Well, it looks like gzip does indeed have an algorithmic specification.
This is not exactly my area of expertise, but it looks to me like
there's a good chance we could turn this into an RFC without too much
pain. Anyone interested in picking up this ball and running with it?
-- NB
From: Jean-loup Gailly <jloup(_at_)chorus(_dot_)fr>
To: Nathaniel Borenstein <nsb(_at_)thumper(_dot_)bellcore(_dot_)com>
Subject: Re: Gzip spec available?
The specification of the deflation format is given in the pkzip 1.93a
distribution but it has some bugs. A corrected one is given below.
(It takes some time to really understand the algorithm from the given
specification, but that's all I had available when I wrote zip, and I
had to find the bugs in the documentation by trial and error.) The
gzip file format is documented in algorithm.doc in the gzip
distribution.
Jean-loup
[Note: the imploding format is not used by gzip, but the method
of construction of Huffman trees is referenced in the description
of the deflation format. I will try to give a complete self-contained
description of the deflation format in future versions of gzip.]
Imploding
---------
The Imploding algorithm is actually a combination of two distinct
algorithms. The first algorithm compresses repeated byte
sequences using a sliding dictionary. The second algorithm is
used to compress the encoding of the sliding dictionary ouput,
using multiple Shannon-Fano trees.
The Imploding algorithm can use a 4K or 8K sliding dictionary
size. The dictionary size used can be determined by bit 1 in the
general purpose flag word; a 0 bit indicates a 4K dictionary
while a 1 bit indicates an 8K dictionary.
The Shannon-Fano trees are stored at the start of the compressed
file. The number of trees stored is defined by bit 2 in the
general purpose flag word; a 0 bit indicates two trees stored, a
1 bit indicates three trees are stored. If 3 trees are stored,
the first Shannon-Fano tree represents the encoding of the
Literal characters, the second tree represents the encoding of
the Length information, the third represents the encoding of the
Distance information. When 2 Shannon-Fano trees are stored, the
Length tree is stored first, followed by the Distance tree.
The Literal Shannon-Fano tree, if present is used to represent
the entire ASCII character set, and contains 256 values. This
tree is used to compress any data not compressed by the sliding
dictionary algorithm. When this tree is present, the Minimum
Match Length for the sliding dictionary is 3. If this tree is
not present, the Minimum Match Length is 2.
The Length Shannon-Fano tree is used to compress the Length part
of the (length,distance) pairs from the sliding dictionary
output. The Length tree contains 64 values, ranging from the
Minimum Match Length, to 63 plus the Minimum Match Length.
The Distance Shannon-Fano tree is used to compress the Distance
part of the (length,distance) pairs from the sliding dictionary
output. The Distance tree contains 64 values, ranging from 0 to
63, representing the upper 6 bits of the distance value. The
distance values themselves will be between 0 and the sliding
dictionary size, either 4K or 8K.
The Shannon-Fano trees themselves are stored in a compressed
format. The first byte of the tree data represents the number of
bytes of data representing the (compressed) Shannon-Fano tree
minus 1. The remaining bytes represent the Shannon-Fano tree
data encoded as:
High 4 bits: Number of values at this bit length + 1. (1 - 16)
Low 4 bits: Bit Length needed to represent value + 1. (1 - 16)
The Shannon-Fano codes can be constructed from the bit lengths
using the following algorithm:
1) Sort the Bit Lengths in ascending order, while retaining the
order of the original lengths stored in the file.
2) Generate the Shannon-Fano trees:
Code <- 0
CodeIncrement <- 0
LastBitLength <- 0
i <- number of Shannon-Fano codes - 1 (either 255 or 63)
loop while i >= 0
Code = Code + CodeIncrement
if BitLength(i) <> LastBitLength then
LastBitLength=BitLength(i)
CodeIncrement = 1 shifted left (16 - LastBitLength)
ShannonCode(i) = Code
i <- i - 1
end loop
3) Reverse the order of all the bits in the above ShannonCode()
vector, so that the most significant bit becomes the least
significant bit. For example, the value 0x1234 (hex) would
become 0x2C48 (hex).
4) Restore the order of Shannon-Fano codes as originally stored
within the file.
Example:
This example will show the encoding of a Shannon-Fano tree
of size 8. Notice that the actual Shannon-Fano trees used
for Imploding are either 64 or 256 entries in size.
Example: 0x02, 0x42, 0x01, 0x13
The first byte indicates 3 values in this table. Decoding the
bytes:
0x42 = 5 codes of 3 bits long
0x01 = 1 code of 2 bits long
0x13 = 2 codes of 4 bits long
This would generate the original bit length array of:
(3, 3, 3, 3, 3, 2, 4, 4)
There are 8 codes in this table for the values 0 thru 7. Using the
algorithm to obtain the Shannon-Fano codes produces:
Reversed Order Original
Val Sorted Constructed Code Value Restored Length
--- ------ ----------------- -------- -------- ------
0: 2 1100000000000000 11 101 3
1: 3 1010000000000000 101 001 3
2: 3 1000000000000000 001 110 3
3: 3 0110000000000000 110 010 3
4: 3 0100000000000000 010 100 3
5: 3 0010000000000000 100 11 2
6: 4 0001000000000000 1000 1000 4
7: 4 0000000000000000 0000 0000 4
The values in the Val, Order Restored and Original Length columns
now represent the Shannon-Fano encoding tree that can be used for
decoding the Shannon-Fano encoded data. How to parse the
variable length Shannon-Fano values from the data stream is beyond the
scope of this document. (See the references listed at the end of
this document for more information.) However, traditional decoding
schemes used for Huffman variable length decoding, such as the
Greenlaw algorithm, can be succesfully applied.
The compressed data stream begins immediately after the
compressed Shannon-Fano data. The compressed data stream can be
interpreted as follows:
loop until done
read 1 bit from input stream.
if this bit is non-zero then (encoded data is literal data)
if Literal Shannon-Fano tree is present
read and decode character using Literal Shannon-Fano tree.
otherwise
read 8 bits from input stream.
copy character to the output stream.
otherwise (encoded data is sliding dictionary match)
if 8K dictionary size
read 7 bits for offset Distance (lower 7 bits of offset).
otherwise
read 6 bits for offset Distance (lower 6 bits of offset).
using the Distance Shannon-Fano tree, read and decode the
upper 6 bits of the Distance value.
using the Length Shannon-Fano tree, read and decode
the Length value.
Length <- Length + Minimum Match Length
if Length = 63 + Minimum Match Length
read 8 bits from the input stream,
add this value to Length.
move backwards Distance+1 bytes in the output stream, and
copy Length characters from this position to the output
stream. (if this position is before the start of the output
stream, then assume that all the data before the start of
the output stream is filled with zeros).
end loop
Deflating
---------
The Deflate algorithm is similar to the Implode algorithm using
a sliding dictionary of up to 32K with secondary compression
from Huffman/Shannon-Fano codes.
The compressed data is stored in blocks with a header describing
the block and the Huffman codes used in the data block. The header
format is as follows:
Bit 0: Last Block bit This bit is set to 1 if this is the last
compressed block in the data.
Bits 1-2: Block type
00 (0) - Block is stored - All stored data is byte aligned.
Skip bits until next byte, then next word = block length,
followed by the ones compliment of the block length word.
Remaining data in block is the stored data.
01 (1) - Use fixed Huffman codes for literal and distance codes.
Lit Code Bits Dist Code Bits
--------- ---- --------- ----
0 - 143 8 0 - 31 5
144 - 255 9
256 - 279 7
280 - 287 8
Literal codes 286-287 and distance codes 30-31 are never
used but participate in the huffman construction.
10 (2) - Dynamic Huffman codes. (See expanding Huffman codes)
11 (3) - Reserved - Flag a "Error in compressed data" if seen.
Expanding Huffman Codes
-----------------------
If the data block is stored with dynamic Huffman codes, the Huffman
codes are sent in the following compressed format:
5 Bits: # of Literal codes sent - 257 (257 - 286)
All other codes are never sent.
5 Bits: # of Dist codes - 1 (1 - 32)
4 Bits: # of Bit Length codes - 4 (4 - 19)
The Huffman codes are sent as bit lengths and the codes are built as
described in the implode algorithm. The bit lengths themselves are
compressed with Huffman codes. There are 19 bit length codes:
0 - 15: Represent bit lengths of 0 - 15
16: Copy the previous bit length 3 - 6 times.
The next 2 bits indicate repeat length (0 = 3, ... ,3 = 6)
Example: Codes 8, 16 (+2 bits 11), 16 (+2 bits 10) will
expand to 12 bit lengths of 8 (1 + 6 + 5)
17: Repeat a bit length of 0 for 3 - 10 times. (3 bits of length)
18: Repeat a bit length of 0 for 11 - 138 times (7 bits of length)
The lengths of the bit length codes are sent packed 3 bits per value
(0 - 7) in the following order:
16, 17, 18, 0, 8, 7, 9, 6, 10, 5, 11, 4, 12, 3, 13, 2, 14, 1, 15
The Huffman codes should be built as described in the Implode algorithm
except codes are assigned starting at the shortest bit length, i.e. the
shortest code should be all 0's rather than all 1's. Also, codes with
a bit length of zero do not participate in the tree construction. The
codes are then used to decode the bit lengths for the literal and distance
tables.
The bit lengths for the literal tables are sent first with the number
of entries sent described by the 5 bits sent earlier. There are up
to 286 literal characters; the first 256 represent the respective 8
bit character, code 256 represents the End-Of-Block code, the remaining
29 codes represent copy lengths of 3 thru 258. There are up to 30
distance codes representing distances from 1 thru 32k as described
below.
Length Codes
------------
Extra Extra Extra Extra
Code Bits Length Code Bits Lengths Code Bits Lengths Code Bits Length(s)
---- ---- ------ ---- ---- ------- ---- ---- ------- ---- ---- ---------
257 0 3 265 1 11,12 273 3 35-42 281 5 131-162
258 0 4 266 1 13,14 274 3 43-50 282 5 163-194
259 0 5 267 1 15,16 275 3 51-58 283 5 195-226
260 0 6 268 1 17,18 276 3 59-66 284 5 227-257
261 0 7 269 2 19-22 277 4 67-82 285 0 258
262 0 8 270 2 23-26 278 4 83-98
263 0 9 271 2 27-30 279 4 99-114
264 0 10 272 2 31-34 280 4 115-130
Distance Codes
--------------
Extra Extra Extra Extra
Code Bits Dist Code Bits Dist Code Bits Distance Code Bits Distance
---- ---- ---- ---- ---- ------ ---- ---- -------- ---- ---- --------
0 0 1 8 3 17-24 16 7 257-384 24 11 4097-6144
1 0 2 9 3 25-32 17 7 385-512 25 11 6145-8192
2 0 3 10 4 33-48 18 8 513-768 26 12 8193-12288
3 0 4 11 4 49-64 19 8 769-1024 27 12 12289-16384
4 1 5,6 12 5 65-96 20 9 1025-1536 28 13 16385-24576
5 1 7,8 13 5 97-128 21 9 1537-2048 29 13 24577-32768
6 2 9-12 14 6 129-192 22 10 2049-3072
7 2 13-16 15 6 193-256 23 10 3073-4096
The compressed data stream begins immediately after the
compressed header data. The compressed data stream can be
interpreted as follows:
do
read header from input stream.
if stored block
skip bits until byte aligned
read count and 1's compliment of count
copy count bytes data block
otherwise
loop until end of block code sent
decode literal character from input stream
if literal < 256
copy character to the output stream
otherwise
if literal = end of block
break from loop
otherwise
decode distance from input stream
move backwards distance bytes in the output stream, and
copy length characters from this position to the output
stream.
end loop
while not last block