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root/middleware-offline/trunk/_src/eidmw/FreeImagePTEiD/Source/ZLib/algorithm.txt
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1 | 1. Compression algorithm (deflate) |

2 | |

3 | The deflation algorithm used by gzip (also zip and zlib) is a variation of |

4 | LZ77 (Lempel-Ziv 1977, see reference below). It finds duplicated strings in |

5 | the input data. The second occurrence of a string is replaced by a |

6 | pointer to the previous string, in the form of a pair (distance, |

7 | length). Distances are limited to 32K bytes, and lengths are limited |

8 | to 258 bytes. When a string does not occur anywhere in the previous |

9 | 32K bytes, it is emitted as a sequence of literal bytes. (In this |

10 | description, `string' must be taken as an arbitrary sequence of bytes, |

11 | and is not restricted to printable characters.) |

12 | |

13 | Literals or match lengths are compressed with one Huffman tree, and |

14 | match distances are compressed with another tree. The trees are stored |

15 | in a compact form at the start of each block. The blocks can have any |

16 | size (except that the compressed data for one block must fit in |

17 | available memory). A block is terminated when deflate() determines that |

18 | it would be useful to start another block with fresh trees. (This is |

19 | somewhat similar to the behavior of LZW-based _compress_.) |

20 | |

21 | Duplicated strings are found using a hash table. All input strings of |

22 | length 3 are inserted in the hash table. A hash index is computed for |

23 | the next 3 bytes. If the hash chain for this index is not empty, all |

24 | strings in the chain are compared with the current input string, and |

25 | the longest match is selected. |

26 | |

27 | The hash chains are searched starting with the most recent strings, to |

28 | favor small distances and thus take advantage of the Huffman encoding. |

29 | The hash chains are singly linked. There are no deletions from the |

30 | hash chains, the algorithm simply discards matches that are too old. |

31 | |

32 | To avoid a worst-case situation, very long hash chains are arbitrarily |

33 | truncated at a certain length, determined by a runtime option (level |

34 | parameter of deflateInit). So deflate() does not always find the longest |

35 | possible match but generally finds a match which is long enough. |

36 | |

37 | deflate() also defers the selection of matches with a lazy evaluation |

38 | mechanism. After a match of length N has been found, deflate() searches for |

39 | a longer match at the next input byte. If a longer match is found, the |

40 | previous match is truncated to a length of one (thus producing a single |

41 | literal byte) and the process of lazy evaluation begins again. Otherwise, |

42 | the original match is kept, and the next match search is attempted only N |

43 | steps later. |

44 | |

45 | The lazy match evaluation is also subject to a runtime parameter. If |

46 | the current match is long enough, deflate() reduces the search for a longer |

47 | match, thus speeding up the whole process. If compression ratio is more |

48 | important than speed, deflate() attempts a complete second search even if |

49 | the first match is already long enough. |

50 | |

51 | The lazy match evaluation is not performed for the fastest compression |

52 | modes (level parameter 1 to 3). For these fast modes, new strings |

53 | are inserted in the hash table only when no match was found, or |

54 | when the match is not too long. This degrades the compression ratio |

55 | but saves time since there are both fewer insertions and fewer searches. |

56 | |

57 | |

58 | 2. Decompression algorithm (inflate) |

59 | |

60 | 2.1 Introduction |

61 | |

62 | The key question is how to represent a Huffman code (or any prefix code) so |

63 | that you can decode fast. The most important characteristic is that shorter |

64 | codes are much more common than longer codes, so pay attention to decoding the |

65 | short codes fast, and let the long codes take longer to decode. |

66 | |

67 | inflate() sets up a first level table that covers some number of bits of |

68 | input less than the length of longest code. It gets that many bits from the |

69 | stream, and looks it up in the table. The table will tell if the next |

70 | code is that many bits or less and how many, and if it is, it will tell |

71 | the value, else it will point to the next level table for which inflate() |

72 | grabs more bits and tries to decode a longer code. |

73 | |

74 | How many bits to make the first lookup is a tradeoff between the time it |

75 | takes to decode and the time it takes to build the table. If building the |

76 | table took no time (and if you had infinite memory), then there would only |

77 | be a first level table to cover all the way to the longest code. However, |

78 | building the table ends up taking a lot longer for more bits since short |

79 | codes are replicated many times in such a table. What inflate() does is |

80 | simply to make the number of bits in the first table a variable, and then |

81 | to set that variable for the maximum speed. |

82 | |

83 | For inflate, which has 286 possible codes for the literal/length tree, the size |

84 | of the first table is nine bits. Also the distance trees have 30 possible |

85 | values, and the size of the first table is six bits. Note that for each of |

86 | those cases, the table ended up one bit longer than the ``average'' code |

87 | length, i.e. the code length of an approximately flat code which would be a |

88 | little more than eight bits for 286 symbols and a little less than five bits |

89 | for 30 symbols. |

90 | |

91 | |

92 | 2.2 More details on the inflate table lookup |

93 | |

94 | Ok, you want to know what this cleverly obfuscated inflate tree actually |

95 | looks like. You are correct that it's not a Huffman tree. It is simply a |

96 | lookup table for the first, let's say, nine bits of a Huffman symbol. The |

97 | symbol could be as short as one bit or as long as 15 bits. If a particular |

98 | symbol is shorter than nine bits, then that symbol's translation is duplicated |

99 | in all those entries that start with that symbol's bits. For example, if the |

100 | symbol is four bits, then it's duplicated 32 times in a nine-bit table. If a |

101 | symbol is nine bits long, it appears in the table once. |

102 | |

103 | If the symbol is longer than nine bits, then that entry in the table points |

104 | to another similar table for the remaining bits. Again, there are duplicated |

105 | entries as needed. The idea is that most of the time the symbol will be short |

106 | and there will only be one table look up. (That's whole idea behind data |

107 | compression in the first place.) For the less frequent long symbols, there |

108 | will be two lookups. If you had a compression method with really long |

109 | symbols, you could have as many levels of lookups as is efficient. For |

110 | inflate, two is enough. |

111 | |

112 | So a table entry either points to another table (in which case nine bits in |

113 | the above example are gobbled), or it contains the translation for the symbol |

114 | and the number of bits to gobble. Then you start again with the next |

115 | ungobbled bit. |

116 | |

117 | You may wonder: why not just have one lookup table for how ever many bits the |

118 | longest symbol is? The reason is that if you do that, you end up spending |

119 | more time filling in duplicate symbol entries than you do actually decoding. |

120 | At least for deflate's output that generates new trees every several 10's of |

121 | kbytes. You can imagine that filling in a 2^15 entry table for a 15-bit code |

122 | would take too long if you're only decoding several thousand symbols. At the |

123 | other extreme, you could make a new table for every bit in the code. In fact, |

124 | that's essentially a Huffman tree. But then you spend too much time |

125 | traversing the tree while decoding, even for short symbols. |

126 | |

127 | So the number of bits for the first lookup table is a trade of the time to |

128 | fill out the table vs. the time spent looking at the second level and above of |

129 | the table. |

130 | |

131 | Here is an example, scaled down: |

132 | |

133 | The code being decoded, with 10 symbols, from 1 to 6 bits long: |

134 | |

135 | A: 0 |

136 | B: 10 |

137 | C: 1100 |

138 | D: 11010 |

139 | E: 11011 |

140 | F: 11100 |

141 | G: 11101 |

142 | H: 11110 |

143 | I: 111110 |

144 | J: 111111 |

145 | |

146 | Let's make the first table three bits long (eight entries): |

147 | |

148 | 000: A,1 |

149 | 001: A,1 |

150 | 010: A,1 |

151 | 011: A,1 |

152 | 100: B,2 |

153 | 101: B,2 |

154 | 110: -> table X (gobble 3 bits) |

155 | 111: -> table Y (gobble 3 bits) |

156 | |

157 | Each entry is what the bits decode as and how many bits that is, i.e. how |

158 | many bits to gobble. Or the entry points to another table, with the number of |

159 | bits to gobble implicit in the size of the table. |

160 | |

161 | Table X is two bits long since the longest code starting with 110 is five bits |

162 | long: |

163 | |

164 | 00: C,1 |

165 | 01: C,1 |

166 | 10: D,2 |

167 | 11: E,2 |

168 | |

169 | Table Y is three bits long since the longest code starting with 111 is six |

170 | bits long: |

171 | |

172 | 000: F,2 |

173 | 001: F,2 |

174 | 010: G,2 |

175 | 011: G,2 |

176 | 100: H,2 |

177 | 101: H,2 |

178 | 110: I,3 |

179 | 111: J,3 |

180 | |

181 | So what we have here are three tables with a total of 20 entries that had to |

182 | be constructed. That's compared to 64 entries for a single table. Or |

183 | compared to 16 entries for a Huffman tree (six two entry tables and one four |

184 | entry table). Assuming that the code ideally represents the probability of |

185 | the symbols, it takes on the average 1.25 lookups per symbol. That's compared |

186 | to one lookup for the single table, or 1.66 lookups per symbol for the |

187 | Huffman tree. |

188 | |

189 | There, I think that gives you a picture of what's going on. For inflate, the |

190 | meaning of a particular symbol is often more than just a letter. It can be a |

191 | byte (a "literal"), or it can be either a length or a distance which |

192 | indicates a base value and a number of bits to fetch after the code that is |

193 | added to the base value. Or it might be the special end-of-block code. The |

194 | data structures created in inftrees.c try to encode all that information |

195 | compactly in the tables. |

196 | |

197 | |

198 | Jean-loup Gailly Mark Adler |

199 | jloup@gzip.org madler@alumni.caltech.edu |

200 | |

201 | |

202 | References: |

203 | |

204 | [LZ77] Ziv J., Lempel A., ``A Universal Algorithm for Sequential Data |

205 | Compression,'' IEEE Transactions on Information Theory, Vol. 23, No. 3, |

206 | pp. 337-343. |

207 | |

208 | ``DEFLATE Compressed Data Format Specification'' available in |

209 | http://www.ietf.org/rfc/rfc1951.txt |

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