1 files changed, 115 insertions, 7 deletions

diff --git a/algorithm.doc b/algorithm.txt
index 01902af..cdc830b 100644
--- a/algorithm.doc
+++ b/algorithm.txt
@@ -1,6 +1,6 @@
 1. Compression algorithm (deflate)
 
-The deflation algorithm used by zlib (also zip and gzip) is a variation of
+The deflation algorithm used by gzip (also zip and zlib) is a variation of
 LZ77 (Lempel-Ziv 1977, see reference below). It finds duplicated strings in
 the input data.  The second occurrence of a string is replaced by a
 pointer to the previous string, in the form of a pair (distance,
@@ -35,12 +35,12 @@ parameter of deflateInit). So deflate() does not always find the longest
 possible match but generally finds a match which is long enough.
 
 deflate() also defers the selection of matches with a lazy evaluation
-mechanism. After a match of length N has been found, deflate() searches for a
-longer match at the next input byte. If a longer match is found, the
+mechanism. After a match of length N has been found, deflate() searches for
+a longer match at the next input byte. If a longer match is found, the
 previous match is truncated to a length of one (thus producing a single
-literal byte) and the longer match is emitted afterwards.  Otherwise,
-the original match is kept, and the next match search is attempted only
-N steps later.
+literal byte) and the process of lazy evaluation begins again. Otherwise,
+the original match is kept, and the next match search is attempted only N
+steps later.
 
 The lazy match evaluation is also subject to a runtime parameter. If
 the current match is long enough, deflate() reduces the search for a longer
@@ -57,6 +57,8 @@ but saves time since there are both fewer insertions and fewer searches.
 
 2. Decompression algorithm (inflate)
 
+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
@@ -91,8 +93,114 @@ interesting to see if optimizing the first level table for other
 applications gave values within a bit or two of the flat code size.
 
 
+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  
+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  
+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  
+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  
+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  
+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  
+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  
+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  
+fill out the table vs. the time spent looking at the second level and above of
+the table.
+
+Here is an example, scaled down:
+
+The code being decoded, with 10 symbols, from 1 to 6 bits long:
+
+A: 0
+B: 10
+C: 1100
+D: 11010
+E: 11011
+F: 11100
+G: 11101
+H: 11110
+I: 111110
+J: 111111
+
+Let's make the first table three bits long (eight entries):
+
+000: A,1
+001: A,1
+010: A,1
+011: A,1
+100: B,2
+101: B,2
+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  
+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.
+
+Table X is two bits long since the longest code starting with 110 is five bits
+long:
+
+00: C,1
+01: C,1
+10: D,2
+11: E,2
+
+Table Y is three bits long since the longest code starting with 111 is six  
+bits long:
+
+000: F,2
+001: F,2
+010: G,2
+011: G,2
+100: H,2
+101: H,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  
+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  
+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  
+compactly in the tables.
+
+
 Jean-loup Gailly        Mark Adler
-gzip@prep.ai.mit.edu    madler@alumni.caltech.edu
+jloup@gzip.org          madler@alumni.caltech.edu
 
 
 References: