199767f8919635c4928607450d9e0abb932109ceToomas Soome1. Compression algorithm (deflate)
199767f8919635c4928607450d9e0abb932109ceToomas SoomeThe deflation algorithm used by gzip (also zip and zlib) is a variation of
199767f8919635c4928607450d9e0abb932109ceToomas SoomeLZ77 (Lempel-Ziv 1977, see reference below). It finds duplicated strings in
199767f8919635c4928607450d9e0abb932109ceToomas Soomethe input data. The second occurrence of a string is replaced by a
199767f8919635c4928607450d9e0abb932109ceToomas Soomepointer to the previous string, in the form of a pair (distance,
199767f8919635c4928607450d9e0abb932109ceToomas Soomelength). Distances are limited to 32K bytes, and lengths are limited
199767f8919635c4928607450d9e0abb932109ceToomas Soometo 258 bytes. When a string does not occur anywhere in the previous
199767f8919635c4928607450d9e0abb932109ceToomas Soome32K bytes, it is emitted as a sequence of literal bytes. (In this
199767f8919635c4928607450d9e0abb932109ceToomas Soomedescription, `string' must be taken as an arbitrary sequence of bytes,
199767f8919635c4928607450d9e0abb932109ceToomas Soomeand is not restricted to printable characters.)
199767f8919635c4928607450d9e0abb932109ceToomas SoomeLiterals or match lengths are compressed with one Huffman tree, and
199767f8919635c4928607450d9e0abb932109ceToomas Soomematch distances are compressed with another tree. The trees are stored
199767f8919635c4928607450d9e0abb932109ceToomas Soomein a compact form at the start of each block. The blocks can have any
199767f8919635c4928607450d9e0abb932109ceToomas Soomesize (except that the compressed data for one block must fit in
199767f8919635c4928607450d9e0abb932109ceToomas Soomeavailable memory). A block is terminated when deflate() determines that
199767f8919635c4928607450d9e0abb932109ceToomas Soomeit would be useful to start another block with fresh trees. (This is
199767f8919635c4928607450d9e0abb932109ceToomas Soomesomewhat similar to the behavior of LZW-based _compress_.)
199767f8919635c4928607450d9e0abb932109ceToomas SoomeDuplicated strings are found using a hash table. All input strings of
199767f8919635c4928607450d9e0abb932109ceToomas Soomelength 3 are inserted in the hash table. A hash index is computed for
199767f8919635c4928607450d9e0abb932109ceToomas Soomethe next 3 bytes. If the hash chain for this index is not empty, all
199767f8919635c4928607450d9e0abb932109ceToomas Soomestrings in the chain are compared with the current input string, and
199767f8919635c4928607450d9e0abb932109ceToomas Soomethe longest match is selected.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeThe hash chains are searched starting with the most recent strings, to
199767f8919635c4928607450d9e0abb932109ceToomas Soomefavor small distances and thus take advantage of the Huffman encoding.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeThe hash chains are singly linked. There are no deletions from the
199767f8919635c4928607450d9e0abb932109ceToomas Soomehash chains, the algorithm simply discards matches that are too old.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeTo avoid a worst-case situation, very long hash chains are arbitrarily
199767f8919635c4928607450d9e0abb932109ceToomas Soometruncated at a certain length, determined by a runtime option (level
199767f8919635c4928607450d9e0abb932109ceToomas Soomeparameter of deflateInit). So deflate() does not always find the longest
199767f8919635c4928607450d9e0abb932109ceToomas Soomepossible match but generally finds a match which is long enough.
199767f8919635c4928607450d9e0abb932109ceToomas Soomedeflate() also defers the selection of matches with a lazy evaluation
199767f8919635c4928607450d9e0abb932109ceToomas Soomemechanism. After a match of length N has been found, deflate() searches for
199767f8919635c4928607450d9e0abb932109ceToomas Soomea longer match at the next input byte. If a longer match is found, the
199767f8919635c4928607450d9e0abb932109ceToomas Soomeprevious match is truncated to a length of one (thus producing a single
199767f8919635c4928607450d9e0abb932109ceToomas Soomeliteral byte) and the process of lazy evaluation begins again. Otherwise,
199767f8919635c4928607450d9e0abb932109ceToomas Soomethe original match is kept, and the next match search is attempted only N
199767f8919635c4928607450d9e0abb932109ceToomas SoomeThe lazy match evaluation is also subject to a runtime parameter. If
199767f8919635c4928607450d9e0abb932109ceToomas Soomethe current match is long enough, deflate() reduces the search for a longer
199767f8919635c4928607450d9e0abb932109ceToomas Soomematch, thus speeding up the whole process. If compression ratio is more
199767f8919635c4928607450d9e0abb932109ceToomas Soomeimportant than speed, deflate() attempts a complete second search even if
199767f8919635c4928607450d9e0abb932109ceToomas Soomethe first match is already long enough.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeThe lazy match evaluation is not performed for the fastest compression
199767f8919635c4928607450d9e0abb932109ceToomas Soomemodes (level parameter 1 to 3). For these fast modes, new strings
199767f8919635c4928607450d9e0abb932109ceToomas Soomeare inserted in the hash table only when no match was found, or
199767f8919635c4928607450d9e0abb932109ceToomas Soomewhen the match is not too long. This degrades the compression ratio
199767f8919635c4928607450d9e0abb932109ceToomas Soomebut saves time since there are both fewer insertions and fewer searches.
199767f8919635c4928607450d9e0abb932109ceToomas Soome2. Decompression algorithm (inflate)
199767f8919635c4928607450d9e0abb932109ceToomas Soome2.1 Introduction
199767f8919635c4928607450d9e0abb932109ceToomas SoomeThe key question is how to represent a Huffman code (or any prefix code) so
199767f8919635c4928607450d9e0abb932109ceToomas Soomethat you can decode fast. The most important characteristic is that shorter
199767f8919635c4928607450d9e0abb932109ceToomas Soomecodes are much more common than longer codes, so pay attention to decoding the
199767f8919635c4928607450d9e0abb932109ceToomas Soomeshort codes fast, and let the long codes take longer to decode.
199767f8919635c4928607450d9e0abb932109ceToomas Soomeinflate() sets up a first level table that covers some number of bits of
199767f8919635c4928607450d9e0abb932109ceToomas Soomeinput less than the length of longest code. It gets that many bits from the
199767f8919635c4928607450d9e0abb932109ceToomas Soomestream, and looks it up in the table. The table will tell if the next
199767f8919635c4928607450d9e0abb932109ceToomas Soomecode is that many bits or less and how many, and if it is, it will tell
199767f8919635c4928607450d9e0abb932109ceToomas Soomethe value, else it will point to the next level table for which inflate()
199767f8919635c4928607450d9e0abb932109ceToomas Soomegrabs more bits and tries to decode a longer code.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeHow many bits to make the first lookup is a tradeoff between the time it
199767f8919635c4928607450d9e0abb932109ceToomas Soometakes to decode and the time it takes to build the table. If building the
199767f8919635c4928607450d9e0abb932109ceToomas Soometable took no time (and if you had infinite memory), then there would only
199767f8919635c4928607450d9e0abb932109ceToomas Soomebe a first level table to cover all the way to the longest code. However,
199767f8919635c4928607450d9e0abb932109ceToomas Soomebuilding the table ends up taking a lot longer for more bits since short
199767f8919635c4928607450d9e0abb932109ceToomas Soomecodes are replicated many times in such a table. What inflate() does is
199767f8919635c4928607450d9e0abb932109ceToomas Soomesimply to make the number of bits in the first table a variable, and then
199767f8919635c4928607450d9e0abb932109ceToomas Soometo set that variable for the maximum speed.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeFor inflate, which has 286 possible codes for the literal/length tree, the size
199767f8919635c4928607450d9e0abb932109ceToomas Soomeof the first table is nine bits. Also the distance trees have 30 possible
199767f8919635c4928607450d9e0abb932109ceToomas Soomevalues, and the size of the first table is six bits. Note that for each of
199767f8919635c4928607450d9e0abb932109ceToomas Soomethose cases, the table ended up one bit longer than the ``average'' code
199767f8919635c4928607450d9e0abb932109ceToomas Soomelength, i.e. the code length of an approximately flat code which would be a
199767f8919635c4928607450d9e0abb932109ceToomas Soomelittle more than eight bits for 286 symbols and a little less than five bits
199767f8919635c4928607450d9e0abb932109ceToomas Soomefor 30 symbols.
199767f8919635c4928607450d9e0abb932109ceToomas Soome2.2 More details on the inflate table lookup
199767f8919635c4928607450d9e0abb932109ceToomas SoomeOk, you want to know what this cleverly obfuscated inflate tree actually
199767f8919635c4928607450d9e0abb932109ceToomas Soomelooks like. You are correct that it's not a Huffman tree. It is simply a
199767f8919635c4928607450d9e0abb932109ceToomas Soomelookup table for the first, let's say, nine bits of a Huffman symbol. The
199767f8919635c4928607450d9e0abb932109ceToomas Soomesymbol could be as short as one bit or as long as 15 bits. If a particular
199767f8919635c4928607450d9e0abb932109ceToomas Soomesymbol is shorter than nine bits, then that symbol's translation is duplicated
199767f8919635c4928607450d9e0abb932109ceToomas Soomein all those entries that start with that symbol's bits. For example, if the
199767f8919635c4928607450d9e0abb932109ceToomas Soomesymbol is four bits, then it's duplicated 32 times in a nine-bit table. If a
199767f8919635c4928607450d9e0abb932109ceToomas Soomesymbol is nine bits long, it appears in the table once.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeIf the symbol is longer than nine bits, then that entry in the table points
199767f8919635c4928607450d9e0abb932109ceToomas Soometo another similar table for the remaining bits. Again, there are duplicated
199767f8919635c4928607450d9e0abb932109ceToomas Soomeentries as needed. The idea is that most of the time the symbol will be short
199767f8919635c4928607450d9e0abb932109ceToomas Soomeand there will only be one table look up. (That's whole idea behind data
199767f8919635c4928607450d9e0abb932109ceToomas Soomecompression in the first place.) For the less frequent long symbols, there
199767f8919635c4928607450d9e0abb932109ceToomas Soomewill be two lookups. If you had a compression method with really long
199767f8919635c4928607450d9e0abb932109ceToomas Soomesymbols, you could have as many levels of lookups as is efficient. For
199767f8919635c4928607450d9e0abb932109ceToomas Soomeinflate, two is enough.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeSo a table entry either points to another table (in which case nine bits in
199767f8919635c4928607450d9e0abb932109ceToomas Soomethe above example are gobbled), or it contains the translation for the symbol
199767f8919635c4928607450d9e0abb932109ceToomas Soomeand the number of bits to gobble. Then you start again with the next
199767f8919635c4928607450d9e0abb932109ceToomas Soomeungobbled bit.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeYou may wonder: why not just have one lookup table for how ever many bits the
199767f8919635c4928607450d9e0abb932109ceToomas Soomelongest symbol is? The reason is that if you do that, you end up spending
199767f8919635c4928607450d9e0abb932109ceToomas Soomemore time filling in duplicate symbol entries than you do actually decoding.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeAt least for deflate's output that generates new trees every several 10's of
199767f8919635c4928607450d9e0abb932109ceToomas Soomekbytes. You can imagine that filling in a 2^15 entry table for a 15-bit code
199767f8919635c4928607450d9e0abb932109ceToomas Soomewould take too long if you're only decoding several thousand symbols. At the
199767f8919635c4928607450d9e0abb932109ceToomas Soomeother extreme, you could make a new table for every bit in the code. In fact,
199767f8919635c4928607450d9e0abb932109ceToomas Soomethat's essentially a Huffman tree. But then you spend too much time
199767f8919635c4928607450d9e0abb932109ceToomas Soometraversing the tree while decoding, even for short symbols.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeSo the number of bits for the first lookup table is a trade of the time to
199767f8919635c4928607450d9e0abb932109ceToomas Soomefill out the table vs. the time spent looking at the second level and above of
199767f8919635c4928607450d9e0abb932109ceToomas SoomeHere is an example, scaled down:
199767f8919635c4928607450d9e0abb932109ceToomas SoomeThe code being decoded, with 10 symbols, from 1 to 6 bits long:
199767f8919635c4928607450d9e0abb932109ceToomas SoomeLet's make the first table three bits long (eight entries):
199767f8919635c4928607450d9e0abb932109ceToomas Soome110: -> table X (gobble 3 bits)
199767f8919635c4928607450d9e0abb932109ceToomas Soome111: -> table Y (gobble 3 bits)
199767f8919635c4928607450d9e0abb932109ceToomas SoomeEach entry is what the bits decode as and how many bits that is, i.e. how
199767f8919635c4928607450d9e0abb932109ceToomas Soomemany bits to gobble. Or the entry points to another table, with the number of
199767f8919635c4928607450d9e0abb932109ceToomas Soomebits to gobble implicit in the size of the table.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeTable X is two bits long since the longest code starting with 110 is five bits
199767f8919635c4928607450d9e0abb932109ceToomas SoomeTable Y is three bits long since the longest code starting with 111 is six
199767f8919635c4928607450d9e0abb932109ceToomas SoomeSo what we have here are three tables with a total of 20 entries that had to
199767f8919635c4928607450d9e0abb932109ceToomas Soomebe constructed. That's compared to 64 entries for a single table. Or
199767f8919635c4928607450d9e0abb932109ceToomas Soomecompared to 16 entries for a Huffman tree (six two entry tables and one four
199767f8919635c4928607450d9e0abb932109ceToomas Soomeentry table). Assuming that the code ideally represents the probability of
199767f8919635c4928607450d9e0abb932109ceToomas Soomethe symbols, it takes on the average 1.25 lookups per symbol. That's compared
199767f8919635c4928607450d9e0abb932109ceToomas Soometo one lookup for the single table, or 1.66 lookups per symbol for the
199767f8919635c4928607450d9e0abb932109ceToomas SoomeHuffman tree.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeThere, I think that gives you a picture of what's going on. For inflate, the
199767f8919635c4928607450d9e0abb932109ceToomas Soomemeaning of a particular symbol is often more than just a letter. It can be a
199767f8919635c4928607450d9e0abb932109ceToomas Soomebyte (a "literal"), or it can be either a length or a distance which
199767f8919635c4928607450d9e0abb932109ceToomas Soomeindicates a base value and a number of bits to fetch after the code that is
199767f8919635c4928607450d9e0abb932109ceToomas Soomeadded to the base value. Or it might be the special end-of-block code. The
199767f8919635c4928607450d9e0abb932109ceToomas Soomedata structures created in inftrees.c try to encode all that information
199767f8919635c4928607450d9e0abb932109ceToomas Soomecompactly in the tables.
199767f8919635c4928607450d9e0abb932109ceToomas SoomeJean-loup Gailly Mark Adler
199767f8919635c4928607450d9e0abb932109ceToomas Soomejloup@gzip.org madler@alumni.caltech.edu
199767f8919635c4928607450d9e0abb932109ceToomas Soome[LZ77] Ziv J., Lempel A., ``A Universal Algorithm for Sequential Data
199767f8919635c4928607450d9e0abb932109ceToomas SoomeCompression,'' IEEE Transactions on Information Theory, Vol. 23, No. 3,
199767f8919635c4928607450d9e0abb932109ceToomas Soome``DEFLATE Compressed Data Format Specification'' available in