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5.5 Deflating - Method 8 | |
------------------------ | |
5.5.1 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. | |
5.5.2 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. | |
5.5.3 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 - 256 (256 - 286) | |
All other codes are never sent. | |
5 Bits: # of Dist codes - 1 (1 - 32) | |
4 Bits: # of Bit Length codes - 3 (3 - 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 | |
5.5.4 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 | |
if data descriptor exists | |
skip bits until byte aligned | |
read crc and sizes | |
endif |
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5.3 Imploding - Method 6 | |
------------------------ | |
5.3.1 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 output, | |
using multiple Shannon-Fano trees. | |
5.3.2 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. | |
5.3.3 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. | |
5.3.4 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. | |
5.3.5 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. | |
5.3.6 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. | |
5.3.7 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) | |
5.3.8 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 successfully applied. | |
5.3.9 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 |
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