Best Utility:
Bernd Meyer
Monash University, Melbourne, Australia
1/832 Blackburn Rd
Clayton, VIC 3168
Australia
http://byron.csse.monash.edu.au/
Judges' Comments:
To build:
make bmeyer
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. See the extra build lines
in the Makefile, and read the author's comments below.
If you cannot work out hwo 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 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.
To run:
In a video window (white text on black background):
./bmeyer < michael.pgm > michael.glic
Compare the michael.pgm to the screen output.
To test that you are compressing and decompressing the same way the
author was, try
./bmeyer < lenna.glic
Also try in a reverse video window:
./bmeyer < michael.pgm 2>/dev/null | ./bmeyer > new.pgm
Compare the michael.pgm to the screen output. Compare the new.pgm file
to the michael.pgm file.
Create a large reverse video xterm, say 200 columns wide and try:
./bmeyer 200 < lavabus.pgm > lavabus.glic
Produce an even smaller output:
./bmeyer -2 200 < lavabus.pgm > lavabus.glic2
Decompress that smaller glic-file:
./bmeyer -2 200 < lavabus.glic2 > new.pgm
Compare the new.pgm file to the lavabus.pgm file by viewing
them.
Don't even think of supplying different compression factors (the
dashed argument) for compression and decompression! You've been warned.
Selected Author's Comments:
GLICBAWLS
A) 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:
./bmeyer < michael.pgm > michael.glic
and then
./bmeyer < 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
./bmeyer 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 tbe 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
./bmeyer -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.
./bmeyer -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
./bmeyer -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 WARNING WARNING WARNING WARNING WARNING 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. *
* *
*****************************************************************
B) 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.
C) 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
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 #define's 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....[0]
D) Bugs, Assumptions and TODOs
==============================
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-losslessy 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, 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.
E) 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). [1][2][3]
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/decoded[4].
[0] Yes, this could be seen as a challenge....
[1] Actually, the weight is pow(0.8,D)/s, where s is the sigma
used for en/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....
[2] 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.
[3] 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".
[4] 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.
####################################################################
Photo Credit:
Lavabus was taken by the judge, Landon Curt Noll. Michael was
provided by the author. Lenna is a 1972 Playboy centerfold.
michael.pgm
The author's Godchild and nephew.
lavabus.pgm
A bus that was trapped by lava from Kilauea volcano in
Hawaii, USA. 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.)