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Using GPUs For General-Purpose Computing

Paul Tinsley writes "After seeing the press releases from both Nvidia and ATI announcing their next generation video card offerings, it got me to thinking about what else could be done with that raw processing power. These new cards weigh in with transistor counts of 220 and 160 million (respectively) with the P4 EE core at a count of 29 million. What could my video card be doing for me while I am not playing the latest 3d games? A quick search brought me to some preliminary work done at the University of Washington with a GeForce4 TI 4600 pitted against a 1.5GHz P4. My Favorite excerpt from the paper: 'For a 1500x1500 matrix, the GPU outperforms the CPU by a factor of 3.2.' A PDF of the paper is available here."

53 of 396 comments (clear)

  1. The day is saved by drsmack1 · · Score: 5, Funny

    Now I finally have a use for the 20 Voodoo 2 cards I have in a box in the basement. Now I can have my very own supercomputer. I just need some six pci slot motherboards.... Instant cluster!

    1. Re:The day is saved by PygmySurfer · · Score: 5, Funny

      Unless those Voodoo 2s have magically grown T&L units, they're not going to do you much good.

      Maybe they have. They've been trapped in that box together in the basement for a long time.

    2. Re:The day is saved by Directrix1 · · Score: 4, Interesting

      Doesn't anybody find it annoying that 3-D operation is being hardwired into the video card to begin with? Why aren't we making 200million transistor math coprocessors with high bus speeds, uncoupled from the video card. This way we wouldn't have to keep getting a new video card every time we want to upgrade our systems 3-d performance. Since these operations are highly symmetric, you could put in an array of these into one machine to incrementally upgrade. Also, this would make the issue of how to access your GPU to use for other purposes irrelevant, as it would be a math coprocessor expected to be used as such anyways. And the best reason for doing it this way: OpenGL (and DirectX too) could become more of a thick software layer on top of the generic coprocessor, and since the coprocessors would eventually standardize on common instruction set, you wouldn't need a new version of OpenGL or DirectX for every new coprocessor release. What do you guys think?

      --
      Occam's razor is the blind faith in the natural selection of least resistance and in universal oversimplification. -- EF
    3. Re:The day is saved by Metasquares · · Score: 4, Insightful
      This way we wouldn't have to keep getting a new video card every time we want to upgrade our systems 3-d performance.
      I think you've just answered your own question.
  2. What?!?!?! by DarkHelmet · · Score: 5, Funny
    What? Matrix operations run faster on a massively parallel form of vector processor over a general purpose processor? How can that be?

    Intel's been telling me for years that I need faster hardware from THEM to get the job done...

    You mean........ they were lying?!?!?

    CRAP!

    --
    /^[A-Z0-9._%+-]+@[A-Z0-9.-]+\.[A-Z]{2,4}$/i
    1. Re:What?!?!?! by Anonymous Coward · · Score: 5, Funny

      Don't worry, the Intel processor is *much* faster at the internet thingy. Graphics cards only do the upload to screen thing, and everyone knows the internet is all about downloading.

      And besides, nobody needs or wants Matrix operations anyway. Did you see how bad Matrix Reloaded was? That was *just* reloading, imagine how bad Matrix Multiplying is. You get the idea.

  3. Link to previous discussion on same/similar sub... by 8282now · · Score: 5, Informative
  4. Googled HTML by balster+neb · · Score: 5, Informative

    Here's a HTML version of the PDF, thanks to Google.

  5. video stuff by rexguo · · Score: 4, Interesting

    At my work place, I'm looking into using the GPUs to do video analysis. Things like cut-scene detection, generating multi-resolution versions of a video frame, applying video effects and other proprietary technologies that were previously done in CPU. The combination of pixel shaders and floating-point buffers really make GPUs a Super-SIMD machine if you know how to exploit it.

    --
    www.rexguo.com - Technologist + Designer
  6. As has been said many time before ... by keltor · · Score: 5, Insightful

    The GPU are very fast ... at performing vector and matrix calculations. This is the whole point. If general computing CPUs were capable of doing vector or matrix calcs very efficiently, we would probably not have GPUs.

    1. Re:As has been said many time before ... by lazy_arabica · · Score: 5, Interesting
      The GPU are very fast ... at performing vector and matrix calculations. This is the whole point. If general computing CPUs were capable of doing vector or matrix calcs very efficiently, we would probably not have GPUs.
      Yes. But 3D graphics are not the only use of these mathematical objects ; I wonder if it would be possible to use a GPU to perform video encoding or digital sound manipulation at a higher speed, as both operations require matrices. I'm also sure they could take advantage of these processors vector manipulation capabilities.
  7. 178 Million in the P4EE by 2megs · · Score: 5, Insightful

    The Pentium 4 EE actually has 178 million transistors, which puts it in between ATI's and NVIDIA's latest.

    In all of this, keep in mind that there's computing and there's computing...the kind of computing power in a GPU is excellent for doing the same numeric computation to every element of a large vector or matrix, not so much for branchy decisiony type things like walking a binary tree. You wouldn't want to run a database on something structured like a GPU (or an old vector-processing Cray), but something like a simulation of weather or molecular modeliing could be perfect for it.

    The similarities of a GPU to a vector processing system bring up an interesting possibility...could Fortran see a renaissance for writing shader programs?

    1. Re:178 Million in the P4EE by Knightmare · · Score: 5, Informative

      Yes, it's true that it has that many transistors BUT, only 29 million of them are part of the core, the rest is memory. The transistor count on the video cards does not count the ram.

    2. Re:178 Million in the P4EE by gunix · · Score: 5, Insightful

      Well, it's like UNIX, it's userfriendly, it's just selects it's friends very carefully.
      IMHO, the perfect friend is someone interested in maximum performance and knows how to program and knows something about computer hardware.

      Have you looked at fortran 90, 95 or 2000?

      --
      Evolution of Language Through The Ages: 6000 BC : ungh, grrf, booga 2000 AD : grep, awk, sed
  8. Website on this topic by Anonymous Coward · · Score: 5, Informative

    General-purpose computation using graphics hardware has been a significant topic of study for the last few years. Pointers to a lot of papers and discussion on the subject are available at: www.gpgpu.org

  9. Re:Not the Point by JonoPlop · · Score: 4, Interesting
    The whole point of graphic cards is that they have a dedicated purpose. Using the cards for anything that is general purpose is like using a motorcycle to tow a pop-up camper.

    No, it's like using your pop-up camper for storage space when you're using it on holidays.

  10. While not playing games? by pyrrhonist · · Score: 4, Funny
    What could my video card be doing for me while I am not playing the latest 3d games?

    Two words: virtual pr0n

    --
    Show me on the doll where his noodly appendage touched you.
  11. Hacking the GPU by nihilogos · · Score: 5, Informative

    Is a course being offered at caltech since last summer on using gpus for numerical work. Course page is here.

    --
    :wq
  12. What comes next. by CherniyVolk · · Score: 5, Funny


    "Utilize the sheer computing power of your video card!"

    New market blitz, hmmmm.

    SETI ports their code, and within five days their average completed work units increase 1000 fold. 13 hours later, they have evidence of intelligent life at 30000 locations within one degree.

    Microsoft gets the hint, and comes out with a brilliant plan to utilize GPUs to speed up their OS and add bells and whistles to their UI.

    And, once again, Apple and Quartz Extreme is ignored.

    1. Re:What comes next. by Barbarian · · Score: 4, Funny

      Then they throw away the results because the gpu's are not able to calculate at double precision floating point, but only at 24 or 32 bits.

  13. It's nice, but could be nicer by Anonymous Coward · · Score: 5, Informative

    Before you get excited just remember how asymmetric the APG bus is. Those GPUs will be at much better use when we get them as 64bit pci cards.

  14. Re:Not the Point by Amiga+Lover · · Score: 4, Insightful

    The whole point of graphic cards is that they have a dedicated purpose. Using the cards for anything that is general purpose is like using a motorcycle to tow a pop-up camper.


    What's relevant is that to the processor on a graphics card, its dedicated purpose is simply a bunch of logic. There's no dedicated "this must be used for pixels only, all else is waste" logic inherent in the system. there are MANY purposes for which the same/similar logic that applies in generating 3D imagery can be used, and that seems the purpose of this paper. Run THOSE type operations on the GPU. Some things they won't be able to do well no doubt - but those they can, they can do extremely well.

  15. Not just the GPU : the RAM by ratboot · · Score: 5, Interesting

    What's interesting with new video cards it's their memory capacity, 128 or 256 MB and that this memory is accessible on some new cards at 900 MHz with a data path of 256 bit (which is a lot faster than a CPU with DDR 400 installed).

  16. Wow by cubicledrone · · Score: 5, Interesting

    All that processing power, and the latest games still run at about 22 frames per second, if that.

    The CPU can do six billion instructions a second, the GPU can do 18 billion, and every last cycle is being used to stuff a 40MB texture into memory faster. What a waste. Yeah, the walls are even more green and slimy. Whoop-de-fucking-do.

    Would it be great if all that processing power could be used for something other than yet-another-graphics-demo?

    Like, maybe some new and innovative gameplay?

    --
    Business isn't willing to pay for products, innovation and careers, so we get brands, mortgage commercials and layoffs.
    1. Re:Wow by PitaBred · · Score: 4, Insightful

      You don't seem to understand that GPU's are very specific purpose computing devices. They aren't like a general purpose processor like you CPU. They crunch matrices, and that's about it. Even all the programmable stuff is just putting parameters on the matrix churning.

  17. audio stuff by RobPiano · · Score: 4, Interesting

    At my work we do audio stuff. It would be really neat if I could do some of the more complicated audio analysis (FFT etc) that requires lots of vector math using the video cards gpu. There is probably even some way you could sync the timing for multimedia stuff.

    I know nothing about CPU design though

  18. This is BIG by macrealist · · Score: 5, Insightful

    Creating a way to use the specialize GPUs for vector processing that is not graphics related is ingenious. Like a lot of great ideas, it is sooo obvious AFTER you see some one else do it.

    Don't miss the point that this is not intended for general purpose computing. Don't port OoO to the graphics chip.

    Where it is huge is in signal processing. FPGAs have begun replacing even the G4s in this area recently because of the huge gains in speed vs. power consumption an FPGA affords. However, FPGAs are not bought and used as is, and end up costing a significant amount (of development time/money) to become useful. Being able to use these commodity GPUs for vector processing creates a very desirable price/processing power/power consumption option. If I were nVIDIA or ATI, I would be shoveling these guys money to continue their work.

    --
    I am living proof of the Peter Principle
  19. Siggraph 2003 by Adam_Trask · · Score: 5, Informative
    Check out the publication list in Siggraph 2003. There is a whole section named "Computation on GPUs" (papers listed below). And the papers for Siggraph 2004 should be out shortly.

    If you have a matrix solver, there is no telling what you can do. And i remember, these papers show that the speed is faster than the matrix calculations of the same stuff using the CPU.

    # Linear Algebra Operators for GPU Implementation of Numerical Algorithms
    Jens Krüger, Rüdiger Westermann

    # Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid
    Jeff Bolz, Ian Farmer, Eitan Grinspun, Peter Schröder

    # Nonlinear Optimization Framework for Image-Based Modeling on Programmable Graphics Hardware
    Karl E. Hillesland, Sergey Molinov, Radek Grzeszczuk

  20. http://www.gpgpu.org/ is a great resource by aancsiid · · Score: 4, Interesting

    http://www.gpgpu.org/ is a great resource for general purpose graphics processor usage.

  21. Not so... by oboylet · · Score: 4, Interesting
    High-powered GPUs can make for really good general-purpose devices.

    Apple's Newton had no CPU, only a GPU that was more than adequate.

    Ideas like these are good in general. I'd like to see the industry move away from the CPU-as-chief status quo. Amigas were years ahead of their time in large part because the emphasis wasn't as much on central processing. The CPU did only what it was supposed to do -- hand out instructions to the gfx and audio subsystems.

    Hardly using a "motorcycle to tow a pop-up camper." If anything, the conventional wisdom is, "when all you have is a hammer, everything looks like a nail."

  22. and a sourceforge project too by Lord+Prox · · Score: 4, Informative

    BrookGPU
    from the BrookGPU website...
    As the programmability and performance of modern GPUs continues to increase, many researchers are looking to graphics hardware to solve problems previously performed on general purpose CPUs. In many cases, performing general purpose computation on graphics hardware can provide a significant advantage over implementations on traditional CPUs. However, if GPUs are to become a powerful processing resource, it is important to establish the correct abstraction of the hardware; this will encourage efficient application design as well as an optimizable interface for hardware designers.

    From what I understand this project it aimed at making an abstraction layer for GUP hardware so writing code to run on it is easier and standardsied.

  23. Imagine... by rokzy · · Score: 4, Interesting

    a beowulf cluster of them.

    seriously, we have a 16 node beowulf cluster and each node has an unnecessarily good graphics card in them. a lot of the calculations are matrix-based e.g. several variables each 1xthousands (1D) or hundredsxhundreds (2D).

    how feasible and worthwhile do you think it would be to tap into the extra processing power?

  24. Pseudo repost by grape+jelly · · Score: 4, Informative

    I thought this looked familiar:

    http://developers.slashdot.org/developers/03/12/21 /169200.shtml?tid=152&tid=185

    At least, I would imagine most of the comments would be the same or similar....

  25. Finally by Pan+T.+Hose · · Score: 5, Funny

    Using GPUs For General-Purpose Computing

    I'm glad that finally they started to use the General-Purpose Unit. What took them so long?

    --
    Sincerely,
    Pan Tarhei Hosé, PhD.
    "Homo sum et cogito ergo odi profanum vulgus et libido."
  26. Maybe time for a new generation of math-processor? by Anonymous Coward · · Score: 4, Insightful

    Remember the co-processors? Well, actually I don't (I'm a tad to young). But I know about them.

    Maybe it's time to start making co-processing add-on cards for advanced operations such as matrix mults and other operations that can be done in parallell on a low level. Add to that a couple of hundred megs of RAM and you have a neat little helper when raytracing etc. You could easily emulate the cards if you didn't have them (or needed them). The branchy nature of the program itself would not affect the performance of the co-processor since it should only be used for calculations.

    I for one would like to see this.

  27. Re:Not the Point by kfg · · Score: 5, Funny

    Dude, you obviously have never tried to sleep in a motorcycle.

    KFG

  28. Frogger by BiggerIsBetter · · Score: 4, Interesting

    Some dude wrote Frogger almost entirely in pixel shaders. http://www.beyond3d.com/articles/shadercomp/result s/ (2nd from the bottom).

    --
    Forget thrust, drag, lift and weight. Airplanes fly because of money.
  29. Re:Not the Point-headbanger. by Amiga+Lover · · Score: 4, Insightful

    There is however one thing to keep in mind. Presently our GPU's may have the headroom to play with, but with Apple's Quartz, and Microsoft's Longhorn, let alone what's coming with X. That headroom may disappear, and our video cards will have to go back to being video cards.

    On those operating systems that require them, that could very well be.

    Still makes a nice thought that a linux box without even X installed, but a kickass graphics card, could crunch away doing something 4 times quicker than any windowed machine.

  30. Bass Ackwards? by Anonymous Coward · · Score: 5, Insightful

    Perhaps offloading the CPU to the GPU is the wrong way to look at things? With the apparently imminent arrival of commodity (low power) multi-CPU chips, maybe we should be considering what we need to add to perform graphics more efficiently (ala MMX et al)?

    While it's true that general purpose hardware will never perform as well as or as efficiently as a design specifically targeted to the task (or at least it better not), it is also equally as true that eventually general purpose/commodity hardware will achieve a price-performance point where it is more than "good enough" for majority.

  31. Re:Link to previous discussion on same/similar sub by hype7 · · Score: 4, Interesting

    There's some good stuff in there.

    However, it seems a few organisations have actually beaten us to it.

    Apple, for example, uses the 3d aspect of the GPU to accelerate its 2d compositing system with quartz extreme. Microsoft, as usual, announced the feature after Apple shipped it, and with any luck Windows users might have it by 2007

    -- james

  32. GPU = by greppling · · Score: 4, Funny

    Now I finally understand that acronym: General purpose unit!

  33. Re:Unused computing Power? by PitaBred · · Score: 4, Insightful

    Lemme try to help:
    a) Not equal. Apples and oranges. A GPU will do repeated calculations very, very fast, like matrix transforms and the like. A CPU on the other hand will make decisions based on input, rather than just crunching numbers
    b) The main display (the GUI) already uses many tricks on the graphics card. The hard part is making sure that all graphics cards support the features. Things like the xrender extension and such are becoming more common as graphics cards and drivers get "standard" capabilities
    c) Your imagination is the limit as to what it could be used for. Just realize that it's a good data processing unit, not a good program execution unit. Use each for their strengths.
    d) Modified? With new cards/drivers, all it takes is OpenGL calls to start taking advantage of this power. All it really takes is someone who knows what they're doing and has a bit of inspiration.

  34. Re:Maybe time for a new generation of math-process by BlueJay465 · · Score: 4, Informative

    Well they already make DSP cards for audio processing. Simply do a google(TM) search for "DSP card" and you will get several vendors.

    I can't imagine it would take a whole lot to hack them for just their processing power outside of audio applications.

  35. transistor counts through the ages by nothings · · Score: 5, Informative
    Transistor counts keep growing, so I keep updating this and reposting it about once a year.

    486 : 1.2 million transistors
    Pentium : 3 million transistors
    Pentium Pro : 5.5 million transistors
    Pentium 2 : 7.5 million transistors
    Nvidia TNT2 : 9 million transistors
    Alpha 21164 : 9.3 million (1994)
    Alpha 21264 : 15.2 million (1998)
    Geforce 256 : 23 million transistors
    Pentium 3 : 28 million transistors
    Pentium 4 : 42 million transistors
    P4 Northwood : 55 million transistors
    GeForce 3 : 57 million transistors
    GeForce 4 : 63 million transistors
    Radeon 9700 : 110 million transistors
    GeForce FX : 125 million transistors
    P4 Prescott : 125 million transistors
    Radeon X800 : 160 million transistors
    P4 EE : 178 million transistors
    GeForce 6800 : 220 million transistors
    here's the non-sucky version since <ecode> doesn't actually preserve spacing like <pre>.
  36. I think I speak for many of us by Sycraft-fu · · Score: 5, Insightful

    When I say oh shut the fuck up.

    Sorry for the flames, but seriously, I get so damn sick of all the "all new games suck" whiners. Look, there are legit reasons to want new technology. It is nice to have better graphics, more realistic sound, etc. It is NICE to have game that looks and sounds more like reality. Yes, that doesn't make the game great, but that doesn't mean it's worthless.

    What's more, don't pretend like all modern games suck while old games ruled. That's a bunch of bullshit. Sure, there are plenty of modern games that suck, but guess what? There are tons of old games that suck too. Thing is, you just tend to forget about them. You remember the greats that you enjoyed or heard about, the ones that helped shape gaming today. You forget all the utter shit that was released, just as is released today.

    So get off it. If you don't like nice graphics, fine. Stick with old games, no one is forcing you to upgrade. But don't pretend like there is no reason to want better graphics in games.

    1. Re:I think I speak for many of us by Tim+C · · Score: 5, Insightful

      Hear, hear.

      There's something that's always puzzled me a little about this site - attached to every single article about some new piece of PC tech - a faster processor, better graphics card, etc - there are a number of comments bemoaning the advance. All of them saying that people don't need the power/speed they have already, that they personally are just fine with 4 year old hardware, or, in this case, that better graphics don't make for better games. Hell, the same is true for mobile phones - I've lost count of the number of comments bemoaning advances in them, too.

      It's funny, but I thought this was supposed to be a site for geeks; aren't geeks supposed to *like* newer, better toys?

      To get back on topic - no, better graphics are not sufficient for a better game. However, if the gameplay is there, then they can certainly make the experience more enjoyable. Would Quake have been as much fun if it was rendered in wireframes?

      Better graphics help add to the sense of realisim, making the game a more immersive experience. The whole point of the majority of games is entertainment and (to an extent) escapism. Additionally, what a lot of people like the grand-parent poster seem to forget is that most of the big-name game engines are licensed for use in a number of games. Let people like id spend their time and money coming up with the most graphically intensive, realistic engine they can. Think Doom 3'll suck because the gameplay will be crap? Fine, then wait for someone to license the engine and create a better game with it. In the meantime, please shut up and remember that there are those of us who like things to be pretty, as well as useful/well made/fun/(good at $primaryPurpose)

      Good graphics on their own won't make a good game, but they will help make a good game great.

  37. Let me check my notes... by Impeesa · · Score: 4, Interesting

    I did a paper on the topic of general-purpose GPU programming for my parallel computing course just this last semester here, interestingly enough. I believe our research indicated that even a single PCI card was so badly throttled by the bus throughput that it was basically useless. AGP does a lot better taking data in, but it's still pretty costly sending data back to the CPU. I have a feeling your proposed setup will be a whole lot more feasible if/when PCI Express becomes mainstream.

  38. Re:Maybe time for a new generation of math-process by pe1chl · · Score: 4, Insightful

    What I remember about co-processing cards and "intelligent peripheral cards" (like raid controllers or network cards with an onboard processor) is this:

    There is a certain overhead because a communications protocol is to be established between the main processor and the co-processor. For simple tasks the main processor often stops and waits for the co-processor to complete the task and retrieves the results. For more complicated tasks, the main processor continues but later an interrupt occurs that the main processor must service.

    You must be very careful or the extra overhead of this communication makes the execution of the task slower than without the co-processor. This is certainly going to happen at some time in the future, when you increase central processor power all the time but keep using the same co-processor.

    For example, your matrix co-processor needs to be fed the matrix data, start working, and tell it is finished. Your performance would not only be limited by the processor speed, but also by the bus transfer rate, and by the impact those fast bus transfers have on the CPU-memory bandwidth available and the on-CPU cache validity.
    When you are unlucky, the next CPU you buy is faster in performing the task itself.

  39. Dual Core by BrookHarty · · Score: 4, Interesting

    With Dual Core CPU's going to be the norm, why not a Dual Core GPU for even faster gfx cards? With everyone wanting 16x antialiasing at 1600x1200 to get over 100fps, its gonna take some very powerful GPU's (or some dual cores).

    Even with the ATI 800XT, 1600x1200 can dip below 30FPS with AA/AF on higher settings. Still a ways to go for that full virtual reality look.

  40. Audio DSP by buserror · · Score: 4, Informative

    I've been thinking about using the GPU for audio DSP work for some time, even got to a point where I could transform some signal by "rendering" it into a texture (in a simple way, I could mix two sounds using the alpha as factor).
    The problem is that these cards are made to be "write only" and that basicaly fetching back anything from them is *very* slow, which makes them totaly useless for the purpose, since you *kmow* the results are there, but you can't fetch them in an usefull/fast maneer.
    I wonder if it's deliberate, to sell the "pro" cards they use for the rendering farms

  41. Re:Link to previous discussion on same/similar sub by Crazy+Eight · · Score: 5, Informative

    QE is cool, but it doesn't do anything similar at all to what they're talking about here. FFTs on an NV30 are only incidentally related to texture mapping window contents. Check out gpgpu.org or BrookGPU. In a sense, the idea is to treat modern graphics hardware as the next step beyond SIMD instruction sets. Incidentally, e17 exploited (hardware) GL rendering of 2D graphics via evas a bit before Apple put that into OS X.

  42. Commodore 64 by curator_thew · · Score: 5, Interesting


    This concept was being used back in 1988. The Commodore 64 (1mhz 6510, a 6502 like micro processor) had a peripheral 5.25 disk drive called the 1541, which itself had a 1mhz 6510 cpu in it, connected via. a serial link.

    It became common practice to introduce fast loaders: these were partially resident in the C64, and also in the 1541: effectively replacing the 1541's limited firmware.

    However, demo programmers figured out how to utilise the 1541: one particular demo involved uploading program to the 1541 at start, then upon ever screen rewrite, uploading vectors to the 1541, which the 1541 would perform calculations in parallel with the C64, then at the end of the screen, the C64 fetch the results from the 1541, and incorporate them into the next screen frame.

    Equally, GPU provides similar capability if so used.

  43. Interesting work that raises some questions... by thurin_the_destroyer · · Score: 4, Informative

    Having done a similar work for my final year project this year, I have some experience attempting general purpose computation on a GPU. The results that I recieved when comparing the CPU with the GPU were very different with many of the applications coming in at 7-15 times slower on the GPU. Further, I discovered some problems which I mention below:

    ! Matrix results
    As in mentioned earlier in the report, the graphics pipeline does not support a branch instruction. So with a limitied number of assembly instructions that can be executed in each stage of the pipeline (either 128 or 256 in current cards), how is it possible for them to perform a calculation on a 1500x1500 matrix multiplication. To calculate a single result 1500 multiplications would need to take place and if they are really clever about how they encode the data into texture s to optimise access, they would need two texture accesses for even 4 multiplications. By my calculations that is 1875 instructions, where you can only do 128 or 256.

    My tests found that using the Cg compiler provided by NVidia, that a matrix of size 26x26 could be multiplied before the unrolling of the for loop exceed the 256 limitation.

    One aspect that my evaluation did not get to examine was the possiblity of reading partial results back from the framebuffer to the texture memory along with loading a slightly modified program to generate the next partial result. They don't mention if they used this strategy so I assume that they don't.

    ! Inclusion of a branch instruction
    Even if a branch instruction were to be included into the vertex and fragment stages of the pipeline, it would cause serious timing issues. As student of Computer Science, I have been taught that the pipeline operates at the speed of the slowest stage and from designing simple pipelined ALUs, I see the logic behind it. However, if a branch instruction is included then the fragment processing stage could become the slowest as the pipeline stalls waiting for the fragment processor to output its information into the framebuffer. I believe it for this reason that the GPU designers specifically did not include a branch instruction.

    ! Accuracy
    My work also found a serious accuracy issue with attempting compuation on the GPU. Firstly, the GPU hardware represents all number in the pipeline as floating point values. As many of you can probably guess, this brings up the ever present problem of 'floating point error'. The interface between GPU and CPU are traditionally 8-bit values. Once they are imported into the 32-bit floating point pipeline the representation has them falling between 0 and 1, meaning that these numbers must be scaled up to their intended representations (integers between 0 and 255 for example) before computation can begin. Combine these two necessary operations and what I saw was a serious accuracy issue where five of my nine results(in the 3x3 matrix) were one integer value out.

    While I don't claim to be an expert on these matters, I do think there is the possiblity of using commodity graphics cards for general purpose computation. However, using hardware that is not designed for this purpose holds some serious constraints in my opinion. Anyone who cares to look at my work can find it here