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diff --git a/src/3rdparty/zlib/doc/algorithm.txt b/src/3rdparty/zlib/doc/algorithm.txt new file mode 100644 index 0000000000..34960bddac --- /dev/null +++ b/src/3rdparty/zlib/doc/algorithm.txt @@ -0,0 +1,209 @@ +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://www.ietf.org/rfc/rfc1951.txt |