+++ /dev/null
-1. Compression algorithm (deflate)
-
-The deflation algorithm used by gzip (also zip and zlib) 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 process of lazy evaluation begins again. 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)
-
-2.1 Introduction
-
-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.
-
-
-2.2 More details on the inflate table lookup
-
-Ok, you want to know what this cleverly obfuscated inflate tree actually
-looks like. You are correct that it's not a Huffman tree. It is simply a
-lookup table for the first, let's say, nine bits of a Huffman symbol. The
-symbol could be as short as one bit or as long as 15 bits. If a particular
-symbol is shorter than nine bits, then that symbol's translation is duplicated
-in all those entries that start with that symbol's bits. For example, if the
-symbol is four bits, then it's duplicated 32 times in a nine-bit table. If a
-symbol is nine bits long, it appears in the table once.
-
-If the symbol is longer than nine bits, then that entry in the table points
-to another similar table for the remaining bits. Again, there are duplicated
-entries as needed. The idea is that most of the time the symbol will be short
-and there will only be one table look up. (That's whole idea behind data
-compression in the first place.) For the less frequent long symbols, there
-will be two lookups. If you had a compression method with really long
-symbols, you could have as many levels of lookups as is efficient. For
-inflate, two is enough.
-
-So a table entry either points to another table (in which case nine bits in
-the above example are gobbled), or it contains the translation for the symbol
-and the number of bits to gobble. Then you start again with the next
-ungobbled bit.
-
-You may wonder: why not just have one lookup table for how ever many bits the
-longest symbol is? The reason is that if you do that, you end up spending
-more time filling in duplicate symbol entries than you do actually decoding.
-At least for deflate's output that generates new trees every several 10's of
-kbytes. You can imagine that filling in a 2^15 entry table for a 15-bit code
-would take too long if you're only decoding several thousand symbols. At the
-other extreme, you could make a new table for every bit in the code. In fact,
-that's essentially a Huffman tree. But then you spend two much time
-traversing the tree while decoding, even for short symbols.
-
-So the number of bits for the first lookup table is a trade of the time to
-fill out the table vs. the time spent looking at the second level and above of
-the table.
-
-Here is an example, scaled down:
-
-The code being decoded, with 10 symbols, from 1 to 6 bits long:
-
-A: 0
-B: 10
-C: 1100
-D: 11010
-E: 11011
-F: 11100
-G: 11101
-H: 11110
-I: 111110
-J: 111111
-
-Let's make the first table three bits long (eight entries):
-
-000: A,1
-001: A,1
-010: A,1
-011: A,1
-100: B,2
-101: B,2
-110: -> table X (gobble 3 bits)
-111: -> table Y (gobble 3 bits)
-
-Each entry is what the bits decode to and how many bits that is, i.e. how
-many bits to gobble. Or the entry points to another table, with the number of
-bits to gobble implicit in the size of the table.
-
-Table X is two bits long since the longest code starting with 110 is five bits
-long:
-
-00: C,1
-01: C,1
-10: D,2
-11: E,2
-
-Table Y is three bits long since the longest code starting with 111 is six
-bits long:
-
-000: F,2
-001: F,2
-010: G,2
-011: G,2
-100: H,2
-101: H,2
-110: I,3
-111: J,3
-
-So what we have here are three tables with a total of 20 entries that had to
-be constructed. That's compared to 64 entries for a single table. Or
-compared to 16 entries for a Huffman tree (six two entry tables and one four
-entry table). Assuming that the code ideally represents the probability of
-the symbols, it takes on the average 1.25 lookups per symbol. That's compared
-to one lookup for the single table, or 1.66 lookups per symbol for the
-Huffman tree.
-
-There, I think that gives you a picture of what's going on. For inflate, the
-meaning of a particular symbol is often more than just a letter. It can be a
-byte (a "literal"), or it can be either a length or a distance which
-indicates a base value and a number of bits to fetch after the code that is
-added to the base value. Or it might be the special end-of-block code. The
-data structures created in inftrees.c try to encode all that information
-compactly in the tables.
-
-
-Jean-loup Gailly Mark Adler
-jloup@gzip.org 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
projects / rrdtool.git / blobdiff