LZMA Докладчик : Гареев Роман

LZMA (Lempel-Ziv-Markov chain-Algorithm) 7z(7-Zip) LZMA SDK 2 /31

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LZMA: LZ77(Sliding Window) Deflate: Zip and Gzip Range Encoding 5

Jacob ZivAbraham Lempel LZ77 (Sliding Window) 6 /31

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. 7 /31

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”) 8 /31

a10.4 a20.2 a30.2 a40.1 a50.1 Hu ff man Coding a5 a4 a3 a2 a1 a45 a345 a2345 a /31

Phillip Katz Deflate: Zip and Gzip 10 /31

( сдвиг, длина, символ ) Закодированный текст … old...she needs..then…there… the new... Текст для пр … Режимы : Normal High-compression Fast ⇒ ( сдвиг, длина ) 11 /31 Режимы сжатия : Без сжатия Сжатие с фиксированным размером таблиц Сжатие с индивидуальными таблицами, создаваемыми для текущей информации

“range encoding” “Handbook of Data Compression” David Salomon, Giovanni Motta 12 /31

Закодированный текст … … the new... Текст для пр … “hash-chain”, “binary-tree” 13 /31 bt2 Binary Tree with 2 bytes hashing bt3 Binary Tree with 3 bytes hashing bt4 Binary Tree with 4 bytes hashing hc4 Hash Chain with 4 bytes hashing LZMA индекс

14 /31 Hash-chain XY 123 …… …… … … 24 …

15 /31 …abm…abcd2…abcx…abcd1…aby… Binary-tree abm… abcd2… abcd1… abm… abcx… abm… abcx… aby…

Пример реализации LZMA( реализация на JAVA из LZMA SDK) 16 /31

LZMA SDK 2004 ANSI-C/C++/C#/Java lzma.exe lzma.txt 7zFormat.txt history.txt 17 /31

Основные характеристики LZMA SDK Различный размер словаря Предполагаемая скорость сжатия : около 2MB/s на 2 GHz CPU Предполагаемая скорость распаковки : MB/s на 2 GHz Core 2 или AMD Athlon MB/s на 200 MHz RISC Небольшое количество затрат памяти для распаковки (16 KB + размер словаря ) Поддержка многопоточности 18 /31

Основные опции LZMA SDK a{N} Режим сжатия. 0, 1, 2 fast, normal, max -d{N} -si -so -mf{MF_ID} 19 /31 MF_ID Memory Description bt2 d * MB Binary Tree с 2 байтным хэшированием bt3 d * MB Binary Tree с 3 байтным хэшированием bt4 d * MB Binary Tree с 4 байтным хэшированием hc4 d * MB Hash Chain с 4 байтным хэшированием

20 /31 Lasse Collin

Сравнение Gzip, Bzip2 и LZMA AMD mobile Athlon XP MB RAM Linux gzip 1.3.3, bzip , LZMA SDK 4.17 (lzmash) Обращалось внимание на : размер файлов после сжатия время распаковки память, требуемая для распаковки обычный формат, который все знают 21 /31

Tar archive OpenOffice.org 1.1.4(Linux) (203 MB) 22 /31 gzipbzip2lzmash 140,6%35,8%31,7% 239,9%34,9%29,2% 339,3%34,5%28,0% 438,2%34,3%27,4% 537,5%34,2%26,7% 637,2%34,1%26,4% 737,1%34,1%26,1% 837,1%34,0%25,7% 937,0%34,0%25,4% Compressed size / Uncompressed size * 100%

Tar archive OpenOffice.org 1.1.4(Linux) (203 MB) 23 /31 gzipbzip2lzmash 111.5s1m 26s0m 58s 212.0s1m 40s2m 7s 313.7s1m 54s4m 58s 415.1s2m 5s5m 26s 518.4s2m 11s6m 47s 624.5s2m 18s7m 30s 729.4s2m 25s8m 24s 845.5s2m 32s10m 59s 966.9s2m 37s12m 20s Compression time gzipbzip2lzmash 13.3s16.5s11.3s 23.3s24.2s10.5s 33.3s29.2s10.5s 43.3s32.1s10.4s 53.2s34.2s10.2s 63.2s35.4s10.2s 73.2s36.5s10.1s 83.2s37.5s10.0s 93.1s38.2s10.0s Decompression time

Tar archive The Linux kernel source (199 MB) 24 /31 gzipbzip2lzmash 127,8%21,1% 226,5%19,7%18,7% 325,7%19,1%16,7% 423,9%18,7%16,1% 522,9%18,4%15,6% 622,6%18,2%15,2% 722,5%18,1%14,8% 822,4%17,9%14,5% 922,4%17,8%14,3% Compressed size / Uncompressed size * 100%

Tar archive The Linux kernel source (199 MB) 25 /31 gzipbzip2lzmash 18.3s1m 9s0m 45s 28.7s1m 22s1m 45s 39.8s1m 34s5m 10s 411.1s1m 45s5m 43s 513.8s1m 57s7m 39s 617.8s2m 2s8m 23s 720.7s2m 11s9m 11s 829.7s2m 21s11m 34s 940.9s2m 26s12m 31s Compression time gzipbzip2lzmash 12.8s12.8s7.7s 22.7s19.4s6.9s 32.6s23.8s6.4s 42.5s26.4s6.3s 52.5s28.3s6.3s 62.4s29.6s6.2s 72.4s30.6s6.2s 82.4s31.3s6.1s 92.4s32.1s6.1s Decompression time

XMMS binary package (5.2 MB)(Slackware 10.1) 26 /31 gzipbzip2lzmash 139,3%32,8%26,0% 238,4%29,3%20,7% 337,7%28,0%18,8% 436,9%27,0%18,3% 536,2%26,6%18,0% 636,0%26,1%17,9% 735,9%26,0%17,9% 835,9%25,7%17,8% 935,8%25,2%17,8% Compressed size / Uncompressed size * 100%

XMMS binary package (5.2 MB)(Slackware 10.1) 27 /31 gzipbzip2lzmash 10.3s2.4s1.4s 20.3s2.9s2.7s 30.4s3.2s6.2s 40.4s3.3s6.6s 50.5s4.6s8.2s 60.7s5.6s8.5s 70.8s4.7s8.6s 81.1s4.9s10.5s 91.8s5.1s10.5s Compression time gzipbzip2lzmash 10.1s0.4s0.3s 20.1s0.6s0.2s 30.1s0.7s0.2s 40.1s0.8s0.2s 50.1s0.9s0.2s 60.1s0.9s0.2s 70.1s0.9s0.2s 80.1s1.0s0.2s 90.1s1.0s0.2s Decompression time

XMMS source tarball (15.2 MB) 28 /31 gzipbzip2lzmash 129,5%23,2%21,2% 228,6%19,9%13,3% 327,9%18,3%12,0% 426,4%17,2%11,3% 525,7%16,7%10,8% 625,4%16,2%10,3% 725,3%15,7%9,7% 825,3%15,4%9,6% 925,3%15,1%9,6% Compressed size / Uncompressed size * 100%

XMMS source tarball (15.2 MB) 29 /31 gzipbzip2lzmash 10.7s6.1s3.5s 20.7s7.3s6.0s 30.8s8.5s19.0s 40.9s9.9s19.9s 51.1s11.2s28.9s 61.4s11.0s30.1s 71.7s12.5s30.9s 82.5s15.9s41.7s 92.9s17.5s41.7s Compression time gzipbzip2lzmash 10.2s1.0s0.6s 20.2s1.5s0.4s 30.2s1.9s0.4s 40.2s2.1s0.4s 50.2s2.3s0.4s 60.2s2.5s0.4s 70.2s2.6s0.4s 80.2s2.7s0.4s 90.2s2.8s0.4s Decompression time

Memory requirements 30 /31 gzipbzip2lzmash 1<1 MB2 MB 2<1 MB2 MB12 MB 3<1 MB3 MB12 MB 4<1 MB4 MB16 MB 5<1 MB5 MB26 MB 6<1 MB5 MB45 MB 7<1 MB6 MB83 MB 8<1 MB7 MB159 MB 9<1 MB7 MB311 MB RAM usage on compression gzipbzip2lzmash 1<1 MB1 MB 2<1 MB2 MB 3<1 MB2 MB1 MB 4<1 MB2 MB 5<1 MB3 MB 6<1 MB3 MB5 MB 7<1 MB3 MB9 MB 8<1 MB4 MB17 MB 9<1 MB4 MB33 MB RAM usage on decompression

Спасибо за внимание ! 31 /31