
| 965 | unsigned state2 = (state << kNumPosBitsMax) + posState;\r |
| 966 | \r |
| 967 | The decoder uses the following code flow scheme to select exact \r |
| 968 | type of LITERAL or MATCH:\r |
| 969 | \r |
| 970 | IsMatch[state2] decode\r |
| 971 | 0 - the Literal\r |
| 972 | 1 - the Match\r |
| 973 | IsRep[state] decode\r |
| 974 | 0 - Simple Match\r |
| 975 | 1 - Rep Match\r |
| 976 | IsRepG0[state] decode\r |
| 977 | 0 - the distance is rep0\r |
| 978 | IsRep0Long[state2] decode\r |
| 979 | 0 - Short Rep Match\r |
| 980 | 1 - Rep Match 0\r |
| 981 | 1 - \r |
| 982 | IsRepG1[state] decode\r |
| 983 | 0 - Rep Match 1\r |
| 984 | 1 - \r |
| 985 | IsRepG2[state] decode\r |
| 986 | 0 - Rep Match 2\r |
| 987 | 1 - Rep Match 3\r |
| 988 | \r |
| 989 | \r |
| 990 | LITERAL symbol\r |
| 991 | --------------\r |
| 992 | If the value "0" was decoded with IsMatch[state2] decoding, we have "LITERAL" type.\r |
| 993 | \r |
| 994 | At first the LZMA decoder must check that it doesn't exceed \r |
| 995 | specified uncompressed size:\r |
| 996 | \r |
| 997 | if (unpackSizeDefined && unpackSize == 0)\r |
| 998 | return LZMA_RES_ERROR;\r |
| 999 | \r |
| 1000 | Then it decodes literal value and puts it to sliding window:\r |
| 1001 | \r |
| 1002 | DecodeLiteral(state, rep0);\r |
| 1003 | \r |
| 1004 | Then the decoder must update the "state" value and "unpackSize" value;\r |
| 1005 | \r |
| 1006 | state = UpdateState_Literal(state);\r |
| 1007 | unpackSize--;\r |
| 1008 | \r |
| 1009 | Then the decoder must go to the begin of main loop to decode next Match or Literal.\r |
| 1010 | \r |
| 1011 | \r |
| 1012 | Simple Match\r |
| 1013 | ------------\r |
| 1014 | \r |
| 1015 | If the value "1" was decoded with IsMatch[state2] decoding,\r |
| 1016 | we have the "Simple Match" type.\r |
| 1017 | \r |
| 1018 | The distance history table is updated with the following scheme:\r |
| 1019 | \r |
| 1020 | rep3 = rep2;\r |
| 1021 | rep2 = rep1;\r |
| 1022 | rep1 = rep0;\r |
| 1023 | \r |
| 1024 | The zero-based length is decoded with "LenDecoder":\r |
| 1025 | \r |
| 1026 | len = LenDecoder.Decode(&RangeDec, posState);\r |
| 1027 | \r |
| 1028 | The state is update with UpdateState_Match function:\r |
| 1029 | \r |
| 1030 | state = UpdateState_Match(state);\r |
| 1031 | \r |
| 1032 | and the new "rep0" value is decoded with DecodeDistance:\r |
| 1033 | \r |
| 1034 | rep0 = DecodeDistance(len);\r |
| 1035 | \r |
| 1036 | That "rep0" will be used as zero-based distance for current match.\r |
| 1037 | \r |
| 1038 | If the value of "rep0" is equal to 0xFFFFFFFF, it means that we have \r |
| 1039 | "End of stream" marker, so we can stop decoding and check finishing \r |
| 1040 | condition in Range Decoder:\r |
| 1041 | \r |
| 1042 | if (rep0 == 0xFFFFFFFF)\r |
| 1043 | return RangeDec.IsFinishedOK() ?\r |
| 1044 | LZMA_RES_FINISHED_WITH_MARKER :\r |
| 1045 | LZMA_RES_ERROR;\r |
| 1046 | \r |
| 1047 | If uncompressed size is defined, LZMA decoder must check that it doesn't \r |
| 1048 | exceed that specified uncompressed size:\r |
| 1049 | \r |
| 1050 | if (unpackSizeDefined && unpackSize == 0)\r |
| 1051 | return LZMA_RES_ERROR;\r |
| 1052 | \r |
| 1053 | Also the decoder must check that "rep0" value is not larger than dictionary size\r |
| 1054 | and is not larger than the number of already decoded bytes:\r |
| 1055 | \r |
| 1056 | if (rep0 >= dictSize || !OutWindow.CheckDistance(rep0))\r |
| 1057 | return LZMA_RES_ERROR;\r |
| 1058 | \r |
| 1059 | Then the decoder must copy match bytes as described in \r |
| 1060 | "The match symbols copying" section.\r |
| 1061 | \r |
| 1062 | \r |
| 1063 | Rep Match\r |
| 1064 | ---------\r |
| 1065 | \r |
| 1066 | If the LZMA decoder has decoded the value "1" with IsRep[state] variable,\r |
| 1067 | we have "Rep Match" type.\r |
| 1068 | \r |
| 1069 | At first the LZMA decoder must check that it doesn't exceed \r |
| 1070 | specified uncompressed size:\r |
| 1071 | \r |
| 1072 | if (unpackSizeDefined && unpackSize == 0)\r |
| 1073 | return LZMA_RES_ERROR;\r |
| 1074 | \r |
| 1075 | Also the decoder must return error, if the LZ window is empty:\r |
| 1076 | \r |
| 1077 | if (OutWindow.IsEmpty())\r |
| 1078 | return LZMA_RES_ERROR;\r |
| 1079 | \r |
| 1080 | If the match type is "Rep Match", the decoder uses one of the 4 variables of\r |
| 1081 | distance history table to get the value of distance for current match.\r |
| 1082 | And there are 4 corresponding ways of decoding flow. \r |
| 1083 | \r |
| 1084 | The decoder updates the distance history with the following scheme \r |
| 1085 | depending from type of match:\r |
| 1086 | \r |
| 1087 | - "Rep Match 0" or "Short Rep Match":\r |
| 1088 | ; LZMA doesn't update the distance history \r |
| 1089 | \r |
| 1090 | - "Rep Match 1":\r |
| 1091 | UInt32 dist = rep1;\r |
| 1092 | rep1 = rep0;\r |
| 1093 | rep0 = dist;\r |
| 1094 | \r |
| 1095 | - "Rep Match 2":\r |
| 1096 | UInt32 dist = rep2;\r |
| 1097 | rep2 = rep1;\r |
| 1098 | rep1 = rep0;\r |
| 1099 | rep0 = dist;\r |
| 1100 | \r |
| 1101 | - "Rep Match 3":\r |
| 1102 | UInt32 dist = rep3;\r |
| 1103 | rep3 = rep2;\r |
| 1104 | rep2 = rep1;\r |
| 1105 | rep1 = rep0;\r |
| 1106 | rep0 = dist;\r |
| 1107 | \r |
| 1108 | Then the decoder decodes exact subtype of "Rep Match" using "IsRepG0", "IsRep0Long",\r |
| 1109 | "IsRepG1", "IsRepG2".\r |
| 1110 | \r |
| 1111 | If the subtype is "Short Rep Match", the decoder updates the state, puts \r |
| 1112 | the one byte from window to current position in window and goes to next \r |
| 1113 | MATCH/LITERAL symbol (the begin of main loop):\r |
| 1114 | \r |
| 1115 | state = UpdateState_ShortRep(state);\r |
| 1116 | OutWindow.PutByte(OutWindow.GetByte(rep0 + 1));\r |
| 1117 | unpackSize--;\r |
| 1118 | continue;\r |
| 1119 | \r |
| 1120 | In other cases (Rep Match 0/1/2/3), it decodes the zero-based \r |
| 1121 | length of match with "RepLenDecoder" decoder:\r |
| 1122 | \r |
| 1123 | len = RepLenDecoder.Decode(&RangeDec, posState);\r |
| 1124 | \r |
| 1125 | Then it updates the state:\r |
| 1126 | \r |
| 1127 | state = UpdateState_Rep(state);\r |
| 1128 | \r |
| 1129 | Then the decoder must copy match bytes as described in \r |
| 1130 | "The Match symbols copying" section.\r |
| 1131 | \r |
| 1132 | \r |
| 1133 | The match symbols copying\r |
| 1134 | -------------------------\r |
| 1135 | \r |
| 1136 | If we have the match (Simple Match or Rep Match 0/1/2/3), the decoder must\r |
| 1137 | copy the sequence of bytes with calculated match distance and match length.\r |
| 1138 | If uncompressed size is defined, LZMA decoder must check that it doesn't \r |
| 1139 | exceed that specified uncompressed size:\r |
| 1140 | \r |
| 1141 | len += kMatchMinLen;\r |
| 1142 | bool isError = false;\r |
| 1143 | if (unpackSizeDefined && unpackSize < len)\r |
| 1144 | {\r |
| 1145 | len = (unsigned)unpackSize;\r |
| 1146 | isError = true;\r |
| 1147 | }\r |
| 1148 | OutWindow.CopyMatch(rep0 + 1, len);\r |
| 1149 | unpackSize -= len;\r |
| 1150 | if (isError)\r |
| 1151 | return LZMA_RES_ERROR;\r |
| 1152 | \r |
| 1153 | Then the decoder must go to the begin of main loop to decode next MATCH or LITERAL.\r |
| 1154 | \r |
| 1155 | \r |
| 1156 | \r |
| 1157 | NOTES\r |
| 1158 | -----\r |
| 1159 | \r |
| 1160 | This specification doesn't describe the variant of decoder implementation \r |
| 1161 | that supports partial decoding. Such partial decoding case can require some \r |
| 1162 | changes in "end of stream" condition checks code. Also such code \r |
| 1163 | can use additional status codes, returned by decoder.\r |
| 1164 | \r |
| 1165 | This specification uses C++ code with templates to simplify describing.\r |
| 1166 | The optimized version of LZMA decoder doesn't need templates.\r |
| 1167 | Such optimized version can use just two arrays of CProb variables:\r |
| 1168 | 1) The dynamic array of CProb variables allocated for the Literal Decoder.\r |
| 1169 | 2) The one common array that contains all other CProb variables.\r |
| 1170 | \r |
| 1171 | \r |
| 1172 | References: \r |
| 1173 | \r |
| 1174 | 1. G. N. N. Martin, Range encoding: an algorithm for removing redundancy \r |
| 1175 | from a digitized message, Video & Data Recording Conference, \r |
| 1176 | Southampton, UK, July 24-27, 1979.\r |