Compression notes

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These are primarily notes
It won't be complete in any sense.
It exists to contain fragments of useful information.

Stuff vaguely related to storing, hosting, and transferring files and media:


Utilities and file formats (rather than methods and algorithms)

This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

General purpose


Commonly used, mostly because it caught on is so well in the mid-nineties it became a generic brand name.

Created by PKWare, as PKZIP, though many will know the WinZip product (not from PKWare. There was some compatibility kerfuffle about encryption at the time). (verify)

There have been a bunch of revisions/additions (see version history), and the amount of underlying compression formats has increased over time.

Of the compression formats, some are outdated, many are specialized, and there is optional encryption.

This also means not everything can open every zip file. To avoid compatibility problems, ZIP files created for compatibility are based on DEFLATE, so has basically not changed in twenty years.

compression methods

General purpose, little point because basic deflate is usually better:

  • 0: Store (no compression)
  • 1: Shrink
  • 2: Reduce (compression factor 1)
  • 3: Reduce (compression factor 2)
  • 4: Reduce (compression factor 3)
  • 5: Reduce (compression factor 4)
  • 6: Implode

General purpose, more common:

  • 8: Deflate (the one that everything supports)
  • 9: Deflate64 ('Enhanced deflate')
  • 14: LZMA
  • 98: PPMd (since WinZip version 11(verify))
  • 12: bzip2 (since WinZip version 11(verify))

Media-specific compression methods:

  • 96: Compressed lossless JPEG
  • 97: WavPack


  • 10: Old IBM TERSE
  • 18: New IBM TERSE
  • 19: IBM LZ77 z
  • 7: "Reserved for Tokenizing compression algorithm" (?)

multi-part ZIP

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Multipart zip files were once used to get over the maximum size of a medium, in particular floppies but also CDs, maximum supported/allowed file size (e.g. email attachments, FAT32).

(Note that multi-part ZIPs are now often created as Zip64 for large-file reasons(verify))

split zip

These are typically named z01, z02, etc., and the .zip is the last part (not the first as would be quite sensible to assume).

These files are mostly just the compressed bytes split at arbitrary points, except that the offsets in each part's headers are relative to the start of that part.

Which means that just concatenating them together does not make a correct zip file, though a script that fixes the offsets while concatenating, or even fixes them after naive concatentation, is relatively simple, and there are tools to do both.

Ideally your uncompressor just knows about split multipart zip, though, because it's fewer steps.

spanned zip

Spanned zip is the same as the above in terms of file contents, different only in the file naming, specifically all parts have the same name, but reside on different media.

For example, a set of floppies all have on them, which happen to be sequential parts known only via physical labeling on the floppies.

Relatively rare in that it's impractical to keep all these files on one medium (you'ld keep them in separate directories, or more probably, rename them to be able to handle them).

See also [1]


7zip (when handing non-7z zips)

doesn't create multi-part zip, it simply splits the whole stream at arbitrary points (doesn't alter the offsets),
names them,, etc.
7zip obviously understands what it made itself
For other tools you would directly concatenate these files, which creates a correct single zip file.


This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

From the WinZip team, based roughly on ZIP but different enough to be a separate format.

Not widely supported.


Compresses better than ZIP, also proprietary but comparably available, so was used instead of ZIP in certain areas.

Uses LZ and PPM(d)


The .7z format archive focuses on LZMA, which performs noticably better than ZIP's classical DEFLATE, and regularly a little better than other alternatives such as RAR, bz2, gzip, and others.

The 7zip program is useful as an interface that handles many formats, but the 7zip format itself is not supported by many others.

The 7zip interface uses plugins to support external formats. When you use it from the CLI and have multiple 7z commands, the difference is that:

  • 7z
    : the variant you can tell to use plugins
can read/write .7z, .zip, .gz, .bz2, .tar files, and reads from .rar, .cab, .iso, .arj, .lzh, .chm, .Z, .cpio, .rpm, .deb, and .nsis
  • 7za
    : a standalone variant, which handles only .7z, .zip, .gz, .bz2, .tar, .lzma, .cab, .Z
  • 7zr
    : a lightweight standalone version that handles only .7z
  • 7zg
    : GUI

In general (e.g. linux CLI) you can use 7z (some package only 7za) and forget about the rest.


Based on DEFLATE, which is a combination of LZ77 and Huffman coding.

Fairly widely supported (things like WinRAR and 7zip can also open these).

Compression amount/speed tradeoff:

  • has -1 to -9 (and also --fast and --best, respectively 1 and 9)
  • particularly -8 and -9 seem to take a lot more time than is worth it compression-wise.
  • default is -6, which seems a practical choice


Based on BWT and Huffman.

Generally gives better compression than deflate (e.g. gzip, classic/compatible ZIP), and a little more resource-intensive.

Things like WinRAR and 7zip can also open these.

Compression amount/speed tradeoff:

  • -9 is the default (verify)
  • compression seems to level off to sub-percent size differences at and above -7
  • Time taken seems to be fairly linear from -1 to -9. if you only care about having compression at all, you could just use -1 (it's perhaps twice the speed of -9)

This seems to mean there's not a sweet spot (as clear as e.g. with gzip) without specifically valuing time over drive space, or the other way around.



Used around OSX



Seen in the nineties, rarely used now.

Had useful multi-file handling before ZIP really did, so saw use distributing software, e.g. in BBSes.

There was a successor named JAR, not to be confused with the Java -related JAR archives.


Seen in the late nineties, early noughties. Similar to RAR in that it outperforms ZIP, but RAR is more popular.


Used on the Amiga and for some software releases.

Now rarely used in the west, but still used in Japan, and there was is an LZH compressed folder extension for WinXP, analogous to zipped folder support in windows in the west.

There was a successor named LHx, then LH.


LZMA compressor.

In terms of compression per time spent

lzip -0 is comparable to gzip -6
lzip -3 is comparable to bzip2 -9 / xz -3
lzip -9 is comparable to xz -9(verify)

Apparently also seems a little better at error recovery(verify) [2]

lzip and zx are both LZMA family, xz is more recent though there are arguments why it's not the best design as an archiver, whereas lzip just does just the thing it does.

Parallelized variants, and speed versus compression


  • if you care more about speed: pigz -3
  • if you care more about space: lbzip2 -9 (-9 is the default, so is optional to specify)
  • if you care even more about space, you're probably already an xz user and have no speed expectations.

Parallelized variants:

  • for bzip2 there's lbzip2 and pbzip2
  • for gzip there's pigz
  • for lzip there's plzip
  • for xz thre's pxz and pixz

Some details:

  • pigz speed: pigz -3 is ~50% faster than the default -6, at still decent compression
  • pigz -11 is zopfli, a few percent better but much slower
  • lbzip2:
speed barely changes with compression level, so you may as well use -9, also the default
(-1 seems slightly slower than the rest, even. Yeah, weird)
memory hungrier than others, also at (many-thread) decompression
  • pigz versus lbzip2 - draw your own conclusions from below and tests on your own typical data(!), but it seems:
lbzip2 compresses better at all settings (one test file: lbzip2:24% pigz:35%)
pigz -3 noticably faster than lbzip2 at all settings ((verify))
pigz -7 (and higher) are slower than lbzip2
I've heard that lbzip2 scales better with cores so on beefy dedicates cases would then be faster; TODO: check
  • pbzip2 is slower than lbzip2 at higher compression, similar speed at lower compression
  • pxz and pixz are slower than the above at higher compression (...what did you expect?)
(more comparable at lower compression - have not checked to what degree)

Quick and dirty benchmarks:

(on tmpfs, so negligible IO) on a 218MB, fairly compressible floating point number data file

On an AMD FX6300:

  • pigz -1 compresses it to 80MB (36%) in 1.0sec
  • pigz -2 compresses it to 77MB in 1.1sec
  • pigz -3 compresses it to 76MB in 1.3sec
  • pigz -4 compresses it to 75MB in 1.4sec
  • pigz -5 compresses it to 75MB in 1.8sec
  • pigz -6 compresses it to 75MB in 2.2sec
  • pigz -7 compresses it to 75MB in 2.4sec
  • pigz -8 compresses it to 75MB in 4.2sec
  • pigz -9 compresses it to 75MB (34%) in 11.5sec
  • lbzip2 -1 compresses it to 55MB (25%) in 3.0 sec (yes, slower than -6!)
  • lbzip2 -2 compresses it to 51MB in 2.7 sec
  • lbzip2 -6 compresses it to 48MB in 2.7 sec
  • lbzip2 -9 compresses it to 46MB (21%) in 2.8sec
  • pbzip2 -6 compresses it to 48MB in 3.3sec

Similar tests on a dual Xeon E5645 were approximately twice as fast, so it seems to scale roughly linearly, going by passmark score.

Less practical nerdery

This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

There is a whole set of compression types that are exercises in getting very high compression at the cost of a bunch of time.

They are usually barely command line utilities, let alone easy to use.

These include:

...and many others.


This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

Lossless methods

Entropy coding (minimum redundancy coding)

This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

Mostly per-symbol coding - where a symbol are logical parts of the input, regularly fixed-size things, e.g. a character or byte in a file, a pixel of an image, etc.

Probably the most common symbol-style coding, contrasted with variable-run coding, which is often dictionary coding.

Modified code


See also:

Adaptive Huffman (a.k.a. Dynamic Huffman)

See also:


Similar to Huffman in concept and complexity.

A little easier to implement, so a nicer programming exercise, yet Huffman typically performs better.

See also:

Elias, a.k.a. Shannon-Fano-Elias

See also:

Golomb coding

Rice coding

universal codes

In itself mostly a propery

Fibonacci coding

Elias gamma coding

Exp-Golomb (Exponential-Golomb)

Range encoding

Arithmetic coding

Dictionary coding

Dictionary coders work by building up a dictionary of "this short code means this longer data".

The method of building that dictionary varies, and most of the work is in making a dictionary that is efficient for a given set of data.


Primarily combines LZ77 and Huffman coding.

Used in ZIP, zlib, gzip, PNG, and others.

See also RFC 1951

Modern compressors may still produce standard deflate streams for compatibility. For example, ZIP's deflate is still the most uniquitously supported coding in ZIP files, #zopfli can be used as a drop-in in gzip (and in theory zip).

(ZIP also uses Deflate64 (see its #compression_methods), which is a relatively minor variation)

LZ family and variants

Referring to an approach that Abraham Lempel, and Jacob Ziv used, and various others since.

LZ77 and LZ78 (a.k.a. LZ1 and LZ2)

Refer to the original algorithms described in publications by Lempel and Ziv in 1977 and 1978.


Short for Lempel, Ziv, Welch, refers to an extension of LZ78 described in 1984 by Terry Welch.

Used in various place, including GIF, TIFF, Unix compress, and various others.

Limited adoption because implementations were due to patents from 1983 to 2003 (or 2004, depending on where you lived).

See also:


Lempel-Ziv-Storer-Szymanski (1984)

Used by PKZip, ARJ, ZOO, LHarc


Lempel-Ziv-Markovchain Algorithm (since 1998)

Still much like LZ77/deflate, but with smarter dictionary building(verify).

Default method in 7Zip. An optional method in some new versions of the ZIP format.


LZW variant (letters stand for Miller, Wegman)


LZW variant (letters stand for all prefixes)


Syllable-based LZW variant



Built for very fast decompression (and can do it in-place(verify)).

Compression speed more at a tradeoff, though typically used at lower compression settings, to e.g. get ~half the compression ration of gzip at ~four times the speed, because usually the point is a CPU-cheap way to store more data / move it faster.

You can also make it work harder to get compression ratio ant time quite comparable to gzip -- while retaining the high-speed low-resource decompression.


Largely comparable to LZO, but designed for more constrained memory use (verify)


Basically a variant of LZO - fast to decompress, but even during compression it prefers speed over compression ratio (by not being as exhaustive as typical DEFLATE style compression).

You can think of it as a "what compression can I get at minimal CPU cost?", in that it can compress at hundreds of MByte/s per modern core (order of magnitude).

It is an option in things like ZFS, a filesystem that's biased to archiving, so where a little CPU and memory overhead on writes are considered worth it. ZFS also tries to (quickly, early in the data) detect when no compression should be used at all, which adds to the 'minimal CPU cost' aspect.

Comparison between LZO and LZ4 seems to be:

  • LZ4 is done faster
  • LZO can compress a little better
  • LZO uses less memory


Variant of LZ4

  • same cheap decompression speed
  • typically 20% better compression, but at 5x to 10x slower compression speeds
  • no fast decision to not compress (verify), so e.g. in ZFS you generally don't want it over LZ4

...i.e. it's meant to save storage cost for archiving and backups, on hosts that otherwise don't use their CPU much.

...where explicit compression (e.g. throw it at bzip2 or xz) may be equally sensible. (There seems no hurry to get it into ZFS)


(1995) Used in Amiga archives, Microsoft Cabinets, Microsoft Compressed HTML (.chm), Microsoft Ebook format (.lit), and one of the options in the WIM disk image format.


Lempel-Ziv Ross Williams (1991), which itself has seven variants.


Letters stand for Jeff Bonwick. Derived from LZRW (specifically LZRW1)

Used in ZFS.


Reduced Offset Lempel-Ziv


zstd (Zstandard) is a LZ77-family compressor, aiming to be a fast compressor and in particular a fast decompressor, at zlib-like compression levels.

Very roughly:

at one end it has lzo / lz4 speeds, but compresses more
at the other end it has zlib/bzip2 compression (but faster than those)

Note that part of that speed comes from multicore being standard part, rather than an afterthought from another project, yet these compressors exist for gzip, bzip2 (and narrow the difference at the latter end).

There are other footnotes, e.g. that of compression, decompression memory.

zstd makes sense within certain systems, because of the lower CPU (and/or; tradeoff with) higher speed at almost the same compression as zlib.

See also:


zopfli, brotli

This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

These are meant for the web.

zopfli produces a standard DEFLATE stream (often then wrapped in zlib/gzip) that tends to squeeze out a little more compression than zlib/gzip at their max settings, by exhausting more alternatives - which also makes it much slower.

It is intended for things you compress once, then serve many times, e.g. on the web for woff, PNG and such. Certainly not for on-the-fly compression or one-time transfers.

Brotli is built for fast on-the-fly text compression, and tuned with dictionaries that do better at some very common strings on the web. It tends to shave 20% more off HTML, JS, and CSS.

Which is comparable to zlib/gzip/DEFLATE on its lighter settings, except brotli's is meant to decompress faster, and have low and well bound resource requirements (not unique features, but can be a useful combination for some purposes).(verify)

See also:


Burrows-Wheeler transform (BWT)

See Searching_algorithms#Burrows-Wheeler_Transform

Being reversible and putting similar patterns near each other, using the BWT as a step in compression algorithms makes sense, and is indeed used: bzip2 is built around it.

Prediction by Partial Matching (PPM)

PPM is the concept, PPM(n) is PPMd

Dynamic Markov Compression (DMC)

Context tree weighting (CTW)

Context Mixing (CM)


High compression, who-cares-about-speed

Consider file-serving purposes you compress once, then serve millions of times.

You pay mostly for transfer, so it pays to try your hardest once to compress it.

This is a big argument behind pre-compressed zlib through HTTP - and specifically zopfli for your most-served stuff.

Similarly, archive and backup spend CPU compressing exactly once, and mostly pay long-term storage space (disk, or even just the physical rooms to put them in).

This means high compression ratios save the most cost, and you want to look at bzip2, 7z, LZMA and PPMd methods, maybe xz or ZPAQ, over things like gzip, lz4, zstd.

While these tend to not parallelize as brilliantly as some specialized variants, if you have cores to spare you may get more compression within the same timespan, which can be a no-brainer. See e.g. Compression_notes#Parallelized_variants.2C_and_speed_versus_compression for the kind of tradeoffs -- but test on your own data.

On CPU and memory difference under higher compression

The higher compression settings tend to mean "search more exhaustively within the given data to see if there is a slightly better solution".

This means the highest compression almost always means significantly lower compression speed - but often little to no difference in decompression speed.

But, under methods that involve lookup tables, it can make a real difference to the memory used in decompression and compression.

And with quickly-diminishing returns in compression.

The quickly diminishing returns are quickly not worth the extra CPU time and/or memory use.

Or responsiveness. Things like LZ4 have no parameters, which is good when you want guarantees like 'is always done in what seems like negligible time'.

It does mean lower compression, because they only really focus on redundancy within a shortish window, rather than the best possible solution for a large amount of data.

This is also part of why there is often more difference between compression methods, than there is within a method at different compression levels.

There is still an argument for cases where you will read/send/serve the result many times - it will eventually make up for the initial investment (or when storage is more expensive to your bottom line than CPU power, which should be basically never). This is why things like png crushers exist, the reason behind zopfli, and why you may wish to sometimes use zx or lzip for software distribution.

Generic tools may not even let you try this, e.g. bzip2 settings barely matter, and for good reason.

High speed, reasonable compression

(see above)

These can make sense in systems

where CPU is generally not the bottleneck, so spending a little CPU on light data compression is almost free
and/or tend to write as much as they read (e.g. storage/database systems)

For example

for database and storage systems, since these are often relatively dedicated, and tend to have a core or two to spare.
and/or when it lowers network transmission (bandwidth and interrupt load)

  • LZO (see above)
  • LZF (see above)
  • LZ4
(e.g. compresses similarly to e.g. FastLZ, QuickLZ in less time)
e.g. used in ZFS's transparent data compression
  • snappy (previously zippy) seems similar to LZ4
  • zstd and gipfeli seems to intentionally aim at more compression than LZ4/snappy at speeds still higher than typical DEFLATE'. (verify)

Note that some of these have the footnote "If you've got a core or two to spare."

Which on dedicated storage servers is typically true, while on workhorses might take a few percent off your general performance.

See also:

Lossy methods

Note that lossy (sometimes 'lossful') methods often employ lossless coding of some perceptual approximation.

Transparency is the quality of compressed data being functionally indistinguishable from the original - a lack of (noticeable) artifacts. Since this is a perceptual quality, this isn't always easy to quantify.

Ideally, lossy compression balances transparency and low size/bitrate, and some methods will search for the the compression level at which a good balance happens.

Floating point compression

Floating point data, particularly when higher-dimensional, has a tendency to be large.

And also to have smooth, easily modelled patterns.

Very clean floating point data may compress well, even using completely general-purpose compression that doesn't know it's floating point data.

Noisier data less so, but methods that know it's dealing with floating point may do better.

Note that floating point compression can be essentially lossless.

There is often also the option for lossy compression. Conceptually, you can shave bits off the mantissa. The tradeoff may be worth it, particularly when you know the data was noisy to start with.





Bi-level images

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  • ITU T.88, Information technology - Coded representation of picture and audio information - Lossy/lossless coding of bi-level images

See also:

Note that DjVu's CJB2 is a variation of this format.

CCITT Group 3 and 4

This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

(Note CCITT is now ITU-T)


  • ITU-T T.4, Standardization of Group 3 facsimile terminals for document transmission
  • ITU-T T.6, Facsimile coding schemes and coding control functions for Group 4 facsimile apparatus

Published in 1988, parts of the fax standard were updated in 1992, 1993. Actual fax machines need to conform to a larger number of standards.

See also

containers and/or compression


Pack200 is a compression scheme for Java (specified in JSR 200), which seems to specialize in informed/logical compression of bytecode, (and bytecode within JARs)

Pack200 plus gzip compress these things better than gzip alone.

It's used with JWS, among other things

See also:

See also