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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.
String: a sequence of arbitrary 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 <length, backward distance>. 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.
+---+ | | <-- 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
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.
Symbol Code ------ ---- A 10 B 0 C 110 D 111I.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 2Step 2 computes the following next_code values:
N next_code[N] - ------------ 1 0 2 0 3 2 4 14Step 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
first bit BFINAL next 2 bits BTYPENote 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 <length = 5, distance = 2> adds X,Y,X,Y,X to the output
stream.
We now specify each compression method in turn.
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.
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
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.
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.
A compliant decompressor must accept the full range of possible values defined in the previous section, and must accept blocks of arbitrary size.
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.
[2] Ziv J., Lempel A., "A Universal Algorithm for Sequential Data Compression", IEEE Transactions on Information Theory, Vol. 23, No. 3, pp. 337-343.
[3] Gailly, J.-L., and Adler, M., ZLIB documentation and sources, available in ftp://ftp.uu.net/pub/archiving/zip/doc/
[4] Gailly, J.-L., and Adler, M., GZIP documentation and sources, available as gzip-*.tar in ftp://prep.ai.mit.edu/pub/gnu/
[5] Schwartz, E. S., and Kallick, B. "Generating a canonical prefix encoding." Comm. ACM, 7,3 (Mar. 1964), pp. 166-169.
[6] Hirschberg and Lelewer, "Efficient decoding of prefix codes," Comm. ACM, 33,4, April 1990, pp. 449-459.
Phil Katz designed the deflate format. Jean-Loup Gailly and Mark Adler wrote the related software described in this specification. Glenn Randers-Pehrson converted this document to RFC and HTML format.
Aladdin Enterprises 203 Santa Margarita Ave. Menlo Park, CA 94025 Phone: (415) 322-0103 (AM only) FAX: (415) 322-1734 EMail: <ghost@aladdin.com>Questions about the technical content of this specification can be sent by email to:
Jean-Loup Gailly <jloup@gzip.org> and Mark Adler <madler@alumni.caltech.edu>Editorial comments on this specification can be sent by email to:
L. Peter Deutsch <ghost@aladdin.com> and Glenn Randers-Pehrson <randeg@alumni.rpi.edu>