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