freebsd/gnu/usr.bin/gzip/algorithm.doc

1. Algorithm

The deflation algorithm used by zip and gzip 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,
length).  Distances are limited to 32K bytes, and lengths are limited
to 258 bytes. When a string does not occur anywhere in the previous
32K bytes, it is emitted as a sequence of literal bytes.  (In this
description, 'string' must be taken as an arbitrary sequence of bytes,
and is not restricted to printable characters.)

Literals or match lengths are compressed with one Huffman tree, and
match distances are compressed with another tree. The trees are stored
in a compact form at the start of each block. The blocks can have any
size (except that the compressed data for one block must fit in
available memory). A block is terminated when zip determines that it
would be useful to start another block with fresh trees. (This is
somewhat similar to compress.)

Duplicated strings are found using a hash table. All input strings of
length 3 are inserted in the hash table. A hash index is computed for
the next 3 bytes. If the hash chain for this index is not empty, all
strings in the chain are compared with the current input string, and
the longest match is selected.

The hash chains are searched 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 runtime option (zip -1
to -9). So zip does not always find the longest possible match but
generally finds a match which is long enough.

zip also defers the selection of matches with a lazy evaluation
mechanism. After a match of length N has been found, zip 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.

The lazy match evaluation is also subject to a runtime parameter. If
the current match is long enough, zip reduces the search for a longer
match, thus speeding up the whole process. If compression ratio is more
important than speed, zip attempts a complete second search even if
the first match is already long enough.

The lazy match evaluation is not performed for the fastest compression
modes (speed options -1 to -3). For these fast modes, new strings
are inserted 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. gzip file format

The pkzip format imposes a lot of overhead in various headers, which
are useful for an archiver but not necessary when only one file is
compressed. gzip uses a much simpler structure. Numbers are in little
endian format, and bit 0 is the least significant bit.
A gzip file is a sequence of compressed members. Each member has the
following structure:

2 bytes  magic header  0x1f, 0x8b (\037 \213)  
1 byte   compression method (0..7 reserved, 8 = deflate)
1 byte   flags
            bit 0 set: file probably ascii text
            bit 1 set: continuation of multi-part gzip file
            bit 2 set: extra field present
            bit 3 set: original file name present
            bit 4 set: file comment present
            bit 5 set: file is encrypted
            bit 6,7:   reserved
4 bytes  file modification time in Unix format
1 byte   extra flags (depend on compression method)
1 byte   operating system on which compression took place

2 bytes  optional part number (second part=1)
2 bytes  optional extra field length
? bytes  optional extra field
? bytes  optional original file name, zero terminated
? bytes  optional file comment, zero terminated
12 bytes optional encryption header
? bytes  compressed data
4 bytes  crc32
4 bytes  uncompressed input size modulo 2^32

The format was designed to allow single pass compression without any
backwards seek, and without a priori knowledge of the uncompressed
input size or the available size on the output media. If input does
not come from a regular disk file, the file modification time is set
to the time at which compression started.

The time stamp is useful mainly when one gzip file is transferred over
a network. In this case it would not help to keep ownership
attributes. In the local case, the ownership attributes are preserved
by gzip when compressing/decompressing the file. A time stamp of zero
is ignored.

Bit 0 in the flags is only an optional indication, which can be set by
a small lookahead in the input data. In case of doubt, the flag is
cleared indicating binary data. For systems which have different
file formats for ascii text and binary data, the decompressor can
use the flag to choose the appropriate format.

The extra field, if present, must consist of one or more subfields,
each with the following format:

  subfield id   : 2 bytes
  subfield size : 2 bytes  (little-endian format)
  subfield data

The subfield id can consist of two letters with some mnemonic value.
Please send any such id to jloup@chorus.fr. Ids with a zero second
byte are reserved for future use. The following ids are defined:

  Ap (0x41, 0x70) : Apollo file type information

The subfield size is the size of the subfield data and does not
include the id and the size itself. The field 'extra field length' is
the total size of the extra field, including subfield ids and sizes.

It must be possible to detect the end of the compressed data with any
compression format, regardless of the actual size of the compressed
data. If the compressed data cannot fit in one file (in particular for
diskettes), each part starts with a header as described above, but
only the last part has the crc32 and uncompressed size. A decompressor
may prompt for additional data for multipart compressed files. It is
desirable but not mandatory that multiple parts be extractable
independently so that partial data can be recovered if one of the
parts is damaged. This is possible only if no compression state is
kept from one part to the other. The compression-type dependent flags
can indicate this.

If the file being compressed is on a file system with case insensitive
names, the original name field must be forced to lower case. There is
no original file name if the data was compressed from standard input.

Compression is always performed, even if the compressed file is
slightly larger than the original. The worst case expansion is
a few bytes for the gzip file header, plus 5 bytes every 32K block,
or an expansion ratio of 0.015% for large files. Note that the actual
number of used disk blocks almost never increases.

The encryption is that of zip 1.9. For the encryption check, the
last byte of the decoded encryption header must be zero. The time
stamp of an encrypted file might be set to zero to avoid giving a clue
about the construction of the random header.

Jean-loup Gailly
jloup@chorus.fr

References:

[LZ77] Ziv J., Lempel A., "A Universal Algorithm for Sequential Data
Compression", IEEE Transactions on Information Theory", Vol. 23, No. 3,
pp. 337-343.

APPNOTE.TXT documentation file in PKZIP 1.93a. It is available by
ftp in ftp.cso.uiuc.edu:/pc/exec-pc/pkz193a.exe [128.174.5.59]
Use "unzip pkz193a.exe APPNOTE.TXT" to extract.