ioccc/2000/bmeyer

To build:

make

To use:

./bmeyer

Try:

In a video window (white text on black background):

./try.sh

The script will suggest you compare the output of the program with images, prompting you to press any key to continue so that you may do so.

Judges' remarks:

Don't even think of supplying different compression factors (the dashed argument) for compression and decompression! You've been warned.

The author recommended on linux/x86, glibc 2.0, libc4/5:

bmeyer: bmeyer.c
	CC -DY="__setfpucw(0x127f)" -O6 $? -o $@ -lm

However many compilers use -O3 as the maximum level for -O optimization.

And on linux/x86, glibc 2.1:

bmeyer: bmeyer.c
	gcc -DY='int x=0x127f; __asm__ ("fldcw %0" : : "m" (*&x))'  $? -o $@ -lm

Compile with the maximum possible optimization on your system. If your system has 80-bit internal representation of floating point values (x86, some Motorola processors) and you want the compressed format to be portable across platforms, you need to set your FPU to use 64 bit mode. Read the author's remarks below for more details.

If you cannot work out how to get into 64 bit mode, you can try using -ffloat-store if you compile with GCC (this may have a performance penalty). The resulting binary will have a good chance to produce portable files, but due to the resulting double-rounding (first internally set to 80 bit, then to 64 bit on writing the value to memory), there is a small but very real chance any given file produced might not be portable.

The Makefile defaults to -O3 and no asm() call.

Author's remarks:

This program is called GLICBAWLS

Function

GLICBAWLS stands for "Grey Level Image Compression By Adaptive Weighted Least Squares".

And that's exactly what this program does --- feed it a .PGM file (either raw [i.e. P5] or ASCII [i.e. P2]) on stdin, and it will output a compressed version to stdout. Feed it a compressed file on stdin, and it will decompress it to stdout --- as either raw or ASCII .PGM, depending on what format it was compressed from. For example:

./glicbawls < michael.pgm > michael.glic

and then

./glicbawls < michael.glic > michael.decoded.pgm

As it turns out, glicbawls compresses greyscale images (or, more precisely, "natural" greyscale images) better than any other program I am aware of (with the exception of the not-yet-published program developed for my PhD thesis). Of course, this might take some time, so a progress indicator is provided. To make things more interesting, instead of a boring bar or percentage display, an ASCII rendition of the image being compressed/decompressed is output to stderr (assuming white text on black background). If you have trouble recognizing the image, try squinting at it ;-).

If you still have trouble, simply use a terminal or xterm with more than 80 columns, and tell glicbawls about it by giving the number of columns as an argument. For example

./glicbawls 260 <lavabus.pgm >lavabus.glic

will allow glicbawls to use up to 260 columns, which makes things much more recognizable.

Still running out of space? Need to compress those images just a tad more? And maybe you can handle some loss due to the compression? If so, you can use glicbawls' "near lossless" compression mode. In that mode, the decoded pixel values are allowed to differ from the originals, but there is an upper limit on the magnitude of the difference. For example, if a maximum error of 2 is allowed, an original pixel value of 37 could be decoded as 35, 36, 37, 38 or 39. In order to use this mode, simply give the maximum allowed error as an argument, with a dash (-) before it. For example:

./glicbawls -2 < graph.pgm > graph.2.glic

will compress in a way that allows decompression with a maximum error of two. You can combine both types of arguments, i.e.:

./glicbawls -3 180 < graph.pgm >graph.3.glic

will compress with a maximum error of 3, using a 180 column terminal for the progress display, and:

./glicbawls -3 180 < graph.3.glic > graph.3maxerr.pgm

will decompress the result on such a terminal.

But wait, there is more --- you can also feed glicbawls .PPM files (i.e. colour images), raw or ASCII, your choice. glicbawls will compress and decompress them just fine. However, it only does "reasonably well" on them; It beats PNG easily, but there are certainly programs out there that can compress colour images considerably better. And don't even think about using it for so-called "artistic" images (i.e. anything that wasn't scanned from a photo or camera)....

WARNING

glicball is rather CPU and FPU intensive. Don't run it on anything slow. Things start to be usable around 300+MHz, with 600+ being highly desirable.

Compile Instructions

Unlike most compression program, glicbawls makes heavy use of floating point maths --- and not all FPUs are created equal. Most importantly, the x86 and 68k FPUs use 80 bit floating point formats internally, while most other processors use IEEE 64 bit formats by default. If not taken care of, this means that a glicbawls file compressed on one CPU cannot generally be decompressed on another.

Fortunately, just about all current FPUs can be put into IEEE 64 bit mode (or at least something close enough for glicbawls). Unfortunately, there is no standard way of doing so. For this reason, the build file contains three compile lines; one for machines that already use 64 bit mode by default (most RISC processors), one for linux/x86 machines using libc4, libc5 or glibc2.0, and one for linux/x86 machines using glibc2.1 (glibc2.1 no longer exports the __setfpucw() function, necessitating the use of gcc inline assembly. *Grumble*).

So, if you are building on a machine that does not, by default, use IEEE 64 bit floating point doubles, you'll have to define Y to be a command that switches it into that mode. If you fail to do so, your glicbawls executable will still be able to decompress its own compressed files, but you may be unable to exchange files with glicbawls on other machines.

Obfuscation

Most of the obfuscation of this program was driven by the desperate struggle to fit all of glicbawls' features into code that fits the IOCCC's size limits. All identifiers' names are single-character, which was only possible by ruthless exploitation of scope. There is a function M() that handles nearly all input from stdin, handles all output to stdout, and also recursively calculates one of the mathematical expressions needed for error modelling. There is a function that calculates (A^(-1)*b)*x with A being a matrix and b and x being vectors, and does so in a very efficient way --- but one would be hard pressed to find it. There is an arithmetic coder that is even less recognizable. A lot of loop variables don't get initialized, but instead the code is arranged in such a way that they just happen to have the right value when control flow reaches the loops. Lots of functions use the same two global scratch variables. Variables change their meaning all the time, and the differences between compressing and decompressing are handled in rather subtle ways all over the program. The string that holds the ASCII values for displaying the progress image doubles as a description on how to find a pixel's causal neighbours. And then there are a few #defines that really are just in there to save a few characters, but as an added "benefit" make the source ever more unreadable.

In short --- running it through the preprocessor and the pretty-printer will give you something that looks slightly less like line noise and slightly more like a C program, but unless you are a true wizard, it is unlikely to gain you any insights into what is actually going on....¹

Bugs, Assumptions and TODO

glicbawls assumes that characters are 8 bit wide, and that the character set used is ASCII. If one of these isn't true, all hell will break loose.

The .PGM headers are not checked very thoroughly --- glicbawls will happily try to encode lots of files that it shouldn't touch. The old adage of "garbage in, garbage out" holds in that case. Furthermore, even if glicbawls detects an incorrect input, it fails to provide a meaningful error message, and instead simply aborts.

When decompressing a near-lossless encoded image, the maximum allowed error is required as a command line parameter. This should really be saved in the compressed file!

glicbawls relies on the decimal representation of all integers having less than 255 digits. While ANSI C does not guarantee this, it seems rather unlikely that anyone in the foreseeable future would use images with 10^255 rows, columns or different levels of grey. Also, it is assumed that any integer used can be cast to a double and back without loss of precision. This limits the number of rows, columns and grey levels to 9 quintillion, which should also be sufficient for the next few years.

There is a theoretical chance that you might get a division by zero error. You have a MUCH better chance of getting hit by lightning the very second you realize that you just won a few million in a lottery. But if it happens to you, don't say I didn't warn you! Instead, go out and buy a lightning rod and a lottery ticket ;-)

At one point, a pointer to int is used as the target of a "%1[#]" conversion in a scanf(3), which makes gcc rather unhappy, but shouldn't really cause anyone any trouble. The same goes for a couple of assignments which are used as truth values.

Algorithm

An exhaustive explanation of the algorithm used would go beyond the scope of an info file, and would also be quite difficult in pure ASCII, so the following is just a rough outline, and contains some compression-speak...

The image is handled in scanline ordering. For each pixel, an expected value is calculated by creating a least squares predictor of order 12 based on all of the previously encoded/decoded pixels. However, the contribution of each pixel is weighted according to its Manhattan-distance from the current pixel, D. That weight used is pow(0.8,D). ^{2 3 4}

In a similar way, the prediction errors for all previous pixels are combined --- a weighted average (with weight pow(0.7,D)) of the squares of all previous prediction errors is taken, and the square root of the (appropriately scaled) result is called sigma.

The predicted value and sigma are then used as the parameters of a Student or t-distribution (which is similar to a normal distribution, but has more weight in the tails), providing a probability distribution for the current pixel.

Next, the possible interval of values for the current pixel is halved, and through integration of the probability distribution, a probability is calculated for the pixel value being in the lower half. During encoding, the actual value is examined, and the result encoded using an arithmetic coder. During decoding, the arithmetic decoder provides the information which half the actual value is in. In both cases, the interval borders are adjusted accordingly, the arithmetic coder/decoder updated, and the interval halving repeated until the precise value has been en/decoded⁵ .

Photo Credit:

Lavabus was taken by the judge, Landon Curt Noll. Michael was provided by the author. Lenna is a 1972 Playboy centerfold (doesn't show very much).

• michael.pgm

  The author's Godchild and nephew.

• lavabus.pgm

  A bus that was trapped by lava from Kilauea volcano in Hawaii, US. Nobody was in the bus at the time, BTW. Photo date: 1981.

• lenna.glic

  A November 1972 Playboy centerfold was scanned in long ago and has been used for image compression research since then. Playboy originally threatened to prosecute unauthorized use, but eventually granted that, having been in use for image compression testing for so long, it was now a useful benchmark. (Note: This picture doesn't show very much.)

Copyright and CC BY-SA 4.0 License:

This file is Copyright (c) 2023 by Landon Curt Noll. All Rights Reserved. You are free to share and adapt this file under the terms of this license:

Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)

For more information, see: https://creativecommons.org/licenses/by-sa/4.0/

---

1. Yes, this could be seen as a challenge.... ↩︎

2. Actually, the weight is pow(0.8,D)/s, where s is the sigma used for encoding/decoding the particular previous pixel. Dividing by s is a rather arbitrary action justified only by the improvement in results. Mathematically, I can only justify dividing by s^2, or not dividing at all.... ↩︎

3. Obviously, these least squares predictors are not calculated from scratch for each pixel. Some clever reuse of earlier results allows O(1) calculation, rather than the O(previous_rows*columns) this description would suggest. ↩︎

4. As anyone who has ever tried local least squares knows from bitter experience, there is a lot of numerical instability associated with them. So glicbawls adds a bias towards an averaging predictor to the equation system the least squares predictor is calculated from. The weight that is given to this bias is constantly adjusted throughout coding/decoding, thus justifying the 'a' in glicbawls. ↩︎

5. In the case of near-lossless coding, the interval is not necessarily halved, but rather split at a convenient point (the split points are chosen in such a way as to minimise the expected number of bits needed for coding). Also, the iteration ends as soon as the interval is small enough to guarantee decoding within the requested maximum error. ↩︎