Lzip Compressed Format and the 'application/lzip' Media Type
draft-diaz-lzip-08
| Document | Type | Active Internet-Draft (individual) | |
|---|---|---|---|
| Author | Antonio Diaz Diaz | ||
| Last updated | 2023-06-26 | ||
| RFC stream | (None) | ||
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draft-diaz-lzip-08
Internet Engineering Task Force (IETF) A. Diaz
INTERNET-DRAFT draft-diaz-lzip-08 GNU Project
Category: Informational June 2023
Expiration date: 2023-12-28
Lzip Compressed Format and the 'application/lzip' Media Type
Abstract
Lzip is a lossless compressed data format designed for data sharing,
long-term archiving, and parallel compression/decompression. Lzip
uses LZMA compression and can achieve higher compression ratios than
gzip. Lzip provides accurate and robust 3-factor integrity checking.
This document describes the lzip format and registers a media type, a
content coding, and a structured syntax suffix to be used when
transporting lzip-compressed content via MIME or HTTP.
Status of This Memo
This document is not an Internet Standards Track specification; it is
published for informational purposes.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Not all documents
approved by the IESG are candidates for any level of Internet
Standard; see Section 2 of RFC 7841.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
http://www.rfc-editor.org/info/rfc<rfc-no>.
Comments are solicited and should be addressed to the lzip's mailing
list at lzip-bug@nongnu.org and/or the author.
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Copyright Notice
Copyright (c) 2023 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(http://trustee.ietf.org/license-info) in effect on the date of
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described in the Simplified BSD License.
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provisions of BCP 78 and BCP 79. Internet-Drafts are working
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Purpose . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2. Compliance . . . . . . . . . . . . . . . . . . . . . . . 4
2. File Format . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Format of the LZMA stream in lzip files . . . . . . . . . . . 5
3.1. What is coded . . . . . . . . . . . . . . . . . . . . . 6
3.2. The coding contexts . . . . . . . . . . . . . . . . . . 8
3.3. The range decoder . . . . . . . . . . . . . . . . . . . 10
3.4. Decoding and checking the LZMA stream . . . . . . . . . 10
3.5. Compression . . . . . . . . . . . . . . . . . . . . . . 10
4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 10
4.1. The 'application/lzip' Media Type . . . . . . . . . . . 11
4.2. Content Coding . . . . . . . . . . . . . . . . . . . . . 12
4.3. Structured Syntax Suffix . . . . . . . . . . . . . . . . 12
5. Security Considerations . . . . . . . . . . . . . . . . . . . 12
6. References . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.1. Normative References . . . . . . . . . . . . . . . . . . 14
6.2. Informative References . . . . . . . . . . . . . . . . . 14
Appendix A. Reference Source Code . . . . . . . . . . . . . . . 15
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 24
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 24
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1. Introduction
Lzip is a lossless compressed data format similar to gzip [RFC1952].
Lzip is designed for data sharing, long-term archiving, parallel
compression/decompression, and limited random access to the data.
Lzip can achieve higher compression ratios than gzip. Lzip provides
accurate and robust 3-factor integrity checking.
Lzip is designed to maximize interoperability between compliant
implementations. The file format is as simple as possible (but not
simpler); it only includes the fields required to decode and check
the data and does not contain any optional field nor specifies any
optional behavior. The maximum dictionary size is 512 MiB so that
any lzip file can be decompressed on 32-bit machines.
Lzip uses a simplified and marker-terminated form of the
Lempel-Ziv-Markov chain-Algorithm (LZMA) stream format. The original
LZMA algorithm and stream format were developed by Igor Pavlov. LZMA
is much like deflate (the algorithm of gzip) with two main
differences that account for its higher compression ratio. First,
LZMA can use a dictionary size thousands of times larger than
deflate. Second, LZMA uses a range encoder as its last stage instead
of the less efficient (but faster) Huffman coding used by deflate.
1.1. Purpose
The purpose of this document is to define a lossless compressed data
format that is a) independent of the CPU type, operating system, file
system, and character set and b) suitable for file compression and
pipe and streaming compression, using the LZMA algorithm. The text
of the specification assumes a basic background in programming at the
level of bits and other primitive data representations.
The data can be produced or consumed, even for an arbitrarily long
sequentially presented input data stream, using only an a priori
bounded amount of intermediate storage, and hence can be used in data
communications or similar structures, such as Unix filters.
The data format defined by this specification allows both efficient
parallel compression/decompression and random access to blocks of
compressed data by means of multimember files and a distributed
index.
This specification is intended for use by implementors of software to
compress data into lzip format and/or decompress data from lzip
format. The lzip format is supported by one free software reference
implementation (the lzip tool) written in portable C++ (C++11), and
by several free software implementations written in portable C (C99),
all of them available at [LZIP]. The reference implementation has
been in stable status since 2009, and is widely deployed.
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Also, to enable the transport of a data object compressed with lzip,
this document registers a media type, a content coding, and a
structured syntax suffix that can be used to identify such content
when it is used in a payload encoded using Multipurpose Internet Mail
Extensions (MIME) or Hypertext Transfer Protocol (HTTP).
1.2. Compliance
A compliant decompressor must be able to accept and decompress any
file that conforms to all the specifications presented here; a
compliant compressor must produce files that conform to all the
specifications presented here.
2. 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
In the diagram below, a box like this:
+---+
| | <-- the vertical bars might be missing
+---+
represents one byte; a box like this:
+==============+
| |
+==============+
represents a variable number of bytes.
In a byte, bit 7 is the most significant bit (MSB), while bit 0 is
the least significant bit (LSB).
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 16 EiB - 1 byte of
uncompressed data. The size of a multimember file is unlimited.
Each member has the following structure:
+-+-+-+-+---+---+===========+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| ID |VN |DS |LZMA stream| CRC32 | Data size | Member size |
+-+-+-+-+---+---+===========+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
All multibyte values are stored in little endian order.
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ID string (the "magic" bytes)
A four byte string, identifying the lzip format, with the value
"LZIP" (0x4C, 0x5A, 0x49, 0x50).
VN (version number, 1 byte)
Just in case something needs to be modified in the future. 1 for
now.
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.
LZMA stream
The LZMA stream, finished by an "End Of Stream" marker. Uses
default values for encoder properties. See Section 3 for a
complete description.
CRC32 (4 bytes)
Cyclic Redundancy Check (CRC) of the original uncompressed data.
Data size (8 bytes)
Size of the original uncompressed data.
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. One easy way for the compressor to
prevent the data size field from overflowing is to limit the
member size to 2 PiB.
3. Format of the LZMA stream in lzip files
The LZMA algorithm has three parameters, called "special LZMA
properties", to adjust it for some kinds of binary data. These
parameters are: 'literal_context_bits' (with a default value of 3),
'literal_pos_state_bits' (with a default value of 0), and
'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 'literal_pos_state_bits' has been optimized away and
does not even appear in the code.
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Lzip finishes the LZMA stream with an "End Of Stream" (EOS) marker
(the distance-length pair 0xFFFFFFFFU, 2), which in conjunction with
the '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. Lzd
is written in C++11 and can be downloaded from the lzip download
directory.
3.1. What is coded
The LZMA stream includes literals, matches, and repeated matches
(matches reusing a recently used distance). There are 7 different
coding sequences:
Bit sequence Name Description
----------------------- -------- --------------------------------
0 + byte literal literal byte
1 + 0 + len + dis match distance-length pair
1 + 1 + 0 + 0 shortrep 1 byte match at latest used
distance
1 + 1 + 0 + 1 + len rep0 len bytes match at latest used
distance
1 + 1 + 1 + 0 + len rep1 len bytes match at second latest
used distance
1 + 1 + 1 + 1 + 0 + len rep2 len bytes match at third latest
used distance
1 + 1 + 1 + 1 + 1 + len rep3 len bytes match at fourth latest
used distance
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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 'len' in the table above) are coded as follows:
Bit sequence Description
-------------- ----------------------
0 + 3 bits lengths from 2 to 9
1 + 0 + 3 bits lengths from 10 to 17
1 + 1 + 8 bits lengths from 18 to 273
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 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 >= 0x80000000).
Then, if the position is >= 2, you encode the remaining 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 >= 4, the remaining bits are encoded as follows.
'direct_bits' is the amount of remaining bits (from 1 to 30) needed
to form a complete distance, and is calculated as (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
>= 128 (slot >= 14)) is context-coded in reverse order (from LSB to
MSB). For distances >= 128, the 'direct_bits - 4' part is encoded
with fixed 0.5 probability.
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Bit sequence Description
--------------------------------- ------------------------------
slot distances from 0 to 3
slot + direct_bits distances from 4 to 127
slot + (direct_bits - 4) + 4 bits distances from 128 to 2^32 - 1
3.2. The coding contexts
These contexts ('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:
state
A state machine ('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.
pos_state
Value of the 2 least significant bits of the current position in
the decoded data.
literal_state
Value of the 3 most significant bits of the latest byte decoded.
len_state
Coded value of the current match length (length - 2), with a
maximum of 3. The resulting value is in the range 0 to 3.
The types of previous sequences corresponding to each state are shown
in the following table. '!literal' is any sequence except a literal
byte. 'rep' is any one of 'rep0', 'rep1', 'rep2', or 'rep3'. The
last type in each line is the most recent.
State Types of previous sequences
----- ---------------------------------------------
0 literal, literal, literal
1 match, literal, literal
2 rep or (!literal, shortrep), literal, literal
3 literal, shortrep, literal, literal
4 match, literal
5 rep or (!literal, shortrep), literal
6 literal, shortrep, literal
7 literal, match
8 literal, rep
9 literal, shortrep
10 !literal, match
11 !literal, (rep or shortrep)
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The contexts for decoding the type of coding sequence are:
Name Indices Used when
-------- ---------------- -------------------
bm_match state, pos_state sequence start
bm_rep state after sequence 1
bm_rep0 state after sequence 11
bm_rep1 state after sequence 111
bm_rep2 state after sequence 1111
bm_len state, pos_state after sequence 110
The contexts for decoding distances are:
Name Indices Used when
----------- ------------------- ---------------------------
bm_dis_slot len_state, bit tree distance start
bm_dis reverse bit tree after slots 4 to 13
bm_align reverse bit tree for distances >= 128, after
fixed probability bits
There are two separate sets of contexts for lengths ('Len_model' in
the source). One for normal matches, the other for repeated matches.
The contexts in each Len_model are (see 'decode_len' in the source):
Name Indices Used when
------- ------------------- -----------------
choice1 none length start
choice2 none after sequence 1
bm_low pos_state, bit tree after sequence 0
bm_mid pos_state, bit tree after sequence 10
bm_high bit tree after sequence 11
The context array 'bm_literal' is special. In principle it acts as a
normal bit tree context, the one selected by '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 'match_byte'
(the byte at the latest used distance), until a bit is decoded that
is different from its corresponding bit in 'match_byte'. After the
first difference is found, the rest of the byte is decoded using the
normal bit tree context. (See 'decode_matched' in the source).
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3.3. The range decoder
The LZMA stream is consumed one byte at a time by the range decoder.
(See '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 'decode_bit' in the source).
The range decoder state consists of two unsigned 32-bit variables:
'range' (representing the most significant part of the range size not
yet decoded) and 'code' (representing the current point within
'range'). 'range' is initialized to 2^32 - 1, and 'code' is
initialized to 0.
The range encoder produces a first 0 byte that must be ignored by the
range decoder. (See the 'Range_decoder' constructor in the source).
3.4. 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 '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
must read and decode the member trailer, and check that the three
integrity factors stored there (CRC, data size, and member size)
match those computed from the data.
3.5. Compression
Compression consists in describing the uncompressed data as a
succession of coding sequences from the set shown in Section 3.1, and
then encoding them using a range encoder. The fast encoder in the
reference implementation shows how this can be done in almost the
simplest way possible; issuing the longest match found, or a literal
byte if no match is found, and repeating until all the data have been
compressed. More sophisticated choosing of the coding sequences may
achieve higher compression ratios.
4. IANA Considerations
IANA is asked to make three registrations, as described below.
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4.1. The 'application/lzip' Media Type
The 'application/lzip' media type identifies a block of data that is
compressed using lzip compression. The data are a stream of bytes as
described in this document. IANA is asked to add the following entry
to the standards tree of the "Media Types" registry:
Type name: application
Subtype name: lzip
Required parameters: N/A
Optional parameters: N/A
Encoding considerations: binary
Security considerations: See Section 5 of this RFC
Interoperability considerations: N/A
Published specification: this RFC
Applications that use this media type:
Any application that desires to reduce the size of data
Fragment Identifier Considerations: N/A
Restrictions on Usage: N/A
Provisional Registrations: N/A
Additional information:
Deprecated alias names for this type: application/x-lzip
Magic number(s): First 4 bytes (0x4C, 0x5A, 0x49, 0x50)
File extension(s): lz, tlz (equivalent to tar.lz)
Macintosh File Type Code(s): N/A
Object Identifier(s) or OID(s): N/A
Intended Usage: COMMON
Other Information & Comments: See [LZIP]
Author: Antonio Diaz Diaz
Change Controller: IETF
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4.2. Content Coding
IANA is asked to add the following entry to the "HTTP Content Coding
Registry" within the "Hypertext Transfer Protocol (HTTP) Parameters"
registry:
Name: lzip
Description: A stream of bytes compressed using lzip compression
Pointer to specification text: this RFC
4.3. Structured Syntax Suffix
IANA is asked to add the following entry to the "Structured Syntax
Suffix" registry:
Name: lzip
+suffix: +lzip
References: this RFC
Encoding Considerations: binary
Interoperability Considerations: N/A
Fragment Identifier Considerations:
The syntax and semantics of fragment identifiers specified for
+lzip should be as specified for 'application/lzip'.
(At publication of this document, there is no fragment
identification syntax defined for 'application/lzip'.)
Security Considerations: See Section 5 of this RFC
Contact: See Author's Address of this RFC
Author/Change Controller: IETF
5. Security Considerations
Lzip is a compressed format. Decompressing lzip data may expand them
to a size more than 7000 times larger, risking an out-of-memory or
out-of-disc-space condition. The maximum amount of memory required
to decompress a lzip file is about 512 MiB. Since both the gzip and
lzip formats contain a single data stream, any steps already taken to
avoid such attacks on application/gzip should also work on
application/lzip. One possible measure, already implemented in some
applications, is to set a limit to the decompressed size and stop the
decompression or warn the user if the limit is surpassed.
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This media type does not employ any kind of "active content", but it
can be used to compress any other media type (for example
application/postscript) which could then be interpreted by the
application.
The lzip media type does not need itself any external security
mechanisms. But again, it can be used to compress other media types
requiring them (for example a media type defined for storage of
sensitive medical information).
Most types of files, even plain text files, can be marked with hidden
information. Some formats even include metadata fields for this
purpose. Such information can be used as a watermark to track the
path of the compressed payload. A lzip file does not store any
metadata. Moreover, any non-lzip data appended to the end of the
file is easily detected, and an error can be signaled. But the LZMA
stream inside each lzip member contains an extra first byte that is
ignored by the range decoder (see section 3.3), and can therefore be
(mis)used to store any value. As a consequence, it is possible to
insert tracking information in a lzip file by altering the first LZMA
byte in each member, or by appending to the file as many empty
members as tracking bytes are needed to identify the file. Apart
from this (mis)feature of the LZMA stream, it is not apparent how
this media type could be used to help violate a recipient's privacy.
The lziprecover tool, available at [LZIP], can be used to detect and
remove such tracking information from lzip files.
Because of the nature of the decoding algorithm used by lzip, it is
easy to protect the decoder from invalid memory accesses caused by
corruption in the input data (intentional or not). Size limits need
to be checked at just one place in the decompressor (the decoding of
rep0) to prevent buffer overflows. This inherent safety has been
extensively tested in the reference implementation.
The 'data size' field in the lzip trailer can be faked to be smaller
than the actual decompressed data in an attempt to trigger a buffer
overflow. This is not a problem for most lzip decompressors
(including the reference implementation) because they use 'data size'
only to check the size of the data produced, as an error detection
measure. However, any application that tries to decompress a whole
member in memory must not trust 'data size' and must always avoid
decompressing beyond the end of the buffer because, even if 'data
size' is correct, decompressing corrupt data may produce more
decompressed data than expected, and may cause a buffer overflow.
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Applications that send secret data (passwords, cookies) compressed
over an encrypted channel should be careful not to allow the
compressed size to be used as a side-channel to learn features of the
secret data. For example, an attacker that knows the size of the
secret data can distinguish ASCII text from high-entropy binary data
by their different compressibility. Applications should especially
avoid mixing secret data with attacker-supplied data in the same
compressed stream intended to be sent over an encrypted channel,
because an attacker who can observe the length of the ciphertext can
potentially reconstruct the secret data.
6. References
6.1. Normative References
[LZIP] Diaz, A., "Lzip", <http://www.nongnu.org/lzip/lzip.html>.
6.2. Informative References
[RFC1952] Deutsch, P., "GZIP file format specification version 4.3",
RFC 1952, DOI 10.17487/RFC1952, May 1996,
<http://www.rfc-editor.org/info/rfc1952>.
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Appendix A. Reference Source Code
<CODE BEGINS>
/* Lzd - Educational decompressor for the lzip format
Copyright (C) 2013-2023 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
#define PROGVERSION "1.3"
class State
{
int st;
public:
enum { states = 12 };
State() : st( 0 ) {}
int operator()() const { return st; }
bool is_char() const { return st < 7; }
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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;
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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 Lzip_header[6]; // 0-3 magic bytes
// 4 version
// 5 coded dictionary size
typedef uint8_t Lzip_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
{
unsigned long long member_pos;
uint32_t code;
uint32_t range;
public:
Range_decoder() : member_pos( 6 ), code( 0 ), range( 0xFFFFFFFFU )
{
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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;
}
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
{
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 );
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}
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
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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 );
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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
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{
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 ) )
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{ 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) 2023 Antonio Diaz Diaz.\n"
"License 2-clause BSD.\n"
"This is free software: you are free to change and redistribute "
"it.\nThere 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 < 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; // 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; }
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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 < 20; ++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;
}
<CODE ENDS>
Acknowledgements
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), and Igor Pavlov (for putting all the
above together in LZMA).
Author's Address
Antonio Diaz Diaz
GNU Project
Email: antonio@gnu.org
Expiration date: 2023-12-28
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