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diff --git a/zlib/doc/algorithm.txt b/zlib/doc/algorithm.txt deleted file mode 100644 index c97f495..0000000 --- a/zlib/doc/algorithm.txt +++ /dev/null @@ -1,209 +0,0 @@ -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 key question is how to represent a Huffman code (or any prefix code) so -that you can decode fast. The most important characteristic 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 then -to set that variable for the maximum speed. - -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. - - -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 too 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 as 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 -http://tools.ietf.org/html/rfc1951 |