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1176 lines
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1176 lines
36 KiB
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4 years ago
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LZMA specification (DRAFT version)
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----------------------------------
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Author: Igor Pavlov
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Date: 2013-07-28
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This specification defines the format of LZMA compressed data and lzma file format.
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Notation
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--------
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We use the syntax of C++ programming language.
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We use the following types in C++ code:
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unsigned - unsigned integer, at least 16 bits in size
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int - signed integer, at least 16 bits in size
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UInt64 - 64-bit unsigned integer
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UInt32 - 32-bit unsigned integer
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UInt16 - 16-bit unsigned integer
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Byte - 8-bit unsigned integer
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bool - boolean type with two possible values: false, true
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lzma file format
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================
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The lzma file contains the raw LZMA stream and the header with related properties.
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The files in that format use ".lzma" extension.
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The lzma file format layout:
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Offset Size Description
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0 1 LZMA model properties (lc, lp, pb) in encoded form
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1 4 Dictionary size (32-bit unsigned integer, little-endian)
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5 8 Uncompressed size (64-bit unsigned integer, little-endian)
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13 Compressed data (LZMA stream)
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LZMA properties:
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name Range Description
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lc [0, 8] the number of "literal context" bits
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lp [0, 4] the number of "literal pos" bits
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pb [0, 4] the number of "pos" bits
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dictSize [0, 2^32 - 1] the dictionary size
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The following code encodes LZMA properties:
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void EncodeProperties(Byte *properties)
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{
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properties[0] = (Byte)((pb * 5 + lp) * 9 + lc);
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Set_UInt32_LittleEndian(properties + 1, dictSize);
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}
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If the value of dictionary size in properties is smaller than (1 << 12),
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the LZMA decoder must set the dictionary size variable to (1 << 12).
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#define LZMA_DIC_MIN (1 << 12)
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unsigned lc, pb, lp;
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UInt32 dictSize;
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UInt32 dictSizeInProperties;
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void DecodeProperties(const Byte *properties)
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{
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unsigned d = properties[0];
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if (d >= (9 * 5 * 5))
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throw "Incorrect LZMA properties";
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lc = d % 9;
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d /= 9;
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pb = d / 5;
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lp = d % 5;
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dictSizeInProperties = 0;
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for (int i = 0; i < 4; i++)
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dictSizeInProperties |= (UInt32)properties[i + 1] << (8 * i);
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dictSize = dictSizeInProperties;
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if (dictSize < LZMA_DIC_MIN)
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dictSize = LZMA_DIC_MIN;
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}
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If "Uncompressed size" field contains ones in all 64 bits, it means that
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uncompressed size is unknown and there is the "end marker" in stream,
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that indicates the end of decoding point.
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In opposite case, if the value from "Uncompressed size" field is not
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equal to ((2^64) - 1), the LZMA stream decoding must be finished after
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specified number of bytes (Uncompressed size) is decoded. And if there
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is the "end marker", the LZMA decoder must read that marker also.
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The new scheme to encode LZMA properties
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----------------------------------------
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If LZMA compression is used for some another format, it's recommended to
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use a new improved scheme to encode LZMA properties. That new scheme was
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used in xz format that uses the LZMA2 compression algorithm.
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The LZMA2 is a new compression algorithm that is based on the LZMA algorithm.
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The dictionary size in LZMA2 is encoded with just one byte and LZMA2 supports
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only reduced set of dictionary sizes:
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(2 << 11), (3 << 11),
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(2 << 12), (3 << 12),
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...
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(2 << 30), (3 << 30),
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(2 << 31) - 1
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The dictionary size can be extracted from encoded value with the following code:
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dictSize = (p == 40) ? 0xFFFFFFFF : (((UInt32)2 | ((p) & 1)) << ((p) / 2 + 11));
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Also there is additional limitation (lc + lp <= 4) in LZMA2 for values of
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"lc" and "lp" properties:
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if (lc + lp > 4)
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throw "Unsupported properties: (lc + lp) > 4";
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There are some advantages for LZMA decoder with such (lc + lp) value
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limitation. It reduces the maximum size of tables allocated by decoder.
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And it reduces the complexity of initialization procedure, that can be
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important to keep high speed of decoding of big number of small LZMA streams.
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It's recommended to use that limitation (lc + lp <= 4) for any new format
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that uses LZMA compression. Note that the combinations of "lc" and "lp"
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parameters, where (lc + lp > 4), can provide significant improvement in
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compression ratio only in some rare cases.
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The LZMA properties can be encoded into two bytes in new scheme:
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Offset Size Description
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0 1 The dictionary size encoded with LZMA2 scheme
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1 1 LZMA model properties (lc, lp, pb) in encoded form
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The RAM usage
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=============
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The RAM usage for LZMA decoder is determined by the following parts:
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1) The Sliding Window (from 4 KiB to 4 GiB).
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2) The probability model counter arrays (arrays of 16-bit variables).
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3) Some additional state variables (about 10 variables of 32-bit integers).
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The RAM usage for Sliding Window
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--------------------------------
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There are two main scenarios of decoding:
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1) The decoding of full stream to one RAM buffer.
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If we decode full LZMA stream to one output buffer in RAM, the decoder
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can use that output buffer as sliding window. So the decoder doesn't
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need additional buffer allocated for sliding window.
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2) The decoding to some external storage.
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If we decode LZMA stream to external storage, the decoder must allocate
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the buffer for sliding window. The size of that buffer must be equal
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or larger than the value of dictionary size from properties of LZMA stream.
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In this specification we describe the code for decoding to some external
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storage. The optimized version of code for decoding of full stream to one
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output RAM buffer can require some minor changes in code.
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The RAM usage for the probability model counters
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------------------------------------------------
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The size of the probability model counter arrays is calculated with the
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following formula:
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size_of_prob_arrays = 1846 + 768 * (1 << (lp + lc))
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Each probability model counter is 11-bit unsigned integer.
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If we use 16-bit integer variables (2-byte integers) for these probability
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model counters, the RAM usage required by probability model counter arrays
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can be estimated with the following formula:
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RAM = 4 KiB + 1.5 KiB * (1 << (lp + lc))
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For example, for default LZMA parameters (lp = 0 and lc = 3), the RAM usage is
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RAM_lc3_lp0 = 4 KiB + 1.5 KiB * 8 = 16 KiB
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The maximum RAM state usage is required for decoding the stream with lp = 4
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and lc = 8:
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RAM_lc8_lp4 = 4 KiB + 1.5 KiB * 4096 = 6148 KiB
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If the decoder uses LZMA2's limited property condition
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(lc + lp <= 4), the RAM usage will be not larger than
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RAM_lc_lp_4 = 4 KiB + 1.5 KiB * 16 = 28 KiB
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The RAM usage for encoder
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-------------------------
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There are many variants for LZMA encoding code.
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These variants have different values for memory consumption.
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Note that memory consumption for LZMA Encoder can not be
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smaller than memory consumption of LZMA Decoder for same stream.
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The RAM usage required by modern effective implementation of
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LZMA Encoder can be estimated with the following formula:
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Encoder_RAM_Usage = 4 MiB + 11 * dictionarySize.
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But there are some modes of the encoder that require less memory.
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LZMA Decoding
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=============
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The LZMA compression algorithm uses LZ-based compression with Sliding Window
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and Range Encoding as entropy coding method.
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Sliding Window
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--------------
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LZMA uses Sliding Window compression similar to LZ77 algorithm.
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LZMA stream must be decoded to the sequence that consists
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of MATCHES and LITERALS:
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- a LITERAL is a 8-bit character (one byte).
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The decoder just puts that LITERAL to the uncompressed stream.
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- a MATCH is a pair of two numbers (DISTANCE-LENGTH pair).
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The decoder takes one byte exactly "DISTANCE" characters behind
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current position in the uncompressed stream and puts it to
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uncompressed stream. The decoder must repeat it "LENGTH" times.
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The "DISTANCE" can not be larger than dictionary size.
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And the "DISTANCE" can not be larger than the number of bytes in
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the uncompressed stream that were decoded before that match.
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In this specification we use cyclic buffer to implement Sliding Window
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for LZMA decoder:
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class COutWindow
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{
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Byte *Buf;
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UInt32 Pos;
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UInt32 Size;
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bool IsFull;
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public:
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unsigned TotalPos;
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COutStream OutStream;
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COutWindow(): Buf(NULL) {}
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~COutWindow() { delete []Buf; }
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void Create(UInt32 dictSize)
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{
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Buf = new Byte[dictSize];
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Pos = 0;
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Size = dictSize;
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IsFull = false;
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TotalPos = 0;
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}
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void PutByte(Byte b)
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{
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TotalPos++;
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Buf[Pos++] = b;
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if (Pos == Size)
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{
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Pos = 0;
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IsFull = true;
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}
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OutStream.WriteByte(b);
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}
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Byte GetByte(UInt32 dist) const
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{
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return Buf[dist <= Pos ? Pos - dist : Size - dist + Pos];
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}
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void CopyMatch(UInt32 dist, unsigned len)
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{
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for (; len > 0; len--)
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PutByte(GetByte(dist));
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}
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bool CheckDistance(UInt32 dist) const
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{
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return dist <= Pos || IsFull;
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}
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bool IsEmpty() const
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{
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return Pos == 0 && !IsFull;
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}
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};
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In another implementation it's possible to use one buffer that contains
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Sliding Window and the whole data stream after uncompressing.
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Range Decoder
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-------------
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LZMA algorithm uses Range Encoding (1) as entropy coding method.
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LZMA stream contains just one very big number in big-endian encoding.
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LZMA decoder uses the Range Decoder to extract a sequence of binary
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symbols from that big number.
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The state of the Range Decoder:
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struct CRangeDecoder
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{
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UInt32 Range;
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UInt32 Code;
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InputStream *InStream;
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bool Corrupted;
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}
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The notes about UInt32 type for the "Range" and "Code" variables:
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It's possible to use 64-bit (unsigned or signed) integer type
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for the "Range" and the "Code" variables instead of 32-bit unsigned,
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but some additional code must be used to truncate the values to
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low 32-bits after some operations.
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If the programming language does not support 32-bit unsigned integer type
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(like in case of JAVA language), it's possible to use 32-bit signed integer,
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but some code must be changed. For example, it's required to change the code
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that uses comparison operations for UInt32 variables in this specification.
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The Range Decoder can be in some states that can be treated as
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"Corruption" in LZMA stream. The Range Decoder uses the variable "Corrupted":
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(Corrupted == false), if the Range Decoder has not detected any corruption.
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(Corrupted == true), if the Range Decoder has detected some corruption.
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The reference LZMA Decoder ignores the value of the "Corrupted" variable.
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So it continues to decode the stream, even if the corruption can be detected
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in the Range Decoder. To provide the full compatibility with output of the
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reference LZMA Decoder, another LZMA Decoder implementations must also
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ignore the value of the "Corrupted" variable.
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The LZMA Encoder is required to create only such LZMA streams, that will not
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lead the Range Decoder to states, where the "Corrupted" variable is set to true.
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The Range Decoder reads first 5 bytes from input stream to initialize
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the state:
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void CRangeDecoder::Init()
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{
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Corrupted = false;
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if (InStream->ReadByte() != 0)
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Corrupted = true;
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Range = 0xFFFFFFFF;
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Code = 0;
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for (int i = 0; i < 4; i++)
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Code = (Code << 8) | InStream->ReadByte();
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if (Code == Range)
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Corrupted = true;
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}
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The LZMA Encoder always writes ZERO in initial byte of compressed stream.
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That scheme allows to simplify the code of the Range Encoder in the
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LZMA Encoder.
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After the last bit of data was decoded by Range Decoder, the value of the
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"Code" variable must be equal to 0. The LZMA Decoder must check it by
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calling the IsFinishedOK() function:
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bool IsFinishedOK() const { return Code == 0; }
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If there is corruption in data stream, there is big probability that
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the "Code" value will be not equal to 0 in the Finish() function. So that
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check in the IsFinishedOK() function provides very good feature for
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corruption detection.
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The value of the "Range" variable before each bit decoding can not be smaller
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than ((UInt32)1 << 24). The Normalize() function keeps the "Range" value in
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described range.
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#define kTopValue ((UInt32)1 << 24)
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void CRangeDecoder::Normalize()
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{
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if (Range < kTopValue)
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{
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Range <<= 8;
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Code = (Code << 8) | InStream->ReadByte();
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}
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}
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Notes: if the size of the "Code" variable is larger than 32 bits, it's
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required to keep only low 32 bits of the "Code" variable after the change
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in Normalize() function.
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If the LZMA Stream is not corrupted, the value of the "Code" variable is
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always smaller than value of the "Range" variable.
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But the Range Decoder ignores some types of corruptions, so the value of
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the "Code" variable can be equal or larger than value of the "Range" variable
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for some "Corrupted" archives.
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LZMA uses Range Encoding only with binary symbols of two types:
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1) binary symbols with fixed and equal probabilities (direct bits)
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2) binary symbols with predicted probabilities
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The DecodeDirectBits() function decodes the sequence of direct bits:
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UInt32 CRangeDecoder::DecodeDirectBits(unsigned numBits)
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{
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UInt32 res = 0;
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do
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{
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Range >>= 1;
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Code -= Range;
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UInt32 t = 0 - ((UInt32)Code >> 31);
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Code += Range & t;
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if (Code == Range)
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Corrupted = true;
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Normalize();
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res <<= 1;
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res += t + 1;
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}
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while (--numBits);
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return res;
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}
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The Bit Decoding with Probability Model
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---------------------------------------
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The task of Bit Probability Model is to estimate probabilities of binary
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symbols. And then it provides the Range Decoder with that information.
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The better prediction provides better compression ratio.
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The Bit Probability Model uses statistical data of previous decoded
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symbols.
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That estimated probability is presented as 11-bit unsigned integer value
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that represents the probability of symbol "0".
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#define kNumBitModelTotalBits 11
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Mathematical probabilities can be presented with the following formulas:
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probability(symbol_0) = prob / 2048.
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|
probability(symbol_1) = 1 - Probability(symbol_0) =
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= 1 - prob / 2048 =
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= (2048 - prob) / 2048
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where the "prob" variable contains 11-bit integer probability counter.
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||
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||
|
It's recommended to use 16-bit unsigned integer type, to store these 11-bit
|
||
|
probability values:
|
||
|
|
||
|
typedef UInt16 CProb;
|
||
|
|
||
|
Each probability value must be initialized with value ((1 << 11) / 2),
|
||
|
that represents the state, where probabilities of symbols 0 and 1
|
||
|
are equal to 0.5:
|
||
|
|
||
|
#define PROB_INIT_VAL ((1 << kNumBitModelTotalBits) / 2)
|
||
|
|
||
|
The INIT_PROBS macro is used to initialize the array of CProb variables:
|
||
|
|
||
|
#define INIT_PROBS(p) \
|
||
|
{ for (unsigned i = 0; i < sizeof(p) / sizeof(p[0]); i++) p[i] = PROB_INIT_VAL; }
|
||
|
|
||
|
|
||
|
The DecodeBit() function decodes one bit.
|
||
|
The LZMA decoder provides the pointer to CProb variable that contains
|
||
|
information about estimated probability for symbol 0 and the Range Decoder
|
||
|
updates that CProb variable after decoding. The Range Decoder increases
|
||
|
estimated probability of the symbol that was decoded:
|
||
|
|
||
|
#define kNumMoveBits 5
|
||
|
|
||
|
unsigned CRangeDecoder::DecodeBit(CProb *prob)
|
||
|
{
|
||
|
unsigned v = *prob;
|
||
|
UInt32 bound = (Range >> kNumBitModelTotalBits) * v;
|
||
|
unsigned symbol;
|
||
|
if (Code < bound)
|
||
|
{
|
||
|
v += ((1 << kNumBitModelTotalBits) - v) >> kNumMoveBits;
|
||
|
Range = bound;
|
||
|
symbol = 0;
|
||
|
}
|
||
|
else
|
||
|
{
|
||
|
v -= v >> kNumMoveBits;
|
||
|
Code -= bound;
|
||
|
Range -= bound;
|
||
|
symbol = 1;
|
||
|
}
|
||
|
*prob = (CProb)v;
|
||
|
Normalize();
|
||
|
return symbol;
|
||
|
}
|
||
|
|
||
|
|
||
|
The Binary Tree of bit model counters
|
||
|
-------------------------------------
|
||
|
|
||
|
LZMA uses a tree of Bit model variables to decode symbol that needs
|
||
|
several bits for storing. There are two versions of such trees in LZMA:
|
||
|
1) the tree that decodes bits from high bit to low bit (the normal scheme).
|
||
|
2) the tree that decodes bits from low bit to high bit (the reverse scheme).
|
||
|
|
||
|
Each binary tree structure supports different size of decoded symbol
|
||
|
(the size of binary sequence that contains value of symbol).
|
||
|
If that size of decoded symbol is "NumBits" bits, the tree structure
|
||
|
uses the array of (2 << NumBits) counters of CProb type.
|
||
|
But only ((2 << NumBits) - 1) items are used by encoder and decoder.
|
||
|
The first item (the item with index equal to 0) in array is unused.
|
||
|
That scheme with unused array's item allows to simplify the code.
|
||
|
|
||
|
unsigned BitTreeReverseDecode(CProb *probs, unsigned numBits, CRangeDecoder *rc)
|
||
|
{
|
||
|
unsigned m = 1;
|
||
|
unsigned symbol = 0;
|
||
|
for (unsigned i = 0; i < numBits; i++)
|
||
|
{
|
||
|
unsigned bit = rc->DecodeBit(&probs[m]);
|
||
|
m <<= 1;
|
||
|
m += bit;
|
||
|
symbol |= (bit << i);
|
||
|
}
|
||
|
return symbol;
|
||
|
}
|
||
|
|
||
|
template <unsigned NumBits>
|
||
|
class CBitTreeDecoder
|
||
|
{
|
||
|
CProb Probs[(unsigned)1 << NumBits];
|
||
|
|
||
|
public:
|
||
|
|
||
|
void Init()
|
||
|
{
|
||
|
INIT_PROBS(Probs);
|
||
|
}
|
||
|
|
||
|
unsigned Decode(CRangeDecoder *rc)
|
||
|
{
|
||
|
unsigned m = 1;
|
||
|
for (unsigned i = 0; i < NumBits; i++)
|
||
|
m = (m << 1) + rc->DecodeBit(&Probs[m]);
|
||
|
return m - ((unsigned)1 << NumBits);
|
||
|
}
|
||
|
|
||
|
unsigned ReverseDecode(CRangeDecoder *rc)
|
||
|
{
|
||
|
return BitTreeReverseDecode(Probs, NumBits, rc);
|
||
|
}
|
||
|
};
|
||
|
|
||
|
|
||
|
LZ part of LZMA
|
||
|
---------------
|
||
|
|
||
|
LZ part of LZMA describes details about the decoding of MATCHES and LITERALS.
|
||
|
|
||
|
|
||
|
The Literal Decoding
|
||
|
--------------------
|
||
|
|
||
|
The LZMA Decoder uses (1 << (lc + lp)) tables with CProb values, where
|
||
|
each table contains 0x300 CProb values:
|
||
|
|
||
|
CProb *LitProbs;
|
||
|
|
||
|
void CreateLiterals()
|
||
|
{
|
||
|
LitProbs = new CProb[(UInt32)0x300 << (lc + lp)];
|
||
|
}
|
||
|
|
||
|
void InitLiterals()
|
||
|
{
|
||
|
UInt32 num = (UInt32)0x300 << (lc + lp);
|
||
|
for (UInt32 i = 0; i < num; i++)
|
||
|
LitProbs[i] = PROB_INIT_VAL;
|
||
|
}
|
||
|
|
||
|
To select the table for decoding it uses the context that consists of
|
||
|
(lc) high bits from previous literal and (lp) low bits from value that
|
||
|
represents current position in outputStream.
|
||
|
|
||
|
If (State > 7), the Literal Decoder also uses "matchByte" that represents
|
||
|
the byte in OutputStream at position the is the DISTANCE bytes before
|
||
|
current position, where the DISTANCE is the distance in DISTANCE-LENGTH pair
|
||
|
of latest decoded match.
|
||
|
|
||
|
The following code decodes one literal and puts it to Sliding Window buffer:
|
||
|
|
||
|
void DecodeLiteral(unsigned state, UInt32 rep0)
|
||
|
{
|
||
|
unsigned prevByte = 0;
|
||
|
if (!OutWindow.IsEmpty())
|
||
|
prevByte = OutWindow.GetByte(1);
|
||
|
|
||
|
unsigned symbol = 1;
|
||
|
unsigned litState = ((OutWindow.TotalPos & ((1 << lp) - 1)) << lc) + (prevByte >> (8 - lc));
|
||
|
CProb *probs = &LitProbs[(UInt32)0x300 * litState];
|
||
|
|
||
|
if (state >= 7)
|
||
|
{
|
||
|
unsigned matchByte = OutWindow.GetByte(rep0 + 1);
|
||
|
do
|
||
|
{
|
||
|
unsigned matchBit = (matchByte >> 7) & 1;
|
||
|
matchByte <<= 1;
|
||
|
unsigned bit = RangeDec.DecodeBit(&probs[((1 + matchBit) << 8) + symbol]);
|
||
|
symbol = (symbol << 1) | bit;
|
||
|
if (matchBit != bit)
|
||
|
break;
|
||
|
}
|
||
|
while (symbol < 0x100);
|
||
|
}
|
||
|
while (symbol < 0x100)
|
||
|
symbol = (symbol << 1) | RangeDec.DecodeBit(&probs[symbol]);
|
||
|
OutWindow.PutByte((Byte)(symbol - 0x100));
|
||
|
}
|
||
|
|
||
|
|
||
|
The match length decoding
|
||
|
-------------------------
|
||
|
|
||
|
The match length decoder returns normalized (zero-based value)
|
||
|
length of match. That value can be converted to real length of the match
|
||
|
with the following code:
|
||
|
|
||
|
#define kMatchMinLen 2
|
||
|
|
||
|
matchLen = len + kMatchMinLen;
|
||
|
|
||
|
The match length decoder can return the values from 0 to 271.
|
||
|
And the corresponded real match length values can be in the range
|
||
|
from 2 to 273.
|
||
|
|
||
|
The following scheme is used for the match length encoding:
|
||
|
|
||
|
Binary encoding Binary Tree structure Zero-based match length
|
||
|
sequence (binary + decimal):
|
||
|
|
||
|
0 xxx LowCoder[posState] xxx
|
||
|
1 0 yyy MidCoder[posState] yyy + 8
|
||
|
1 1 zzzzzzzz HighCoder zzzzzzzz + 16
|
||
|
|
||
|
LZMA uses bit model variable "Choice" to decode the first selection bit.
|
||
|
|
||
|
If the first selection bit is equal to 0, the decoder uses binary tree
|
||
|
LowCoder[posState] to decode 3-bit zero-based match length (xxx).
|
||
|
|
||
|
If the first selection bit is equal to 1, the decoder uses bit model
|
||
|
variable "Choice2" to decode the second selection bit.
|
||
|
|
||
|
If the second selection bit is equal to 0, the decoder uses binary tree
|
||
|
MidCoder[posState] to decode 3-bit "yyy" value, and zero-based match
|
||
|
length is equal to (yyy + 8).
|
||
|
|
||
|
If the second selection bit is equal to 1, the decoder uses binary tree
|
||
|
HighCoder to decode 8-bit "zzzzzzzz" value, and zero-based
|
||
|
match length is equal to (zzzzzzzz + 16).
|
||
|
|
||
|
LZMA uses "posState" value as context to select the binary tree
|
||
|
from LowCoder and MidCoder binary tree arrays:
|
||
|
|
||
|
unsigned posState = OutWindow.TotalPos & ((1 << pb) - 1);
|
||
|
|
||
|
The full code of the length decoder:
|
||
|
|
||
|
class CLenDecoder
|
||
|
{
|
||
|
CProb Choice;
|
||
|
CProb Choice2;
|
||
|
CBitTreeDecoder<3> LowCoder[1 << kNumPosBitsMax];
|
||
|
CBitTreeDecoder<3> MidCoder[1 << kNumPosBitsMax];
|
||
|
CBitTreeDecoder<8> HighCoder;
|
||
|
|
||
|
public:
|
||
|
|
||
|
void Init()
|
||
|
{
|
||
|
Choice = PROB_INIT_VAL;
|
||
|
Choice2 = PROB_INIT_VAL;
|
||
|
HighCoder.Init();
|
||
|
for (unsigned i = 0; i < (1 << kNumPosBitsMax); i++)
|
||
|
{
|
||
|
LowCoder[i].Init();
|
||
|
MidCoder[i].Init();
|
||
|
}
|
||
|
}
|
||
|
|
||
|
unsigned Decode(CRangeDecoder *rc, unsigned posState)
|
||
|
{
|
||
|
if (rc->DecodeBit(&Choice) == 0)
|
||
|
return LowCoder[posState].Decode(rc);
|
||
|
if (rc->DecodeBit(&Choice2) == 0)
|
||
|
return 8 + MidCoder[posState].Decode(rc);
|
||
|
return 16 + HighCoder.Decode(rc);
|
||
|
}
|
||
|
};
|
||
|
|
||
|
The LZMA decoder uses two instances of CLenDecoder class.
|
||
|
The first instance is for the matches of "Simple Match" type,
|
||
|
and the second instance is for the matches of "Rep Match" type:
|
||
|
|
||
|
CLenDecoder LenDecoder;
|
||
|
CLenDecoder RepLenDecoder;
|
||
|
|
||
|
|
||
|
The match distance decoding
|
||
|
---------------------------
|
||
|
|
||
|
LZMA supports dictionary sizes up to 4 GiB minus 1.
|
||
|
The value of match distance (decoded by distance decoder) can be
|
||
|
from 1 to 2^32. But the distance value that is equal to 2^32 is used to
|
||
|
indicate the "End of stream" marker. So real largest match distance
|
||
|
that is used for LZ-window match is (2^32 - 1).
|
||
|
|
||
|
LZMA uses normalized match length (zero-based length)
|
||
|
to calculate the context state "lenState" do decode the distance value:
|
||
|
|
||
|
#define kNumLenToPosStates 4
|
||
|
|
||
|
unsigned lenState = len;
|
||
|
if (lenState > kNumLenToPosStates - 1)
|
||
|
lenState = kNumLenToPosStates - 1;
|
||
|
|
||
|
The distance decoder returns the "dist" value that is zero-based value
|
||
|
of match distance. The real match distance can be calculated with the
|
||
|
following code:
|
||
|
|
||
|
matchDistance = dist + 1;
|
||
|
|
||
|
The state of the distance decoder and the initialization code:
|
||
|
|
||
|
#define kEndPosModelIndex 14
|
||
|
#define kNumFullDistances (1 << (kEndPosModelIndex >> 1))
|
||
|
#define kNumAlignBits 4
|
||
|
|
||
|
CBitTreeDecoder<6> PosSlotDecoder[kNumLenToPosStates];
|
||
|
CProb PosDecoders[1 + kNumFullDistances - kEndPosModelIndex];
|
||
|
CBitTreeDecoder<kNumAlignBits> AlignDecoder;
|
||
|
|
||
|
void InitDist()
|
||
|
{
|
||
|
for (unsigned i = 0; i < kNumLenToPosStates; i++)
|
||
|
PosSlotDecoder[i].Init();
|
||
|
AlignDecoder.Init();
|
||
|
INIT_PROBS(PosDecoders);
|
||
|
}
|
||
|
|
||
|
At first stage the distance decoder decodes 6-bit "posSlot" value with bit
|
||
|
tree decoder from PosSlotDecoder array. It's possible to get 2^6=64 different
|
||
|
"posSlot" values.
|
||
|
|
||
|
unsigned posSlot = PosSlotDecoder[lenState].Decode(&RangeDec);
|
||
|
|
||
|
The encoding scheme for distance value is shown in the following table:
|
||
|
|
||
|
posSlot (decimal) /
|
||
|
zero-based distance (binary)
|
||
|
0 0
|
||
|
1 1
|
||
|
2 10
|
||
|
3 11
|
||
|
|
||
|
4 10 x
|
||
|
5 11 x
|
||
|
6 10 xx
|
||
|
7 11 xx
|
||
|
8 10 xxx
|
||
|
9 11 xxx
|
||
|
10 10 xxxx
|
||
|
11 11 xxxx
|
||
|
12 10 xxxxx
|
||
|
13 11 xxxxx
|
||
|
|
||
|
14 10 yy zzzz
|
||
|
15 11 yy zzzz
|
||
|
16 10 yyy zzzz
|
||
|
17 11 yyy zzzz
|
||
|
...
|
||
|
62 10 yyyyyyyyyyyyyyyyyyyyyyyyyy zzzz
|
||
|
63 11 yyyyyyyyyyyyyyyyyyyyyyyyyy zzzz
|
||
|
|
||
|
where
|
||
|
"x ... x" means the sequence of binary symbols encoded with binary tree and
|
||
|
"Reverse" scheme. It uses separated binary tree for each posSlot from 4 to 13.
|
||
|
"y" means direct bit encoded with range coder.
|
||
|
"zzzz" means the sequence of four binary symbols encoded with binary
|
||
|
tree with "Reverse" scheme, where one common binary tree "AlignDecoder"
|
||
|
is used for all posSlot values.
|
||
|
|
||
|
If (posSlot < 4), the "dist" value is equal to posSlot value.
|
||
|
|
||
|
If (posSlot >= 4), the decoder uses "posSlot" value to calculate the value of
|
||
|
the high bits of "dist" value and the number of the low bits.
|
||
|
|
||
|
If (4 <= posSlot < kEndPosModelIndex), the decoder uses bit tree decoders.
|
||
|
(one separated bit tree decoder per one posSlot value) and "Reverse" scheme.
|
||
|
In this implementation we use one CProb array "PosDecoders" that contains
|
||
|
all CProb variables for all these bit decoders.
|
||
|
|
||
|
if (posSlot >= kEndPosModelIndex), the middle bits are decoded as direct
|
||
|
bits from RangeDecoder and the low 4 bits are decoded with a bit tree
|
||
|
decoder "AlignDecoder" with "Reverse" scheme.
|
||
|
|
||
|
The code to decode zero-based match distance:
|
||
|
|
||
|
unsigned DecodeDistance(unsigned len)
|
||
|
{
|
||
|
unsigned lenState = len;
|
||
|
if (lenState > kNumLenToPosStates - 1)
|
||
|
lenState = kNumLenToPosStates - 1;
|
||
|
|
||
|
unsigned posSlot = PosSlotDecoder[lenState].Decode(&RangeDec);
|
||
|
if (posSlot < 4)
|
||
|
return posSlot;
|
||
|
|
||
|
unsigned numDirectBits = (unsigned)((posSlot >> 1) - 1);
|
||
|
UInt32 dist = ((2 | (posSlot & 1)) << numDirectBits);
|
||
|
if (posSlot < kEndPosModelIndex)
|
||
|
dist += BitTreeReverseDecode(PosDecoders + dist - posSlot, numDirectBits, &RangeDec);
|
||
|
else
|
||
|
{
|
||
|
dist += RangeDec.DecodeDirectBits(numDirectBits - kNumAlignBits) << kNumAlignBits;
|
||
|
dist += AlignDecoder.ReverseDecode(&RangeDec);
|
||
|
}
|
||
|
return dist;
|
||
|
}
|
||
|
|
||
|
|
||
|
|
||
|
LZMA Decoding modes
|
||
|
-------------------
|
||
|
|
||
|
There are 2 types of LZMA streams:
|
||
|
|
||
|
1) The stream with "End of stream" marker.
|
||
|
2) The stream without "End of stream" marker.
|
||
|
|
||
|
And the LZMA Decoder supports 3 modes of decoding:
|
||
|
|
||
|
1) The unpack size is undefined. The LZMA decoder stops decoding after
|
||
|
getting "End of stream" marker.
|
||
|
The input variables for that case:
|
||
|
|
||
|
markerIsMandatory = true
|
||
|
unpackSizeDefined = false
|
||
|
unpackSize contains any value
|
||
|
|
||
|
2) The unpack size is defined and LZMA decoder supports both variants,
|
||
|
where the stream can contain "End of stream" marker or the stream is
|
||
|
finished without "End of stream" marker. The LZMA decoder must detect
|
||
|
any of these situations.
|
||
|
The input variables for that case:
|
||
|
|
||
|
markerIsMandatory = false
|
||
|
unpackSizeDefined = true
|
||
|
unpackSize contains unpack size
|
||
|
|
||
|
3) The unpack size is defined and the LZMA stream must contain
|
||
|
"End of stream" marker
|
||
|
The input variables for that case:
|
||
|
|
||
|
markerIsMandatory = true
|
||
|
unpackSizeDefined = true
|
||
|
unpackSize contains unpack size
|
||
|
|
||
|
|
||
|
The main loop of decoder
|
||
|
------------------------
|
||
|
|
||
|
The main loop of LZMA decoder:
|
||
|
|
||
|
Initialize the LZMA state.
|
||
|
loop
|
||
|
{
|
||
|
// begin of loop
|
||
|
Check "end of stream" conditions.
|
||
|
Decode Type of MATCH / LITERAL.
|
||
|
If it's LITERAL, decode LITERAL value and put the LITERAL to Window.
|
||
|
If it's MATCH, decode the length of match and the match distance.
|
||
|
Check error conditions, check end of stream conditions and copy
|
||
|
the sequence of match bytes from sliding window to current position
|
||
|
in window.
|
||
|
Go to begin of loop
|
||
|
}
|
||
|
|
||
|
The reference implementation of LZMA decoder uses "unpackSize" variable
|
||
|
to keep the number of remaining bytes in output stream. So it reduces
|
||
|
"unpackSize" value after each decoded LITERAL or MATCH.
|
||
|
|
||
|
The following code contains the "end of stream" condition check at the start
|
||
|
of the loop:
|
||
|
|
||
|
if (unpackSizeDefined && unpackSize == 0 && !markerIsMandatory)
|
||
|
if (RangeDec.IsFinishedOK())
|
||
|
return LZMA_RES_FINISHED_WITHOUT_MARKER;
|
||
|
|
||
|
LZMA uses three types of matches:
|
||
|
|
||
|
1) "Simple Match" - the match with distance value encoded with bit models.
|
||
|
|
||
|
2) "Rep Match" - the match that uses the distance from distance
|
||
|
history table.
|
||
|
|
||
|
3) "Short Rep Match" - the match of single byte length, that uses the latest
|
||
|
distance from distance history table.
|
||
|
|
||
|
The LZMA decoder keeps the history of latest 4 match distances that were used
|
||
|
by decoder. That set of 4 variables contains zero-based match distances and
|
||
|
these variables are initialized with zero values:
|
||
|
|
||
|
UInt32 rep0 = 0, rep1 = 0, rep2 = 0, rep3 = 0;
|
||
|
|
||
|
The LZMA decoder uses binary model variables to select type of MATCH or LITERAL:
|
||
|
|
||
|
#define kNumStates 12
|
||
|
#define kNumPosBitsMax 4
|
||
|
|
||
|
CProb IsMatch[kNumStates << kNumPosBitsMax];
|
||
|
CProb IsRep[kNumStates];
|
||
|
CProb IsRepG0[kNumStates];
|
||
|
CProb IsRepG1[kNumStates];
|
||
|
CProb IsRepG2[kNumStates];
|
||
|
CProb IsRep0Long[kNumStates << kNumPosBitsMax];
|
||
|
|
||
|
The decoder uses "state" variable value to select exact variable
|
||
|
from "IsRep", "IsRepG0", "IsRepG1" and "IsRepG2" arrays.
|
||
|
The "state" variable can get the value from 0 to 11.
|
||
|
Initial value for "state" variable is zero:
|
||
|
|
||
|
unsigned state = 0;
|
||
|
|
||
|
The "state" variable is updated after each LITERAL or MATCH with one of the
|
||
|
following functions:
|
||
|
|
||
|
unsigned UpdateState_Literal(unsigned state)
|
||
|
{
|
||
|
if (state < 4) return 0;
|
||
|
else if (state < 10) return state - 3;
|
||
|
else return state - 6;
|
||
|
}
|
||
|
unsigned UpdateState_Match (unsigned state) { return state < 7 ? 7 : 10; }
|
||
|
unsigned UpdateState_Rep (unsigned state) { return state < 7 ? 8 : 11; }
|
||
|
unsigned UpdateState_ShortRep(unsigned state) { return state < 7 ? 9 : 11; }
|
||
|
|
||
|
The decoder calculates "state2" variable value to select exact variable from
|
||
|
"IsMatch" and "IsRep0Long" arrays:
|
||
|
|
||
|
unsigned posState = OutWindow.TotalPos & ((1 << pb) - 1);
|
||
|
unsigned state2 = (state << kNumPosBitsMax) + posState;
|
||
|
|
||
|
The decoder uses the following code flow scheme to select exact
|
||
|
type of LITERAL or MATCH:
|
||
|
|
||
|
IsMatch[state2] decode
|
||
|
0 - the Literal
|
||
|
1 - the Match
|
||
|
IsRep[state] decode
|
||
|
0 - Simple Match
|
||
|
1 - Rep Match
|
||
|
IsRepG0[state] decode
|
||
|
0 - the distance is rep0
|
||
|
IsRep0Long[state2] decode
|
||
|
0 - Short Rep Match
|
||
|
1 - Rep Match 0
|
||
|
1 -
|
||
|
IsRepG1[state] decode
|
||
|
0 - Rep Match 1
|
||
|
1 -
|
||
|
IsRepG2[state] decode
|
||
|
0 - Rep Match 2
|
||
|
1 - Rep Match 3
|
||
|
|
||
|
|
||
|
LITERAL symbol
|
||
|
--------------
|
||
|
If the value "0" was decoded with IsMatch[state2] decoding, we have "LITERAL" type.
|
||
|
|
||
|
At first the LZMA decoder must check that it doesn't exceed
|
||
|
specified uncompressed size:
|
||
|
|
||
|
if (unpackSizeDefined && unpackSize == 0)
|
||
|
return LZMA_RES_ERROR;
|
||
|
|
||
|
Then it decodes literal value and puts it to sliding window:
|
||
|
|
||
|
DecodeLiteral(state, rep0);
|
||
|
|
||
|
Then the decoder must update the "state" value and "unpackSize" value;
|
||
|
|
||
|
state = UpdateState_Literal(state);
|
||
|
unpackSize--;
|
||
|
|
||
|
Then the decoder must go to the begin of main loop to decode next Match or Literal.
|
||
|
|
||
|
|
||
|
Simple Match
|
||
|
------------
|
||
|
|
||
|
If the value "1" was decoded with IsMatch[state2] decoding,
|
||
|
we have the "Simple Match" type.
|
||
|
|
||
|
The distance history table is updated with the following scheme:
|
||
|
|
||
|
rep3 = rep2;
|
||
|
rep2 = rep1;
|
||
|
rep1 = rep0;
|
||
|
|
||
|
The zero-based length is decoded with "LenDecoder":
|
||
|
|
||
|
len = LenDecoder.Decode(&RangeDec, posState);
|
||
|
|
||
|
The state is update with UpdateState_Match function:
|
||
|
|
||
|
state = UpdateState_Match(state);
|
||
|
|
||
|
and the new "rep0" value is decoded with DecodeDistance:
|
||
|
|
||
|
rep0 = DecodeDistance(len);
|
||
|
|
||
|
That "rep0" will be used as zero-based distance for current match.
|
||
|
|
||
|
If the value of "rep0" is equal to 0xFFFFFFFF, it means that we have
|
||
|
"End of stream" marker, so we can stop decoding and check finishing
|
||
|
condition in Range Decoder:
|
||
|
|
||
|
if (rep0 == 0xFFFFFFFF)
|
||
|
return RangeDec.IsFinishedOK() ?
|
||
|
LZMA_RES_FINISHED_WITH_MARKER :
|
||
|
LZMA_RES_ERROR;
|
||
|
|
||
|
If uncompressed size is defined, LZMA decoder must check that it doesn't
|
||
|
exceed that specified uncompressed size:
|
||
|
|
||
|
if (unpackSizeDefined && unpackSize == 0)
|
||
|
return LZMA_RES_ERROR;
|
||
|
|
||
|
Also the decoder must check that "rep0" value is not larger than dictionary size
|
||
|
and is not larger than the number of already decoded bytes:
|
||
|
|
||
|
if (rep0 >= dictSize || !OutWindow.CheckDistance(rep0))
|
||
|
return LZMA_RES_ERROR;
|
||
|
|
||
|
Then the decoder must copy match bytes as described in
|
||
|
"The match symbols copying" section.
|
||
|
|
||
|
|
||
|
Rep Match
|
||
|
---------
|
||
|
|
||
|
If the LZMA decoder has decoded the value "1" with IsRep[state] variable,
|
||
|
we have "Rep Match" type.
|
||
|
|
||
|
At first the LZMA decoder must check that it doesn't exceed
|
||
|
specified uncompressed size:
|
||
|
|
||
|
if (unpackSizeDefined && unpackSize == 0)
|
||
|
return LZMA_RES_ERROR;
|
||
|
|
||
|
Also the decoder must return error, if the LZ window is empty:
|
||
|
|
||
|
if (OutWindow.IsEmpty())
|
||
|
return LZMA_RES_ERROR;
|
||
|
|
||
|
If the match type is "Rep Match", the decoder uses one of the 4 variables of
|
||
|
distance history table to get the value of distance for current match.
|
||
|
And there are 4 corresponding ways of decoding flow.
|
||
|
|
||
|
The decoder updates the distance history with the following scheme
|
||
|
depending from type of match:
|
||
|
|
||
|
- "Rep Match 0" or "Short Rep Match":
|
||
|
; LZMA doesn't update the distance history
|
||
|
|
||
|
- "Rep Match 1":
|
||
|
UInt32 dist = rep1;
|
||
|
rep1 = rep0;
|
||
|
rep0 = dist;
|
||
|
|
||
|
- "Rep Match 2":
|
||
|
UInt32 dist = rep2;
|
||
|
rep2 = rep1;
|
||
|
rep1 = rep0;
|
||
|
rep0 = dist;
|
||
|
|
||
|
- "Rep Match 3":
|
||
|
UInt32 dist = rep3;
|
||
|
rep3 = rep2;
|
||
|
rep2 = rep1;
|
||
|
rep1 = rep0;
|
||
|
rep0 = dist;
|
||
|
|
||
|
Then the decoder decodes exact subtype of "Rep Match" using "IsRepG0", "IsRep0Long",
|
||
|
"IsRepG1", "IsRepG2".
|
||
|
|
||
|
If the subtype is "Short Rep Match", the decoder updates the state, puts
|
||
|
the one byte from window to current position in window and goes to next
|
||
|
MATCH/LITERAL symbol (the begin of main loop):
|
||
|
|
||
|
state = UpdateState_ShortRep(state);
|
||
|
OutWindow.PutByte(OutWindow.GetByte(rep0 + 1));
|
||
|
unpackSize--;
|
||
|
continue;
|
||
|
|
||
|
In other cases (Rep Match 0/1/2/3), it decodes the zero-based
|
||
|
length of match with "RepLenDecoder" decoder:
|
||
|
|
||
|
len = RepLenDecoder.Decode(&RangeDec, posState);
|
||
|
|
||
|
Then it updates the state:
|
||
|
|
||
|
state = UpdateState_Rep(state);
|
||
|
|
||
|
Then the decoder must copy match bytes as described in
|
||
|
"The Match symbols copying" section.
|
||
|
|
||
|
|
||
|
The match symbols copying
|
||
|
-------------------------
|
||
|
|
||
|
If we have the match (Simple Match or Rep Match 0/1/2/3), the decoder must
|
||
|
copy the sequence of bytes with calculated match distance and match length.
|
||
|
If uncompressed size is defined, LZMA decoder must check that it doesn't
|
||
|
exceed that specified uncompressed size:
|
||
|
|
||
|
len += kMatchMinLen;
|
||
|
bool isError = false;
|
||
|
if (unpackSizeDefined && unpackSize < len)
|
||
|
{
|
||
|
len = (unsigned)unpackSize;
|
||
|
isError = true;
|
||
|
}
|
||
|
OutWindow.CopyMatch(rep0 + 1, len);
|
||
|
unpackSize -= len;
|
||
|
if (isError)
|
||
|
return LZMA_RES_ERROR;
|
||
|
|
||
|
Then the decoder must go to the begin of main loop to decode next MATCH or LITERAL.
|
||
|
|
||
|
|
||
|
|
||
|
NOTES
|
||
|
-----
|
||
|
|
||
|
This specification doesn't describe the variant of decoder implementation
|
||
|
that supports partial decoding. Such partial decoding case can require some
|
||
|
changes in "end of stream" condition checks code. Also such code
|
||
|
can use additional status codes, returned by decoder.
|
||
|
|
||
|
This specification uses C++ code with templates to simplify describing.
|
||
|
The optimized version of LZMA decoder doesn't need templates.
|
||
|
Such optimized version can use just two arrays of CProb variables:
|
||
|
1) The dynamic array of CProb variables allocated for the Literal Decoder.
|
||
|
2) The one common array that contains all other CProb variables.
|
||
|
|
||
|
|
||
|
References:
|
||
|
|
||
|
1. G. N. N. Martin, Range encoding: an algorithm for removing redundancy
|
||
|
from a digitized message, Video & Data Recording Conference,
|
||
|
Southampton, UK, July 24-27, 1979.
|