2.1 Introduction
-The real question is, given a Huffman tree, how to decode fast. The most
-important realization is that shorter codes are much more common than
-longer codes, so pay attention to decoding the short codes fast, and let
-the long codes take longer to decode.
+The key question is how to represent a Huffman code (or any prefix code) so
+that you can decode fast. The most important characteristic is that shorter
+codes are much more common than longer codes, so pay attention to decoding the
+short codes fast, and let the long codes take longer to decode.
inflate() sets up a first level table that covers some number of bits of
input less than the length of longest code. It gets that many bits from the
be 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 short
codes are replicated many times in such a table. What inflate() does is
-simply to make the number of bits in the first table a variable, and set it
-for the maximum speed.
-
-inflate() sends new trees relatively often, so it is possibly set for a
-smaller first level table than an application that has only one tree for
-all the data. For inflate, which has 286 possible codes for the
-literal/length tree, the size of the first table is nine bits. Also the
-distance trees have 30 possible values, and the size of the first table is
-six bits. Note that for each of those cases, the table ended up one bit
-longer than the ``average'' code length, i.e. the code length of an
-approximately flat code which would be a little more than eight bits for
-286 symbols and a little less than five bits for 30 symbols. It would be
-interesting to see if optimizing the first level table for other
-applications gave values within a bit or two of the flat code size.
+simply to make the number of bits in the first table a variable, and then
+to set that variable for the maximum speed.
+
+For inflate, which has 286 possible codes for the literal/length tree, the size
+of the first table is nine bits. Also the distance trees have 30 possible
+values, and the size of the first table is six bits. Note that for each of
+those cases, the table ended up one bit longer than the ``average'' code
+length, i.e. the code length of an approximately flat code which would be a
+little more than eight bits for 286 symbols and a little less than five bits
+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.
110: -> table X (gobble 3 bits)
111: -> table Y (gobble 3 bits)
-Each entry is what the bits decode to 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.
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
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.
pp. 337-343.
``DEFLATE Compressed Data Format Specification'' available in
-ftp://ds.internic.net/rfc/rfc1951.txt
+http://www.ietf.org/rfc/rfc1951.txt
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