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diff --git a/lib/libz/algorithm.doc b/lib/libz/algorithm.doc new file mode 100644 index 00000000000..01902aff666 --- /dev/null +++ b/lib/libz/algorithm.doc @@ -0,0 +1,105 @@ +1. Compression algorithm (deflate) + +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.) + +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 the behavior of LZW-based _compress_.) + +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. + +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. + +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. + +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. + +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. + +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. + + +2. Decompression algorithm (inflate) + +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. + +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. + +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. + +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. + + +Jean-loup Gailly Mark Adler +gzip@prep.ai.mit.edu madler@alumni.caltech.edu + + +References: + +[LZ77] Ziv J., Lempel A., ``A Universal Algorithm for Sequential Data +Compression,'' IEEE Transactions on Information Theory, Vol. 23, No. 3, +pp. 337-343. + +``DEFLATE Compressed Data Format Specification'' available in +ftp://ds.internic.net/rfc/rfc1951.txt |