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CVS patchset: 5197
CVS date: 2001/11/21 19:43:12

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+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