Source code
Revision control
Copy as Markdown
Other Tools
LZMA specification (DRAFT version)↩
----------------------------------↩
↩
Author: Igor Pavlov↩
Date: 2015-06-14↩
↩
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:↩
↩
bool CRangeDecoder::Init()↩
{↩
Corrupted = false;↩
Range = 0xFFFFFFFF;↩
Code = 0;↩
↩
Byte b = InStream->ReadByte();↩
↩
for (int i = 0; i < 4; i++)↩
Code = (Code << 8) | InStream->ReadByte();↩
↩
if (b != 0 || Code == Range)↩
Corrupted = true;↩
return b == 0;↩
}↩
↩
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. If initial byte is not equal to ZERO, the LZMA Decoder must↩
stop decoding and report error.↩
↩
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.↩