\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 11 February 2018
@set VERSION 1.20

@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
* Output::                 Meaning of lzip's output
* 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
* Trailing data::          Extra data appended to the file
* 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{} 2008-2018 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 can compress about as fast as gzip
@w{(lzip -0)}, or compress most files more than bzip2 @w{(lzip -9)}.
Decompression speed is intermediate between gzip and bzip2. Lzip is
better than gzip and bzip2 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
@xref{Data safety,,,lziprecover}.
@end ifnothtml

@item
The lzip format is as simple as possible (but not simpler). The lzip
manual provides the source 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 end-of-stream marker, provide a 3 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 @w{1.5 MiB} at most. The
amount of memory required for decompression is about @w{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 decompressed files. Integrity testing of concatenated
compressed files is also supported.

Lzip can produce multimember files, and lziprecover can safely recover
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 multimember output. The members so created are
large, about @w{2 PiB} each.


@node Output
@chapter Meaning of lzip's output
@cindex output

The output of lzip looks like this:

@example
lzip -v foo
  foo:  6.676:1, 14.98% ratio, 85.02% saved, 450560 in, 67493 out.

lzip -tvv foo.lz
  foo.lz:  6.676:1, 14.98% ratio, 85.02% saved.  ok
@end example

The meaning of each field is as follows:

@table @code
@item N:1
The compression ratio @w{(uncompressed_size / compressed_size)}, shown
as N to 1.

@item ratio
The inverse compression ratio @w{(compressed_size / uncompressed_size)},
shown as a percentage. A decimal ratio is easily obtained by moving the
decimal point two places to the left; @w{14.98% = 0.1498}.

@item saved
The space saved by compression @w{(1 - ratio)}, shown as a percentage.

@item in
The size of the uncompressed data. When decompressing or testing, it is
shown as @code{decompressed}. Note that lzip always prints the
uncompressed size before the compressed size when compressing,
decompressing, testing or listing.

@item out
The size of the compressed data. When decompressing or testing, it is
shown as @code{compressed}.

@end table

When decompressing or testing at verbosity level 4 (-vvvv), the
dictionary size used to compress the file and the CRC32 of the
uncompressed data are also shown.

LANGUAGE NOTE: Uncompressed = not compressed = plain data; it may never
have been compressed. Decompressed is used to refer to data which have
undergone the process of decompression.


@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

@noindent
@samp{-} used as a @var{file} argument means standard input. It can be
mixed with other @var{files} and is read just once, the first time it
appears in the command line.

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.

@anchor{--trailing-error}
@item -a
@itemx --trailing-error
Exit with error status 2 if any remaining input is detected after
decompressing the last member. Such remaining input is usually trailing
garbage that can be safely ignored. @xref{concat-example}.

@item -b @var{bytes}
@itemx --member-size=@var{bytes}
When compressing, 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 @w{100 kB} to @w{2 PiB}. Defaults to @w{2 PiB}.

@item -c
@itemx --stdout
Compress or decompress to standard output; keep input files unchanged.
If compressing several files, each file is compressed independently.
This option is needed when reading from a named pipe (fifo) or from a
device. Use it also to recover as much of the decompressed data as
possible when decompressing a corrupt file.

@item -d
@itemx --decompress
Decompress the specified files. If a file does not exist or can't be
opened, lzip continues decompressing the rest of the files. If a file
fails to decompress, or is a terminal, lzip exits immediately without
decompressing the rest of the files.

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

@item -F
@itemx --recompress
When compressing, 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 -l
@itemx --list
Print the uncompressed size, compressed size and percentage saved of the
specified files. Trailing data are ignored. The values produced are
correct even for multimember files. If more than one file is given, a
final line containing the cumulative sizes is printed. With @samp{-v},
the dictionary size, the number of members in the file, and the amount
of trailing data (if any) are also printed. With @samp{-vv}, the
positions and sizes of each member in multimember files are also
printed. @samp{-lq} can be used to verify quickly (without
decompressing) the structural integrity of the specified files. (Use
@samp{--test} to verify the data integrity). @samp{-alq} additionally
verifies that none of the specified files contain trailing data.

@item -m @var{bytes}
@itemx --match-length=@var{bytes}
When compressing, 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,
or a file named @samp{@var{file}.lz} when compressing. A second
@samp{.lz} extension is not added if @samp{@var{file}} already ends in
@samp{.lz} or @samp{.tlz}. When compressing and splitting the output in
volumes, several files named @samp{@var{file}00001.lz},
@samp{@var{file}00002.lz}, etc, are created.

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

@item -s @var{bytes}
@itemx --dictionary-size=@var{bytes}
When compressing, set the dictionary size limit in bytes. Lzip will use
the smallest possible dictionary size for each file without exceeding
this limit. Valid values range from @w{4 KiB} to @w{512 MiB}. Values 12
to 29 are interpreted as powers of two, meaning 2^12 to 2^29 bytes. 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
@w{(@var{bytes} / 8)} 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}
When compressing, 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}. Input files are kept
unchanged. Each volume is a complete, maybe multimember, lzip file. A
small volume size may degrade compression ratio, so use it only when
needed. Valid values range from @w{100 kB} to @w{4 EiB}.

@item -t
@itemx --test
Check integrity of the specified files, 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 files. If a file
fails the test, does not exist, can't be opened, or is a terminal, lzip
continues checking the rest of the files. A final diagnostic is shown at
verbosity level 1 or higher if any file fails the test when testing
multiple files.

@item -v
@itemx --verbose
Verbose mode.@*
When compressing, show the compression ratio and size for each file
processed.@*
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 data (if any) both in hexadecimal and as a string of printable
ASCII characters.@*
Two or more @samp{-v} options show the progress of (de)compression.

@item -0 .. -9
Set the compression parameters (dictionary size and match length limit)
as shown in the table below. The default compression level is @samp{-6}.
Note that @samp{-9} can be much slower than @samp{-0}. These options
have no effect when decompressing, testing or listing.

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{--dictionary-size} and
@samp{--match-length} 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.

@item --loose-trailing
When decompressing, testing or listing, allow trailing data whose first
bytes are so similar to the magic bytes of a lzip header that they can
be confused with a corrupt header. Use this option if a file triggers a
"corrupt header" error and the cause is not indeed a corrupt header.

@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 way
is to make it so complicated that there are no obvious deficiencies. The
first method is far more difficult.@*
--- 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 their 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 may become 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 also helps that the LZMA data stream as used by lzip
is extraordinarily safe. It provides embedded error detection. Any
distance larger than the dictionary size acts as a forbidden symbol,
allowing the decompressor to detect the approximate position of errors,
and leaving very little work for the check sequence (CRC and data sizes)
in the detection of errors. Lzip is usually able to detect all posible
bit flips in the compressed data without resorting to the check
sequence. It would be difficult to write an automatic recovery tool like
lziprecover for the gzip format. And, as far as I know, it has never
been written.

Lzip, like gzip and bzip2, uses a CRC32 to check the integrity of the
decompressed data because it provides more accurate error detection than
CRC64 up to a compressed size of about @w{16 GiB}, a size larger than
that of most files. In the case of lzip, the additional detection
capability of the decompressor reduces the probability of undetected
errors more than a million times beyond what the CRC32 alone provides.

The lzip format is designed for long-term archiving. Therefore it
excludes any unneeded features that may interfere with the future
extraction of the decompressed 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 CRC for the header is not only a bad idea, it is an
error; it circumvents the HD of the CRC and may prevent the extraction
of perfectly good data. For example, if the CRC 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.

@item Metadata

The gzip format stores some metadata, like the modification time of the
original file or the operating system on which compression took place.
This complicates reproducible compression (obtaining identical
compressed output from identical input).

@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 @w{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 multimember 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 Accurate and robust error detection

The lzip format provides 3 factor integrity checking and the
decompressors report mismatches in each factor separately. This way if
just one byte in one factor fails but the other two factors match the
data, it probably means that the data are intact and the corruption just
affects the mismatching factor (CRC or data size) in the check sequence.

@item Multiple implementations

Just like the lzip format provides 3 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.

Additionally, the three implementations have been extensively tested
with
@uref{http://www.nongnu.org/lzip/manual/lziprecover_manual.html#Unzcrash,,unzcrash},
valgrind and @samp{american fuzzy lop} without finding a single
vulnerability or false negative.
@ifnothtml
@xref{Unzcrash,,,lziprecover}.
@end ifnothtml

@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 (the "magic" bytes)
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 multimember 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. In
particular @samp{literal_pos_state_bits} has been optimized away and
does not even appear in the code.

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.
@xref{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, multibit 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, so I'll begin
explaining a simpler version of the encoding.

Imagine you need to code a number from 0 to @w{2^32 - 1}, and you want
to do it in a way that produces shorter codes for the smaller numbers.
You may first send the position of the most significant bit that is set
to 1, which you may find by making a bit scan from the left (from the
MSB). A position of 0 means that the number is 0 (no bit is set), 1
means the LSB is the first bit set (the number is 1), and 32 means the
MSB is set (i.e., the number is @w{>= 0x80000000}). Let's call this bit
position a "slot". Then, if slot is @w{> 1}, you send the remaining
@w{slot - 1} bits. Let's call these bits "direct_bits" because they are
coded directly by value instead of indirectly by position.

The inconvenient of this simple method is that it needs 6 bits to code
the slot, but it just uses 33 of the 64 possible values, wasting almost
half of the codes.

The intelligent trick of LZMA is that it encodes the position of the
most significant bit set, along with the value of the next bit, in the
same 6 bits that would take to encode the position alone. This seems to
need 66 slots (2 * position + next_bit), but for slots 0 and 1 there is
no next bit, so the number of needed slots is 64 (0 to 63).

The 6 bits representing this "slot number" are then context-coded. If
the distance is @w{>= 4}, the remaining bits are coded as follows.
@samp{direct_bits} is the amount of remaining bits (from 0 to 30) needed
to form a complete distance, and is calculated as @w{(slot >> 1) - 1}.
If a distance needs 6 or more direct_bits, the last 4 bits are coded
separately. The last piece (all the direct_bits for distances 4 to 127
or the last 4 bits for distances @w{>= 128}) is context-coded in reverse
order (from LSB to MSB). For distances @w{>= 128}, the
@w{@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 @w{(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 @w{(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 Trailing data
@chapter Extra data appended to the file
@cindex trailing data

Sometimes extra data are found appended to a lzip file after the last
member. Such trailing data may be:

@itemize @bullet
@item
Padding added to make the file size a multiple of some block size, for
example when writing to a tape. It is safe to append any amount of
padding zero bytes to a lzip file.

@item
Useful data added by the user; a cryptographically secure hash, a
description of file contents, etc. It is safe to append any amount of
text to a lzip file as long as none of the first four bytes of the text
match the corresponding byte in the string "LZIP", and the text does not
contain any zero bytes (null characters). Nonzero bytes and zero bytes
can't be safely mixed in trailing data.

@item
Garbage added by some not totally successful copy operation.

@item
Malicious data added to the file in order to make its total size and
hash value (for a chosen hash) coincide with those of another file.

@item
In rare cases, trailing data could be the corrupt header of another
member. In multimember or concatenated files the probability of
corruption happening in the magic bytes is 5 times smaller than the
probability of getting a false positive caused by the corruption of the
integrity information itself. Therefore it can be considered to be below
the noise level. Additionally, the test used by lzip to discriminate
trailing data from a corrupt header has a Hamming distance (HD) of 3,
and the 3 bit flips must happen in different magic bytes for the test to
fail. In any case, the option @samp{--trailing-error} guarantees that
any corrupt header will be detected.
@end itemize

Trailing data are in no way part of the lzip file format, but tools
reading lzip files are expected to behave as correctly and usefully as
possible in the presence of trailing data.

Trailing data can be safely ignored in most cases. In some cases, like
that of user-added data, they are expected to be ignored. In those cases
where a file containing trailing data must be rejected, the option
@samp{--trailing-error} can be used. @xref{--trailing-error}.


@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 don't 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 multimember
with a member size of @w{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 device in /dev/sdc and send the output to
@samp{file.lz}.

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

@sp 1
@anchor{concat-example}
@noindent
Example 6: The right way of concatenating the decompressed output of two
or more compressed files. @xref{Trailing data}.

@example
Don't do this
  cat file1.lz file2.lz file3.lz | lzip -d
Do this instead
  lzip -cd file1.lz file2.lz file3.lz
@end example

@sp 1
@noindent
Example 7: Decompress @samp{file.lz} partially until @w{10 KiB} of
decompressed data are produced.

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

@sp 1
@noindent
Example 8: 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 9: Create a multivolume compressed tar archive with a volume
size of @w{1440 KiB}.

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

@sp 1
@noindent
Example 10: Extract a multivolume compressed tar archive.

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

@sp 1
@noindent
Example 11: Create a multivolume compressed backup of a large database
file with a volume size of @w{650 MB}, where each volume is a
multimember file with a member size of @w{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) 2013-2018 Antonio Diaz Diaz.

    This program is free software. Redistribution and use in source and
    binary forms, with or without modification, are permitted provided
    that the following conditions are met:

    1. Redistributions of source code must retain the above copyright
    notice, this list of conditions and the following disclaimer.

    2. Redistributions in binary form must reproduce the above copyright
    notice, this list of conditions and the following disclaimer in the
    documentation and/or other materials provided with the distribution.

    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,
  literal_pos_state_bits = 0,				// not used
  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 ); }

  unsigned decode( const int num_bits )
    {
    unsigned symbol = 0;
    for( int i = num_bits; i > 0; --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;
    }

  unsigned decode_bit( Bit_model & bm )
    {
    unsigned 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;
    }

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

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

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

  unsigned 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_;
  bool pos_wrapped;

  void flush_data();

  uint8_t peek( const unsigned distance ) const
    {
    if( pos > distance ) return buffer[pos - distance - 1];
    if( pos_wrapped ) return buffer[dictionary_size + pos - distance - 1];
    return 0;			// prev_byte of first byte
    }

  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 ),
    pos_wrapped( false )
    {}

  ~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; pos_wrapped = true; }
    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+1];
  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
          {
          if( rdec.decode_bit( bm_len[state()][pos_state] ) == 0 ) // 4th bit
            { state.set_short_rep(); put_byte( peek( rep0 ) ); continue; }
          }
        else
          {
          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;
          }
        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 );
        rep0 = rdec.decode_tree( bm_dis_slot[len_state], dis_slot_bits );
        if( rep0 >= start_dis_model )
          {
          const unsigned dis_slot = rep0;
          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 ),
                                               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 >= pos && !pos_wrapped ) )
          { 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) 2018 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;				// verify 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 );		// decode LZMA stream
    if( !decoder.decode_member() )
      { std::fputs( "Data error\n", stderr ); return 2; }

    File_trailer trailer;			// verify 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, "Error closing stdout: %s\n", std::strerror( errno ) );
      return 1; }
  return 0;
  }
@end verbatim


@node Concept index
@unnumbered Concept index

@printindex cp

@bye
