All posts by msoos

On hyper-binary resolution

Hyper-binary resolution is actually quite straightforward, or at least appears to be. Let’s take the following example. The clauses in our database are the following:

-a V b
-a V c
-b V -c V g
-b V -c V d
-d V g

Let’s set a to true, and see what happens. Immediately, b and c get set to true through binary clauses. If we now propagate g through the clause -b V -c V g, we ought to do hyper-binary resolution straight away, and add the clause -a V g — some call this lazy hyper-binary resolution. Good, one more binary clause!

But then… So now we have nothing to propagate using only binary clauses, we have to propagate using a long clause, -b V -c V d. As good citizens, we also do (lazy) hyper-binary resolution, coming up with the clause -a V d. Good, one more binary clause! One slight glitch now… d propagates to g, using a binary clause. But this means that setting a can propagate to g without -a V g, the first hyper-binary clause we added! So the first hyper-binary clause we added is in fact useless, it needs to be removed. If we applied transitive reduction, it would remove the first hyper-binary clause -a V g automatically.

Let’s go a bit deeper here. How could we have avoided adding the first hyper-binary clause? The obvious answer is: we should have started with -b V -c V d instead of -b V -c V g. But how easy would have it been to know (i.e. calculate) that starting with that different long clause would have made our work easier? I am not sure it would have been easy to know. And of course the example above is very trivial. It could be made much-much more complicated: g could have been reached with any number of hyper-binary resolutions from d — so simple binary look-ahead would not have helped.

I am stuck here. Any ideas?

A nifty way of saving time with OpenCL

In OpenCL, the platform for using the graphics card as a form of highly parallelised machine, reading and writing to the memory of the card is very expensive. For this reason, the OpenCL standard offers a set of highly flexible ways of writing and reading data to- and from the OpenCL device. Using these flexible systems takes time to get used to, but seem to be necessary to get the most out of the graphics card.

The Problem

If data needs to be processed, a standard way of pushing it through the compute device is to use two instances of an OpenCL kernel: while one is executing, the system is reading out the finished data and uploading the new data to compute for the other kernel. Then the kernels switch places, kernel 2 is processing, while data is read-written for kernel 1. This requires the programmer to index every data piece (since there are now two of them), and make sure to get the last iteration right. This latter is tricky, because even if there is no longer data to process, kernel 2 may still be executing even though kernel 1 can now be stopped.

These difficulties make the system tricky to get right, though not impossible. In this blogpost I would like to share with you a nifty trick I have found that completely eliminates this complexity, significantly cleaning up code, while keeping the same speed.

The Solution

Since OpenCL 1.1, OpenCL supports multithreading. While managing threads is one of the most dreaded parts of programming, OpenMP makes things extremely simple. The architecture we will need is the following:

  1. A single-kernel system that churns through data. Let us call this Worker
  2. A simple class that keeps in mind which data pieces have been finished with. Let us call this Dealer

There will be two Workers, and one Dealer. When the Worker requests data from the Dealer, it does it inside a critical OpenMP directive. The Dealer is simply initialised with the data to read through, and deals this data out to the Worker upon request, and marks the data piece as ‘done’. If there are no more data to work on, the Worker exits. The only tricky part is the startup, which should look like:

//Don't allow dynamic number of threads
omp_set_dynamic(0);

//Set the number of threads we need
omp_set_num_threads(2);

//Initialise Dealer
Dealer dealer(my_options);

#pragma omp parallel
{
  int thread = omp_get_thread_num();
  int num_threads = omp_get_num_threads();

  Worker worker(&dealer, my_options);
  worker.compute();
}

It’s really simple, and works on all platforms where OpenMP is supported, which is pretty much everything, including Windows, Linux, embedded devices, etc. The really nice part about this architecture though is that it allows for way more than just getting around the problems with multiple kernels in the same source code.

The advantages

First of all, this architecture allows for the Dealer to do much more than just deal out data. You can set the number of threads to 3, set the workers to do their stuff, and wake up the Dealer every 5 seconds to dump the data, for instance. This only needs a “while(!finished) { wait(5sec); dump_my_data();}” loop in Dealer. Since the other threads can simply continue working while Dealer is writing to disk, this may be quite an important advantage in case the data you are generating is large. Similarly, Dealer could pre-load the data from disk that is to be dealt out to Workers.

Another very nice advantage of the above is that there can be any number of Workers, which sounds crazy until you get your hands on a multi-GPU computer. To take advantage of all GPUs in the system, the Workers simply need to be paremetrised with the device number that we wish to use. For example, if we have two OpenCL devices on a machine, we need to launch 4 threads, with device numbers 0,0 and 1,1. If the data chunks to compute are small relative to the overall data, e.g. data chunks need approx. 1 minute to process, but the overall data takes more than an hour, the dealer will distribute the load pretty evenly among the GPUs, so the GPUs can be even of a mixed speed, and it won’t affect the overall finish time much.

Conclusions

Although the proposed architecture uses multi-threading, something that most programmers fear (sometimes rightly so), it leads to a significantly cleaner and more flexible code that can do more with less. Using this architecture, the code should be easier to write, maintain, and extend — something all good programmers strive for.

AMD’s OpenCL heaven and hell

I have been using the AMD’s OpenCL platform for a while now, so I’ll try to write a little overview of what I think is good and bad about OpenCL in general and AMD’s OpenCL implementation in particular.

Update: AMD was working on the issues below, and temporarily fixed some of them. They are broken again, and I gave up trying to help them. They would need more engineers to fix these issues on a permanent basis.

The good

  • The speed of execution is unbeatable. I can easily get 10x better speeds than current top-of-the-line desktop CPUs. And that’s not just saving on buying the CPU and all the peripherals (memory, motherboard, etc.), but also on power, which can easily be more expensive than the upfront cost of new machines
  • Once a C/C++ template code is written, OpenCL is easy to start using. There are no difficult systems to master from the main program’s perspective, only a couple of well-named functions like clEnqueueWriteBuffer
  • The OpenCL documentation from Khronos is very well written. They even provide a handy reference card that is well made, too
  • There are many books available. I’ve bought The OpenCL programming guide, though I got bored from its first part (describing the specification), and never got to the supposedly interesting second part, so I can’t yet recommend it
  • The AMD programming guide is simply great. It lists all the important factors like register usage of kernel vs. register-limited wavefronts on the compute unit. It is basically a compressed bible, written by someone extremely knowledgeable in the subject, probably some core AMD engineer(s). I highly recommend reading it
  • OpenCL 1.1 supports mulithreading and is easy to multi-thread. I have turned a program that was single-threaded and used only one GPU into a multi-GPU, multi-threaded system in only two days with OpenMP
  • The GNU debugger can be used to debug the OpenCL kernel if the CPU is chosen as the target platform. This is extremely useful and considerably cuts down on development time.

So much for the good part. For something that is still in its infancy — it has only been around for about 3.5 years — the above is quite impressive. Apparently, others think it’s impressive, too, as OpenCL is already a leading solution for GPGPU developers.  Now let’s get to the bad part.

The bad

  • Warning and errors are sometimes silently eaten. This is very frustrating. For example, I passed a constant memory piece as clCreateBuffer&clEnqueueWriteBuffer, but the size of the buffer was larger than the specified maximum (which for constants is pretty low, a couple of KB). What error message did I get? None. The kernel executed ‘fine’, with the slight glitch that it didn’t do anything, at all, just returned immediately — with CL_SUCCESS, naturally. I have hit this errors-get-eaten bug multiple times, with multiple kinds of bugs. So, if my code doesn’t work, it’s hard to know what is wrong
  • AMD supplies debugging and analysis essentially only for Windows and Visual Studio. I have actually shelled out money on a Windows license (first time in my life) only to get these running, but then I realised I would also need a Visual Studio license, for a mere thousand dollars, to use all tools. However, after seeing the greatness of the KernelAnalyzer which I can reliably crash any moment, and gives no information other than what I can already see from the ISA file, I thought… maybe it’s not worth the money
  • Valgrind gives a lot of warnings when launched on a program that uses AMD’s OpenCL implementation. This makes debugging a lot harder, because OpenCL copies a lot of data between the GPU and the CPU, and if you got the numbers wrong, there is nothing to tell you why your data is garbage. The best would be if the AMD APP SDK was valgrind-clean, and when instructed to use the CPU as the OpenCL platform it would detect memory access errors even in the OpenCL kernel.
  • Global memory usage of the kernel really makes a big difference. I thought that although it’s slow, it’s not a big deal. I was wrong. It’s really slow. I can make my program go 10-20% faster just by replacing something like “x = y; x ^= z;” with “x = y^z”, where “x” is global memory, and “y” and “z” are both registers. This was completely new to me. It also gives you a hint at the intelligence of the ‘optimising’ compiler of the AMD APP SDK. But more on that later.

Now that the bad part is out of the way, it’s time for what’s really ugly.

The ugly

  • The ‘optimising’ compiler in the AMD APP SDK can essentially be treated as a random function. It sometimes gives me faster code, sometimes a much slower one, and I can make it switch from one to the other with what essentially amounts to comments in the code. This is like letting a random monster eat your code then treating what came out of the monster as something to benchmark/test. Don’t be surprised if what comes out is, well, quite inedible. This ‘slight’ problem can be evaded if you simply ask the compiler not to ‘optimise’, by passing the “-cl-opt-disable” option. Sometimes optimisation helps, but when debugging performance problems, it’s best to get rid of it. My current main setup doesn’t use the optimiser and I get approx 3x faster code this way. My other code is speeded up by a factor of 1.8x with the optimiser — though it’s only a slow, sort-of backup implementation anyway
  • You have to copy-paste code. Last time I copy-pasted code was when I was 12, programming Pascal. The reason for this is that in the function declaration&definition you have to specify whether the parameter is a register, a global, or a constant. Since you might want to use the same function twice, once with a constant parameter, once with a global one, you have no other choice than to copy-paste. Oh, yes, you could use a #define, but I am not sure that’s cleaner in any way. You also have to copy-paste if you want the same function, but with a slightly different ending. Putting an ‘if’ at the diverging point and passing a parameter to control the ‘if’ will be considerably slower (yes, the compiler is that bad)
  • AMD’s fglrx dirvers on Linux are about as stable as a house of cards in high wind. If it doesn’t crash, that’s a good day. I can make it crash just by launching a video player, but I have more ‘fancy’ ways (e.g. pushing 2 button combinations) of reliably crashing it, too. However, the ‘radeon’ driver which is stable on Linux doesn’t work with OpenCL.Thanks to this, I actually have to reboot my machine to watch any video — and I thought those days (Windows 95?) were over
  • AMD APP SDK on Linux is about as stable as their driver. For example, compiling&launching a program on the 2.6 version uses 150% CPU and forces the kernel to launch 3 kworker(=kernel worker) threads, each eating up 50% CPU, completely using up a 3-core machine. However, the same exact program can be compiled&launched on the 2.5 version, eating exactly 1% CPU and forcing no kworker usage

Conclusions

The OpenCL architecture is clean, usable and user-friendly. Unfortunately, the current AMD OpenCL implementation is bad. I hope this will improve in the future, and as more and more people start using it, the bugs will eventually be reported, triaged, and fixed. As the number of people that buy a particular card for its OpenCL capabilities increase, for instance because games start using OpenCL as a way to speed up certain physics calculations, the makers of these cards will eventually be forced to fix the bugs and make development easier. Until then, we might have to keep on suffering for the speedups we get.

[paypal-donation]

Thoughts on SAT@home

If you have ever wondered how your multi-month SAT problem could be solved, the answer is here: SAT@home by some kind Russian researchers! This idea has been brewing in my head, we even started a mini-project with a  friendly American researcher, but we never got it into a working condition :(. It’s great that someone took the time to do it, though. Creating such a setup has some easier and harder parts. Setting up a BOINC server is not that hard, but it needs to run 24/7, which is difficult, unless you are department head at a university or you have a company behind you. Then the scripts need to be written, which is relatively easy to do, but testing and debugging is time-consuming. The really hard part, though, is how to distribute the workload. Treatises could be written on that, and the one above uses the simplest method, that of cutting up the problem along a couple of variables. It’s a good start, I think: starting easy is always the best way to start — the first automobile didn’t try to achieve 300km/h speeds, and it didn’t have to.

In the long run, I guess the setups will get more and more complicated, combining many techniques from cutting on variables, to clause sharing with a multitude of clause usefulness heuristics, to sharing parameter usefulness statistics. Workshares themselves could eventually be diversified, some doing ‘simple’ search without resolution, some doing only resolution (and clause cleaning?), some doing only (specific) simplification algorithms such as subsumption or strengthening, some doing data analysis on the current state of the problem such as reachability analysis, number of gates or other higher-level elements such as adders in the problem, etc. In other words, there are many ways to improve this. Maybe even a common interface to such a system could be laid down where different SAT solvers could be plugged in and used without notice.

A friend of mine has once written me a mail describing his work, which essentially talks about paying for a webpage not by looking at adverts, but by running a javascript program. The idea is, of course, that we could write a SAT solver in javascript, and make people run the script by putting it on a well-visited webpage. The server would then distribute SAT problems to the javascripts, which would send some computed data back (like learnt clauses), while the person is surfing the page. Cheap (maybe even free) and essentially unlimited CPU time for hard problems. We could use it to answer some fun math questions, or break some cryptographic systems, for example… just have to find someone crazy enough to write a SAT solver in javascript! :)

CCC Camp’11

In case you’ve missed it, the CCC Camp was a great opportunity to meet people both working in security and otherwise. I have even met a very kind Taiwanese researcher who worked on SAT and Gröbner basis: in fact, if you haven’t had the chance to read this paper, I highly recommend it. A set of kind Taiwanese researchers recommended this paper to me, and I think it’s the most interesting SAT paper I have read in the past year.

We at SRLabs have made two releases during this camp, one that breaks GPRS encryption, and one that breaks smart card ROM encryption. I was involved with the first release, essentially working on the crypto part. In case you are interested in the videos, the one on GPRS is uploaded here, and the one on smart card ROM encryption is here. This reminds me of something: the videos from the MIT SAT/SMT Summer School are missing :( Well, given my fail there, maybe that’s a good thing :)