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Hear such events MSN 3289 ordered 17th cavalry silver gundog bits 8 offset 17, 3 extra bits 28 offset 16385, 13 extra bits The format allows either a default or a custom Huffman code. The default code lengths are as follows: Literal length 0 8 bits 144 9 bits 256 7 bits 280 8 bits Offset 0 5 bits If a custom Huffman table is used, then the table is transmitted as a sequence of code lengths. That sequence is itself compressed by run length encoding using another Huffman code to encode the literals and run lengths. It uses a 19 symbol alphabet: 0 code lengths of 0 16 copy the previous code 3 times, followed by 2 extra bits 17 copy 3 times, 3 extra bits 18 copy 11 times, 7 extra bits The Huffman table for these codes are sent as a sequence of up to 19-bit numbers. This sequence is further compressed by reordering the sequence that the values most likely to be 0 are at the end, and sending the sequence only up to the last nonzero value. A 4 bit number indicates the sequence length. The order is: 16, 18, 8, 9, 10, 11, 12, 13, 14, 15. All Huffman codes are packed LSB to MSB order. zip and gzip take option -1 through -9 to select compression level at the expense of speed. All options produce compressed data deflate format which decompresses at the same speed with the same algorithm. The difference is that with the higher options, the compressor spends more time looking for encodings that compress better. A typical implementation keep a list of 3 byte matches a hash table and test the following data to find the longest match. With a higher option, the compressor spend more time searching. It is also sometimes possible to improve compression by encoding a literal even if a match is found, if it results a longer match starting at the next byte. Such testing also increases compression time. kzip performs extreme level of optimizations like this. Compressed sizes and compression times on a 2 GHz T3200 are shown below for the 14 file Calgary corpus. Program Size Time zip -1,194 .17 sec. zip -2,151 .23 zip -3,115 .25 zip -4,072 .25 zip -5,041 .33 zip -6,028 .40 zip -7,025 .42 zip -8,021 .50 zip -9,020 .67 kzip 978 24 unzip .10 LZMA. LZMA is the native compression mode of 7-zip. Although 7-zip is open source, the algorithm was never well documented or described until it was analyzed by Bloom Aug. 2010. Compression is improved over LZ77 by using a longer history buffer optimal parsing, shorter codes for recently repeated matches literal exclusion after matches, and arithmetic coding. Optimal parsing. Simple LZ77 uses greedy parsing. The next byte is always coded using the longest match found the history buffer. 7-zip uses look-ahead to consider a shorter match or a literal if it allows a longer match to be coded afterward with a shorter total code length. Matias and Sahinalp proved that for any dictionary encoding method with the prefix property, that there is a fast algorithm that optimally parses the input into the minimum number of phrases by looking only at the lengths of the next two phrases considered. A dictionary has the prefix property if for any phrase it, all of its prefixes are also the dictionary. LZ77 and LZW both have this property. However, optimal parsing is more difficult to achieve practice because phrases have different code lengths, that the minimum number of phrases does not necessarily give the best compression. Repeated matches. 7-zip uses shorter codes to code the 3 most recent matches place of the LZ77 offset. the case of the most recent match, the match length can be as small as 1. Literal exclusion after matches. 7-zip uses a literal to code the first literal after the match. The idea is that the literal to be coded is known to be different than the predicted byte following the match the history buffer. ordinary context model would incorrectly assign a high probability to the predicted byte, which would waste code space. To prevent this, the coded literal is exclusive-ored with the predicted byte. Coding. 7-zip uses a binary arithmetic coder. It first codes one of 4 possible choices: literal, match, rep or short rep A literal code is followed by the 8 bits of the coded byte MSB to LSB order. A match is coded as a length followed by the offset, each using a variable length code which the length of the binary value