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| Original file line number | Diff line number | Diff line change |
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| 1. Compression algorithm (deflate) | ||
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| The deflation algorithm used by zlib (also zip and gzip) is a variation of | ||
| LZ77 (Lempel-Ziv 1977, see reference below). It finds duplicated strings in | ||
| the input data. The second occurrence of a string is replaced by a | ||
| pointer to the previous string, in the form of a pair (distance, | ||
| length). Distances are limited to 32K bytes, and lengths are limited | ||
| to 258 bytes. When a string does not occur anywhere in the previous | ||
| 32K bytes, it is emitted as a sequence of literal bytes. (In this | ||
| description, 'string' must be taken as an arbitrary sequence of bytes, | ||
| and is not restricted to printable characters.) | ||
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| Literals or match lengths are compressed with one Huffman tree, and | ||
| match distances are compressed with another tree. The trees are stored | ||
| in a compact form at the start of each block. The blocks can have any | ||
| size (except that the compressed data for one block must fit in | ||
| available memory). A block is terminated when deflate() determines that | ||
| it would be useful to start another block with fresh trees. (This is | ||
| somewhat similar to compress.) | ||
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| Duplicated strings are found using a hash table. All input strings of | ||
| length 3 are inserted in the hash table. A hash index is computed for | ||
| the next 3 bytes. If the hash chain for this index is not empty, all | ||
| strings in the chain are compared with the current input string, and | ||
| the longest match is selected. | ||
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| The hash chains are searched starting with the most recent strings, to | ||
| favor small distances and thus take advantage of the Huffman encoding. | ||
| The hash chains are singly linked. There are no deletions from the | ||
| hash chains, the algorithm simply discards matches that are too old. | ||
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| To avoid a worst-case situation, very long hash chains are arbitrarily | ||
| truncated at a certain length, determined by a runtime option (level | ||
| parameter of deflateInit). So deflate() does not always find the longest | ||
| possible match but generally finds a match which is long enough. | ||
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| deflate() also defers the selection of matches with a lazy evaluation | ||
| mechanism. After a match of length N has been found, deflate() searches for a | ||
| longer match at the next input byte. If a longer match is found, the | ||
| previous match is truncated to a length of one (thus producing a single | ||
| literal byte) and the longer match is emitted afterwards. Otherwise, | ||
| the original match is kept, and the next match search is attempted only | ||
| N steps later. | ||
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| The lazy match evaluation is also subject to a runtime parameter. If | ||
| the current match is long enough, deflate() reduces the search for a longer | ||
| match, thus speeding up the whole process. If compression ratio is more | ||
| important than speed, deflate() attempts a complete second search even if | ||
| the first match is already long enough. | ||
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| The lazy match evaluation is not performed for the fastest compression | ||
| modes (level parameter 1 to 3). For these fast modes, new strings | ||
| are inserted in the hash table only when no match was found, or | ||
| when the match is not too long. This degrades the compression ratio | ||
| but saves time since there are both fewer insertions and fewer searches. | ||
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| 2. Decompression algorithm (inflate) | ||
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| The real question is given a Huffman tree, how to decode fast. The most | ||
| important realization is that shorter codes are much more common than | ||
| longer codes, so pay attention to decoding the short codes fast, and let | ||
| the long codes take longer to decode. | ||
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| inflate() sets up a first level table that covers some number of bits of | ||
| input less than the length of longest code. It gets that many bits from the | ||
| stream, and looks it up in the table. The table will tell if the next | ||
| code is that many bits or less and how many, and if it is, it will tell | ||
| the value, else it will point to the next level table for which inflate() | ||
| grabs more bits and tries to decode a longer code. | ||
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| How many bits to make the first lookup is a tradeoff between the time it | ||
| takes to decode and the time it takes to build the table. If building the | ||
| table took no time (and if you had infinite memory), then there would only | ||
| be a first level table to cover all the way to the longest code. However, | ||
| building the table ends up taking a lot longer for more bits since short | ||
| codes are replicated many times in such a table. What inflate() does is | ||
| simply to make the number of bits in the first table a variable, and set it | ||
| for the maximum speed. | ||
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| inflate() sends new trees relatively often, so it is possibly set for a | ||
| smaller first level table than an application that has only one tree for | ||
| all the data. For inflate, which has 286 possible codes for the | ||
| literal/length tree, the size of the first table is nine bits. Also the | ||
| distance trees have 30 possible values, and the size of the first table is | ||
| six bits. Note that for each of those cases, the table ended up one bit | ||
| longer than the "average" code length, i.e. the code length of an | ||
| approximately flat code which would be a little more than eight bits for | ||
| 286 symbols and a little less than five bits for 30 symbols. It would be | ||
| interesting to see if optimizing the first level table for other | ||
| applications gave values within a bit or two of the flat code size. | ||
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| Jean-loup Gailly Mark Adler | ||
| gzip@prep.ai.mit.edu madler@alumni.caltech.edu | ||
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| References: | ||
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| [LZ77] Ziv J., Lempel A., "A Universal Algorithm for Sequential Data | ||
| Compression", IEEE Transactions on Information Theory", Vol. 23, No. 3, | ||
| pp. 337-343. | ||
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| "DEFLATE Compressed Data Format Specification" available in | ||
| ftp://ds.internic.net/rfc/rfc1951.txt |
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