1. Compression algorithm (deflate)The deflation algorithm used by gzip (also zip and zlib) is a variation ofLZ77 (Lempel-Ziv 1977, see reference below). It finds duplicated strings inthe input data.  The second occurrence of a string is replaced by apointer to the previous string, in the form of a pair (distance,length).  Distances are limited to 32K bytes, and lengths are limitedto 258 bytes. When a string does not occur anywhere in the previous32K bytes, it is emitted as a sequence of literal bytes.  (In thisdescription, `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, andmatch distances are compressed with another tree. The trees are storedin a compact form at the start of each block. The blocks can have anysize (except that the compressed data for one block must fit inavailable memory). A block is terminated when deflate() determines thatit would be useful to start another block with fresh trees. (This issomewhat similar to the behavior of LZW-based _compress_.)Duplicated strings are found using a hash table. All input strings oflength 3 are inserted in the hash table. A hash index is computed forthe next 3 bytes. If the hash chain for this index is not empty, allstrings in the chain are compared with the current input string, andthe longest match is selected.The hash chains are searched starting with the most recent strings, tofavor small distances and thus take advantage of the Huffman encoding.The hash chains are singly linked. There are no deletions from thehash chains, the algorithm simply discards matches that are too old.To avoid a worst-case situation, very long hash chains are arbitrarilytruncated at a certain length, determined by a runtime option (levelparameter of deflateInit). So deflate() does not always find the longestpossible match but generally finds a match which is long enough.deflate() also defers the selection of matches with a lazy evaluationmechanism. After a match of length N has been found, deflate() searches fora longer match at the next input byte. If a longer match is found, theprevious match is truncated to a length of one (thus producing a singleliteral byte) and the process of lazy evaluation begins again. Otherwise,the original match is kept, and the next match search is attempted only Nsteps later.The lazy match evaluation is also subject to a runtime parameter. Ifthe current match is long enough, deflate() reduces the search for a longermatch, thus speeding up the whole process. If compression ratio is moreimportant than speed, deflate() attempts a complete second search even ifthe first match is already long enough.The lazy match evaluation is not performed for the fastest compressionmodes (level parameter 1 to 3). For these fast modes, new stringsare inserted in the hash table only when no match was found, orwhen the match is not too long. This degrades the compression ratiobut saves time since there are both fewer insertions and fewer searches.2. Decompression algorithm (inflate)2.1 IntroductionThe key question is how to represent a Huffman code (or any prefix code) sothat you can decode fast.  The most important characteristic is that shortercodes are much more common than longer codes, so pay attention to decoding theshort codes fast, and let the long codes take longer to decode.inflate() sets up a first level table that covers some number of bits ofinput less than the length of longest code.  It gets that many bits from thestream, and looks it up in the table.  The table will tell if the nextcode is that many bits or less and how many, and if it is, it will tellthe 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 ittakes to decode and the time it takes to build the table.  If building thetable took no time (and if you had infinite memory), then there would onlybe 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 shortcodes are replicated many times in such a table.  What inflate() does issimply to make the number of bits in the first table a variable, and  thento set that variable for the maximum speed.For inflate, which has 286 possible codes for the literal/length tree, the sizeof the first table is nine bits.  Also the distance trees have 30 possiblevalues, and the size of the first table is six bits.  Note that for each ofthose cases, the table ended up one bit longer than the ``average'' codelength, i.e. the code length of an approximately flat code which would be alittle more than eight bits for 286 symbols and a little less than five bitsfor 30 symbols.2.2 More details on the inflate table lookupOk, you want to know what this cleverly obfuscated inflate tree actuallylooks like.  You are correct that it's not a Huffman tree.  It is simply alookup table for the first, let's say, nine bits of a Huffman symbol.  Thesymbol could be as short as one bit or as long as 15 bits.  If a particularsymbol is shorter than nine bits, then that symbol's translation is duplicatedin all those entries that start with that symbol's bits.  For example, if thesymbol is four bits, then it's duplicated 32 times in a nine-bit table.  If asymbol is nine bits long, it appears in the table once.If the symbol is longer than nine bits, then that entry in the table pointsto another similar table for the remaining bits.  Again, there are duplicatedentries as needed.  The idea is that most of the time the symbol will be shortand there will only be one table look up.  (That's whole idea behind datacompression in the first place.)  For the less frequent long symbols, therewill be two lookups.  If you had a compression method with really longsymbols, you could have as many levels of lookups as is efficient.  Forinflate, two is enough.So a table entry either points to another table (in which case nine bits inthe above example are gobbled), or it contains the translation for the symboland the number of bits to gobble.  Then you start again with the nextungobbled bit.You may wonder: why not just have one lookup table for how ever many bits thelongest symbol is?  The reason is that if you do that, you end up spendingmore 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 ofkbytes.  You can imagine that filling in a 2^15 entry table for a 15-bit codewould take too long if you're only decoding several thousand symbols.  At theother 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 timetraversing the tree while decoding, even for short symbols.So the number of bits for the first lookup table is a trade of the time tofill out the table vs. the time spent looking at the second level and above ofthe table.Here is an example, scaled down:The code being decoded, with 10 symbols, from 1 to 6 bits long:A: 0B: 10C: 1100D: 11010E: 11011F: 11100G: 11101H: 11110I: 111110J: 111111Let's make the first table three bits long (eight entries):000: A,1001: A,1010: A,1011: A,1100: B,2101: B,2110: -> 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. howmany bits to gobble.  Or the entry points to another table, with the number ofbits to gobble implicit in the size of the table.Table X is two bits long since the longest code starting with 110 is five bitslong:00: C,101: C,110: D,211: E,2Table Y is three bits long since the longest code starting with 111 is sixbits long:000: F,2001: F,2010: G,2011: G,2100: H,2101: H,2110: I,3111: J,3So what we have here are three tables with a total of 20 entries that had tobe constructed.  That's compared to 64 entries for a single table.  Orcompared to 16 entries for a Huffman tree (six two entry tables and one fourentry table).  Assuming that the code ideally represents the probability ofthe symbols, it takes on the average 1.25 lookups per symbol.  That's comparedto one lookup for the single table, or 1.66 lookups per symbol for theHuffman tree.There, I think that gives you a picture of what's going on.  For inflate, themeaning of a particular symbol is often more than just a letter.  It can be abyte (a "literal"), or it can be either a length or a distance whichindicates a base value and a number of bits to fetch after the code that isadded to the base value.  Or it might be the special end-of-block code.  Thedata structures created in inftrees.c try to encode all that informationcompactly in the tables.Jean-loup Gailly        Mark Adlerjloup@gzip.org          madler@alumni.caltech.eduReferences:[LZ77] Ziv J., Lempel A., ``A Universal Algorithm for Sequential DataCompression,'' IEEE Transactions on Information Theory, Vol. 23, No. 3,pp. 337-343.``DEFLATE Compressed Data Format Specification'' available inhttp://www.ietf.org/rfc/rfc1951.txt