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. |