LZMA Докладчик : Гареев Роман email: [email protected].

LZMA

Докладчик: Гареев Роман email: [email protected]

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LZMA (Lempel-Ziv-Markov chain-

Algorithm)

7z(7-Zip)

LZMA SDK

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LZMA:LZ77(Sliding Window)Deflate: Zip and GzipRange Encoding

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Jacob Ziv

Abraham Lempel

LZ77 (Sliding Window)

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In computer science and information theory, data compression, source coding, or bit-rate reduction involves encoding information using fewer bits than the original representation. Compression can be either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by identifying marginally important information and removing it.

Compression is useful because it helps reduce the consumption of resources such as data space or transmission capacity. Because compressed data must be decompressed to be used, this extra processing imposes computational or other costs through decompression. For instance, a compression scheme for video may require expensive hardware for the video to be decompressed fast enough to be viewed as it is being decompressed, and the option to decompress the video in full before watching it may be inconvenient or require additional storage. The design of data compression schemes involve trade-offs among various factors, including the degree of compression, the amount of distortion introduced (e.g., when using lossy data compression), and the computational resources required to compress and uncompress the data.

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Закодированный текст… sir sid eastman easily t eases sea sick seals … Текст для …

(16, 3, “e”)

Закодированный текст… sir sid eastman easily tease s sea sick seals …. Текст для …

sir sid eastman ⇒ (0,0,“s”)

s ir sid eastman e ⇒ (0,0,“i”)

si r sid eastman ea ⇒ (0,0,“r”)

sir sid eastman eas ⇒ (0,0,“ ”)

sir sid eastman easi ⇒ (4,2,“d”)

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a1 0.4

a2 0.2

a3 0.2

a4 0.1

a5 0.1

Huffman Coding

a5

a4

a3

a2

a1

a45

a345

a2345

a12345

0.4

0.1

0.20.2

0.1

0.2

0.4

0.6

1.0

0

1

1

0

01

1

0

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Phillip Katz

Deflate: Zip and Gzip

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(сдвиг, длина, символ)

Закодированный текст… old ...she needs..then…there… the new... Текст для пр…

Режимы:

Normal

High-compression

Fast

⇒ (сдвиг, длина)

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Режимы сжатия:

•Без сжатия

•Сжатие с фиксированным размером таблиц

•Сжатие с индивидуальными таблицами, создаваемыми для текущей информации

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“range encoding”

“Handbook of Data Compression” David Salomon, Giovanni Motta

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Закодированный текст… … the new... Текст для пр…

“hash-chain”, “binary-tree”

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bt2 Binary Tree with 2 bytes hashing



hc4 Hash Chain with 4 bytes hashing

LZMA

индекс

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Hash-chain

XY 123 … … 123

… …

…

…

24 …

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…abm…abcd2…abcx…abcd1…aby… 11 24 30 57 78

62

62

62

62

62

11

24

11

57

30

24

24

11

57

30

11

11

30

24

78

Binary-tree

abm…

abm…

abcd2…

abcd2…

abcd2…

abcd1…

abcd1…

abm…

abm…

abcx…

abcx…

abm…

abcx…

aby…

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Пример реализации LZMA(реализация на JAVA из LZMA SDK)

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LZMA SDK

2004 ANSI-C/C++/C#/Java lzma.exe lzma.txt 7zFormat.txt history.txt

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Основные характеристики LZMA SDK

Различный размер словаря Предполагаемая скорость сжатия: около 2MB/s на 2

GHz CPU Предполагаемая скорость распаковки:

20-30 MB/s на 2 GHz Core 2 или AMD Athlon 64

1-2 MB/s на 200 MHz RISC Небольшое количество затрат памяти для

распаковки(16 KB + размер словаря) Поддержка многопоточности

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Основные опции LZMA SDK

a{N} Режим сжатия. 0, 1, 2 fast, normal, max -d{N} -si -so -mf{MF_ID}

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MF_ID Memory Description

bt2 d * 9.5 + 4MB Binary Tree с 2 байтным хэшированием bt3 d * 11.5 + 4MB Binary Tree с 3 байтным хэшированием bt4 d * 11.5 + 4MB Binary Tree с 4 байтным хэшированием hc4 d * 7.5 + 4MB Hash Chain с 4 байтным хэшированием

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http://tukaani.org

Lasse Collin

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Сравнение Gzip, Bzip2 и LZMA

AMD mobile Athlon XP2400+ 512 MB RAM Linux 2.6.12 gzip 1.3.3, bzip2 1.0.3, LZMA SDK 4.17 (lzmash)

Обращалось внимание на: размер файлов после сжатия время распаковки память, требуемая для распаковки обычный формат, который все знают

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Tar archive OpenOffice.org 1.1.4(Linux) (203 MB)

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gzip bzip2 lzmash

1 40,6% 35,8% 31,7%

2 39,9% 34,9% 29,2%

3 39,3% 34,5% 28,0%

4 38,2% 34,3% 27,4%

5 37,5% 34,2% 26,7%

6 37,2% 34,1% 26,4%

7 37,1% 34,1% 26,1%

8 37,1% 34,0% 25,7%

9 37,0% 34,0% 25,4%

Compressed size / Uncompressed size * 100%

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Tar archive OpenOffice.org 1.1.4(Linux) (203 MB)

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gzip bzip2 lzmash

1 11.5s 1m 26s 0m 58s

2 12.0s 1m 40s 2m 7s

3 13.7s 1m 54s 4m 58s

4 15.1s 2m 5s 5m 26s

5 18.4s 2m 11s 6m 47s

6 24.5s 2m 18s 7m 30s

7 29.4s 2m 25s 8m 24s

8 45.5s 2m 32s 10m 59s

9 66.9s 2m 37s 12m 20s

Compression time

gzip bzip2 lzmash

1 3.3s 16.5s 11.3s

2 3.3s 24.2s 10.5s

3 3.3s 29.2s 10.5s

4 3.3s 32.1s 10.4s

5 3.2s 34.2s 10.2s

6 3.2s 35.4s 10.2s

7 3.2s 36.5s 10.1s

8 3.2s 37.5s 10.0s

9 3.1s 38.2s 10.0s

Decompression time

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Tar archive The Linux kernel 2.6.11.0 source (199 MB)

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gzip bzip2 lzmash

1 27,8% 21,1% 21,1%

2 26,5% 19,7% 18,7%

3 25,7% 19,1% 16,7%

4 23,9% 18,7% 16,1%

5 22,9% 18,4% 15,6%

6 22,6% 18,2% 15,2%

7 22,5% 18,1% 14,8%

8 22,4% 17,9% 14,5%

9 22,4% 17,8% 14,3%


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Tar archive The Linux kernel 2.6.11.0 source (199 MB)

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gzip bzip2 lzmash

1 8.3s 1m 9s 0m 45s

2 8.7s 1m 22s 1m 45s

3 9.8s 1m 34s 5m 10s

4 11.1s 1m 45s 5m 43s

5 13.8s 1m 57s 7m 39s

6 17.8s 2m 2s 8m 23s

7 20.7s 2m 11s 9m 11s

8 29.7s 2m 21s 11m 34s

9 40.9s 2m 26s 12m 31s

Compression time

gzip bzip2 lzmash

1 2.8s 12.8s 7.7s

2 2.7s 19.4s 6.9s

3 2.6s 23.8s 6.4s

4 2.5s 26.4s 6.3s

5 2.5s 28.3s 6.3s

6 2.4s 29.6s 6.2s

7 2.4s 30.6s 6.2s

8 2.4s 31.3s 6.1s

9 2.4s 32.1s 6.1s

Decompression time

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XMMS 1.2.10 binary package (5.2 MB)(Slackware 10.1)

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gzip bzip2 lzmash

1 39,3% 32,8% 26,0%

2 38,4% 29,3% 20,7%

3 37,7% 28,0% 18,8%

4 36,9% 27,0% 18,3%

5 36,2% 26,6% 18,0%

6 36,0% 26,1% 17,9%

7 35,9% 26,0% 17,9%

8 35,9% 25,7% 17,8%

9 35,8% 25,2% 17,8%


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XMMS 1.2.10 binary package (5.2 MB)(Slackware 10.1)

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gzip bzip2 lzmash

1 0.3s 2.4s 1.4s

2 0.3s 2.9s 2.7s

3 0.4s 3.2s 6.2s

4 0.4s 3.3s 6.6s

5 0.5s 4.6s 8.2s

6 0.7s 5.6s 8.5s

7 0.8s 4.7s 8.6s

8 1.1s 4.9s 10.5s

9 1.8s 5.1s 10.5s

Compression time

gzip bzip2 lzmash

1 0.1s 0.4s 0.3s

2 0.1s 0.6s 0.2s

3 0.1s 0.7s 0.2s

4 0.1s 0.8s 0.2s

5 0.1s 0.9s 0.2s

6 0.1s 0.9s 0.2s

7 0.1s 0.9s 0.2s

8 0.1s 1.0s 0.2s

9 0.1s 1.0s 0.2s

Decompression time

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XMMS 1.2.10 source tarball (15.2 MB)

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gzip bzip2 lzmash

1 29,5% 23,2% 21,2%

2 28,6% 19,9% 13,3%

3 27,9% 18,3% 12,0%

4 26,4% 17,2% 11,3%

5 25,7% 16,7% 10,8%

6 25,4% 16,2% 10,3%

7 25,3% 15,7% 9,7%

8 25,3% 15,4% 9,6%

9 25,3% 15,1% 9,6%


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XMMS 1.2.10 source tarball (15.2 MB)

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gzip bzip2 lzmash

1 0.7s 6.1s 3.5s

2 0.7s 7.3s 6.0s

3 0.8s 8.5s 19.0s

4 0.9s 9.9s 19.9s

5 1.1s 11.2s 28.9s

6 1.4s 11.0s 30.1s

7 1.7s 12.5s 30.9s

8 2.5s 15.9s 41.7s

9 2.9s 17.5s 41.7s

Compression time

gzip bzip2 lzmash

1 0.2s 1.0s 0.6s

2 0.2s 1.5s 0.4s

3 0.2s 1.9s 0.4s

4 0.2s 2.1s 0.4s

5 0.2s 2.3s 0.4s

6 0.2s 2.5s 0.4s

7 0.2s 2.6s 0.4s

8 0.2s 2.7s 0.4s

9 0.2s 2.8s 0.4s

Decompression time

30

Memory requirements

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gzip bzip2 lzmash

1 <1 MB 2 MB 2 MB

2 <1 MB 2 MB 12 MB

3 <1 MB 3 MB 12 MB

4 <1 MB 4 MB 16 MB

5 <1 MB 5 MB 26 MB

6 <1 MB 5 MB 45 MB

7 <1 MB 6 MB 83 MB

8 <1 MB 7 MB 159 MB

9 <1 MB 7 MB 311 MB

RAM usage on compression

gzip bzip2 lzmash

1 <1 MB 1 MB 1 MB

2 <1 MB 2 MB 2 MB

3 <1 MB 2 MB 1 MB

4 <1 MB 2 MB 2 MB

5 <1 MB 3 MB 3 MB

6 <1 MB 3 MB 5 MB

7 <1 MB 3 MB 9 MB

8 <1 MB 4 MB 17 MB

9 <1 MB 4 MB 33 MB

RAM usage on decompression

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Спасибо за внимание!

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LZMA Докладчик : Гареев Роман email: [email protected].

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Transcript of LZMA Докладчик : Гареев Роман email: [email protected].