Archive for the ‘parallel programming’ Category

Intel’s Xeon Phi – GPU level power without the hassle?

November 13th, 2012

Intel have finally released the Xeon Phi – an accelerator card based on 60 or so customised Intel cores to give around a Teraflop of double precision performance.  That’s comparable to the latest cards from NVIDIA (1.3 Teraflops according to http://www.theregister.co.uk/2012/11/12/nvidia_tesla_k20_k20x_gpu_coprocessors/) but with one key difference—you don’t need to learn any new languages or technologies to take advantage of it (although you can do so if you wish)!

The Xeon Phi uses good, old fashioned High Performance Computing technologies that we’ve been using for years such as OpenMP and MPI.  There’s no need to completely recode your algorithms in CUDA or OpenCL to get a performance boost…just a sprinkling of OpenMP pragmas might be enough in many cases.  Obviously it will take quite a bit of work to squeeze every last drop of performance out of the thing but this might just be the realisation of ‘personal supercomputer’ we’ve all been waiting for.

Here are some links I’ve found so far — would love to see what everyone else has come up with.  I’ll update as I find more

I also note that the Xeon Phi uses AVX extensions but with a wider vector width of 512 bytes so if you’ve been taking advantage of that technology in your code (using one of these techniques perhaps) you’ll reap the benefits there too.

I, for one, am very excited and can’t wait to get my hands on one!  Thoughts, comments and links gratefully received!

3 comments

Vectorising code to take advantage of modern CPUs (AVX and SSE)

August 24th, 2012

I’ve been playing with AVX vectorisation on Sandy Bridge CPUs off and on for a while now and thought that I’d write up a little of what I’ve discovered.  The basic idea of vectorisation is that each core in a modern CPU can operate on multiple values (i.e. a vector) simultaneously per instruction cycle.

Sandy bridge (and the newer Ivy Bridge) processors have 256bit wide vector units which means that each CORE can perform certain operations on up to eight 32-bit floats or four 64-bit doubles per clock cycle.  So, on a quad core you have 4 vector units (one per core) and could operate on up to 16 doubles or 32 floats per clock cycle.

This all sounds great so how does a programmer actually make use of this neat hardware trick?  There are many routes:-

Intrinsics

At the ‘close to the metal’ level you code for these vector units using instructions called AVX intrinsics.  This is relatively difficult and leads to none-portable code if you are not careful.

Auto-vectorisation in compilers

Since working with intrinsics is such hard work, why not let the compiler take the strain? Many modern compilers can automatically vectorize your C, C++ or Fortran code including gcc, PGI and Intel. Sometimes all you need to do is add an extra switch at compile time and reap the speed benefits. In truth, vectorization isn’t always automatic and the programmer needs to give the compiler some assistance but it is a lot easier than hand-coding intrinsics.

Intel SPMD Program Compiler (ispc)

There is a midway point between automagic vectorisation and having to use intrinsics. Intel have a free compiler called ispc (http://ispc.github.com/) that allows you to write compute kernels in a modified subset of C. These kernels are then compiled to make use of vectorised instruction sets. Programming using ispc feels a little like using OpenCL or CUDA. I figured out how to hook it up to MATLAB a few months ago and developed a version of the Square Root function that is almost twice as fast as MATLAB’s own version for sandy bridge i7 processors.

Vectorised Libraries

Vendors of numerical libraries are steadily applying vectorisation techniques in order to maximise performance.  If the execution speed of your application depends upon these library functions, you may get a significant speed boost simply by updating to the latest version of the library and recompiling with the relevant compiler flags.

CUDA for x86

Another route to vectorised code is to make use of the PGI Compiler’s support for x86 CUDA.  What you do is take CUDA kernels written for NVIDIA GPUs and use the PGI Compiler to compile these kernels for x86 processors.  The resulting executables take advantage of vectorisation.  In essence, the vector units of the CPU are acting like CUDA cores–which they sort of are anyway!

The PGI compilers also have technology which they call PGI Unified binary which allows you to use NVIDIA GPUs when present or default to using multi-core x86 if no GPU is present.

  • PGI CUDA-x86 – PGI’s main page for their CUDA on x86 technologies

OpenCL for x86 processors

Yet another route to vectorisation would be to use Intel’s OpenCL implementation which takes OpenCL kernels and compiles them down to take advantage of vector units (http://software.intel.com/en-us/blogs/2011/09/26/autovectorization-in-intel-opencl-sdk-15/).  The AMD OpenCL implementation may also do this but I haven’t tried it and haven’t had chance to research it yet.

WalkingRandomly posts

I’ve written a couple of blog posts that made use of this technology.

Miscellaneous resources

There is other stuff out there but the above covers everything that I have used so far.  I’ll finish by saying that everyone interested in vectorisation should check out this website…It’s the bible!

Research Articles on SSE/AVX vectorisation

I found the following research articles useful/interesting.  I’ll add to this list over time as I dig out other articles.

5 comments

Intel’s new OpenCL SDK gives access to on-die GPU

April 26th, 2012

Intel have just released their OpenCL Software Development Kit (SDK) for Intel processors.  The good news is that this version targets the on-die GPU as well as the CPU allowing truly heterogeneous programming.  The bad news is that the GPU goodness is for 3rd Generation ‘Ivy Bridge‘ Processors only– us backward Sandy Bridge users have been left in the cold :(

A quick scan through the release notes reveals the following:-

  • OpenCL access to the on-die GPU part is currently for Windows only. Linux users only have CPU support at the moment.
  • No access to the GPU part of Sandy Bridge Processors via this implementation.
  • The GPU part has single precision only (I guess we’ll see many more mixed-precision algorithms from now on)

I don’t have access to an Ivy Bridge processor and so can’t have a play but I’m looking forward to seeing how much performance OpenCL programmers can squeeze out of this new implementation.

Other WalkingRandomly posts on GPU computing

2 comments

Using Intel’s SPMD Compiler (ispc) with MATLAB on Linux

December 28th, 2011

Modern CPUs are capable of parallel processing at multiple levels with the most obvious being the fact that a typical CPU contains multiple processor cores.  My laptop, for example, contains a quad-core Intel Sandy Bridge i7 processor and so has 4 processor cores. You may be forgiven for thinking that, with 4 cores, my laptop can do up to 4 things simultaneously but life isn’t quite that simple.

The first complication is hyper-threading where each physical core appears to the operating system as two or more virtual cores.  For example, the processor in my laptop is capable of using hyper-threading and so I have access to up to 8 virtual cores!  I have heard stories where unscrupulous sales people have passed off a 4 core CPU with hyperthreading as being as good as an 8 core CPU…. after all, if you fire up the Windows Task Manager you can see 8 cores and so there you have it!  However, this is very far from the truth since what you really have is 4 real cores with 4 brain damaged cousins.  Sometimes the brain damaged cousins can do something useful but they are no substitute for physical cores.  There is a great explanation of this technology at makeuseof.com.

The second complication is the fact that each physical processor core contains a SIMD (Single Instruction Multiple Data) lane of a certain width. SIMD lanes, aka  SIMD units or vector units, can process several numbers simultaneously with a single instruction rather than only one a time.  The 256-bit wide SIMD lanes on my laptop’s processor, for example, can operate on up to 8 single (or 4 double) precision numbers per instruction.  Since each physical core has its own SIMD lane this means that a 4 core processor could theoretically operate on up to 32 single precision (or 16 double precision) numbers per clock cycle!

So, all we need now is a way of programming for these SIMD lanes!

Intel’s SPMD Program Compiler, ispc, is a free product that allows programmers to take direct advantage of the SIMD lanes in modern CPUS using a C-like syntax.  The speed-ups compared to single-threaded code can be impressive with Intel reporting up to 32 times speed-up (on an i7 quad-core) for a single precision Black-Scholes option pricing routine for example.

Using ispc on MATLAB

Since ispc routines are callable from C, it stands to reason that we’ll be able to call them from MATLAB using mex.  To demonstrate this, I thought that I’d write a sqrt function that works faster than MATLAB’s built-in version.  This is a tall order since the sqrt function is pretty fast and is already multi-threaded.  Taking the square root of 200 million random numbers doesn’t take very long in MATLAB:

>> x=rand(1,200000000)*10;
>> tic;y=sqrt(x);toc
Elapsed time is 0.666847 seconds.

This might not be the most useful example in the world but I wanted to focus on how to get ispc to work from within MATLAB rather than worrying about the details of a more interesting example.

Step 1 – A reference single-threaded mex file

Before getting all fancy, let’s write a nice, straightforward single-threaded mex file in C and see how fast that goes.

#include <math.h>
#include "mex.h"

void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[] )
{
    double *in,*out;
    int rows,cols,num_elements,i; 

    /*Get pointers to input matrix*/
    in = mxGetPr(prhs[0]);
    /*Get rows and columns of input matrix*/
    rows = mxGetM(prhs[0]);
    cols = mxGetN(prhs[0]);
    num_elements = rows*cols;

    /* Create output matrix */
    plhs[0] = mxCreateDoubleMatrix(rows, cols, mxREAL);
    /* Assign pointer to the output */
    out = mxGetPr(plhs[0]);

    for(i=0; i<num_elements; i++)
    {
        out[i] = sqrt(in[i]);
    }
}

Save the above to a text file called sqrt_mex.c and compile using the following command in MATLAB

 mex sqrt_mex.c

Let’s check out its speed:

>> x=rand(1,200000000)*10;
>> tic;y=sqrt_mex(x);toc
Elapsed time is 1.993684 seconds.

Well, it works but it’s quite a but slower than the built-in MATLAB function so we still have some work to do.

Step 2 – Using the SIMD lane on one core via ispc

Using ispc is a two step process.  First of all you need the .ispc program

export void ispc_sqrt(uniform double vin[], uniform double vout[],
                   uniform int count) {
    foreach (index = 0 ... count) {
        vout[index] = sqrt(vin[index]);
    }
}

Save this to a file called ispc_sqrt.ispc and compile it at the Bash prompt using

ispc -O2 ispc_sqrt.ispc -o ispc_sqrt.o -h ispc_sqrt.h --pic

This creates an object file, ispc_sqrt.o, and a header file, ispc_sqrt.h. Now create the mex file in MATLAB

#include <math.h>
#include "mex.h"
#include "ispc_sqrt.h"

void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[] )
{
    double *in,*out;
    int rows,cols,num_elements,i; 

    /*Get pointers to input matrix*/
    in = mxGetPr(prhs[0]);
    /*Get rows and columns of input matrix*/
    rows = mxGetM(prhs[0]);
    cols = mxGetN(prhs[0]);
    num_elements = rows*cols;

    /* Create output matrix */
    plhs[0] = mxCreateDoubleMatrix(rows, cols, mxREAL);
    /* Assign pointer to the output */
    out = mxGetPr(plhs[0]);

    ispc::ispc_sqrt(in,out,num_elements);
}

Call this ispc_sqrt_mex.cpp and compile in MATLAB with the command

 mex ispc_sqrt_mex.cpp ispc_sqrt.o

Let’s see how that does for speed:

>> tic;y=ispc_sqrt_mex(x);toc
Elapsed time is 1.379214 seconds.

So, we’ve improved on the single-threaded mex file a bit (1.37 instead of 2 seconds) but it’s still not enough to beat the MATLAB built-in.  To do that, we are going to have to use the SIMD lanes on all 4 cores simultaneously.

Step 3 – A reference multi-threaded mex file using OpenMP

Let’s step away from ispc for a while and see how we do with something we’ve seen before– a mex file using OpenMP (see here and here for previous articles on this topic).

#include <math.h>
#include "mex.h"
#include <omp.h>

void do_calculation(double in[],double out[],int num_elements)
{
    int i;

#pragma omp parallel for shared(in,out,num_elements)
    for(i=0; i<num_elements; i++){
          out[i] = sqrt(in[i]);
         }
}

void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[] )
{
    double *in,*out;
    int rows,cols,num_elements,i; 

    /*Get pointers to input matrix*/
    in = mxGetPr(prhs[0]);
    /*Get rows and columns of input matrix*/
    rows = mxGetM(prhs[0]);
    cols = mxGetN(prhs[0]);
    num_elements = rows*cols;

    /* Create output matrix */
    plhs[0] = mxCreateDoubleMatrix(rows, cols, mxREAL);
    /* Assign pointer to the output */
    out = mxGetPr(plhs[0]);

    do_calculation(in,out,num_elements);
}

Save this to a text file called openmp_sqrt_mex.c and compile in MATLAB by doing

 mex openmp_sqrt_mex.c CFLAGS="\$CFLAGS -fopenmp" LDFLAGS="\$LDFLAGS -fopenmp"

Let’s see how that does (OMP_NUM_THREADS has been set to 4):

>> tic;y=openmp_sqrt_mex(x);toc
Elapsed time is 0.641203 seconds.

That’s very similar to the MATLAB built-in and I suspect that The Mathworks have implemented their sqrt function in a very similar manner. Theirs will have error checking, complex number handling and what-not but it probably comes down to a for-loop that’s been parallelized using Open-MP.

Step 4 – Using the SIMD lanes on all cores via ispc

To get a ispc program to run on all of my processors cores simultaneously, I need to break the calculation down into a series of tasks. The .ispc file is as follows

task void
ispc_sqrt_block(uniform double vin[], uniform double vout[],
                   uniform int block_size,uniform int num_elems){
    uniform int index_start = taskIndex * block_size;
    uniform int index_end = min((taskIndex+1) * block_size, (unsigned int)num_elems);

    foreach (yi = index_start ... index_end) {
        vout[yi] = sqrt(vin[yi]);
    }
}

export void
ispc_sqrt_task(uniform double vin[], uniform double vout[],
                   uniform int block_size,uniform int num_elems,uniform int num_tasks)
{

    launch[num_tasks] < ispc_sqrt_block(vin, vout, block_size, num_elems) >;
}

Compile this by doing the following at the Bash prompt

ispc -O2 ispc_sqrt_task.ispc -o ispc_sqrt_task.o -h ispc_sqrt_task.h --pic

We’ll need to make use of a task scheduling system. The ispc documentation suggests that you could use the scheduler in Intel’s Threading Building Blocks or Microsoft’s Concurrency Runtime but a basic scheduler is provided with ispc in the form of tasksys.cpp (I’ve also included it in the .tar.gz file in the downloads section at the end of this post), We’ll need to compile this too so do the following at the Bash prompt

g++ tasksys.cpp -O3 -Wall -m64 -c -o tasksys.o -fPIC

Finally, we write the mex file

#include <math.h>
#include "mex.h"
#include "ispc_sqrt_task.h"

void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[] )
{
    double *in,*out;
    int rows,cols,i;

    unsigned int num_elements;
    unsigned int block_size;
    unsigned int num_tasks; 

    /*Get pointers to input matrix*/
    in = mxGetPr(prhs[0]);
    /*Get rows and columns of input matrix*/
    rows = mxGetM(prhs[0]);
    cols = mxGetN(prhs[0]);
    num_elements = rows*cols;

    /* Create output matrix */
    plhs[0] = mxCreateDoubleMatrix(rows, cols, mxREAL);
    /* Assign pointer to the output */
    out = mxGetPr(plhs[0]);

    block_size = 1000000;
    num_tasks = num_elements/block_size;

    ispc::ispc_sqrt_task(in,out,block_size,num_elements,num_tasks);

}

In the above, the input array is divided into tasks where each task takes care of 1 million elements. Our 200 million element test array will, therefore, be split into 200 tasks– many more than I have processor cores. I’ll let the task scheduler worry about how to schedule these tasks efficiently across the cores in my machine. Compile this in MATLAB by doing

mex ispc_sqrt_task_mex.cpp ispc_sqrt_task.o tasksys.o

Now for crunch time:

>> x=rand(1,200000000)*10;
>> tic;ys=sqrt(x);toc   %MATLAB's built-in
Elapsed time is 0.670766 seconds.
>> tic;y=ispc_sqrt_task_mex(x);toc  %my version using ispc
Elapsed time is 0.393870 seconds.

There we have it! A version of the sqrt function that works faster than MATLAB’s own by virtue of the fact that I am now making full use of the SIMD lanes in my laptop’s Sandy Bridge i7 processor thanks to ispc.

Although this example isn’t very useful as it stands, I hope that it shows that using the ispc compiler from within MATLAB isn’t as hard as you might think and is yet another tool in the arsenal of weaponry that can be used to make MATLAB faster.

Final Timings, downloads and links

  • Single threaded: 2.01 seconds
  • Single threaded with ispc: 1.37 seconds
  • MATLAB built-in: 0.67 seconds
  • Multi-threaded with OpenMP (OMP_NUM_THREADS=4): 0.64 seconds
  • Multi-threaded with OpenMP and hyper-threading (OMP_NUM_THREADS=8): 0.55 seconds
  • Task-based multicore with ispc: 0.39 seconds

Finally, here’s some links and downloads

System Specs

  • MATLAB 2011b running on 64 bit linux
  • gcc 4.6.1
  • ispc version 1.1.1
  • Intel Core i7-2630QM with 8Gb RAM
8 comments

MATLAB mex functions using the NAG C Library in Windows

October 24th, 2011

The NAG C Library is one of the largest commercial collections of numerical software currently available and I often find it very useful when writing MATLAB mex files.  “Why is that?” I hear you ask.

One of the main reasons for writing a mex file is to gain more speed over native MATLAB.  However, one of the main problems with writing mex files is that you have to do it in a low level language such as Fortran or C and so you lose much of the ease of use of MATLAB.

In particular, you lose straightforward access to most of the massive collections of MATLAB routines that you take for granted.  Technically speaking that’s a lie because you could use the mex function mexCallMATLAB to call a MATLAB routine from within your mex file but then you’ll be paying a time overhead every time you go in and out of the mex interface.  Since you are going down the mex route in order to gain speed, this doesn’t seem like the best idea in the world.  This is also the reason why you’d use the NAG C Library and not the NAG Toolbox for MATLAB when writing mex functions.

One way out that I use often is to take advantage of the NAG C library and it turns out that it is extremely easy to add the NAG C library to your mex projects on Windows.  Let’s look at a trivial example.  The following code, nag_normcdf.c, uses the NAG function nag_cumul_normal to produce a simplified version of MATLAB’s normcdf function (laziness is all that prevented me from implementing a full replacement).

/* A simplified version of normcdf that uses the NAG C library
 * Written to demonstrate how to compile MATLAB mex files that use the NAG C Library
 * Only returns a normcdf where mu=0 and sigma=1
 * October 2011 Michael Croucher
 * www.walkingrandomly.com
 */

#include <math.h>
#include "mex.h"
#include "nag.h"
#include "nags.h"

void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[] )
{
    double *in,*out;
    int rows,cols,num_elements,i;

    if(nrhs>1)
    {
        mexErrMsgIdAndTxt("NAG:BadArgs","This simplified version of normcdf only takes 1 input argument");
    } 

    /*Get pointers to input matrix*/
    in = mxGetPr(prhs[0]);
    /*Get rows and columns of input matrix*/
    rows = mxGetM(prhs[0]);
    cols = mxGetN(prhs[0]);
    num_elements = rows*cols;

    /* Create output matrix */
    plhs[0] = mxCreateDoubleMatrix(rows, cols, mxREAL);
    /* Assign pointer to the output */
    out = mxGetPr(plhs[0]);

    for(i=0; i<num_elements; i++){
          out[i] = nag_cumul_normal(in[i]);
         }
}

To compile this in MATLAB, just use the following command

 mex nag_normcdf.c CLW6I09DA_nag.lib

If your system is set up the same as mine then the above should ‘just work’ (see System Information at the bottom of this post).  The new function works just as you would expect it to

>> format long
>> format compact
>> nag_normcdf(1)
ans =
   0.841344746068543

Compare the result to normcdf from the statistics toolbox

>> normcdf(1)
ans =
   0.841344746068543

So far so good. I could stop the post here since all I really wanted to do was say ‘The NAG C library is useful for MATLAB mex functions and it’s a doddle to use – here’s a toy example and here’s the mex command to compile it’

However, out of curiosity, I looked to see if my toy version of normcdf was any faster than The Mathworks’ version.  Let there be 10 million numbers:

>> x=rand(1,10000000);

Let’s time how long it takes MATLAB to take the normcdf of those numbers

>> tic;y=normcdf(x);toc
Elapsed time is 0.445883 seconds.
>> tic;y=normcdf(x);toc
Elapsed time is 0.405764 seconds.
>> tic;y=normcdf(x);toc
Elapsed time is 0.366708 seconds.
>> tic;y=normcdf(x);toc
Elapsed time is 0.409375 seconds.

Now let’s look at my toy-version that uses NAG.

>> tic;y=nag_normcdf(x);toc
Elapsed time is 0.544642 seconds.
>> tic;y=nag_normcdf(x);toc
Elapsed time is 0.556883 seconds.
>> tic;y=nag_normcdf(x);toc
Elapsed time is 0.553920 seconds.
>> tic;y=nag_normcdf(x);toc
Elapsed time is 0.540510 seconds.

So my version is slower!  Never mind, I’ll just make my version parallel using OpenMP – Here is the code: nag_normcdf_openmp.c

/* A simplified version of normcdf that uses the NAG C library
 * Written to demonstrate how to compile MATLAB mex files that use the NAG C Library
 * Only returns a normcdf where mu=0 and sigma=1
 * October 2011 Michael Croucher
 * www.walkingrandomly.com
 */

#include <math.h>
#include "mex.h"
#include "nag.h"
#include "nags.h"
#include <omp.h>

void do_calculation(double in[],double out[],int num_elements)
{
    int i,tid;

#pragma omp parallel for shared(in,out,num_elements) private(i,tid)
    for(i=0; i<num_elements; i++){
          out[i] = nag_cumul_normal(in[i]);
         }
}

void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[] )
{
    double *in,*out;
    int rows,cols,num_elements;

    if(nrhs>1)
    {
        mexErrMsgIdAndTxt("NAG_NORMCDF:BadArgs","This simplified version of normcdf only takes 1 input argument");
    } 

    /*Get pointers to input matrix*/
    in = mxGetPr(prhs[0]);
    /*Get rows and columns of input matrix*/
    rows = mxGetM(prhs[0]);
    cols = mxGetN(prhs[0]);
    num_elements = rows*cols;

    /* Create output matrix */
    plhs[0] = mxCreateDoubleMatrix(rows, cols, mxREAL);
    /* Assign pointer to the output */
    out = mxGetPr(plhs[0]);

    do_calculation(in,out,num_elements);
}

Compile that with

 mex  COMPFLAGS="$COMPFLAGS /openmp"  nag_normcdf_openmp.c CLW6I09DA_nag.lib

and on my quad-core machine I get the following timings

>> tic;y=nag_normcdf_openmp(x);toc
Elapsed time is 0.237925 seconds.
>> tic;y=nag_normcdf_openmp(x);toc
Elapsed time is 0.197531 seconds.
>> tic;y=nag_normcdf_openmp(x);toc
Elapsed time is 0.206511 seconds.
>> tic;y=nag_normcdf_openmp(x);toc
Elapsed time is 0.211416 seconds.

This is faster than MATLAB and so normal service is resumed :)

System Information

  • 64bit Windows 7
  • MATLAB 2011b
  • NAG C Library Mark 9 – CLW6I09DAL
  • Visual Studio 2008
  • Intel Core i7-2630QM processor
2 comments

MATLAB functions with built in parallel computing toolbox support

September 11th, 2011

So, you’re the proud owner of a new license for MATLAB’s parallel computing toolbox (PCT) and you are wondering how to get some bang for your buck as quickly as possible.  Sure, you are going to learn about constructs such as parfor and spmd but that takes time and effort.  Wouldn’t it be nice if you could speed up some of your MATLAB code simply by saying ‘Turn parallelisation on’?

It turns out that The Mathworks have been adding support for their parallel computing toolbox all over the place and all you have to do is switch it on (Assuming that you actually have the parallel computing toolbox of course).  For example say you had the following call to fmincon (part of the optimisation toolbox) in your code

[x, fval] = fmincon(@objfun, x0, [], [], [], [], [], [], @confun,opts)

To turn on parallelisation across 2 cores just do

matlabpool 2;
opts = optimset('fmincon');
opts = optimset('UseParallel','always');
[x, fval] = fmincon(@objfun, x0, [], [], [], [], [], [], @confun,opts);

That wasn’t so hard was it?  The speedup (if any) completely depends upon your particular optimization problem.

Why isn’t parallelisation turned on by default?
The next question that might occur to you is ‘Why doesn’t The Mathworks just turn parallelisation on by default?’ After all, although the above modification is straightforward, it does require you to know that this particular function supports parallel execution via the PCT. If you didn’t think to check then your code would be doomed to serial execution forever.

The simple answer to this question is ‘Sometimes the parallel version is slower‘. Take this serial code for example.

objfun = @(x)exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1);
confun = @(x) deal( [1.5+x(1)*x(2)-x(1)-x(2); -x(1)*x(2)-10], [] );
tic;
[x, fval] = fmincon(objfun, x0, [], [], [], [], [], [], confun);
toc

On the machine I am currently sat at (quad core running MATLAB 2011a on Linux) this typically takes around 0.032 seconds to solve. With a problem that trivial my gut feeling is that we are not going to get much out of switching to parallel mode.

objfun = @(x)exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1);
confun = @(x) deal( [1.5+x(1)*x(2)-x(1)-x(2); -x(1)*x(2)-10],[] );

%only do this next line once.  It opens two MATLAB workers
matlabpool 2;

opts = optimset('fmincon');
opts = optimset('UseParallel','always');

tic;
[x, fval] = fmincon(objfun, x0, [], [], [], [], [], [], confun,opts);
toc

Sure enough, this increases execution time dramatically to an average of 0.23 seconds on my machine.  There is always a computational overhead that needs paying when you go parallel and if your problem is too trivial then this overhead costs more than the calculation itself.

So which functions support the Parallel Computing Toolbox?

I wanted a web-page that listed all functions that gain benefit from the Parallel Computing Toolbox but couldn’t find one.  I found some documentation on specific toolboxes such as Parallel Statistics but nothing that covered all of MATLAB in one place.  Here is my attempt at producing such a document.  Feel free to contact me if I have missed anything out.

This covers MATLAB 2011b and is almost certainly incomplete. I’ve only covered toolboxes that I have access to and so some are missing.  Please contact me if you have any extra information.

Bioinformatics Toolbox

Global Optimisation

Image Processing

Optimisation Toolbox

Simulink

  • Running parallel simulations
  • You can increase the speed of diagram updates for models containing large model reference hierarchies by building referenced models that are configured in Accelerator mode in parallel whenever conditions allow.  This is covered in the documentation.

Statistics Toolbox

Other articles about parallel computing in MATLAB from WalkingRandomly

7 comments

MATLAB GPU / CUDA experiences on my laptop – Elementwise operations on the GPU #1

July 27th, 2011

This is part 1 of an ongoing series of articles about MATLAB programming for GPUs using the Parallel Computing Toolbox.  The introduction and index to the series is at http://www.walkingrandomly.com/?p=3730.

Have you ever needed to take the sine of 100 million random numbers?  Me either, but such an operation gives us an excuse to look at the basic concepts of GPU computing with MATLAB and get an idea of the timings we can expect for simple elementwise calculations.

Taking the sine of 100 million numbers on the CPU

Let’s forget about GPUs for a second and look at how this would be done on the CPU using MATLAB.  First, I create 100 million random numbers over a range from 0 to 10*pi and store them in the variable cpu_x;

cpu_x = rand(1,100000000)*10*pi;

Now I take the sine of all 100 million elements of cpu_x using a single command.

cpu_y = sin(cpu_x)

I have to confess that I find the above command very cool. Not only are we looping over a massive array using just a single line of code but MATLAB will also be performing the operation in parallel. So, if you have a multicore machine (and pretty much everyone does these days) then the above command will make good use of many of those cores. Furthermore, this kind of parallelisation is built into the core of MATLAB….no parallel computing toolbox necessary. As an aside, if you’d like to see a list of functions that automatically run in parallel on the CPU then check out my blog post on the issue.

So, how quickly does my 4 core laptop get through this 100 million element array?  We can find out using the MATLAB functions tic and toc. I ran it three times on my laptop and got the following

>> tic;cpu_y = sin(cpu_x);toc
Elapsed time is 0.833626 seconds.
>> tic;cpu_y = sin(cpu_x);toc
Elapsed time is 0.899769 seconds.
>> tic;cpu_y = sin(cpu_x);toc
Elapsed time is 0.916969 seconds.

So the first thing you’ll notice is that the timings vary and I’m not going to go into the reasons why here. What I am going to say is that because of this variation it makes sense to time the calculation a number of times (20 say) and take an average. Let’s do that

sintimes=zeros(1,20);
for i=1:20;tic;cpu_y = sin(cpu_x);sintimes(i)=toc;end
average_time = sum(sintimes)/20

average_time =
    0.8011

So, on average, it takes my quad core laptop just over 0.8 seconds to take the sine of 100 million elements using the CPU.  A couple of points:

  • I note that this time is smaller than any of the three test times I did before running the loop and I’m not really sure why.  I’m guessing that it takes my CPU a short while to decide that it’s got a lot of work to do and ramp up to full speed but further insights are welcomed.
  • While staring at the CPU monitor I noticed that the above calculation never used more than 50% of the available virtual cores.  It’s using all 4 of my physical CPU cores but perhaps if it took advantage of hyperthreading I’d get even better performance?  Changing OMP_NUM_THREADS to 8 before launching MATLAB did nothing to change this.

Taking the sine of 100 million numbers on the GPU

Just like before, we start off by using the CPU to generate the 100 million random numbers1

cpu_x = rand(1,100000000)*10*pi;

The first thing you need to know about GPUs is that they have their own memory that is completely separate from main memory. So, the GPU doesn’t know anything about the array created above. Before our GPU can get to work on our data we have to transfer it from main memory to GPU memory and we acheive this using the gpuArray command.

gpu_x = gpuArray(cpu_x); %this moves our data to the GPU

Once the GPU can see all our data we can apply the sine function to it very easily.

gpu_y = sin(gpu_x)

Finally, we transfer the results back to main memory.

cpu_y = gather(gpu_y)

If, like many of the GPU articles you see in the literature, you don’t want to include transfer times between GPU and host then you time the calculation like this:

tic
gpu_y = sin(gpu_x);
toc

Just like the CPU version, I repeated this calculation several times and took an average. The result was 0.3008 seconds giving a speedup of 2.75 times compared to the CPU version.
If, however, you include the time taken to transfer the input data to the GPU and the results back to the CPU then you need to time as follows

tic
gpu_x = gpuArray(cpu_x);
gpu_y = sin(gpu_x);
cpu_y = gather(gpu_y)
toc

On my system this takes 1.0159 seconds on average– longer than it takes to simply do the whole thing on the CPU. So, for this particular calculation, transfer times between host and GPU swamp the benefits gained by all of those CUDA cores.

Benchmark code
I took the ideas above and wrote a simple benchmark program called sine_test.  The way you call it is as follows

[cpu,gpu_notransfer,gpu_withtransfer] = sin_test(numrepeats,num_elements]

For example, if you wanted to run the benchmarks 20 times on a 1 million element array and return the average times then you just do

>> [cpu,gpu_notransfer,gpu_withtransfer] = sine_test(20,1e6)
cpu =
    0.0085
gpu_notransfer =
    0.0022
gpu_withtransfer =
    0.0116

I then ran this on my laptop for array sizes ranging from 1 million to 100 million and used the results to plot the graph below.
GPU vs CPU for lots of sines

But I wanna write a ‘GPUs are awesome’ paper

So far in this little story things are not looking so hot for the GPU  and yet all of the ‘GPUs are awesome’ papers you’ve ever read seem to disagree with me entirely.  What on earth is going on?  Well, lets take the advice given by csgillespie.wordpress.com and turn it on its head.  How do we get awesome speedup figures from the above benchmarks to help us pump out a ‘GPUs are awesome paper’?

0. Don’t consider transfer times between CPU and GPU.

We’ve already seen that this can ruin performance so let’s not do it shall we?  As long as we explicitly say that we are not including transfer times then we are covered.

1. Use a singlethreaded CPU.

Many papers in the literature compare the GPU version with a single-threaded CPU version and yet I’ve been using all 4 cores of my processor.  Silly me…let’s fix that by running MATLAB in single threaded mode by launching it with the command

matlab -singleCompThread

Now when I run the benchmark for 100 million elements I get the following times

>> [cpu,gpu_no,gpu_with] = sine_test(10,1e8)
cpu =
    2.8875
gpu_no =
    0.3016
gpu_with =
    1.0205

Now we’re talking! I can now claim that my GPU version is over 9 times faster than the CPU version.

2. Use an old CPU.

My laptop has got one of those new-fangled sandy-bridge i7 processors…one of the best classes of CPU you can get for a laptop.  If, however, I was doing these tests at work then I guess I’d be using a GPU mounted in my university Desktop machine.  Obviously I would compare the GPU version of my program with the CPU in the Desktop….an Intel Core 2 Quad Q9650.  Heck its running at 3Ghz which is more Ghz than my laptop so to the casual observer (or a phb) it would look like I was using a more beefed up processor in order to make my comparison fairer.

So, I ran the CPU benchmark on that (in singleCompThread mode obviously) and got 4.009 seconds…noticeably slower than my laptop.  Awesome…I am definitely going to use that figure!

I know what you’re thinking…Mike’s being a fool for the sake of it but csgillespie.wordpress.com puts it like this ‘Since a GPU has (usually) been bought specifically for the purpose of the article, the CPU can be a few years older.’ So, some of those ‘GPU are awesome’ articles will be accidentally misleading us in exactly this manner.

3. Work in single precision.

Yeah I know that you like working with double precision arithmetic but that slows GPUs down.  So, let’s switch to single precision.  Just argue in your paper that single precision is OK for this particular calculation and we’ll be set.  To change the benchmarking code all you need to do is change every instance of

rand(1,num_elems)*10*pi;

to

rand(1,num_elems,'single')*10*pi;

Since we are reputable researchers we will, of course, modify both the CPU and GPU versions to work in single precision.  Timings are below

  • Desktop at work (single thread, single precision): 3.49 seconds
  • Laptop GPU (single precision, not including transfer): 0.122 seconds

OK, so switching to single precision made the CPU version a bit faster but it’s more than doubled GPU performance.  We can now say that the GPU version is over 28 times faster than the CPU version.  Now we have ourselves a bone-fide ‘GPUs are awesome’ paper.

4. Use the best GPU we can find

So far I have been comparing the CPU against the relatively lowly GPU in my laptop.  Obviously, however, if I were to do this for real then I’d get a top of the range Tesla.  It turns out that I know someone who has a Tesla C2050 and so we ran the single precision benchmark on that.  The result was astonishing…0.0295 seconds for 100 million numbers not including transfer times.  The double precision performance for the same calculation on the C2050 was 0.0524 seonds.

5. Write the abstract for our ‘GPUs are awesome’ paper

We took an Nvidia Tesla C2050 GPU and mounted it in a machine containing an Intel Quad Core CPU running at 3Ghz.  We developed a program that performs element-wise trigonometry on arrays of up to 100 million single precision random numbers using both the CPU and the GPU.  The GPU version of our code ran up to 118 times faster than the CPU version.  GPUs are awesome!

Results from different CPUs and GPUs.  Double precision, multi-threaded

I ran the sine_test benchmark on several different systems for 100 million elements.  The CPU was set to be multi-threaded and double precision was used throughout.

sine_test(10,1e8)

GPUs

  • Tesla C2050, Linux, 2011a – 0.7487 seconds including transfers,  0.0524 seconds excluding transfers.
  • GT 555M – 144 CUDA Cores, 3Gb RAM, Windows 7, 2011a (My laptop’s GPU) -1.0205 seconds including transfers, 0.3016 seconds excluding transfers

CPUs

  • Intel Core i7-880 @3.07Ghz, Linux, 2011a – 0.659 seconds
  • Intel Core i7-2630QM, Windows 7, 2011a (My laptop’s CPU) – 0.801 seconds
  • Intel Core 2 Quad Q9650 @ 3.00GHz, Linux – 0.958 seconds

Conclusions

  • MATLAB’s new GPU functions are very easy to use!  No need to learn low-level CUDA programming.
  • It’s very easy to massage CPU vs GPU numbers to look impressive.  Read those ‘GPUs are awesome’ papers with care!
  • In real life you have to consider data transfer times between GPU and CPU since these can dominate overall wall clock time with simple calculations such as those considered here.  The more work you can do on the GPU, the better.
  • My laptop’s GPU is nowhere near as good as I would have liked it to be.  Almost 6 times slower than a Tesla C2050 (excluding data transfer) for elementwise double precision calculations.  Data transfer times seem to about the same though.

Next time

In the next article in the series I’ll look at an element-wise calculation that really is worth doing on the GPU – even using the wimpy GPU in my laptop – and introduce the MATLAB function arrayfun.

Footnote

1 – MATLAB 2011a can’t create random numbers directly on the GPU. I have no doubt that we’ll be able to do this in future versions of MATLAB which will change the nature of this particular calculation somewhat.  Then it will make sense to include the random number generation in the overall benchmark; transfer times to the GPU will be non-existant. In general, however, we’ll still come across plenty of situations where we’ll have a huge array in main memory that needs to be transferred to the GPU for further processing so what we learn here will not be wasted.

Hardware / Software used for the majority of this article

  • Laptop model: Dell XPS L702X
  • CPU: Intel Core i7-2630QM @2Ghz software overclockable to 2.9Ghz. 4 physical cores but total 8 virtual cores due to Hyperthreading.
  • GPU: GeForce GT 555M with 144 CUDA Cores.  Graphics clock: 590Mhz.  Processor Clock:1180 Mhz. 3072 Mb DDR3 Memeory
  • RAM: 8 Gb
  • OS: Windows 7 Home Premium 64 bit.  I’m not using Linux because of the lack of official support for Optimus.
  • MATLAB: 2011a with the parallel computing toolbox

Other GPU articles at Walking Randomly

Thanks to various people at The Mathworks for some useful discussions, advice and tutorials while creating this series of articles.

25 comments

MATLAB GPU / CUDA experiences and tutorials on my laptop – Introduction

July 27th, 2011

These days it seems that you can’t talk about scientific computing for more than 5 minutes without somone bringing up the topic of Graphics Processing Units (GPUs).  Originally designed to make computer games look pretty, GPUs are massively parallel processors that promise to  revolutionise the way we compute.

A brief glance at the specification of a typical laptop suggests why GPUs are the new hotness in numerical computing.  Take my new one for instance, a Dell XPS L702X, which comes with a Quad-Core Intel i7 Sandybridge processor running at up to 2.9Ghz and an NVidia GT 555M with a whopping 144 CUDA cores.  If you went back in time a few years and told a younger version of me that I’d soon own a 148 core laptop then young Mike would be stunned.  He’d also be wondering ‘What’s the catch?’

Of course the main catch is that all processor cores are not created equally.  Those 144 cores in my GPU are, individually, rather wimpy when compared to the ones in the Intel CPU.  It’s the sheer quantity of them that makes the difference.  The question at the forefront of my mind when I received my shiny new laptop was ‘Just how much of a difference?’

Now I’ve seen lots of articles that compare CPUs with GPUs and the GPUs always win…..by a lot!  Dig down into the meat of these articles,  however, and it turns out that things are not as simple as they seem.  Roughly speaking, the abstract of some them could be summed up as ‘We took  a serial algorithm written by a chimpanzee for an old, outdated CPU and spent 6 months parallelising and fine tuning it for a top of the line  GPU.  Our GPU version is up to 150 times faster!‘

Well it would be wouldn’t it?!  In other news, Lewis Hamilton can drive his F1 supercar around Silverstone faster than my dad can in his clapped out 12 year old van!  These articles are so prevalent that csgillespie.wordpress.com recently published an excellent article that summarised everything you should consider when evaluating them.  What you do is take the claimed speed-up, apply a set of common sense questions and thus determine a realistic speedup.  That factor of 150 can end up more like a factor of 8 once you think about it the right way.

That’s not to say that GPUs aren’t powerful or useful…it’s just that maybe they’ve been hyped up a bit too much!

So anyway, back to my laptop.  It doesn’t have a top of the range GPU custom built for scientific computing, instead it has what Notebookcheck.net refers to as a fast middle class graphics card for laptops.  It’s got all of the required bits though….144 cores and CUDA compute level 2.1 so surely it can whip the built in CPU even if it’s just by a little bit?

I decided to find out with a few randomly chosen tests.  I wasn’t aiming for the kind of rigor that would lead to a peer reviewed journal but I did want to follow some basic rules at least

  • I will only choose algorithms that have been optimised and parallelised for both the CPU and the GPU.
  • I will release the source code of the tests so that they can be critised and repeated by others.
  • I’ll do the whole thing in MATLAB using the new GPU functionality in the parallel computing toolbox.  So, to repeat my calculations all you need to do is copy and paste some code.  Using MATLAB also ensures that I’m using good quality code for both CPU and GPU.

The articles

This is the introduction to a set of articles about GPU computing on MATLAB using the parallel computing toolbox.  Links to the rest of them are below and more will be added in the future.

External links of interest to MATLABers with an interest in GPUs

9 comments

Making Mathematica faster with Compile

June 18th, 2011

Over at Sol Lederman’s fantastic new blog, Playing with Mathematica, he shared some code that produced the following figure.

Sol's image

Here’s Sol’s code with an AbsoluteTiming command thrown in.

f[x_, y_] := Module[{},
  If[
   Sin[Min[x*Sin[y], y*Sin[x]]] >
    Cos[Max[x*Cos[y],
       y*Cos[x]]] + (((2 (x - y)^2 + (x + y - 6)^2)/40)^3)/
      6400000 + (12 - x - y)/30, 1, 0]
  ]

 AbsoluteTiming[
\[Delta] = 0.02;
range = 11;
xyPoints = Table[{x, y}, {y, 0, range, \[Delta]}, {x, 0, range, \[Delta]}];
image = Map[f @@ # &, xyPoints, {2}];
]
Rotate[ArrayPlot[image, ColorRules -> {0 -> White, 1 -> Black}], 135 Degree]

This took 8.02 seconds on the laptop I am currently working on (Windows 7 AMD Phenom II N620 Dual core at 2.8Ghz). Note that I am only measuring how long the calculation itself took and am ignoring the time taken to render the image and define the function.

Compiled functions make Mathematica code go faster

Mathematica has a Compile function which does exactly what you’d expect…it produces a compiled version of the function you give it (if it can!). Sol’s function gave it no problems at all.

f = Compile[{{x, _Real}, {y, _Real}}, If[
    Sin[Min[x*Sin[y], y*Sin[x]]] >
     Cos[Max[x*Cos[y],
        y*Cos[x]]] + (((2 (x - y)^2 + (x + y - 6)^2)/40)^3)/
       6400000 + (12 - x - y)/30, 1, 0]
   ];

AbsoluteTiming[
 \[Delta] = 0.02;
 range = 11;
 xyPoints =
  Table[{x, y}, {y, 0, range, \[Delta]}, {x, 0, range, \[Delta]}];
 image = Map[f @@ # &, xyPoints, {2}];
 ]
Rotate[ArrayPlot[image, ColorRules -> {0 -> White, 1 -> Black}],
 135 Degree]

This simple change takes computation time down from 8.02 seconds to 1.23 seconds which is a 6.5 times speed up for hardly any extra coding work. Not too shabby!

Switch to C code to get it even faster

I’m not done yet though! By default the Compile command produces code for the so-called Mathematica Virtual Machine but recent versions of Mathematica allow us to go even further.

Install Visual Studio Express 2010 (and the Windows 7.1 SDK if you are running 64bit Windows) and you can ask Mathematica to convert the function to low level C code, compile it and produce a function object linked to the resulting compiled code. Sounds complicated but is a snap to actually do. Just add

CompilationTarget -> "C"

to the Compile command.

f = Compile[{{x, _Real}, {y, _Real}},
   If[Sin[Min[x*Sin[y], y*Sin[x]]] >
     Cos[Max[x*Cos[y],
        y*Cos[x]]] + (((2 (x - y)^2 + (x + y - 6)^2)/40)^3)/
       6400000 + (12 - x - y)/30, 1, 0]
   , CompilationTarget -> "C"
   ];

AbsoluteTiming[\[Delta] = 0.02;
 range = 11;
 xyPoints =
  Table[{x, y}, {y, 0, range, \[Delta]}, {x, 0, range, \[Delta]}];
 image = Map[f @@ # &, xyPoints, {2}];]
Rotate[ArrayPlot[image, ColorRules -> {0 -> White, 1 -> Black}],
 135 Degree]

On my machine this takes calculation time down to 0.89 seconds which is 9 times faster than the original.

Making the compiled function listable

The current compiled function takes just one x,y pair and returns a result.

In[8]:= f[1, 2]

Out[8]= 1

It can’t directly accept a list of x values and a list of y values. For example for the two points (1,2) and (10,20) I’d like to be able to do f[{1, 10}, {2, 20}] and get the results {1,1}. However what I end up with is an error

f[{1, 10}, {2, 20}]

CompiledFunction::cfsa: Argument {1,10} at position 1 should be a machine-size real number. >>

To fix this I need to make my compiled function listable which is as easy as adding

RuntimeAttributes -> {Listable}

to the function definition.

f = Compile[{{x, _Real}, {y, _Real}},
   If[Sin[Min[x*Sin[y], y*Sin[x]]] >
     Cos[Max[x*Cos[y],
        y*Cos[x]]] + (((2 (x - y)^2 + (x + y - 6)^2)/40)^3)/
       6400000 + (12 - x - y)/30, 1, 0]
   , CompilationTarget -> "C", RuntimeAttributes -> {Listable}
   ];

So now I can pass the entire array to this compiled function at once. No need for Map.

AbsoluteTiming[
 \[Delta] = 0.02;
 range = 11;
 xpoints = Table[x, {x, 0, range, \[Delta]}, {y, 0, range, \[Delta]}];
 ypoints = Table[y, {x, 0, range, \[Delta]}, {y, 0, range, \[Delta]}];
 image = f[xpoints, ypoints];
 ]
Rotate[ArrayPlot[image, ColorRules -> {0 -> White, 1 -> Black}],
 135 Degree]

On my machine this gets calculation time down to 0.28 seconds, a whopping 28.5 times faster than the original. Rendering time is becoming much more of an issue than calculation time in fact!

Parallel anyone?

Simply by adding

Parallelization -> True

to the Compile command I can parallelise the code using threads. Since I have a dual core machine, this might be a good thing to do. Let’s take a look

f = Compile[{{x, _Real}, {y, _Real}},
   If[
    Sin[Min[x*Sin[y], y*Sin[x]]] >
     Cos[Max[x*Cos[y],
        y*Cos[x]]] + (((2 (x - y)^2 + (x + y - 6)^2)/40)^3)/
       6400000 + (12 - x - y)/30, 1, 0]
   , RuntimeAttributes -> {Listable}, CompilationTarget -> "C",
   Parallelization -> True];

AbsoluteTiming[
 \[Delta] = 0.02;
 range = 11;
 xpoints = Table[x, {x, 0, range, \[Delta]}, {y, 0, range, \[Delta]}];
 ypoints = Table[y, {x, 0, range, \[Delta]}, {y, 0, range, \[Delta]}];
 image = f[xpoints, ypoints];
 ]
Rotate[ArrayPlot[image, ColorRules -> {0 -> White, 1 -> Black}],
 135 Degree]

The first time I ran this it was SLOWER than the non-threaded version coming in at 0.33 seconds. Subsequent runs varied and occasionally got as low as 0.244 seconds which is only a few hundredths of a second faster than the original.

If I make the problem bigger, however, by decreasing the size of Delta then we start to see the benefit of parallelisation.

AbsoluteTiming[
 \[Delta] = 0.01;
 range = 11;
 xpoints = Table[x, {x, 0, range, \[Delta]}, {y, 0, range, \[Delta]}];
 ypoints = Table[y, {x, 0, range, \[Delta]}, {y, 0, range, \[Delta]}];
 image = f[xpoints, ypoints];
 ]
Rotate[ArrayPlot[image, ColorRules -> {0 -> White, 1 -> Black}],
 135 Degree]

The above calculation (sans rendering) took 0.988 seconds using a parallelised version of f and 1.24 seconds using a serial version. Rendering took significantly longer! As a comparison lets put a Delta of 0.01 in the original code:

f[x_, y_] := Module[{},
  If[
   Sin[Min[x*Sin[y], y*Sin[x]]] >
    Cos[Max[x*Cos[y],
       y*Cos[x]]] + (((2 (x - y)^2 + (x + y - 6)^2)/40)^3)/
      6400000 + (12 - x - y)/30, 1, 0]
  ]

 AbsoluteTiming[
\[Delta] = 0.01;
range = 11;
xyPoints = Table[{x, y}, {y, 0, range, \[Delta]}, {x, 0, range, \[Delta]}];
image = Map[f @@ # &, xyPoints, {2}];
]
Rotate[ArrayPlot[image, ColorRules -> {0 -> White, 1 -> Black}], 135 Degree]

The calculation time (again, ignoring rendering time) took 32.56 seconds and so our C-compiled, parallel version is almost 33 times faster!

Summary

  • The Compile function can make your code run significantly faster by compiling it for the Mathematica Virtual Machine (MVM).  Note that not every function is suitable for compilation.
  • If you have a C-compiler installed on your machine then you can switch from the MVM to compiled C-code using a single option statement.  The resulting code is even faster
  • Making your functions listable can increase performance.
  • Parallelising your compiled function is easy and can lead to even more speed but only if your problem is of a suitable size.
  • Sol Lederman has a very cool Mathematica blog – check it out!  The code that inspired this blog post originated there.
4 comments

GPU support in Mathematica, Maple, MATLAB and Mathcad Prime

May 6th, 2011

Updated January 4th 2011

It is becoming increasingly common for programmers to make use of GPUs (Graphical Processing Units) to speed up their programs substantially.  There are three major low-level programming libraries that allow you to do this in languages such as C; namely CUDA, OpenCL and Microsoft DirectCompute.  Of these three, CUDA is the most developed but it only works on Nvidia graphics cards.

I am often asked if the major commercial math packages support GPU computing and I find myself writing the same summary email over and over again.  So, here is a very brief breakdown of what is currently on offer.  I plan to expand the information contained in this page over time so if you have any information about GPU computing in these packages then let me know.

MATLAB

Core MATLAB contains no support for GPU computing but several organizations (including The Mathworks themselves) have produced add-on toolboxes that add such support:

  • Jacket – This is a product from a company called AccelerEyes and is possibly the most advanced and well developed GPU solution for MATLAB currently available.  As of version 2.0 it supports both OpenCL and CUDA frameworks.
  • The Mathworks’ Parallel Computing Toolbox (PCT) – If you want to do your MATLAB GPU computing the officially supported way then this is the product you need.  As a bonus, it also allows you to make better use of the multicore processor that almost certainly resides in your machine.  Like many of the offerings on this page, only the CUDA framework is supported so you are out of luck if you don’t have an NVidia graphics card.  Even if you do have an NVidia graphics card then you still might be out of luck since the PCT only supports cards that have compute level 1.3 or above (i.e. double precision only).
  • CULA is a set of GPU-accelerated linear algebra libraries utilizing the NVIDIA CUDA parallel computing architecture and it has a MATLAB interface.
  • GPUmat – This product is completely free but is less developed than the commercial offerings above.  Again. it is CUDA only
  • OpenCL toolbox – The only OpenCL solution for MATLAB I could find.  It is free but development seems to have stalled.

Mathematica

Mathematica 8 has support for both CUDA and OpenCL built in so no need for any add-ons.  Furthermore, it supports both single and double precision GPUs so you can experiment with GPU computing on older, cheaper cards.

Maple

Maple has had some CUDA-only GPU support since version 14.  On the face of it, the CUDA package only appears to contain one accelerated function–Matrix-Matrix multiplication– but when you load this function it accelerates many functions that use matrix-matrix multiply internally.  I’ve never found a definitive list of such functions though.

Mathcad

Mathcad 15 and Mathcad Prime have no support for GPU enhanced computing.

4 comments