\input texinfo @c -*-texinfo-*-
@c %**start of header
@setfilename lzip.info
@documentencoding ISO-8859-15
@settitle Lzip Manual
@finalout
@c %**end of header

@set UPDATED 12 July 2015
@set VERSION 1.17

@dircategory Data Compression
@direntry
* Lzip: (lzip).                 LZMA lossless data compressor
@end direntry


@ifnothtml
@titlepage
@title Lzip
@subtitle LZMA lossless data compressor
@subtitle for Lzip version @value{VERSION}, @value{UPDATED}
@author by Antonio Diaz Diaz

@page
@vskip 0pt plus 1filll
@end titlepage

@contents
@end ifnothtml

@node Top
@top

This manual is for Lzip (version @value{VERSION}, @value{UPDATED}).

@menu
* Introduction::           Purpose and features of lzip
* Invoking lzip::          Command line interface
* Quality assurance::      Design, development and testing of lzip
* File format::            Detailed format of the compressed file
* Algorithm::              How lzip compresses the data
* Stream format::          Format of the LZMA stream in lzip files
* Examples::               A small tutorial with examples
* Problems::               Reporting bugs
* Reference source code::  Source code illustrating stream format
* Concept index::          Index of concepts
@end menu

@sp 1
Copyright @copyright{} 2008-2015 Antonio Diaz Diaz.

This manual is free documentation: you have unlimited permission
to copy, distribute and modify it.


@node Introduction
@chapter Introduction
@cindex introduction

Lzip is a lossless data compressor with a user interface similar to the
one of gzip or bzip2. Lzip is about as fast as gzip, compresses most
files more than bzip2, and is better than both from a data recovery
perspective.

The lzip file format is designed for data sharing and long-term
archiving, taking into account both data integrity and decoder
availability:

@itemize @bullet
@item
The lzip format provides very safe integrity checking and some data
recovery means. The
@uref{http://www.nongnu.org/lzip/manual/lziprecover_manual.html#Data-safety,,lziprecover}
program can repair bit-flip errors (one of the most common forms of data
corruption) in lzip files, and provides data recovery capabilities,
including error-checked merging of damaged copies of a file.
@ifnothtml
@ref{Data safety,,,lziprecover}.
@end ifnothtml

@item
The lzip format is as simple as possible (but not simpler). The lzip
manual provides the code of a simple decompressor along with a detailed
explanation of how it works, so that with the only help of the lzip
manual it would be possible for a digital archaeologist to extract the
data from a lzip file long after quantum computers eventually render
LZMA obsolete.

@item
Additionally the lzip reference implementation is copylefted, which
guarantees that it will remain free forever.
@end itemize

A nice feature of the lzip format is that a corrupt byte is easier to
repair the nearer it is from the beginning of the file. Therefore, with
the help of lziprecover, losing an entire archive just because of a
corrupt byte near the beginning is a thing of the past.

The member trailer stores the 32-bit CRC of the original data, the size
of the original data and the size of the member. These values, together
with the value remaining in the range decoder and the end-of-stream
marker, provide a 4 factor integrity checking which guarantees that the
decompressed version of the data is identical to the original. This
guards against corruption of the compressed data, and against undetected
bugs in lzip (hopefully very unlikely). The chances of data corruption
going undetected are microscopic. Be aware, though, that the check
occurs upon decompression, so it can only tell you that something is
wrong. It can't help you recover the original uncompressed data.

Lzip uses the same well-defined exit status values used by bzip2, which
makes it safer than compressors returning ambiguous warning values (like
gzip) when it is used as a back end for other programs like tar or
zutils.

Lzip will automatically use the smallest possible dictionary size for
each file without exceeding the given limit. Keep in mind that the
decompression memory requirement is affected at compression time by the
choice of dictionary size limit.

The amount of memory required for compression is about 1 or 2 times the
dictionary size limit (1 if input file size is less than dictionary size
limit, else 2) plus 9 times the dictionary size really used. The option
@samp{-0} is special and only requires about 1.5 MiB at most. The amount
of memory required for decompression is about 46 kB larger than the
dictionary size really used.

When compressing, lzip replaces every file given in the command line
with a compressed version of itself, with the name "original_name.lz".
When decompressing, lzip attempts to guess the name for the decompressed
file from that of the compressed file as follows:

@multitable {anyothername} {becomes} {anyothername.out}
@item filename.lz  @tab becomes @tab filename
@item filename.tlz @tab becomes @tab filename.tar
@item anyothername @tab becomes @tab anyothername.out
@end multitable

(De)compressing a file is much like copying or moving it; therefore lzip
preserves the access and modification dates, permissions, and, when
possible, ownership of the file just as "cp -p" does. (If the user ID or
the group ID can't be duplicated, the file permission bits S_ISUID and
S_ISGID are cleared).

Lzip is able to read from some types of non regular files if the
@samp{--stdout} option is specified.

If no file names are specified, lzip compresses (or decompresses) from
standard input to standard output. In this case, lzip will decline to
write compressed output to a terminal, as this would be entirely
incomprehensible and therefore pointless.

Lzip will correctly decompress a file which is the concatenation of two
or more compressed files. The result is the concatenation of the
corresponding uncompressed files. Integrity testing of concatenated
compressed files is also supported.

Lzip can produce multi-member files and safely recover, with
lziprecover, the undamaged members in case of file damage. Lzip can
also split the compressed output in volumes of a given size, even when
reading from standard input. This allows the direct creation of
multivolume compressed tar archives.

Lzip is able to compress and decompress streams of unlimited size by
automatically creating multi-member output. The members so created are
large, about 2 PiB each.


@node Invoking lzip
@chapter Invoking lzip
@cindex invoking
@cindex options
@cindex usage
@cindex version

The format for running lzip is:

@example
lzip [@var{options}] [@var{files}]
@end example

Lzip supports the following options:

@table @code
@item -h
@itemx --help
Print an informative help message describing the options and exit.

@item -V
@itemx --version
Print the version number of lzip on the standard output and exit.

@item -b @var{bytes}
@itemx --member-size=@var{bytes}
Set the member size limit to @var{bytes}. A small member size may
degrade compression ratio, so use it only when needed. Valid values
range from 100 kB to 2 PiB. Defaults to 2 PiB.

@item -c
@itemx --stdout
Compress or decompress to standard output. Needed when reading from a
named pipe (fifo) or from a device. Use it to recover as much of the
uncompressed data as possible when decompressing a corrupt file.

@item -d
@itemx --decompress
Decompress.

@item -f
@itemx --force
Force overwrite of output files.

@item -F
@itemx --recompress
Force re-compression of files whose name already has the @samp{.lz} or
@samp{.tlz} suffix.

@item -k
@itemx --keep
Keep (don't delete) input files during compression or decompression.

@item -m @var{bytes}
@itemx --match-length=@var{bytes}
Set the match length limit in bytes. After a match this long is found,
the search is finished. Valid values range from 5 to 273. Larger values
usually give better compression ratios but longer compression times.

@item -o @var{file}
@itemx --output=@var{file}
When reading from standard input and @samp{--stdout} has not been
specified, use @samp{@var{file}} as the virtual name of the uncompressed
file. This produces a file named @samp{@var{file}} when decompressing, a
file named @samp{@var{file}.lz} when compressing, and several files
named @samp{@var{file}00001.lz}, @samp{@var{file}00002.lz}, etc, when
compressing and splitting the output in volumes.

@item -q
@itemx --quiet
Quiet operation. Suppress all messages.

@item -s @var{bytes}
@itemx --dictionary-size=@var{bytes}
Set the dictionary size limit in bytes. Valid values range from 4 KiB to
512 MiB. Lzip will use the smallest possible dictionary size for each
file without exceeding this limit. Note that dictionary sizes are
quantized. If the specified size does not match one of the valid sizes,
it will be rounded upwards by adding up to (@var{bytes} / 16) to it.

For maximum compression you should use a dictionary size limit as large
as possible, but keep in mind that the decompression memory requirement
is affected at compression time by the choice of dictionary size limit.

@item -S @var{bytes}
@itemx --volume-size=@var{bytes}
Split the compressed output into several volume files with names
@samp{original_name00001.lz}, @samp{original_name00002.lz}, etc, and set
the volume size limit to @var{bytes}. Each volume is a complete, maybe
multi-member, lzip file. A small volume size may degrade compression
ratio, so use it only when needed. Valid values range from 100 kB to 4
EiB.

@item -t
@itemx --test
Check integrity of the specified file(s), but don't decompress them.
This really performs a trial decompression and throws away the result.
Use it together with @samp{-v} to see information about the file.

@item -v
@itemx --verbose
Verbose mode.@*
When compressing, show the compression ratio for each file processed. A
second @samp{-v} shows the progress of compression.@*
When decompressing or testing, further -v's (up to 4) increase the
verbosity level, showing status, compression ratio, dictionary size,
trailer contents (CRC, data size, member size), and up to 6 bytes of
trailing garbage (if any).

@item -0 .. -9
Set the compression parameters (dictionary size and match length limit)
as shown in the table below. Note that @samp{-9} can be much slower than
@samp{-0}. These options have no effect when decompressing.

The bidimensional parameter space of LZMA can't be mapped to a linear
scale optimal for all files. If your files are large, very repetitive,
etc, you may need to use the @samp{--match-length} and
@samp{--dictionary-size} options directly to achieve optimal
performance.

@multitable {Level} {Dictionary size} {Match length limit}
@item Level @tab Dictionary size @tab Match length limit
@item -0 @tab 64 KiB @tab  16 bytes
@item -1 @tab  1 MiB @tab   5 bytes
@item -2 @tab  1.5 MiB @tab   6 bytes
@item -3 @tab  2 MiB @tab   8 bytes
@item -4 @tab  3 MiB @tab  12 bytes
@item -5 @tab  4 MiB @tab  20 bytes
@item -6 @tab  8 MiB @tab  36 bytes
@item -7 @tab 16 MiB @tab  68 bytes
@item -8 @tab 24 MiB @tab 132 bytes
@item -9 @tab 32 MiB @tab 273 bytes
@end multitable

@item --fast
@itemx --best
Aliases for GNU gzip compatibility.

@end table

Numbers given as arguments to options may be followed by a multiplier
and an optional @samp{B} for "byte".

Table of SI and binary prefixes (unit multipliers):

@multitable {Prefix} {kilobyte  (10^3 = 1000)} {|} {Prefix} {kibibyte (2^10 = 1024)}
@item Prefix @tab Value               @tab | @tab Prefix @tab Value
@item k @tab kilobyte  (10^3 = 1000)  @tab | @tab Ki @tab kibibyte (2^10 = 1024)
@item M @tab megabyte  (10^6)         @tab | @tab Mi @tab mebibyte (2^20)
@item G @tab gigabyte  (10^9)         @tab | @tab Gi @tab gibibyte (2^30)
@item T @tab terabyte  (10^12)        @tab | @tab Ti @tab tebibyte (2^40)
@item P @tab petabyte  (10^15)        @tab | @tab Pi @tab pebibyte (2^50)
@item E @tab exabyte   (10^18)        @tab | @tab Ei @tab exbibyte (2^60)
@item Z @tab zettabyte (10^21)        @tab | @tab Zi @tab zebibyte (2^70)
@item Y @tab yottabyte (10^24)        @tab | @tab Yi @tab yobibyte (2^80)
@end multitable

@sp 1
Exit status: 0 for a normal exit, 1 for environmental problems (file not
found, invalid flags, I/O errors, etc), 2 to indicate a corrupt or
invalid input file, 3 for an internal consistency error (eg, bug) which
caused lzip to panic.


@node Quality assurance
@chapter Design, development and testing of lzip
@cindex quality assurance

There are two ways of constructing a software design. One way is to make
it so simple that there are obviously no deficiencies and the other is
to make it so complicated that there are no obvious deficiencies.@*
--- C.A.R. Hoare

Lzip has been designed, written and tested with great care to be the
standard general-purpose compressor for unix-like systems. This chapter
describes the lessons learned from previous compressors (gzip and
bzip2), and their application to the design of lzip.

@sp 1
@section Format design

When gzip was designed in 1992, computers and operating systems were
much less capable than they are today. Gzip tried to work around some of
those limitations, like 8.3 file names, with additional fields in its
file format.

Today those limitations have mostly disappeared, and the format of gzip
has proved to be unnecessarily complicated. It includes fields that were
never used, others that have lost its usefulness, and finally others
that have become too limited.

Bzip2 was designed 5 years later, and its format is simpler than the one
of gzip.

Probably the worst defect of the gzip format from the point of view of
data safety is the variable size of its header. If the byte at offset 3
(flags) of a gzip member gets corrupted, it mat become very difficult to
recover the data, even if the compressed blocks are intact, because it
can't be known with certainty where the compressed blocks begin.

By contrast, the header of a lzip member has a fixed length of 6. The
lzma stream in a lzip member always starts at offset 6, making it
trivial to recover the data even if the whole header becomes corrupt.

Bzip2 also provides a header of fixed length and marks the begin and end
of each compressed block with six magic bytes, making it possible to
find the compressed blocks even in case of file damage. But bzip2 does
not store the size of each compressed block, as lzip does.

Lzip provides better data recovery capabilities than any other gzip-like
compressor because its format has been designed from the beginning to be
simple and safe. It would be very difficult to write an automatic
recovery tool like lziprecover for the gzip format. And, as far as I
know, it has never been writen.

The lzip format is designed for long-term archiving. Therefore it
excludes any unneeded features that may interfere with the future
extraction of the uncompressed data.

@sp 1
@subsection Gzip format (mis)features not present in lzip

@table @samp
@item Multiple algorithms

Gzip provides a CM (Compression Method) field that has never been used
because it is a bad idea to begin with. New compression methods may
require additional fields, making it impossible to implement new methods
and, at the same time, keep the same format. This field does not solve
the problem of format proliferation; it just makes the problem less
obvious.

@item Optional fields in header

Unless special precautions are taken, optional fields are generally a
bad idea because they produce a header of variable size. The gzip header
has 2 fields that, in addition to being optional, are zero-terminated.
This means that if any byte inside the field gets zeroed, or if the
terminating zero gets altered, gzip won't be able to find neither the
header CRC nor the compressed blocks.

@item Optional CRC for the header

Using an optional checksum for the header is not only a bad idea, it is
an error; it may prevent the extraction of perfectly good data. For
example, if the checksum is used and the bit enabling it is reset by a
bit-flip, the header will appear to be intact (in spite of being
corrupt) while the compressed blocks will appear to be totally
unrecoverable (in spite of being intact). Very misleading indeed.

@end table

@subsection Lzip format improvements over gzip and bzip2

@table @samp
@item 64-bit size field

Probably the most frequently reported shortcoming of the gzip format is
that it only stores the least significant 32 bits of the uncompressed
size. The size of any file larger than 4 GiB gets truncated.

Bzip2 does not store the uncompressed size of the file.

The lzip format provides a 64-bit field for the uncompressed size.
Additionaly, lzip produces multi-member output automatically when the
size is too large for a single member, allowing for an unlimited
uncompressed size.

@item Distributed index

The lzip format provides a distributed index that, among other things,
helps plzip to decompress several times faster than pigz and helps
lziprecover do its job. Neither the gzip format nor the bzip2 format do
provide an index.

A distributed index is safer and more scalable than a monolithic index.
The monolithic index introduces a single point of failure in the
compressed file and may limit the number of members or the total
uncompressed size.

@end table

@section Quality of implementation

@table @samp
@item Multiple implementations

Just like the lzip format provides 4 factor protection against
undetected data corruption, the development methodology of the lzip
family of compressors provides 3 factor protection against undetected
programming errors.

Three related but independent compressor implementations, lzip, clzip
and minilzip/lzlib, are developed concurrently. Every stable release of
any of them is subjected to a hundred hours of intensive testing to
verify that it produces identical output to the other two. This
guarantees that all three implement the same algorithm, and makes it
unlikely that any of them may contain serious undiscovered errors. In
fact, no errors have been discovered in lzip since 2009.

@item Dictionary size

Lzip automatically uses the smallest possible dictionary size for each
file. In addition to reducing the amount of memory required for
decompression, this feature also minimizes the probability of being
affected by RAM errors during compression.

@item Exit status

Returning a warning status of 2 is a design flaw of compress that leaked
into the design of gzip. Both bzip2 and lzip are free from this flaw.

@end table


@node File format
@chapter File format
@cindex file format

Perfection is reached, not when there is no longer anything to add, but
when there is no longer anything to take away.@*
--- Antoine de Saint-Exupery

@sp 1
In the diagram below, a box like this:
@verbatim
+---+
|   | <-- the vertical bars might be missing
+---+
@end verbatim

represents one byte; a box like this:
@verbatim
+==============+
|              |
+==============+
@end verbatim

represents a variable number of bytes.

@sp 1
A lzip file consists of a series of "members" (compressed data sets).
The members simply appear one after another in the file, with no
additional information before, between, or after them.

Each member has the following structure:
@verbatim
+--+--+--+--+----+----+=============+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| ID string | VN | DS | Lzma stream | CRC32 |   Data size   |  Member size  |
+--+--+--+--+----+----+=============+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
@end verbatim

All multibyte values are stored in little endian order.

@table @samp
@item ID string
A four byte string, identifying the lzip format, with the value "LZIP"
(0x4C, 0x5A, 0x49, 0x50).

@item VN (version number, 1 byte)
Just in case something needs to be modified in the future. 1 for now.

@item DS (coded dictionary size, 1 byte)
The dictionary size is calculated by taking a power of 2 (the base size)
and substracting from it a fraction between 0/16 and 7/16 of the base
size.@*
Bits 4-0 contain the base 2 logarithm of the base size (12 to 29).@*
Bits 7-5 contain the numerator of the fraction (0 to 7) to substract
from the base size to obtain the dictionary size.@*
Example: 0xD3 = 2^19 - 6 * 2^15 = 512 KiB - 6 * 32 KiB = 320 KiB@*
Valid values for dictionary size range from 4 KiB to 512 MiB.

@item Lzma stream
The lzma stream, finished by an end of stream marker. Uses default
values for encoder properties. @xref{Stream format}, for a complete
description.

@item CRC32 (4 bytes)
CRC of the uncompressed original data.

@item Data size (8 bytes)
Size of the uncompressed original data.

@item Member size (8 bytes)
Total size of the member, including header and trailer. This field acts
as a distributed index, allows the verification of stream integrity, and
facilitates safe recovery of undamaged members from multi-member files.

@end table


@node Algorithm
@chapter Algorithm
@cindex algorithm

In spite of its name (Lempel-Ziv-Markov chain-Algorithm), LZMA is not a
concrete algorithm; it is more like "any algorithm using the LZMA coding
scheme". For example, the option @samp{-0} of lzip uses the scheme in almost
the simplest way possible; issuing the longest match it can find, or a
literal byte if it can't find a match. Inversely, a much more elaborated
way of finding coding sequences of minimum size than the one currently
used by lzip could be developed, and the resulting sequence could also
be coded using the LZMA coding scheme.

Lzip currently implements two variants of the LZMA algorithm; fast
(used by option @samp{-0}) and normal (used by all other compression levels).

The high compression of LZMA comes from combining two basic, well-proven
compression ideas: sliding dictionaries (LZ77/78) and markov models (the
thing used by every compression algorithm that uses a range encoder or
similar order-0 entropy coder as its last stage) with segregation of
contexts according to what the bits are used for.

Lzip is a two stage compressor. The first stage is a Lempel-Ziv coder,
which reduces redundancy by translating chunks of data to their
corresponding distance-length pairs. The second stage is a range encoder
that uses a different probability model for each type of data;
distances, lengths, literal bytes, etc.

Here is how it works, step by step:

1) The member header is written to the output stream.

2) The first byte is coded literally, because there are no previous
bytes to which the match finder can refer to.

3) The main encoder advances to the next byte in the input data and
calls the match finder.

4) The match finder fills an array with the minimum distances before the
current byte where a match of a given length can be found.

5) Go back to step 3 until a sequence (formed of pairs, repeated
distances and literal bytes) of minimum price has been formed. Where the
price represents the number of output bits produced.

6) The range encoder encodes the sequence produced by the main encoder
and sends the produced bytes to the output stream.

7) Go back to step 3 until the input data are finished or until the
member or volume size limits are reached.

8) The range encoder is flushed.

9) The member trailer is written to the output stream.

10) If there are more data to compress, go back to step 1.

@sp 1
@noindent
The ideas embodied in lzip are due to (at least) the following people:
Abraham Lempel and Jacob Ziv (for the LZ algorithm), Andrey Markov (for
the definition of Markov chains), G.N.N. Martin (for the definition of
range encoding), Igor Pavlov (for putting all the above together in
LZMA), and Julian Seward (for bzip2's CLI).


@node Stream format
@chapter Format of the LZMA stream in lzip files
@cindex format of the LZMA stream

The LZMA algorithm has three parameters, called "special LZMA
properties", to adjust it for some kinds of binary data. These
parameters are; @samp{literal_context_bits} (with a default value of 3),
@samp{literal_pos_state_bits} (with a default value of 0), and
@samp{pos_state_bits} (with a default value of 2). As a general purpose
compressor, lzip only uses the default values for these parameters.

Lzip also finishes the LZMA stream with an "End Of Stream" marker (the
distance-length pair 0xFFFFFFFFU, 2), which in conjunction with the
"member size" field in the member trailer allows the verification of
stream integrity. The LZMA stream in lzip files always has these two
features (default properties and EOS marker) and is referred to in this
document as LZMA-302eos or LZMA-lzip.

The second stage of LZMA is a range encoder that uses a different
probability model for each type of symbol; distances, lengths, literal
bytes, etc. Range encoding conceptually encodes all the symbols of the
message into one number. Unlike Huffman coding, which assigns to each
symbol a bit-pattern and concatenates all the bit-patterns together,
range encoding can compress one symbol to less than one bit. Therefore
the compressed data produced by a range encoder can't be split in pieces
that could be individually described.

It seems that the only way of describing the LZMA-302eos stream is
describing the algorithm that decodes it. And given the many details
about the range decoder that need to be described accurately, the source
code of a real decoder seems the only appropriate reference to use.

What follows is a description of the decoding algorithm for LZMA-302eos
streams using as reference the source code of "lzd", an educational
decompressor for lzip files which can be downloaded from the lzip
download directory. The source code of lzd is included in appendix A.
@ref{Reference source code}

@sp 1
@section What is coded

The LZMA stream includes literals, matches and repeated matches (matches
reusing a recently used distance). There are 7 different coding sequences:

@multitable @columnfractions .35 .14 .51
@headitem Bit sequence @tab Name @tab Description
@item 0 + byte @tab literal @tab literal byte
@item 1 + 0 + len + dis @tab match @tab distance-length pair
@item 1 + 1 + 0 + 0 @tab shortrep @tab 1 byte match at latest used
distance
@item 1 + 1 + 0 + 1 + len @tab rep0 @tab len bytes match at latest used
distance
@item 1 + 1 + 1 + 0 + len @tab rep1 @tab len bytes match at second
latest used distance
@item 1 + 1 + 1 + 1 + 0 + len @tab rep2 @tab len bytes match at third
latest used distance
@item 1 + 1 + 1 + 1 + 1 + len @tab rep3 @tab len bytes match at fourth
latest used distance
@end multitable

@sp 1
In the following tables, multi-bit sequences are coded in normal order,
from MSB to LSB, except where noted otherwise.

Lengths (the @samp{len} in the table above) are coded as follows:

@multitable @columnfractions .5 .5
@headitem Bit sequence @tab Description
@item 0 + 3 bits @tab lengths from 2 to 9
@item 1 + 0 + 3 bits @tab lengths from 10 to 17
@item 1 + 1 + 8 bits @tab lengths from 18 to 273
@end multitable

@sp 1
The coding of distances is a little more complicated. LZMA divides the
interval between any two powers of 2 into 2 halves, named slots. As
possible distances range from 0 to (2^32 - 1), there are 64 slots (0 to
63). The slot number is context-coded in 6 bits. @samp{direct_bits} are
the remaining bits (from 0 to 30) needed to form a complete distance,
and are calculated as (slot >> 1) - 1. If a distance needs 6 or more
direct_bits, the last 4 bits are coded separately. The last piece
(direct_bits for distances 4 to 127 or the last 4 bits for distances >=
128) is context-coded in reverse order (from LSB to MSB). For distances
>= 128, the @samp{direct_bits - 4} part is coded with fixed 0.5
probability.

@multitable @columnfractions .5 .5
@headitem Bit sequence @tab Description
@item slot @tab distances from 0 to 3
@item slot + direct_bits @tab distances from 4 to 127
@item slot + (direct_bits - 4) + 4 bits @tab distances from 128 to
2^32 - 1
@end multitable

@sp 1
@section The coding contexts

These contexts (@samp{Bit_model} in the source), are integers or arrays
of integers representing the probability of the corresponding bit being 0.

The indices used in these arrays are:

@table @samp
@item state
A state machine (@samp{State} in the source) with 12 states (0 to 11),
coding the latest 2 to 4 types of sequences processed. The initial state
is 0.

@item pos_state
Value of the 2 least significant bits of the current position in the
decoded data.

@item literal_state
Value of the 3 most significant bits of the latest byte decoded.

@item len_state
Coded value of length (length - 2), with a maximum of 3. The resulting
value is in the range 0 to 3.

@end table


In the following table, @samp{!literal} is any sequence except a literal
byte. @samp{rep} is any one of @samp{rep0}, @samp{rep1}, @samp{rep2} or
@samp{rep3}. The types of previous sequences corresponding to each state
are:

@multitable {State} {rep or (!literal, shortrep), literal, literal}
@headitem State @tab Types of previous sequences
@item  0 @tab literal, literal, literal
@item  1 @tab match, literal, literal
@item  2 @tab rep or (!literal, shortrep), literal, literal
@item  3 @tab literal, shortrep, literal, literal
@item  4 @tab match, literal
@item  5 @tab rep or (!literal, shortrep), literal
@item  6 @tab literal, shortrep, literal
@item  7 @tab literal, match
@item  8 @tab literal, rep
@item  9 @tab literal, shortrep
@item 10 @tab !literal, match
@item 11 @tab !literal, (rep or shortrep)
@end multitable

@sp 1
The contexts for decoding the type of coding sequence are:

@multitable @columnfractions .2 .4 .4
@headitem Name @tab Indices @tab Used when
@item bm_match @tab state, pos_state @tab sequence start
@item bm_rep @tab state @tab after sequence 1
@item bm_rep0 @tab state @tab after sequence 11
@item bm_rep1 @tab state @tab after sequence 111
@item bm_rep2 @tab state @tab after sequence 1111
@item bm_len @tab state, pos_state @tab after sequence 110
@end multitable

@sp 1
The contexts for decoding distances are:

@multitable @columnfractions .2 .4 .4
@headitem Name @tab Indices @tab Used when
@item bm_dis_slot @tab len_state, bit tree @tab distance start
@item bm_dis @tab reverse bit tree @tab after slots 4 to 13
@item bm_align @tab reverse bit tree @tab for distances >= 128, after
fixed probability bits
@end multitable

@sp 1
There are two separate sets of contexts for lengths (@samp{Len_model} in
the source). One for normal matches, the other for repeated matches. The
contexts in each Len_model are (see @samp{decode_len} in the source):

@multitable @columnfractions .2 .4 .4
@headitem Name @tab Indices @tab Used when
@item choice1 @tab none @tab length start
@item choice2 @tab none @tab after sequence 1
@item bm_low @tab pos_state, bit tree @tab after sequence 0
@item bm_mid @tab pos_state, bit tree @tab after sequence 10
@item bm_high @tab bit tree @tab after sequence 11
@end multitable

@sp 1
The context array @samp{bm_literal} is special. In principle it acts as
a normal bit tree context, the one selected by @samp{literal_state}. But
if the previous decoded byte was not a literal, two other bit tree
contexts are used depending on the value of each bit in
@samp{match_byte} (the byte at the latest used distance), until a bit is
decoded that is different from its corresponding bit in
@samp{match_byte}. After the first difference is found, the rest of the
byte is decoded using the normal bit tree context. (See
@samp{decode_matched} in the source).

@sp 1
@section The range decoder

The LZMA stream is consumed one byte at a time by the range decoder.
(See @samp{normalize} in the source). Every byte consumed produces a
variable number of decoded bits, depending on how well these bits agree
with their context. (See @samp{decode_bit} in the source).

The range decoder state consists of two unsigned 32-bit variables;
@code{range} (representing the most significant part of the range size
not yet decoded), and @code{code} (representing the current point within
@code{range}). @code{range} is initialized to (2^32 - 1), and
@code{code} is initialized to 0.

The range encoder produces a first 0 byte that must be ignored by the
range decoder. This is done by shifting 5 bytes in the initialization of
@code{code} instead of 4. (See the @samp{Range_decoder} constructor in
the source).

@sp 1
@section Decoding the LZMA stream

After decoding the member header and obtaining the dictionary size, the
range decoder is initialized and then the LZMA decoder enters a loop
(See @samp{decode_member} in the source) where it invokes the range
decoder with the appropriate contexts to decode the different coding
sequences (matches, repeated matches, and literal bytes), until the "End
Of Stream" marker is decoded.


@node Examples
@chapter A small tutorial with examples
@cindex examples

WARNING! Even if lzip is bug-free, other causes may result in a corrupt
compressed file (bugs in the system libraries, memory errors, etc).
Therefore, if the data you are going to compress are important, give the
@samp{--keep} option to lzip and do not remove the original file until
you verify the compressed file with a command like
@w{@samp{lzip -cd file.lz | cmp file -}}.

@sp 1
@noindent
Example 1: Replace a regular file with its compressed version
@samp{file.lz} and show the compression ratio.

@example
lzip -v file
@end example

@sp 1
@noindent
Example 2: Like example 1 but the created @samp{file.lz} is multi-member
with a member size of 1 MiB. The compression ratio is not shown.

@example
lzip -b 1MiB file
@end example

@sp 1
@noindent
Example 3: Restore a regular file from its compressed version
@samp{file.lz}. If the operation is successful, @samp{file.lz} is
removed.

@example
lzip -d file.lz
@end example

@sp 1
@noindent
Example 4: Verify the integrity of the compressed file @samp{file.lz}
and show status.

@example
lzip -tv file.lz
@end example

@sp 1
@noindent
Example 5: Compress a whole floppy in /dev/fd0 and send the output to
@samp{file.lz}.

@example
lzip -c /dev/fd0 > file.lz
@end example

@sp 1
@noindent
Example 6: Decompress @samp{file.lz} partially until 10 KiB of
decompressed data are produced.

@example
lzip -cd file.lz | dd bs=1024 count=10
@end example

@sp 1
@noindent
Example 7: Decompress @samp{file.lz} partially from decompressed byte
10000 to decompressed byte 15000 (5000 bytes are produced).

@example
lzip -cd file.lz | dd bs=1000 skip=10 count=5
@end example

@sp 1
@noindent
Example 8: Create a multivolume compressed tar archive with a volume
size of 1440 KiB.

@example
tar -c some_directory | lzip -S 1440KiB -o volume_name
@end example

@sp 1
@noindent
Example 9: Extract a multivolume compressed tar archive.

@example
lzip -cd volume_name*.lz | tar -xf -
@end example

@sp 1
@noindent
Example 10: Create a multivolume compressed backup of a large database
file with a volume size of 650 MB, where each volume is a multi-member
file with a member size of 32 MiB.

@example
lzip -b 32MiB -S 650MB big_db
@end example


@node Problems
@chapter Reporting bugs
@cindex bugs
@cindex getting help

There are probably bugs in lzip. There are certainly errors and
omissions in this manual. If you report them, they will get fixed. If
you don't, no one will ever know about them and they will remain unfixed
for all eternity, if not longer.

If you find a bug in lzip, please send electronic mail to
@email{lzip-bug@@nongnu.org}. Include the version number, which you can
find by running @w{@code{lzip --version}}.


@node Reference source code
@appendix Reference source code
@cindex reference source code

@verbatim
/*  Lzd - Educational decompressor for the lzip format
    Copyright (C) 2013-2015 Antonio Diaz Diaz.

    This program is free software: you have unlimited permission
    to copy, distribute and modify it.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
*/
/*
    Exit status: 0 for a normal exit, 1 for environmental problems
    (file not found, invalid flags, I/O errors, etc), 2 to indicate a
    corrupt or invalid input file.
*/

#include <algorithm>
#include <cerrno>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <stdint.h>
#include <unistd.h>
#if defined(__MSVCRT__) || defined(__OS2__) || defined(_MSC_VER)
#include <fcntl.h>
#include <io.h>
#endif


class State
  {
  int st;

public:
  enum { states = 12 };
  State() : st( 0 ) {}
  int operator()() const { return st; }
  bool is_char() const { return st < 7; }

  void set_char()
    {
    static const int next[states] = { 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 4, 5 };
    st = next[st];
    }
  void set_match()     { st = ( st < 7 ) ? 7 : 10; }
  void set_rep()       { st = ( st < 7 ) ? 8 : 11; }
  void set_short_rep() { st = ( st < 7 ) ? 9 : 11; }
  };


enum {
  min_dictionary_size = 1 << 12,
  max_dictionary_size = 1 << 29,
  literal_context_bits = 3,
  pos_state_bits = 2,
  pos_states = 1 << pos_state_bits,
  pos_state_mask = pos_states - 1,

  len_states = 4,
  dis_slot_bits = 6,
  start_dis_model = 4,
  end_dis_model = 14,
  modeled_distances = 1 << (end_dis_model / 2),		// 128
  dis_align_bits = 4,
  dis_align_size = 1 << dis_align_bits,

  len_low_bits = 3,
  len_mid_bits = 3,
  len_high_bits = 8,
  len_low_symbols = 1 << len_low_bits,
  len_mid_symbols = 1 << len_mid_bits,
  len_high_symbols = 1 << len_high_bits,
  max_len_symbols = len_low_symbols + len_mid_symbols + len_high_symbols,

  min_match_len = 2,					// must be 2

  bit_model_move_bits = 5,
  bit_model_total_bits = 11,
  bit_model_total = 1 << bit_model_total_bits };

struct Bit_model
  {
  int probability;
  Bit_model() : probability( bit_model_total / 2 ) {}
  };

struct Len_model
  {
  Bit_model choice1;
  Bit_model choice2;
  Bit_model bm_low[pos_states][len_low_symbols];
  Bit_model bm_mid[pos_states][len_mid_symbols];
  Bit_model bm_high[len_high_symbols];
  };


class CRC32
  {
  uint32_t data[256];		// Table of CRCs of all 8-bit messages.

public:
  CRC32()
    {
    for( unsigned n = 0; n < 256; ++n )
      {
      unsigned c = n;
      for( int k = 0; k < 8; ++k )
        { if( c & 1 ) c = 0xEDB88320U ^ ( c >> 1 ); else c >>= 1; }
      data[n] = c;
      }
    }

  void update_buf( uint32_t & crc, const uint8_t * const buffer,
                   const int size ) const
    {
    for( int i = 0; i < size; ++i )
      crc = data[(crc^buffer[i])&0xFF] ^ ( crc >> 8 );
    }
  };

const CRC32 crc32;


typedef uint8_t File_header[6];	// 0-3 magic, 4 version, 5 coded_dict_size

typedef uint8_t File_trailer[20];
			//  0-3  CRC32 of the uncompressed data
			//  4-11 size of the uncompressed data
			// 12-19 member size including header and trailer

class Range_decoder
  {
  uint32_t code;
  uint32_t range;

public:
  Range_decoder() : code( 0 ), range( 0xFFFFFFFFU )
    {
    for( int i = 0; i < 5; ++i ) code = (code << 8) | get_byte();
    }

  uint8_t get_byte() { return std::getc( stdin ); }

  int decode( const int num_bits )
    {
    int symbol = 0;
    for( int i = 0; i < num_bits; ++i )
      {
      range >>= 1;
      symbol <<= 1;
      if( code >= range ) { code -= range; symbol |= 1; }
      if( range <= 0x00FFFFFFU )			// normalize
        { range <<= 8; code = (code << 8) | get_byte(); }
      }
    return symbol;
    }

  int decode_bit( Bit_model & bm )
    {
    int symbol;
    const uint32_t bound = ( range >> bit_model_total_bits ) * bm.probability;
    if( code < bound )
      {
      range = bound;
      bm.probability += (bit_model_total - bm.probability) >> bit_model_move_bits;
      symbol = 0;
      }
    else
      {
      range -= bound;
      code -= bound;
      bm.probability -= bm.probability >> bit_model_move_bits;
      symbol = 1;
      }
    if( range <= 0x00FFFFFFU )				// normalize
      { range <<= 8; code = (code << 8) | get_byte(); }
    return symbol;
    }

  int decode_tree( Bit_model bm[], const int num_bits )
    {
    int symbol = 1;
    for( int i = 0; i < num_bits; ++i )
      symbol = ( symbol << 1 ) | decode_bit( bm[symbol] );
    return symbol - (1 << num_bits);
    }

  int decode_tree_reversed( Bit_model bm[], const int num_bits )
    {
    int symbol = decode_tree( bm, num_bits );
    int reversed_symbol = 0;
    for( int i = 0; i < num_bits; ++i )
      {
      reversed_symbol = ( reversed_symbol << 1 ) | ( symbol & 1 );
      symbol >>= 1;
      }
    return reversed_symbol;
    }

  int decode_matched( Bit_model bm[], const int match_byte )
    {
    Bit_model * const bm1 = bm + 0x100;
    int symbol = 1;
    for( int i = 7; i >= 0; --i )
      {
      const int match_bit = ( match_byte >> i ) & 1;
      const int bit = decode_bit( bm1[(match_bit<<8)+symbol] );
      symbol = ( symbol << 1 ) | bit;
      if( match_bit != bit )
        {
        while( symbol < 0x100 )
          symbol = ( symbol << 1 ) | decode_bit( bm[symbol] );
        break;
        }
      }
    return symbol & 0xFF;
    }

  int decode_len( Len_model & lm, const int pos_state )
    {
    if( decode_bit( lm.choice1 ) == 0 )
      return decode_tree( lm.bm_low[pos_state], len_low_bits );
    if( decode_bit( lm.choice2 ) == 0 )
      return len_low_symbols +
             decode_tree( lm.bm_mid[pos_state], len_mid_bits );
    return len_low_symbols + len_mid_symbols +
           decode_tree( lm.bm_high, len_high_bits );
    }
  };


class LZ_decoder
  {
  unsigned long long partial_data_pos;
  Range_decoder rdec;
  const unsigned dictionary_size;
  uint8_t * const buffer;	// output buffer
  unsigned pos;			// current pos in buffer
  unsigned stream_pos;		// first byte not yet written to stdout
  uint32_t crc_;

  void flush_data();

  uint8_t peek( const unsigned distance ) const
    {
    unsigned i = pos - distance - 1;
    if( pos <= distance ) i += dictionary_size;
    return buffer[i];
    }

  void put_byte( const uint8_t b )
    {
    buffer[pos] = b;
    if( ++pos >= dictionary_size ) flush_data();
    }

public:
  explicit LZ_decoder( const unsigned dict_size )
    :
    partial_data_pos( 0 ),
    dictionary_size( dict_size ),
    buffer( new uint8_t[dictionary_size] ),
    pos( 0 ),
    stream_pos( 0 ),
    crc_( 0xFFFFFFFFU )
    { buffer[dictionary_size-1] = 0; }		// prev_byte of first byte

  ~LZ_decoder() { delete[] buffer; }

  unsigned crc() const { return crc_ ^ 0xFFFFFFFFU; }
  unsigned long long data_position() const { return partial_data_pos + pos; }

  bool decode_member();
  };


void LZ_decoder::flush_data()
  {
  if( pos > stream_pos )
    {
    const unsigned size = pos - stream_pos;
    crc32.update_buf( crc_, buffer + stream_pos, size );
    errno = 0;
    if( std::fwrite( buffer + stream_pos, 1, size, stdout ) != size )
      { std::fprintf( stderr, "Write error: %s\n", std::strerror( errno ) );
        std::exit( 1 ); }
    if( pos >= dictionary_size ) { partial_data_pos += pos; pos = 0; }
    stream_pos = pos;
    }
  }


bool LZ_decoder::decode_member()		// Returns false if error
  {
  Bit_model bm_literal[1<<literal_context_bits][0x300];
  Bit_model bm_match[State::states][pos_states];
  Bit_model bm_rep[State::states];
  Bit_model bm_rep0[State::states];
  Bit_model bm_rep1[State::states];
  Bit_model bm_rep2[State::states];
  Bit_model bm_len[State::states][pos_states];
  Bit_model bm_dis_slot[len_states][1<<dis_slot_bits];
  Bit_model bm_dis[modeled_distances-end_dis_model];
  Bit_model bm_align[dis_align_size];
  Len_model match_len_model;
  Len_model rep_len_model;
  unsigned rep0 = 0;			// rep[0-3] latest four distances
  unsigned rep1 = 0;			// used for efficient coding of
  unsigned rep2 = 0;			// repeated distances
  unsigned rep3 = 0;
  State state;

  while( !std::feof( stdin ) && !std::ferror( stdin ) )
    {
    const int pos_state = data_position() & pos_state_mask;
    if( rdec.decode_bit( bm_match[state()][pos_state] ) == 0 )	// 1st bit
      {
      const uint8_t prev_byte = peek( 0 );
      const int literal_state = prev_byte >> ( 8 - literal_context_bits );
      Bit_model * const bm = bm_literal[literal_state];
      if( state.is_char() )
        put_byte( rdec.decode_tree( bm, 8 ) );
      else
        put_byte( rdec.decode_matched( bm, peek( rep0 ) ) );
      state.set_char();
      }
    else					// match or repeated match
      {
      int len;
      if( rdec.decode_bit( bm_rep[state()] ) != 0 )		// 2nd bit
        {
        if( rdec.decode_bit( bm_rep0[state()] ) != 0 )		// 3rd bit
          {
          unsigned distance;
          if( rdec.decode_bit( bm_rep1[state()] ) == 0 )	// 4th bit
            distance = rep1;
          else
            {
            if( rdec.decode_bit( bm_rep2[state()] ) == 0 )	// 5th bit
              distance = rep2;
            else
              { distance = rep3; rep3 = rep2; }
            rep2 = rep1;
            }
          rep1 = rep0;
          rep0 = distance;
          }
        else
          {
          if( rdec.decode_bit( bm_len[state()][pos_state] ) == 0 ) // 4th bit
            { state.set_short_rep(); put_byte( peek( rep0 ) ); continue; }
          }
        state.set_rep();
        len = min_match_len + rdec.decode_len( rep_len_model, pos_state );
        }
      else					// match
        {
        rep3 = rep2; rep2 = rep1; rep1 = rep0;
        len = min_match_len + rdec.decode_len( match_len_model, pos_state );
        const int len_state = std::min( len - min_match_len, len_states - 1 );
        const int dis_slot =
          rdec.decode_tree( bm_dis_slot[len_state], dis_slot_bits );
        if( dis_slot < start_dis_model ) rep0 = dis_slot;
        else
          {
          const int direct_bits = ( dis_slot >> 1 ) - 1;
          rep0 = ( 2 | ( dis_slot & 1 ) ) << direct_bits;
          if( dis_slot < end_dis_model )
            rep0 += rdec.decode_tree_reversed( bm_dis + rep0 - dis_slot - 1,
                                               direct_bits );
          else
            {
            rep0 += rdec.decode( direct_bits - dis_align_bits ) << dis_align_bits;
            rep0 += rdec.decode_tree_reversed( bm_align, dis_align_bits );
            if( rep0 == 0xFFFFFFFFU )		// marker found
              {
              flush_data();
              return ( len == min_match_len );	// End Of Stream marker
              }
            }
          }
        state.set_match();
        if( rep0 >= dictionary_size || rep0 >= data_position() )
          { flush_data(); return false; }
        }
      for( int i = 0; i < len; ++i ) put_byte( peek( rep0 ) );
      }
    }
  flush_data();
  return false;
  }


int main( const int argc, const char * const argv[] )
  {
  if( argc > 1 )
    {
    std::printf( "Lzd %s - Educational decompressor for the lzip format.\n",
                 PROGVERSION );
    std::printf( "Study the source to learn how a lzip decompressor works.\n"
                 "See the lzip manual for an explanation of the code.\n"
                 "It is not safe to use lzd for any real work.\n"
                 "\nUsage: %s < file.lz > file\n", argv[0] );
    std::printf( "Lzd decompresses from standard input to standard output.\n"
                 "\nCopyright (C) 2015 Antonio Diaz Diaz.\n"
                 "This is free software: you are free to change and redistribute it.\n"
                 "There is NO WARRANTY, to the extent permitted by law.\n"
                 "Report bugs to lzip-bug@nongnu.org\n"
                 "Lzd home page: http://www.nongnu.org/lzip/lzd.html\n" );
    return 0;
    }

#if defined(__MSVCRT__) || defined(__OS2__) || defined(_MSC_VER)
  setmode( fileno( stdin ), O_BINARY );
  setmode( fileno( stdout ), O_BINARY );
#endif

  for( bool first_member = true; ; first_member = false )
    {
    File_header header;
    for( int i = 0; i < 6; ++i ) header[i] = std::getc( stdin );
    if( std::feof( stdin ) || std::memcmp( header, "LZIP\x01", 5 ) != 0 )
      {
      if( first_member )
        { std::fputs( "Bad magic number (file not in lzip format).\n", stderr );
          return 2; }
      break;
      }
    unsigned dict_size = 1 << ( header[5] & 0x1F );
    dict_size -= ( dict_size / 16 ) * ( ( header[5] >> 5 ) & 7 );
    if( dict_size < min_dictionary_size || dict_size > max_dictionary_size )
      { std::fputs( "Invalid dictionary size in member header.\n", stderr );
        return 2; }

    LZ_decoder decoder( dict_size );
    if( !decoder.decode_member() )
      { std::fputs( "Data error\n", stderr ); return 2; }

    File_trailer trailer;
    for( int i = 0; i < 20; ++i ) trailer[i] = std::getc( stdin );
    unsigned crc = 0;
    for( int i = 3; i >= 0; --i ) { crc <<= 8; crc += trailer[i]; }
    unsigned long long data_size = 0;
    for( int i = 11; i >= 4; --i ) { data_size <<= 8; data_size += trailer[i]; }
    if( crc != decoder.crc() || data_size != decoder.data_position() )
      { std::fputs( "CRC error\n", stderr ); return 2; }
    }

  if( std::fclose( stdout ) != 0 )
    { std::fprintf( stderr, "Can't close stdout: %s\n", std::strerror( errno ) );
      return 1; }
  return 0;
  }
@end verbatim


@node Concept index
@unnumbered Concept index

@printindex cp

@bye
