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RFC1951 (DEFLATE)
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RFC1951 (DEFLATE)
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DEFLATE Compressed Data Format Specification version 1.3
Abstract
This specification defines a lossless compressed data format that
compresses data using a combination of the LZ77 algorithm and Huffman
coding, with efficiency comparable to the best currently available
general-purpose compression methods. The data can be produced or
consumed, even for an arbitrarily long sequentially presented input
data stream, using only an a priori bounded amount of intermediate
storage. The format can be implemented readily in a manner not
covered by patents.
1. Introduction
1.1. Purpose
The purpose of this specification is to define a lossless
compressed data format that:
* Is independent of CPU type, operating system, file system,
and character set, and hence can be used for interchange;
* Can be produced or consumed, even for an arbitrarily long
sequentially presented input data stream, using only an a
priori bounded amount of intermediate storage, and hence
can be used in data communications or similar structures
such as Unix filters;
* Compresses data with efficiency comparable to the best
currently available general-purpose compression methods,
and in particular considerably better than the "compress"
program;
* Can be implemented readily in a manner not covered by
patents, and hence can be practiced freely;
* Is compatible with the file format produced by the current
widely used gzip utility, in that conforming decompressors
will be able to read data produced by the existing gzip
compressor.
The data format defined by this specification does not attempt to:
* Allow random access to compressed data;
* Compress specialized data (e.g., raster graphics) as well
as the best currently available specialized algorithms.
A simple counting argument shows that no lossless compression
algorithm can compress every possible input data set. For the
format defined here, the worst case expansion is 5 bytes per 32K-
byte block, i.e., a size increase of 0.015% for large data sets.
English text usually compresses by a factor of 2.5 to 3;
executable files usually compress somewhat less; graphical data
such as raster images may compress much more.
1.2. Intended audience
This specification is intended for use by implementors of software
to compress data into "deflate" format and/or decompress data from
"deflate" format.
The text of the specification assumes a basic background in
programming at the level of bits and other primitive data
representations. Familiarity with the technique of Huffman coding
is helpful but not required.
1.3. Scope
The specification specifies a method for representing a sequence
of bytes as a (usually shorter) sequence of bits, and a method for
packing the latter bit sequence into bytes.
1.4. Compliance
Unless otherwise indicated below, a compliant decompressor must be
able to accept and decompress any data set that conforms to all
the specifications presented here; a compliant compressor must
produce data sets that conform to all the specifications presented
here.
1.5. Definitions of terms and conventions used
Byte: 8 bits stored or transmitted as a unit (same as an octet).
For this specification, a byte is exactly 8 bits, even on machines
which store a character on a number of bits different from eight.
See below, for the numbering of bits within a byte.
String: a sequence of arbitrary bytes.
1.6. Changes from previous versions
There have been no technical changes to the deflate format since
version 1.1 of this specification. In version 1.2, some
terminology was changed. Version 1.3 is a conversion of the
specification to RFC style.
2. Compressed representation overview
A compressed data set consists of a series of blocks, corresponding
to successive blocks of input data. The block sizes are arbitrary,
except that non-compressible blocks are limited to 65,535 bytes.
Each block is compressed using a combination of the LZ77 algorithm
and Huffman coding. The Huffman trees for each block are independent
of those for previous or subsequent blocks; the LZ77 algorithm may
use a reference to a duplicated string occurring in a previous block,
up to 32K input bytes before.
Each block consists of two parts: a pair of Huffman code trees that
describe the representation of the compressed data part, and a
compressed data part. (The Huffman trees themselves are compressed
using Huffman encoding.) The compressed data consists of a series of
elements of two types: literal bytes (of strings that have not been
detected as duplicated within the previous 32K input bytes), and
pointers to duplicated strings, where a pointer is represented as a
pair . The representation used in the
"deflate" format limits distances to 32K bytes and lengths to 258
bytes, but does not limit the size of a block, except for
uncompressible blocks, which are limited as noted above.
Each type of value (literals, distances, and lengths) in the
compressed data is represented using a Huffman code, using one code
tree for literals and lengths and a separate code tree for distances.
The code trees for each block appear in a compact form just before
the compressed data for that block.
3. Detailed specification
3.1. Overall conventions In the diagrams below, a box like this:
+---+
| | <-- the vertical bars might be missing
+---+
represents one byte; a box like this:
+==============+
| |
+==============+
represents a variable number of bytes.
Bytes stored within a computer do not have a "bit order", since
they are always treated as a unit. However, a byte considered as
an integer between 0 and 255 does have a most- and least-
significant bit, and since we write numbers with the most-
significant digit on the left, we also write bytes with the most-
significant bit on the left. In the diagrams below, we number the
bits of a byte so that bit 0 is the least-significant bit, i.e.,
the bits are numbered:
+--------+
|76543210|
+--------+
Within a computer, a number may occupy multiple bytes. All
multi-byte numbers in the format described here are stored with
the least-significant byte first (at the lower memory address).
For example, the decimal number 520 is stored as:
0 1
+--------+--------+
|00001000|00000010|
+--------+--------+
^ ^
| |
| + more significant byte = 2 x 256
+ less significant byte = 8
3.1.1. Packing into bytes
This document does not address the issue of the order in which
bits of a byte are transmitted on a bit-sequential medium,
since the final data format described here is byte- rather than
bit-oriented. However, we describe the compressed block format
in below, as a sequence of data elements of various bit
lengths, not a sequence of bytes. We must therefore specify
how to pack these data elements into bytes to form the final
compressed byte sequence:
* Data elements are packed into bytes in order of
increasing bit number within the byte, i.e., starting
with the least-significant bit of the byte.
* Data elements other than Huffman codes are packed
starting with the least-significant bit of the data
element.
* Huffman codes are packed starting with the most-
significant bit of the code.
In other words, if one were to print out the compressed data as
a sequence of bytes, starting with the first byte at the
*right* margin and proceeding to the *left*, with the most-
significant bit of each byte on the left as usual, one would be
able to parse the result from right to left, with fixed-width
elements in the correct MSB-to-LSB order and Huffman codes in
bit-reversed order (i.e., with the first bit of the code in the
relative LSB position).
3.2. Compressed block format
3.2.1. Synopsis of prefix and Huffman coding
Prefix coding represents symbols from an a priori known
alphabet by bit sequences (codes), one code for each symbol, in
a manner such that different symbols may be represented by bit
sequences of different lengths, but a parser can always parse
an encoded string unambiguously symbol-by-symbol.
We define a prefix code in terms of a binary tree in which the
two edges descending from each non-leaf node are labeled 0 and
1 and in which the leaf nodes correspond one-for-one with (are
labeled with) the symbols of the alphabet; then the code for a
symbol is the sequence of 0's and 1's on the edges leading from
the root to the leaf labeled with that symbol. For example:
/\ Symbol Code
0 1 ------ ----
/ \ A 00
/\ B B 1
0 1 C 011
/ \ D 010
A /\
0 1
/ \
D C
A parser can decode the next symbol from an encoded input
stream by walking down the tree from the root, at each step
choosing the edge corresponding to the next input bit.
Given an alphabet with known symbol frequencies, the Huffman
algorithm allows the construction of an optimal prefix code
(one which represents strings with those symbol frequencies
using the fewest bits of any possible prefix codes for that
alphabet). Such a code is called a Huffman code. (See
reference [1] in Chapter 5, references for additional
information on Huffman codes.)
Note that in the "deflate" format, the Huffman codes for the
various alphabets must not exceed certain maximum code lengths.
This constraint complicates the algorithm for computing code
lengths from symbol frequencies. Again, see Chapter 5,
references for details.
3.2.2. Use of Huffman coding in the "deflate" format
The Huffman codes used for each alphabet in the "deflate"
format have two additional rules:
* All codes of a given bit length have lexicographically
consecutive values, in the same order as the symbols
they represent;
* Shorter codes lexicographically precede longer codes.
We could recode the example above to follow this rule as
follows, assuming that the order of the alphabet is ABCD:
Symbol Code
------ ----
A 10
B 0
C 110
D 111
I.e., 0 precedes 10 which precedes 11x, and 110 and 111 are
lexicographically consecutive.
Given this rule, we can define the Huffman code for an alphabet
just by giving the bit lengths of the codes for each symbol of
the alphabet in order; this is sufficient to determine the
actual codes. In our example, the code is completely defined
by the sequence of bit lengths (2, 1, 3, 3). The following
algorithm generates the codes as integers, intended to be read
from most- to least-significant bit. The code lengths are
initially in tree[I].Len; the codes are produced in
tree[I].Code.
1) Count the number of codes for each code length. Let
bl_count[N] be the number of codes of length N, N >= 1.
2) Find the numerical value of the smallest code for each
code length:
code = 0;
bl_count[0] = 0;
for (bits = 1; bits <= MAX_BITS; bits++) {
code = (code + bl_count[bits-1]) << 1;
next_code[bits] = code;
}
3) Assign numerical values to all codes, using consecutive
values for all codes of the same length with the base
values determined at step 2. Codes that are never used
(which have a bit length of zero) must not be assigned a
value.
for (n = 0; n <= max_code; n++) {
len = tree[n].Len;
if (len != 0) {
tree[n].Code = next_code[len];
next_code[len]++;
}
}
Example:
Consider the alphabet ABCDEFGH, with bit lengths (3, 3, 3, 3,
3, 2, 4, 4). After step 1, we have:
N bl_count[N]
- -----------
2 1
3 5
4 2
Step 2 computes the following next_code values:
N next_code[N]
- ------------
1 0
2 0
3 2
4 14
Step 3 produces the following code values:
Symbol Length Code
------ ------ ----
A 3 010
B 3 011
C 3 100
D 3 101
E 3 110
F 2 00
G 4 1110
H 4 1111
3.2.3. Details of block format
Each block of compressed data begins with 3 header bits
containing the following data:
first bit BFINAL
next 2 bits BTYPE
Note that the header bits do not necessarily begin on a byte
boundary, since a block does not necessarily occupy an integral
number of bytes.
BFINAL is set if and only if this is the last block of the data
set.
BTYPE specifies how the data are compressed, as follows:
00 - no compression
01 - compressed with fixed Huffman codes
10 - compressed with dynamic Huffman codes
11 - reserved (error)
The only difference between the two compressed cases is how the
Huffman codes for the literal/length and distance alphabets are
defined.
In all cases, the decoding algorithm for the actual data is as
follows:
do
read block header from input stream.
if stored with no compression
skip any remaining bits in current partially
processed byte
read LEN and NLEN (see next section)
copy LEN bytes of data to output
otherwise
if compressed with dynamic Huffman codes
read representation of code trees (see
subsection below)
loop (until end of block code recognized)
decode literal/length value from input stream
if value < 256
copy value (literal byte) to output stream
otherwise
if value = end of block (256)
break from loop
otherwise (value = 257..285)
decode distance from input stream
move backwards distance bytes in the output
stream, and copy length bytes from this
position to the output stream.
end loop
while not last block
Note that a duplicated string reference may refer to a string
in a previous block; i.e., the backward distance may cross one
or more block boundaries. However a distance cannot refer past
the beginning of the output stream. (An application using a
preset dictionary might discard part of the output stream; a
distance can refer to that part of the output stream anyway)
Note also that the referenced string may overlap the current
position; for example, if the last 2 bytes decoded have values
X and Y, a string reference with
adds X,Y,X,Y,X to the output stream.
We now specify each compression method in turn.
3.2.4. Non-compressed blocks (BTYPE=00)
Any bits of input up to the next byte boundary are ignored.
The rest of the block consists of the following information:
0 1 2 3 4...
+---+---+---+---+================================+
| LEN | NLEN |... LEN bytes of literal data...|
+---+---+---+---+================================+
LEN is the number of data bytes in the block. NLEN is the
one's complement of LEN.
3.2.5. Compressed blocks (length and distance codes)
As noted above, encoded data blocks in the "deflate" format
consist of sequences of symbols drawn from three conceptually
distinct alphabets: either literal bytes, from the alphabet of
byte values (0..255), or pairs,
where the length is drawn from (3..258) and the distance is
drawn from (1..32,768). In fact, the literal and length
alphabets are merged into a single alphabet (0..285), where
values 0..255 represent literal bytes, the value 256 indicates
end-of-block, and values 257..285 represent length codes
(possibly in conjunction with extra bits following the symbol
code) as follows:
Extra Extra Extra
Code Bits Length(s) Code Bits Lengths Code Bits Length(s)
---- ---- ------ ---- ---- ------- ---- ---- -------
257 0 3 267 1 15,16 277 4 67-82
258 0 4 268 1 17,18 278 4 83-98
259 0 5 269 2 19-22 279 4 99-114
260 0 6 270 2 23-26 280 4 115-130
261 0 7 271 2 27-30 281 5 131-162
262 0 8 272 2 31-34 282 5 163-194
263 0 9 273 3 35-42 283 5 195-226
264 0 10 274 3 43-50 284 5 227-257
265 1 11,12 275 3 51-58 285 0 258
266 1 13,14 276 3 59-66
The extra bits should be interpreted as a machine integer
stored with the most-significant bit first, e.g., bits 1110
represent the value 14.
Extra Extra Extra
Code Bits Dist Code Bits Dist Code Bits Distance
---- ---- ---- ---- ---- ------ ---- ---- --------
0 0 1 10 4 33-48 20 9 1025-1536
1 0 2 11 4 49-64 21 9 1537-2048
2 0 3 12 5 65-96 22 10 2049-3072
3 0 4 13 5 97-128 23 10 3073-4096
4 1 5,6 14 6 129-192 24 11 4097-6144
5 1 7,8 15 6 193-256 25 11 6145-8192
6 2 9-12 16 7 257-384 26 12 8193-12288
7 2 13-16 17 7 385-512 27 12 12289-16384
8 3 17-24 18 8 513-768 28 13 16385-24576
9 3 25-32 19 8 769-1024 29 13 24577-32768
3.2.6. Compression with fixed Huffman codes (BTYPE=01)
The Huffman codes for the two alphabets are fixed, and are not
represented explicitly in the data. The Huffman code lengths
for the literal/length alphabet are:
Lit Value Bits Codes
--------- ---- -----
0 - 143 8 00110000 through
10111111
144 - 255 9 110010000 through
111111111
256 - 279 7 0000000 through
0010111
280 - 287 8 11000000 through
11000111
The code lengths are sufficient to generate the actual codes,
as described above; we show the codes in the table for added
clarity. Literal/length values 286-287 will never actually
occur in the compressed data, but participate in the code
construction.
Distance codes 0-31 are represented by (fixed-length) 5-bit
codes, with possible additional bits as shown in the table
shown in Paragraph 3.2.5, above. Note that distance codes 30-
31 will never actually occur in the compressed data.
3.2.7. Compression with dynamic Huffman codes (BTYPE=10)
The Huffman codes for the two alphabets appear in the block
immediately after the header bits and before the actual
compressed data, first the literal/length code and then the
distance code. Each code is defined by a sequence of code
lengths, as discussed in Paragraph 3.2.2, above. For even
greater compactness, the code length sequences themselves are
compressed using a Huffman code. The alphabet for code lengths
is as follows:
0 - 15: Represent code lengths of 0 - 15
16: Copy the previous code 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 code lengths of 8 (1 + 6 + 5)
17: Repeat a code length of 0 for 3 - 10 times.
(3 bits of length)
18: Repeat a code length of 0 for 11 - 138 times
(7 bits of length)
A code length of 0 indicates that the corresponding symbol in
the literal/length or distance alphabet will not occur in the
block, and should not participate in the Huffman code
construction algorithm given earlier. If only one distance
code is used, it is encoded using one bit, not zero bits; in
this case there is a single code length of one, with one unused
code. One distance code of zero bits means that there are no
distance codes used at all (the data is all literals).
We can now define the format of the block:
5 Bits: HLIT, # of Literal/Length codes - 257 (257 - 286)
5 Bits: HDIST, # of Distance codes - 1 (1 - 32)
4 Bits: HCLEN, # of Code Length codes - 4 (4 - 19)
(HCLEN + 4) x 3 bits: code lengths for the code length
alphabet given just above, in the order: 16, 17, 18,
0, 8, 7, 9, 6, 10, 5, 11, 4, 12, 3, 13, 2, 14, 1, 15
These code lengths are interpreted as 3-bit integers
(0-7); as above, a code length of 0 means the
corresponding symbol (literal/length or distance code
length) is not used.
HLIT + 257 code lengths for the literal/length alphabet,
encoded using the code length Huffman code
HDIST + 1 code lengths for the distance alphabet,
encoded using the code length Huffman code
The actual compressed data of the block,
encoded using the literal/length and distance Huffman
codes
The literal/length symbol 256 (end of data),
encoded using the literal/length Huffman code
The code length repeat codes can cross from HLIT + 257 to the
HDIST + 1 code lengths. In other words, all code lengths form
a single sequence of HLIT + HDIST + 258 values.
3.3. Compliance
A compressor may limit further the ranges of values specified in
the previous section and still be compliant; for example, it may
limit the range of backward pointers to some value smaller than
32K. Similarly, a compressor may limit the size of blocks so that
a compressible block fits in memory.
A compliant decompressor must accept the full range of possible
values defined in the previous section, and must accept blocks of
arbitrary size.
4. Compression algorithm details
While it is the intent of this document to define the "deflate"
compressed data format without reference to any particular
compression algorithm, the format is related to the compressed
formats produced by LZ77 (Lempel-Ziv 1977, see reference [2] below);
since many variations of LZ77 are patented, it is strongly
recommended that the implementor of a compressor follow the general
algorithm presented here, which is known not to be patented per se.
The material in this section is not part of the definition of the
specification per se, and a compressor need not follow it in order to
be compliant.
The compressor terminates a block when it determines that starting a
new block with fresh trees would be useful, or when the block size
fills up the compressor's block buffer.
The compressor uses a chained hash table to find duplicated strings,
using a hash function that operates on 3-byte sequences. At any
given point during compression, let XYZ be the next 3 input bytes to
be examined (not necessarily all different, of course). First, the
compressor examines the hash chain for XYZ. If the chain is empty,
the compressor simply writes out X as a literal byte and advances one
byte in the input. If the hash chain is not empty, indicating that
the sequence XYZ (or, if we are unlucky, some other 3 bytes with the
same hash function value) has occurred recently, the compressor
compares all strings on the XYZ hash chain with the actual input data
sequence starting at the current point, and selects the longest
match.
The compressor searches the hash chains starting with the most recent
strings, to favor small distances and thus take advantage of the
Huffman encoding. The hash chains are singly linked. There are no
deletions from the hash chains; the algorithm simply discards matches
that are too old. To avoid a worst-case situation, very long hash
chains are arbitrarily truncated at a certain length, determined by a
run-time parameter.
To improve overall compression, the compressor optionally defers the
selection of matches ("lazy matching"): after a match of length N has
been found, the compressor searches for a longer match starting at
the next input byte. If it finds a longer match, it truncates the
previous match to a length of one (thus producing a single literal
byte) and then emits the longer match. Otherwise, it emits the
original match, and, as described above, advances N bytes before
continuing.
Run-time parameters also control this "lazy match" procedure. If
compression ratio is most important, the compressor attempts a
complete second search regardless of the length of the first match.
In the normal case, if the current match is "long enough", the
compressor reduces the search for a longer match, thus speeding up
the process. If speed is most important, the compressor inserts new
strings in the hash table only when no match was found, or when the
match is not "too long". This degrades the compression ratio but
saves time since there are both fewer insertions and fewer searches.
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