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Diffstat (limited to 'algorithm.txt')
| -rw-r--r-- | algorithm.txt | 72 |
1 files changed, 36 insertions, 36 deletions
diff --git a/algorithm.txt b/algorithm.txt index a049765..b022dde 100644 --- a/algorithm.txt +++ b/algorithm.txt @@ -91,40 +91,40 @@ for 30 symbols. 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 +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 +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 +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 +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 +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 +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 +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 +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. @@ -154,7 +154,7 @@ Let's make the first table three bits long (eight entries): 110: -> 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. how +Each entry is what the bits decode as 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. @@ -166,7 +166,7 @@ long: 10: D,2 11: E,2 -Table Y is three bits long since the longest code starting with 111 is six +Table Y is three bits long since the longest code starting with 111 is six bits long: 000: F,2 @@ -178,20 +178,20 @@ bits long: 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 +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 +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 +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. |