nest-open-source / nest-cam / 4320010 / lzma / refs/heads/master / . / lzma / DOC / lzma-specification.txt

LZMA specification (DRAFT version) | |

---------------------------------- | |

Author: Igor Pavlov | |

Date: 2013-07-28 | |

This specification defines the format of LZMA compressed data and lzma file format. | |

Notation | |

-------- | |

We use the syntax of C++ programming language. | |

We use the following types in C++ code: | |

unsigned - unsigned integer, at least 16 bits in size | |

int - signed integer, at least 16 bits in size | |

UInt64 - 64-bit unsigned integer | |

UInt32 - 32-bit unsigned integer | |

UInt16 - 16-bit unsigned integer | |

Byte - 8-bit unsigned integer | |

bool - boolean type with two possible values: false, true | |

lzma file format | |

================ | |

The lzma file contains the raw LZMA stream and the header with related properties. | |

The files in that format use ".lzma" extension. | |

The lzma file format layout: | |

Offset Size Description | |

0 1 LZMA model properties (lc, lp, pb) in encoded form | |

1 4 Dictionary size (32-bit unsigned integer, little-endian) | |

5 8 Uncompressed size (64-bit unsigned integer, little-endian) | |

13 Compressed data (LZMA stream) | |

LZMA properties: | |

name Range Description | |

lc [0, 8] the number of "literal context" bits | |

lp [0, 4] the number of "literal pos" bits | |

pb [0, 4] the number of "pos" bits | |

dictSize [0, 2^32 - 1] the dictionary size | |

The following code encodes LZMA properties: | |

void EncodeProperties(Byte *properties) | |

{ | |

properties[0] = (Byte)((pb * 5 + lp) * 9 + lc); | |

Set_UInt32_LittleEndian(properties + 1, dictSize); | |

} | |

If the value of dictionary size in properties is smaller than (1 << 12), | |

the LZMA decoder must set the dictionary size variable to (1 << 12). | |

#define LZMA_DIC_MIN (1 << 12) | |

unsigned lc, pb, lp; | |

UInt32 dictSize; | |

UInt32 dictSizeInProperties; | |

void DecodeProperties(const Byte *properties) | |

{ | |

unsigned d = properties[0]; | |

if (d >= (9 * 5 * 5)) | |

throw "Incorrect LZMA properties"; | |

lc = d % 9; | |

d /= 9; | |

pb = d / 5; | |

lp = d % 5; | |

dictSizeInProperties = 0; | |

for (int i = 0; i < 4; i++) | |

dictSizeInProperties |= (UInt32)properties[i + 1] << (8 * i); | |

dictSize = dictSizeInProperties; | |

if (dictSize < LZMA_DIC_MIN) | |

dictSize = LZMA_DIC_MIN; | |

} | |

If "Uncompressed size" field contains ones in all 64 bits, it means that | |

uncompressed size is unknown and there is the "end marker" in stream, | |

that indicates the end of decoding point. | |

In opposite case, if the value from "Uncompressed size" field is not | |

equal to ((2^64) - 1), the LZMA stream decoding must be finished after | |

specified number of bytes (Uncompressed size) is decoded. And if there | |

is the "end marker", the LZMA decoder must read that marker also. | |

The new scheme to encode LZMA properties | |

---------------------------------------- | |

If LZMA compression is used for some another format, it's recommended to | |

use a new improved scheme to encode LZMA properties. That new scheme was | |

used in xz format that uses the LZMA2 compression algorithm. | |

The LZMA2 is a new compression algorithm that is based on the LZMA algorithm. | |

The dictionary size in LZMA2 is encoded with just one byte and LZMA2 supports | |

only reduced set of dictionary sizes: | |

(2 << 11), (3 << 11), | |

(2 << 12), (3 << 12), | |

... | |

(2 << 30), (3 << 30), | |

(2 << 31) - 1 | |

The dictionary size can be extracted from encoded value with the following code: | |

dictSize = (p == 40) ? 0xFFFFFFFF : (((UInt32)2 | ((p) & 1)) << ((p) / 2 + 11)); | |

Also there is additional limitation (lc + lp <= 4) in LZMA2 for values of | |

"lc" and "lp" properties: | |

if (lc + lp > 4) | |

throw "Unsupported properties: (lc + lp) > 4"; | |

There are some advantages for LZMA decoder with such (lc + lp) value | |

limitation. It reduces the maximum size of tables allocated by decoder. | |

And it reduces the complexity of initialization procedure, that can be | |

important to keep high speed of decoding of big number of small LZMA streams. | |

It's recommended to use that limitation (lc + lp <= 4) for any new format | |

that uses LZMA compression. Note that the combinations of "lc" and "lp" | |

parameters, where (lc + lp > 4), can provide significant improvement in | |

compression ratio only in some rare cases. | |

The LZMA properties can be encoded into two bytes in new scheme: | |

Offset Size Description | |

0 1 The dictionary size encoded with LZMA2 scheme | |

1 1 LZMA model properties (lc, lp, pb) in encoded form | |

The RAM usage | |

============= | |

The RAM usage for LZMA decoder is determined by the following parts: | |

1) The Sliding Window (from 4 KiB to 4 GiB). | |

2) The probability model counter arrays (arrays of 16-bit variables). | |

3) Some additional state variables (about 10 variables of 32-bit integers). | |

The RAM usage for Sliding Window | |

-------------------------------- | |

There are two main scenarios of decoding: | |

1) The decoding of full stream to one RAM buffer. | |

If we decode full LZMA stream to one output buffer in RAM, the decoder | |

can use that output buffer as sliding window. So the decoder doesn't | |

need additional buffer allocated for sliding window. | |

2) The decoding to some external storage. | |

If we decode LZMA stream to external storage, the decoder must allocate | |

the buffer for sliding window. The size of that buffer must be equal | |

or larger than the value of dictionary size from properties of LZMA stream. | |

In this specification we describe the code for decoding to some external | |

storage. The optimized version of code for decoding of full stream to one | |

output RAM buffer can require some minor changes in code. | |

The RAM usage for the probability model counters | |

------------------------------------------------ | |

The size of the probability model counter arrays is calculated with the | |

following formula: | |

size_of_prob_arrays = 1846 + 768 * (1 << (lp + lc)) | |

Each probability model counter is 11-bit unsigned integer. | |

If we use 16-bit integer variables (2-byte integers) for these probability | |

model counters, the RAM usage required by probability model counter arrays | |

can be estimated with the following formula: | |

RAM = 4 KiB + 1.5 KiB * (1 << (lp + lc)) | |

For example, for default LZMA parameters (lp = 0 and lc = 3), the RAM usage is | |

RAM_lc3_lp0 = 4 KiB + 1.5 KiB * 8 = 16 KiB | |

The maximum RAM state usage is required for decoding the stream with lp = 4 | |

and lc = 8: | |

RAM_lc8_lp4 = 4 KiB + 1.5 KiB * 4096 = 6148 KiB | |

If the decoder uses LZMA2's limited property condition | |

(lc + lp <= 4), the RAM usage will be not larger than | |

RAM_lc_lp_4 = 4 KiB + 1.5 KiB * 16 = 28 KiB | |

The RAM usage for encoder | |

------------------------- | |

There are many variants for LZMA encoding code. | |

These variants have different values for memory consumption. | |

Note that memory consumption for LZMA Encoder can not be | |

smaller than memory consumption of LZMA Decoder for same stream. | |

The RAM usage required by modern effective implementation of | |

LZMA Encoder can be estimated with the following formula: | |

Encoder_RAM_Usage = 4 MiB + 11 * dictionarySize. | |

But there are some modes of the encoder that require less memory. | |

LZMA Decoding | |

============= | |

The LZMA compression algorithm uses LZ-based compression with Sliding Window | |

and Range Encoding as entropy coding method. | |

Sliding Window | |

-------------- | |

LZMA uses Sliding Window compression similar to LZ77 algorithm. | |

LZMA stream must be decoded to the sequence that consists | |

of MATCHES and LITERALS: | |

- a LITERAL is a 8-bit character (one byte). | |

The decoder just puts that LITERAL to the uncompressed stream. | |

- a MATCH is a pair of two numbers (DISTANCE-LENGTH pair). | |

The decoder takes one byte exactly "DISTANCE" characters behind | |

current position in the uncompressed stream and puts it to | |

uncompressed stream. The decoder must repeat it "LENGTH" times. | |

The "DISTANCE" can not be larger than dictionary size. | |

And the "DISTANCE" can not be larger than the number of bytes in | |

the uncompressed stream that were decoded before that match. | |

In this specification we use cyclic buffer to implement Sliding Window | |

for LZMA decoder: | |

class COutWindow | |

{ | |

Byte *Buf; | |

UInt32 Pos; | |

UInt32 Size; | |

bool IsFull; | |

public: | |

unsigned TotalPos; | |

COutStream OutStream; | |

COutWindow(): Buf(NULL) {} | |

~COutWindow() { delete []Buf; } | |

void Create(UInt32 dictSize) | |

{ | |

Buf = new Byte[dictSize]; | |

Pos = 0; | |

Size = dictSize; | |

IsFull = false; | |

TotalPos = 0; | |

} | |

void PutByte(Byte b) | |

{ | |

TotalPos++; | |

Buf[Pos++] = b; | |

if (Pos == Size) | |

{ | |

Pos = 0; | |

IsFull = true; | |

} | |

OutStream.WriteByte(b); | |

} | |

Byte GetByte(UInt32 dist) const | |

{ | |

return Buf[dist <= Pos ? Pos - dist : Size - dist + Pos]; | |

} | |

void CopyMatch(UInt32 dist, unsigned len) | |

{ | |

for (; len > 0; len--) | |

PutByte(GetByte(dist)); | |

} | |

bool CheckDistance(UInt32 dist) const | |

{ | |

return dist <= Pos || IsFull; | |

} | |

bool IsEmpty() const | |

{ | |

return Pos == 0 && !IsFull; | |

} | |

}; | |

In another implementation it's possible to use one buffer that contains | |

Sliding Window and the whole data stream after uncompressing. | |

Range Decoder | |

------------- | |

LZMA algorithm uses Range Encoding (1) as entropy coding method. | |

LZMA stream contains just one very big number in big-endian encoding. | |

LZMA decoder uses the Range Decoder to extract a sequence of binary | |

symbols from that big number. | |

The state of the Range Decoder: | |

struct CRangeDecoder | |

{ | |

UInt32 Range; | |

UInt32 Code; | |

InputStream *InStream; | |

bool Corrupted; | |

} | |

The notes about UInt32 type for the "Range" and "Code" variables: | |

It's possible to use 64-bit (unsigned or signed) integer type | |

for the "Range" and the "Code" variables instead of 32-bit unsigned, | |

but some additional code must be used to truncate the values to | |

low 32-bits after some operations. | |

If the programming language does not support 32-bit unsigned integer type | |

(like in case of JAVA language), it's possible to use 32-bit signed integer, | |

but some code must be changed. For example, it's required to change the code | |

that uses comparison operations for UInt32 variables in this specification. | |

The Range Decoder can be in some states that can be treated as | |

"Corruption" in LZMA stream. The Range Decoder uses the variable "Corrupted": | |

(Corrupted == false), if the Range Decoder has not detected any corruption. | |

(Corrupted == true), if the Range Decoder has detected some corruption. | |

The reference LZMA Decoder ignores the value of the "Corrupted" variable. | |

So it continues to decode the stream, even if the corruption can be detected | |

in the Range Decoder. To provide the full compatibility with output of the | |

reference LZMA Decoder, another LZMA Decoder implementations must also | |

ignore the value of the "Corrupted" variable. | |

The LZMA Encoder is required to create only such LZMA streams, that will not | |

lead the Range Decoder to states, where the "Corrupted" variable is set to true. | |

The Range Decoder reads first 5 bytes from input stream to initialize | |

the state: | |

void CRangeDecoder::Init() | |

{ | |

Corrupted = false; | |

if (InStream->ReadByte() != 0) | |

Corrupted = true; | |

Range = 0xFFFFFFFF; | |

Code = 0; | |

for (int i = 0; i < 4; i++) | |

Code = (Code << 8) | InStream->ReadByte(); | |

if (Code == Range) | |

Corrupted = true; | |

} | |

The LZMA Encoder always writes ZERO in initial byte of compressed stream. | |

That scheme allows to simplify the code of the Range Encoder in the | |

LZMA Encoder. | |

After the last bit of data was decoded by Range Decoder, the value of the | |

"Code" variable must be equal to 0. The LZMA Decoder must check it by | |

calling the IsFinishedOK() function: | |

bool IsFinishedOK() const { return Code == 0; } | |

If there is corruption in data stream, there is big probability that | |

the "Code" value will be not equal to 0 in the Finish() function. So that | |

check in the IsFinishedOK() function provides very good feature for | |

corruption detection. | |

The value of the "Range" variable before each bit decoding can not be smaller | |

than ((UInt32)1 << 24). The Normalize() function keeps the "Range" value in | |

described range. | |

#define kTopValue ((UInt32)1 << 24) | |

void CRangeDecoder::Normalize() | |

{ | |

if (Range < kTopValue) | |

{ | |

Range <<= 8; | |

Code = (Code << 8) | InStream->ReadByte(); | |

} | |

} | |

Notes: if the size of the "Code" variable is larger than 32 bits, it's | |

required to keep only low 32 bits of the "Code" variable after the change | |

in Normalize() function. | |

If the LZMA Stream is not corrupted, the value of the "Code" variable is | |

always smaller than value of the "Range" variable. | |

But the Range Decoder ignores some types of corruptions, so the value of | |

the "Code" variable can be equal or larger than value of the "Range" variable | |

for some "Corrupted" archives. | |

LZMA uses Range Encoding only with binary symbols of two types: | |

1) binary symbols with fixed and equal probabilities (direct bits) | |

2) binary symbols with predicted probabilities | |

The DecodeDirectBits() function decodes the sequence of direct bits: | |

UInt32 CRangeDecoder::DecodeDirectBits(unsigned numBits) | |

{ | |

UInt32 res = 0; | |

do | |

{ | |

Range >>= 1; | |

Code -= Range; | |

UInt32 t = 0 - ((UInt32)Code >> 31); | |

Code += Range & t; | |

if (Code == Range) | |

Corrupted = true; | |

Normalize(); | |

res <<= 1; | |

res += t + 1; | |

} | |

while (--numBits); | |

return res; | |

} | |

The Bit Decoding with Probability Model | |

--------------------------------------- | |

The task of Bit Probability Model is to estimate probabilities of binary | |

symbols. And then it provides the Range Decoder with that information. | |

The better prediction provides better compression ratio. | |

The Bit Probability Model uses statistical data of previous decoded | |

symbols. | |

That estimated probability is presented as 11-bit unsigned integer value | |

that represents the probability of symbol "0". | |

#define kNumBitModelTotalBits 11 | |

Mathematical probabilities can be presented with the following formulas: | |

probability(symbol_0) = prob / 2048. | |

probability(symbol_1) = 1 - Probability(symbol_0) = | |

= 1 - prob / 2048 = | |

= (2048 - prob) / 2048 | |

where the "prob" variable contains 11-bit integer probability counter. | |

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. |