lzip/doc/lzip.texi

\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 26 January 2024
@set VERSION 1.24

@dircategory 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

@ifnottex
@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
* Algorithm::              How lzip compresses the data
* File format::            Detailed format of the compressed file
* 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{} 2008-2024 Antonio Diaz Diaz.

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


@node Introduction
@chapter Introduction
@cindex introduction

@uref{http://www.nongnu.org/lzip/lzip.html,,Lzip}
is a lossless data compressor with a user interface similar to the one
of gzip or bzip2. Lzip uses a simplified form of the 'Lempel-Ziv-Markov
chain-Algorithm' (LZMA) stream format to maximize interoperability. The
maximum dictionary size is 512 MiB so that any lzip file can be decompressed
on 32-bit machines. Lzip provides accurate and robust 3-factor integrity
checking. 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. Lzip has been designed, written, and tested with great care to
replace gzip and bzip2 as the standard general-purpose compressed format for
Unix-like systems.

For compressing/decompressing large files on multiprocessor machines
@uref{http://www.nongnu.org/lzip/manual/plzip_manual.html,,plzip} can be
much faster than lzip at the cost of a slightly reduced compression ratio.
@ifnothtml
@xref{Top,plzip manual,,plzip}.
@end ifnothtml

For creation and manipulation of compressed tar archives
@uref{http://www.nongnu.org/lzip/manual/tarlz_manual.html,,tarlz} can be more
efficient than using tar and plzip because tarlz is able to keep the
alignment between tar members and lzip members.
@ifnothtml
@xref{Top,tarlz manual,,tarlz}.
@end ifnothtml

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 program
@uref{http://www.nongnu.org/lzip/manual/lziprecover_manual.html#Data-safety,,lziprecover}
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 automatically uses for each file the largest dictionary size that does
not exceed neither the file size nor the limit given. 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
@option{-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, if you have
appropriate privileges, ownership of the file just as @w{@samp{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 either the
option @option{-c} or the option @option{-o} is specified.

Lzip refuses to read compressed data from a terminal or write compressed
data to a terminal, as this would be entirely incomprehensible and might
leave the terminal in an abnormal state.

Lzip correctly decompresses 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 -tvvv foo.lz
  foo.lz:  6.676:1, 14.98% ratio, 85.02% saved.  450560 out,  67493 in. 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
@w{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
Size of the input data. This is the uncompressed size when compressing, or
the compressed size when decompressing or testing. Note that lzip always
prints the uncompressed size before the compressed size when compressing,
decompressing, testing, or listing.

@item out
Size of the output data. This is the compressed size when compressing, or
the decompressed size when decompressing or testing.

@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
If no file names are specified, lzip compresses (or decompresses) from
standard input to standard output. A hyphen @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. Remember to
prepend @file{./} to any file name beginning with a hyphen, or use @samp{--}.

lzip supports the following
@uref{http://www.nongnu.org/arg-parser/manual/arg_parser_manual.html#Argument-syntax,,options}:
@ifnothtml
@xref{Argument syntax,,,arg_parser}.
@end ifnothtml

@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.
This version number should be included in all bug reports.

@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}. It is advisable
to keep members smaller than RAM size so that they can be repaired with
lziprecover in case of corruption. 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. (The
output consists of a sequence of independently compressed members). This
option (or @option{-o}) 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. @option{-c} overrides @option{-o}
and @option{-S}. @option{-c} has no effect when testing or listing.

@item -d
@itemx --decompress
Decompress the files specified. The integrity of the files specified is
checked. If a file does not exist, can't be opened, or the destination file
already exists and @option{--force} has not been specified, lzip continues
decompressing the rest of the files and exits with error status 1. If a file
fails to decompress, or is a terminal, lzip exits immediately with error
status 2 without decompressing the rest of the files. A terminal is
considered an uncompressed file, and therefore invalid.

@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
files specified. 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 @option{-v}, the dictionary
size, the number of members in the file, and the amount of trailing data (if
any) are also printed. With @option{-vv}, the positions and sizes of each
member in multimember files are also printed.

If any file is damaged, does not exist, can't be opened, or is not regular,
the final exit status is @w{> 0}. @option{-lq} can be used to check quickly
(without decompressing) the structural integrity of the files specified.
(Use @option{--test} to check the data integrity). @option{-alq}
additionally checks that none of the files specified 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}
If @option{-c} has not been also specified, write the (de)compressed output
to @var{file}, automatically creating any missing parent directories; keep
input files unchanged. If compressing several files, each file is compressed
independently. (The output consists of a sequence of independently
compressed members). This option (or @option{-c}) is needed when reading
from a named pipe (fifo) or from a device. @w{@option{-o -}} is equivalent
to @option{-c}. @option{-o} has no effect when testing or listing.

In order to keep backward compatibility with lzip versions prior to 1.22,
when compressing from standard input and no other file names are given, the
extension @samp{.lz} is appended to @var{file} unless it already ends in
@samp{.lz} or @samp{.tlz}. This feature will be removed in a future version
of lzip. Meanwhile, redirection may be used instead of @option{-o} to write
the compressed output to a file without the extension @samp{.lz} in its
name: @w{@samp{lzip < file > foo}}.

When compressing and splitting the output in volumes, @var{file} is used as
a prefix, and several files named @samp{@var{file}00001.lz},
@samp{@var{file}00002.lz}, etc, are created. In this case, only one input
file is allowed.

@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 uses for
each file the largest dictionary size that does not exceed neither the file
size nor 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. Dictionary sizes are quantized so that they can be coded in just one
byte (@pxref{coded-dict-size}). If the size specified does not match one of
the valid sizes, it is 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, and @option{-c} has not been also specified, 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 files specified, but don't decompress them. This
really performs a trial decompression and throws away the result. Use it
together with @option{-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 testing 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 @option{-v} options show the progress of (de)compression.

@item -0 .. -9
Compression level. Set the compression parameters (dictionary size and
match length limit) as shown in the table below. The default compression
level is @option{-6}, equivalent to @w{@option{-s8MiB -m36}}. Note that
@option{-9} can be much slower than @option{-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 options @option{--dictionary-size} and
@option{--match-length} directly to achieve optimal performance.

If several compression levels or @option{-s} or @option{-m} options are
given, the last setting is used. For example @w{@option{-9 -s64MiB}} is
equivalent to @w{@option{-s64MiB -m273}}

@multitable {Level} {Dictionary size (-s)} {Match length limit (-m)}
@item Level @tab Dictionary size (-s) @tab Match length limit (-m)
@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 --empty-error
Exit with error status 2 if any empty member is found in the input files.

@item --marking-error
Exit with error status 2 if the first LZMA byte is non-zero in any member of
the input files. This may be caused by data corruption or by deliberate
insertion of tracking information in the file. Use
@w{@samp{lziprecover --clear-marking}} to clear any such non-zero bytes.

@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 expressed in decimal,
hexadecimal, or octal (using the same syntax as integer constants in C++),
and 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)
@item R @tab ronnabyte  (10^27)       @tab | @tab Ri @tab robibyte  (2^90)
@item Q @tab quettabyte (10^30)       @tab | @tab Qi @tab quebibyte (2^100)
@end multitable

@sp 1
Exit status: 0 for a normal exit, 1 for environmental problems
(file not found, invalid command-line options, I/O errors, etc), 2 to
indicate a corrupt or invalid input file, 3 for an internal consistency
error (e.g., 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 replace gzip
and bzip2 as the standard general-purpose compressed format for Unix-like
systems. This chapter describes the lessons learned from these previous
formats, and their application to the design of lzip. The lzip format
specification has been reviewed carefully and is believed to be free from
design errors.

@sp 1
@section Format design

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

Lziprecover is able to provide unique data recovery capabilities because the
lzip format is extraordinarily safe. The simple and safe design of the file
format complements the embedded error detection provided by the LZMA data
stream. 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
possible 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 optimal accuracy in the detection of
errors 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 several
million times more, resulting in a combined integrity checking optimally
accurate for any member size produced by lzip. Preliminary results suggest
that the lzip format is safe enough to be used in critical safety avionics
systems.

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 Hamming distance (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, then the header seems to be intact
(in spite of being corrupt) while the compressed blocks seem 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 or equal 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.
Additionally, 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

Our civilization depends critically on software; it had better be quality
software.@*
--- Bjarne Stroustrup

@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 method detects most false
positives for corruption. 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, data size, or
member size) in the member trailer.

@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 tested to check 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 adapts the dictionary size to the size of 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. @c key4_mask

@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 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". LZMA compression consists in describing the uncompressed data as a
succession of coding sequences from the set shown in Section @samp{What is
coded} (@pxref{what-is-coded}), and then encoding them using a range
encoder. For example, the option @option{-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 @option{-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) 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 bytes produced 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
During compression, lzip reads data in large blocks (one dictionary size at
a time). Therefore it may block for up to tens of seconds any process
feeding data to it through a pipe. This is normal. The blocking intervals
get longer with higher compression levels because dictionary size increases
(and compression speed decreases) with compression level.

@noindent
The ideas embodied in lzip are due to (at least) the following people:
Abraham Lempel and Jacob Ziv (for the LZ algorithm), Andrei 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 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 one or more independent "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 can
encode in compressed form up to @w{16 EiB - 1 byte} of uncompressed data.
The size of a multimember file is unlimited.

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.

@anchor{coded-dict-size}
@item DS (coded dictionary size, 1 byte)
The dictionary size is calculated by taking a power of 2 (the base size)
and subtracting 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 subtract
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)
Cyclic Redundancy Check (CRC) of the original uncompressed data.

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

@item Member size (8 bytes)
Total size of the member, including header and trailer. This field acts
as a distributed index, improves the checking of stream integrity, and
facilitates the safe recovery of undamaged members from multimember files.
Lzip limits the member size to @w{2 PiB} to prevent the data size field from
overflowing.

@end table


@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 finishes the LZMA stream with an "End Of Stream" (EOS) marker (the
distance-length pair @w{0xFFFFFFFFU, 2}), which in conjunction with the
@samp{member size} field in the member trailer allows the checking of stream
integrity. The EOS marker is the only LZMA marker allowed in lzip files. 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. This
simplified and marker-terminated form of the LZMA stream format has been
chosen to maximize interoperability and safety.

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 described individually.

It seems that the only way of describing the LZMA-302eos stream is to
describe 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 decompressor 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, included in appendix A. @xref{Reference source
code}. Lzd is written in C++11 and can be downloaded from the lzip download
directory.

@sp 1
@section What is coded

@anchor{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 most significant bit (MSB) to least significant bit (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 by
explaining a simpler version of the encoding.

Imagine you need to encode 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 encode 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}). Then, if the position is @w{>= 2}, you encode
the remaining @w{position - 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 encode the
position, 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 in what it calls a "slot"
the position of the most significant bit set, along with the value of the
next bit, using the same 6 bits that would take to encode the position
alone. This seems to need 66 slots (twice the number of positions), but for
positions 0 and 1 there is no next bit, so the number of slots needed 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 encoded as follows.
@samp{direct_bits} is the amount of remaining bits (from 1 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 encoded
separately. The last piece (all the direct_bits for distances 4 to 127
(slots 4 to 13), or the last 4 bits for distances @w{>= 128}
@w{(slot >= 14)}) is context-coded in reverse order (from LSB to MSB). For
distances @w{>= 128}, the @w{@samp{direct_bits - 4}} part is encoded 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 the current match length @w{(length - 2)}, with a maximum
of 3. The resulting value is in the range 0 to 3.

@end table


The types of previous sequences corresponding to each state are shown 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 last type in each line is the most recent.

@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 .35 .45
@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 .3 .5
@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:
@samp{range} (representing the most significant part of the range size
not yet decoded) and @samp{code} (representing the current point within
@samp{range}). @samp{range} is initialized to @w{2^32 - 1}, and
@samp{code} is initialized to 0.

The range encoder produces a first 0 byte that must be ignored by the
range decoder. (See the @samp{Range_decoder} constructor in the source).

@sp 1
@section Decoding and checking 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.

Once the "End Of Stream" marker has been decoded, the decompressor reads and
decodes the member trailer, and checks that the three integrity factors
stored there (CRC, data size, and member size) match those computed from the
data.


@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; an "End Of File" string (to check that the
file has not been truncated), 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 matches 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 @option{--trailing-error} guarantees that
any corrupt header is 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
@option{--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
option @option{--keep} to lzip and don't remove the original file until you
check the compressed file with a command like
@w{@samp{lzip -cd file.lz | cmp file -}}. Most RAM errors happening during
compression can only be detected by comparing the compressed file with the
original because the corruption happens before lzip compresses the RAM
contents, resulting in a valid compressed file containing wrong data.

@sp 1
@noindent
Example 1: Extract all the files from archive @samp{foo.tar.lz}.

@example
  tar -xf foo.tar.lz
or
  lzip -cd foo.tar.lz | tar -xf -
@end example

@sp 1
@noindent
Example 2: 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 3: Like example 2 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 4: 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 5: Check the integrity of the compressed file @samp{file.lz} and
show status.

@example
lzip -tv 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 at
offset 10000 to decompressed byte at offset 14999 (5000 bytes are produced).

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

@sp 1
@noindent
Example 9: Compress a whole device in /dev/sdc and send the output to
@samp{file.lz}.

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

@sp 1
@noindent
Example 10: 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 11: Extract a multivolume compressed tar archive.

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

@sp 1
@noindent
Example 12: 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{@samp{lzip --version}}.


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

@verbatim
/* Lzd - Educational decompressor for the lzip format
   Copyright (C) 2013-2024 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 command-line options, 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 __DJGPP__
#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()
    {
    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;


enum { header_size = 6, trailer_size = 20 };
typedef uint8_t Lzip_header[header_size]; // 0-3 magic bytes
					  //   4 version
					  //   5 coded dictionary size
typedef uint8_t Lzip_trailer[trailer_size];
			//  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
  {
  unsigned long long member_pos;
  uint32_t code;
  uint32_t range;

public:
  Range_decoder()
    : member_pos( header_size ), code( 0 ), range( 0xFFFFFFFFU )
    {
    get_byte();			// discard first byte of the LZMA stream
    for( int i = 0; i < 4; ++i ) code = ( code << 8 ) | get_byte();
    }

  uint8_t get_byte() { ++member_pos; return std::getc( stdin ); }
  unsigned long long member_position() const { return member_pos; }

  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;
    }

  bool decode_bit( Bit_model & bm )
    {
    bool 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
      {
      code -= bound;
      range -= 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 bool match_bit = ( match_byte >> i ) & 1;
      const bool 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 min_match_len +
             decode_tree( lm.bm_low[pos_state], len_low_bits );
    if( decode_bit( lm.choice2 ) == 0 )
      return min_match_len + len_low_symbols +
             decode_tree( lm.bm_mid[pos_state], len_mid_bits );
    return min_match_len + 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; }
  uint8_t get_byte() { return rdec.get_byte(); }
  unsigned long long member_position() const
    { return rdec.member_position(); }

  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 );
    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()	// Return 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
      {
      // literal byte
      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();
      continue;
      }
    // 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 = rdec.decode_len( rep_len_model, pos_state );
      }
    else					// match
      {
      rep3 = rep2; rep2 = rep1; rep1 = rep0;
      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 > 2 || ( argc == 2 && std::strcmp( argv[1], "-d" ) != 0 ) )
    {
    std::printf(
      "Lzd %s - Educational decompressor for the lzip format.\n"
      "Study the source code to learn how a lzip decompressor works.\n"
      "See the lzip manual for an explanation of the code.\n"
      "\nUsage: %s [-d] < file.lz > file\n"
      "Lzd decompresses from standard input to standard output.\n"
      "\nCopyright (C) 2024 Antonio Diaz Diaz.\n"
      "License 2-clause BSD.\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",
      PROGVERSION, argv[0] );
    return 0;
    }

#if defined __MSVCRT__ || defined __OS2__ || defined __DJGPP__
  setmode( STDIN_FILENO, O_BINARY );
  setmode( STDOUT_FILENO, O_BINARY );
#endif

  for( bool first_member = true; ; first_member = false )
    {
    Lzip_header header;				// check header
    for( int i = 0; i < header_size; ++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;					// ignore trailing data
      }
    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; }

    Lzip_trailer trailer;			// check trailer
    for( int i = 0; i < trailer_size; ++i ) trailer[i] = decoder.get_byte();
    int retval = 0;
    unsigned crc = 0;
    for( int i = 3; i >= 0; --i ) crc = ( crc << 8 ) + trailer[i];
    if( crc != decoder.crc() )
      { std::fputs( "CRC mismatch\n", stderr ); retval = 2; }

    unsigned long long data_size = 0;
    for( int i = 11; i >= 4; --i )
      data_size = ( data_size << 8 ) + trailer[i];
    if( data_size != decoder.data_position() )
      { std::fputs( "Data size mismatch\n", stderr ); retval = 2; }

    unsigned long long member_size = 0;
    for( int i = 19; i >= 12; --i )
      member_size = ( member_size << 8 ) + trailer[i];
    if( member_size != decoder.member_position() )
      { std::fputs( "Member size mismatch\n", stderr ); retval = 2; }
    if( retval ) return retval;
    }

  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