Mercurial > cpython-lru_cache-weakref
annotate Modules/zlib/algorithm.txt @ 87690:66c1c9f32567 default tip
Add use_weakref option to functools.lru_cache
The use_weakref option makes lru_cache create weak references to the function
arguments when creating the cache key, which prevents them from staying in the
memory forever even after all other references to them are gone.
This is a proof of concept for http://bugs.python.org/issue19859
| author | Radomir Dopieralski <devel@sheep.art.pl> |
|---|---|
| date | Tue, 03 Dec 2013 16:02:48 +0100 |
| parents | 224aa49f22f1 |
| children |
| rev | line source |
|---|---|
|
36186
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
1 1. Compression algorithm (deflate) |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
3 The deflation algorithm used by gzip (also zip and zlib) is a variation of |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
4 LZ77 (Lempel-Ziv 1977, see reference below). It finds duplicated strings in |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
5 the input data. The second occurrence of a string is replaced by a |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
6 pointer to the previous string, in the form of a pair (distance, |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
7 length). Distances are limited to 32K bytes, and lengths are limited |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
8 to 258 bytes. When a string does not occur anywhere in the previous |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
9 32K bytes, it is emitted as a sequence of literal bytes. (In this |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
10 description, `string' must be taken as an arbitrary sequence of bytes, |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
11 and is not restricted to printable characters.) |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
12 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
13 Literals or match lengths are compressed with one Huffman tree, and |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
14 match distances are compressed with another tree. The trees are stored |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
15 in a compact form at the start of each block. The blocks can have any |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
16 size (except that the compressed data for one block must fit in |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
17 available memory). A block is terminated when deflate() determines that |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
18 it would be useful to start another block with fresh trees. (This is |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
19 somewhat similar to the behavior of LZW-based _compress_.) |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
20 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
21 Duplicated strings are found using a hash table. All input strings of |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
22 length 3 are inserted in the hash table. A hash index is computed for |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
23 the next 3 bytes. If the hash chain for this index is not empty, all |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
24 strings in the chain are compared with the current input string, and |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
25 the longest match is selected. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
26 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
27 The hash chains are searched starting with the most recent strings, to |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
28 favor small distances and thus take advantage of the Huffman encoding. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
29 The hash chains are singly linked. There are no deletions from the |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
30 hash chains, the algorithm simply discards matches that are too old. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
31 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
32 To avoid a worst-case situation, very long hash chains are arbitrarily |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
33 truncated at a certain length, determined by a runtime option (level |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
34 parameter of deflateInit). So deflate() does not always find the longest |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
35 possible match but generally finds a match which is long enough. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
36 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
37 deflate() also defers the selection of matches with a lazy evaluation |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
38 mechanism. After a match of length N has been found, deflate() searches for |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
39 a longer match at the next input byte. If a longer match is found, the |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
40 previous match is truncated to a length of one (thus producing a single |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
41 literal byte) and the process of lazy evaluation begins again. Otherwise, |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
42 the original match is kept, and the next match search is attempted only N |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
43 steps later. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
44 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
45 The lazy match evaluation is also subject to a runtime parameter. If |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
46 the current match is long enough, deflate() reduces the search for a longer |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
47 match, thus speeding up the whole process. If compression ratio is more |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
48 important than speed, deflate() attempts a complete second search even if |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
49 the first match is already long enough. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
50 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
51 The lazy match evaluation is not performed for the fastest compression |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
52 modes (level parameter 1 to 3). For these fast modes, new strings |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
53 are inserted in the hash table only when no match was found, or |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
54 when the match is not too long. This degrades the compression ratio |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
55 but saves time since there are both fewer insertions and fewer searches. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
56 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
57 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
58 2. Decompression algorithm (inflate) |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
59 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
60 2.1 Introduction |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
61 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
62 The key question is how to represent a Huffman code (or any prefix code) so |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
63 that you can decode fast. The most important characteristic is that shorter |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
64 codes are much more common than longer codes, so pay attention to decoding the |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
65 short codes fast, and let the long codes take longer to decode. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
66 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
67 inflate() sets up a first level table that covers some number of bits of |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
68 input less than the length of longest code. It gets that many bits from the |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
69 stream, and looks it up in the table. The table will tell if the next |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
70 code is that many bits or less and how many, and if it is, it will tell |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
71 the value, else it will point to the next level table for which inflate() |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
72 grabs more bits and tries to decode a longer code. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
73 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
74 How many bits to make the first lookup is a tradeoff between the time it |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
75 takes to decode and the time it takes to build the table. If building the |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
76 table took no time (and if you had infinite memory), then there would only |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
77 be a first level table to cover all the way to the longest code. However, |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
78 building the table ends up taking a lot longer for more bits since short |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
79 codes are replicated many times in such a table. What inflate() does is |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
80 simply to make the number of bits in the first table a variable, and then |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
81 to set that variable for the maximum speed. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
82 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
83 For inflate, which has 286 possible codes for the literal/length tree, the size |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
84 of the first table is nine bits. Also the distance trees have 30 possible |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
85 values, and the size of the first table is six bits. Note that for each of |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
86 those cases, the table ended up one bit longer than the ``average'' code |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
87 length, i.e. the code length of an approximately flat code which would be a |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
88 little more than eight bits for 286 symbols and a little less than five bits |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
89 for 30 symbols. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
90 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
91 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
92 2.2 More details on the inflate table lookup |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
93 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
94 Ok, you want to know what this cleverly obfuscated inflate tree actually |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
95 looks like. You are correct that it's not a Huffman tree. It is simply a |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
96 lookup table for the first, let's say, nine bits of a Huffman symbol. The |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
97 symbol could be as short as one bit or as long as 15 bits. If a particular |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
98 symbol is shorter than nine bits, then that symbol's translation is duplicated |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
99 in all those entries that start with that symbol's bits. For example, if the |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
100 symbol is four bits, then it's duplicated 32 times in a nine-bit table. If a |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
101 symbol is nine bits long, it appears in the table once. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
102 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
103 If the symbol is longer than nine bits, then that entry in the table points |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
104 to another similar table for the remaining bits. Again, there are duplicated |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
105 entries as needed. The idea is that most of the time the symbol will be short |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
106 and there will only be one table look up. (That's whole idea behind data |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
107 compression in the first place.) For the less frequent long symbols, there |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
108 will be two lookups. If you had a compression method with really long |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
109 symbols, you could have as many levels of lookups as is efficient. For |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
110 inflate, two is enough. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
111 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
112 So a table entry either points to another table (in which case nine bits in |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
113 the above example are gobbled), or it contains the translation for the symbol |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
114 and the number of bits to gobble. Then you start again with the next |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
115 ungobbled bit. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
116 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
117 You may wonder: why not just have one lookup table for how ever many bits the |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
118 longest symbol is? The reason is that if you do that, you end up spending |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
119 more time filling in duplicate symbol entries than you do actually decoding. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
120 At least for deflate's output that generates new trees every several 10's of |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
121 kbytes. You can imagine that filling in a 2^15 entry table for a 15-bit code |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
122 would take too long if you're only decoding several thousand symbols. At the |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
123 other extreme, you could make a new table for every bit in the code. In fact, |
|
86546
224aa49f22f1
Issue #18527: Upgrade internal copy of zlib to 1.2.8
Christian Heimes <christian@cheimes.de>
parents:
36186
diff
changeset
|
124 that's essentially a Huffman tree. But then you spend too much time |
|
36186
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
125 traversing the tree while decoding, even for short symbols. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
126 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
127 So the number of bits for the first lookup table is a trade of the time to |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
128 fill out the table vs. the time spent looking at the second level and above of |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
129 the table. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
130 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
131 Here is an example, scaled down: |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
132 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
133 The code being decoded, with 10 symbols, from 1 to 6 bits long: |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
134 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
135 A: 0 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
136 B: 10 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
137 C: 1100 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
138 D: 11010 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
139 E: 11011 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
140 F: 11100 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
141 G: 11101 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
142 H: 11110 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
143 I: 111110 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
144 J: 111111 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
145 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
146 Let's make the first table three bits long (eight entries): |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
147 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
148 000: A,1 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
149 001: A,1 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
150 010: A,1 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
151 011: A,1 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
152 100: B,2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
153 101: B,2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
154 110: -> table X (gobble 3 bits) |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
155 111: -> table Y (gobble 3 bits) |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
156 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
157 Each entry is what the bits decode as and how many bits that is, i.e. how |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
158 many bits to gobble. Or the entry points to another table, with the number of |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
159 bits to gobble implicit in the size of the table. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
160 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
161 Table X is two bits long since the longest code starting with 110 is five bits |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
162 long: |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
163 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
164 00: C,1 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
165 01: C,1 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
166 10: D,2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
167 11: E,2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
168 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
169 Table Y is three bits long since the longest code starting with 111 is six |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
170 bits long: |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
171 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
172 000: F,2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
173 001: F,2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
174 010: G,2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
175 011: G,2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
176 100: H,2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
177 101: H,2 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
178 110: I,3 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
179 111: J,3 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
180 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
181 So what we have here are three tables with a total of 20 entries that had to |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
182 be constructed. That's compared to 64 entries for a single table. Or |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
183 compared to 16 entries for a Huffman tree (six two entry tables and one four |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
184 entry table). Assuming that the code ideally represents the probability of |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
185 the symbols, it takes on the average 1.25 lookups per symbol. That's compared |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
186 to one lookup for the single table, or 1.66 lookups per symbol for the |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
187 Huffman tree. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
188 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
189 There, I think that gives you a picture of what's going on. For inflate, the |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
190 meaning of a particular symbol is often more than just a letter. It can be a |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
191 byte (a "literal"), or it can be either a length or a distance which |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
192 indicates a base value and a number of bits to fetch after the code that is |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
193 added to the base value. Or it might be the special end-of-block code. The |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
194 data structures created in inftrees.c try to encode all that information |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
195 compactly in the tables. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
196 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
197 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
198 Jean-loup Gailly Mark Adler |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
199 jloup@gzip.org madler@alumni.caltech.edu |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
200 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
201 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
202 References: |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
203 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
204 [LZ77] Ziv J., Lempel A., ``A Universal Algorithm for Sequential Data |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
205 Compression,'' IEEE Transactions on Information Theory, Vol. 23, No. 3, |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
206 pp. 337-343. |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
207 |
|
81fa47d2d477
Import zlib into Python tree.
Martin v. Löwis <martin@v.loewis.de>
parents:
diff
changeset
|
208 ``DEFLATE Compressed Data Format Specification'' available in |
|
86546
224aa49f22f1
Issue #18527: Upgrade internal copy of zlib to 1.2.8
Christian Heimes <christian@cheimes.de>
parents:
36186
diff
changeset
|
209 http://tools.ietf.org/html/rfc1951 |
