Bzip2

From Wikipedia, the free encyclopedia

Jump to: navigation, search
bzip2
File extension: .bz2, .tar.bz2, .tbz2, .tb2
MIME type: application/x-bzip
Type code: Bzp2
Developed by: Julian Seward
Type of format: data compression
bzip2
Developer: Julian Seward
Latest release: 1.0.4 / December 20, 2006
OS: Cross-platform
Use: data compression
License: Bzip2
Website: www.bzip.org
The correct title of this article is bzip2. The initial letter is shown capitalized due to technical restrictions.

bzip2 is a free software/open source data compression algorithm and program developed by Julian Seward. Seward made the first public release of bzip2, version 0.15, in July 1996. The compressor's stability and popularity grew over the next several years, and Seward released version 1.0 in late 2000.

Contents

[edit] Compression efficiency

bzip2 compresses most files more effectively than more traditional gzip or ZIP but is slower. In this manner it is fairly similar to other recent-generation compression algorithms. Unlike other formats such as RAR or ZIP (and similar to gzip), bzip2 is only a data compressor, not an archiver. The program itself has no facilities for multiple files, encryption or archive-splitting, in the UNIX tradition instead relying on separate external utilities such as tar and GnuPG for these tasks.

In some cases, bzip2 is surpassed by 7z and RAR formats in terms of absolute compression efficiency. According to the author, bzip2 gets within ten to fifteen percent of the "best" class of compression algorithms currently known (PPM), although it is roughly twice as fast at compression and six times faster at decompression.

bzip2 uses the Burrows-Wheeler transform to convert frequently recurring character sequences into strings of identical letters, and then applies a move-to-front transform and finally Huffman coding. In bzip2 the blocks are generally all the same size in plaintext, which can be selected by a command-line argument between 100kB–900kB. Compression blocks are delimited by a 48-bit sequence (magic number) derived from the binary-coded decimal representation of π, 0x314159265359, with the end-of-stream similarly delimited by a value representing sqrt(π), 0x177245385090.

Originally, bzip2's ancestor bzip used arithmetic coding after the blocksort; this was discontinued because of the patent restriction to be replaced by the Huffman coding currently used in bzip2.

[edit] Compression stack

Bzip2 uses several layers of compression techniques stacked on top of each other, which occur in the following order during compression and the reverse order during decompression:

  1. Run-length encoding (RLE), any sequence of four (4) duplicate symbols are adjusted so that the following symbol is replaced by a repeat length of between 0 and 255. Thus the sequence "AAAAAAABBBBCCCD" is replaced with "AAAA\4BBBB\0CCCD". Runs of symbols are always transformed after three consecutive symbols, even if the run-length is set to zero. This transformation is particularly good at taking care of large zeroed areas of files. In the worst case, it can cause a pre-BWT expansion of 1.25 and in the best case a reduction to <0.02 of original size.
  2. Burrows-Wheeler transform (BWT), this is the reversible block-sort that is at the core of bzip2. The block is entirely self contained, with input and output buffers remaining the same size—in bzip2, the operating limit for this stage is 900kB. For the block-sort, a (notional) matrix is created in which row i contains the whole of the buffer, rotated to start from the ith symbol. Following rotation, the rows of the matrix are sorted into alphabetic (numerical) order. A 24-bit pointer is stored marking the starting position for when the block is untransformed. In practice, it is not necessary to construct the full matrix, rather the sort is performed using pointers for each position in the buffer. The output buffer is the last column of the matrix; this contains the whole buffer, but reordered so that it is likely to contain large runs of identical symbols.
  3. Move to front (MTF), again, this transform does not alter the size of the processed block. Each of the symbols in use in the document is placed in an array. When a symbol is processed, it is replaced by its subscript (offset) in the array and that symbol is shuffled to the front of the array. The effect is that long runs of identical symbols are replaced by long runs of small symbols.
  4. Run-length encoding (RLE), long strings of repeated symbols in the output (normally zeros by this time) are replaced by a combination of the symbol and a sequence of two special codes, RUNA and RUNB, which represent the run-length as a binary number greater than one (1). The sequence 0,0,0,0,1 would be represented as 0,RUNB,RUNA,1; RUNB and RUNA representing the value 11 in binary, or three (3) in decimal. The run-length code is terminated by reaching another normal symbol.
  5. Huffman coding, this process replaces fixed length symbols (8-bit bytes) with variable length codes based on the frequency of use. More frequently used codes end up shorter (2-3 bits) whilst rare codes can be allocated up to 20 bits. The codes are selected carefully so that no sequence of bits can be confused for a different code. An additional code is used to mark the end of the stream: if fewer than 256 symbols are in use, then the end-of-stream will be the smallest used value, which could be as low as three (3). The code mappings are allocated as follows:
    0: RUNA
    1: RUNB
    2-257: byte values 0-255
    258: end of stream, finish processing. (could be as low as 3).
  6. Multiple Huffman tables, several identically-sized Huffman tables can be used with a block if the gain from using them is greater than the cost of including the extra table. At least two (2) and up to six (6) tables can be present, with the most appropriate table being reselected before every 50 symbols processed. This has the advantage of having very responsive Huffman dynamics without having to continuously supply new tables, as would be required in DEFLATE. Run-length encoding in the previous step is designed to take care of codes that have an inverse probability of use higher than the shortest code Huffman code in use.
  7. Unary Base 1 encoding, if multiple Huffman tables are in use, the selection of each table (numbered 0..5) is done from a list by a zero-terminated bit run between one (1) and six (6) bits in length. The selection is into a MTF list of the tables. Using this feature results in a maximum expansion of around 1.015, but generally less. This expansion is likely to be greatly over-shadowed by the advantage of selecting more appropriate Huffman tables and the common-case of continuing to use the same Huffman table is represented as a single bit. Rather than unary encoding, effectively this is an extreme form of a Huffman tree where each code has half the probability of the previous code.
  8. Delta encoding (Δ); Huffman code bit-lengths are required to reconstruct each of the used Canonical Huffman tables. Each bit-length is stored as an encoded difference against the previous code bit-length. A zero-bit (0) means that the previous bit-length should be duplicated for the current code, whilst a one-bit (1) means that a further bit should be read and the bit-length incremented or decremented based on that value. In the common case a single bit is used per symbol per table and the worst case—going from length one (1) to length twenty (20)—would require approximately 37 bits. As a result of the earlier MTF encoding, code lengths would start at 2-3bits long (very frequently used codes) and gradually increase, meaning that the delta format is fairly efficient—requiring around 300-bits (38 bytes) per full Huffman table.
  9. Sparse Bit array, a bitmap is used to show which symbols are used inside the block and should be included in the Huffman trees. Binary data is likely to use all 256 symbols representable by a byte, whereas textual data may only use a small subset of available values, perhaps covering the ASCII range between 32 and 126. Storing 256 zero bits would be inefficient if they were mostly unused. A sparse method is used, the 256 symbols are divided up into 16 ranges and only if symbols are used within that block is a 16-bit array included. The presence of each of these 16 ranges is indicated by an additional 16-bit bit array at the front. The total bitmap uses between 32 and 272 bits of storage (4–34 bytes). For contrast, the DEFLATE algorithm would show the absence of a symbol by encoded the symbol as having zero bit-length; this very inefficient with the Delta-encoding used in bzip2 which is the reason for bzip2 having a separate bit array.

[edit] File format

A .bz2 stream consists of a 4-byte header, followed by zero or more compressed blocks, immediately followed by an end-of-stream marker containing a 32-bit CRC for the plaintext whole stream processed. The compressed blocks are bit-aligned and no padding occurs.

/* Paul Sladen, 2007-01-11 */

.magic:16                       = 'BZ' signature/magic number
.version:8                      = 'h' for Bzip2 ('H'uffman coding), '0' for Bzip1 (deprecated)
.hundred_k_blocksize:8          = '1'..'9' block-size 100kB-900kB

.compressed_magic:48            = 0x314159265359 (BCD (pi))
.crc:32                         = checksum for this block
.randomised:1                   = 0=>normal, 1=>randomised (deprecated)
.origPtr:24                     = starting pointer into BWT for after untransform
.huffman_used_map:16            = bitmap, of ranges of 16 bytes, present/not present
.huffman_used_bitmaps:0..256    = bitmap, of symbols used, present/not present (multiples of 16)
.huffman_groups:3               = 2..6 number of different Huffman tables in use
.selectors_used:15              = number of times that the Huffman tables are swapped (each 50 bytes)
*.selector_list:1..6            = zero-terminated bit runs (0..62) of MTF'ed Huffman table (*selectors_used)
.start_huffman_length:5         = 0..20 starting bit length for Huffman deltas
*.delta_bit_length:1..40        = 0=>next symbol; 1=>alter length
                                                { 1=>length--;  0=>length++ } (*(symbols+2)*groups)
.contents:2..∞                  = Huffman encoded data stream until end of block

.eos_magic:48                   = 0x177245385090 (BCD sqrt(pi)
.crc:32                         = checksum for whole stream
.padding:0..7                   = align to whole byte

Note for implementors. Because of the first-stage RLE compression (see above), the maximum length of plaintext that a single 900kB bzip2 block can contain is around 46MB (45,899,235 bytes)! This staggering feat of compression can occur if the whole plaintext consists entirely of repeated values (the resulting .bz2 file in this case is 46 bytes long).[1]

[edit] Use

In Unix, bzip2 can be used combined with or independently of tar: bzip2 file to compress and bzip2 -d file.bz2 to uncompress (the alias bunzip2 for decompression may also be used).

bzip2's command line flags are mostly the same as in gzip. So, to extract from a bzip2-compressed tar-file:

bzcat archivefile.tar.bz2 | tar -xvf -

To create a bzip2-compressed tar-file:

tar -cvf - filenames | bzip2 > archivefile.tar.bz2

GNU tar supports a -j flag, which allows creation of tar.bz2 files without a pipeline:

tar -cvjf archivefile.tar.bz2 file-list

Decompressing in GNU tar:

tar -xvjf archivefile.tar.bz2

[edit] Implementations

[edit] See also

[edit] External links

[edit] References

  1. ^ $ dd if=/dev/zero bs=45899235 count=1 | bzip2 -vvvv | wc -c

    A even smaller file of 40 bytes can be achieved by using a input containing entirely values of 251, an apparent compression ratio of 1147480:1.

Personal tools