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VexCL is a C++ vector expression template library for OpenCL/CUDA
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VexCL is vector expression template library for OpenCL. It has been created for ease of OpenCL developement with C++. VexCL strives to reduce amount of boilerplate code needed to develop OpenCL applications. The library provides convenient and intuitive notation for vector arithmetic, reduction, and sparse matrix-vector multiplication. Multi-device and even multi-platform computations are supported. See Doxygen-generated documentation at


Consider classical hello world problem for OpenCL: addition of two vectors. This is pure OpenCL implementation. Note that I used official C++ bindings here; C variant would be much more verbose. And this is the same problem solved with VexCL. I rest my case :).

Selection of compute devices

You can select any number of available compute devices, which satisfy provided filters. Filter is a functor returning bool and acting on a cl::Device parameter. Several standard filters are provided, such as device type or name filter, double precision support etc. Filters can be combined with logical operators. In the example below all devices with names matching "Radeon" and supporting double precision are selected:

#include <vexcl/vexcl.hpp>
using namespace vex;
int main() {
    vex::Context ctx(Filter::Name("Radeon") && Filter::DoublePrecision);
    std::cout << ctx << std::endl;

vex::Context object holds list of initialized OpenCL contexts and command queues for each filtered device. If you just need list of available devices without creating contexts and queues on them, then look for device_list() function in documenation.

If you wish to obtain exclusive access to your devices (across all processes that use VexCL library), just wrap your device filter in Filter::Exclusive function call:

vex::Context ctx( Filter::Exclusive( Filter::Platform("NVIDIA") && Filter::DoublePrecision ) );

Memory allocation and vector arithmetic

Once you initialized VexCL context, you can allocate OpenCL buffers on the associated devices. vex::vector constructor accepts std::vector of cl::CommandQueue. The contents of the created vector will be partitioned between each queue (presumably, each of the provided queues is linked with separate device). Size of each partition will be proportional to relative device bandwidth. Device bandwidth is measured first time it is requested by launch of small test kernel.

Multi-platform computation is supported (that is, you can spread your vectors across devices by different vendors), but should be used with caution: all computations will be performed with the speed of the slowest device selected.

In the example below host vector is allocated and initialized, then copied to all GPU devices found in the system. A couple of empty device vectors are allocated as well:

const size_t n = 1 << 20;
std::vector<double> x(n);
std::generate(x.begin(), x.end(), [](){ return (double)rand() / RAND_MAX; });

vex::Context ctx(Filter::Type(CL_DEVICE_TYPE_GPU));

vex::vector<double> X(ctx.queue(), x);
vex::vector<double> Y(ctx.queue(), n);
vex::vector<double> Z(ctx.queue(), n);

You can now use simple vector arithmetic with device vectors. For every expression you use, appropriate kernel is compiled (first time it is encountered in your program) and called automagically. If you want to see sources of the generated kernels on the standard output, define VEXCL_SHOW_KERNELS macro before including VexCL headers.

Vectors are processed in parallel across all devices they were allocated on:

Y = 42;
Z = sqrt(2 * X) + cos(Y);

You can copy the result back to host or you can use vector::operator[] to read (or write) vector elements directly. Though latter technique is very ineffective and should be used for debugging purposes only.

copy(Z, x);
assert(x[42] == Z[42]);

Another frequently performed operation is reduction of a vector expression to single value, such as summation. This can be done with Reductor class:

Reductor<double,SUM> sum(ctx.queue());
Reductor<double,MAX> max(ctx.queue());

std::cout << max(fabs(X) - 0.5) << std::endl;
std::cout << sum(sqrt(2 * X) + cos(Y)) << std::endl;

Stencil convolution

Stencil convolution operation comes in handy in many situations. For example, it allows us to apply a moving average filter to a device vector. All you need is to construct a vex::stencil object:

// Moving average with 5-points window.
std::vector<double> sdata(5, 0.2);
stencil(ctx.queue(), sdata, sdata.size() / 2);

vex::vector<double> x(ctx.queue(), 1024 * 1024);
vex::vector<double> y(ctx.queue(), 1024 * 1024);

x = 1;
y = x * s; // convolve x with s

Sparse matrix-vector multiplication

One of the most common operations in linear algebra is matrix-vector multiplication. Class SpMat holds representation of a sparse matrix, spanning several devices. In the example below it is used for solution of a system of linear equations with conjugate gradients method:

typedef double real;
// Solve system of linear equations A u = f with conjugate gradients method.
// Input matrix is represented in CSR format (parameters row, col, and val).
void cg_gpu(
        const std::vector<size_t> &row,   // Indices to col and val vectors.
        const std::vector<size_t> &col,   // Column numbers of non-zero elements.
        const std::vector<real>   &val,   // Values of non-zero elements.
        const std::vector<real>   &rhs,   // Right-hand side.
        std::vector<real> &x              // In: initial approximation; out: result.
    // Init OpenCL.
    vex::Context ctx(Filter::Type(CL_DEVICE_TYPE_GPU));

    // Move data to compute devices.
    size_t n = x.size();
    vex::SpMat<real>  A(ctx.queue(), n, n,,,;
    vex::vector<real> f(ctx.queue(), rhs);
    vex::vector<real> u(ctx.queue(), x);
    vex::vector<real> r(ctx.queue(), n);
    vex::vector<real> p(ctx.queue(), n);
    vex::vector<real> q(ctx.queue(), n);

    Reductor<real,MAX> max(ctx.queue());
    Reductor<real,SUM> sum(ctx.queue());

    // Solve equation Au = f with conjugate gradients method.
    real rho1, rho2;
    r = f - A * u;

    for(uint iter = 0; max(fabs(r)) > 1e-8 && iter < n; iter++) {
        rho1 = sum(r * r);

        if (iter == 0) {
            p = r;
        } else {
            real beta = rho1 / rho2;
            p = r + beta * p;

        q = A * p;

        real alpha = rho1 / sum(p * q);

        u += alpha * p;
        r -= alpha * q;

        rho2 = rho1;

    // Get result to host.
    copy(u, x);

User-defined functions

Simple arithmetic expressions are sometimes not enough. Imagine that you need to count how many elements in vector x are greater that their counterparts in vector y. This may be achieved by introduction of custom function. In order to build such a function, you need to supply its body, its return type and types of its arguments. After that, you can apply the function to any valid vector expressions:

// Function body has to be defined at global scope, and it has to be of `extern
// const char[]` type. This allows us to use it as a template parameter.
extern const char greater_body[] = "return prm1 > prm2 ? 1 : 0;";
UserFunction<greater_body, size_t(float, float)> greater;

size_t count_if_greater(
    const Reductor<size_t, SUM> &sum,
    const vex::vector<float> &x,
    const vex::vector<float> &y
    return sum(greater(x, y));

You could also write sum(greater(x + y, 5 * y)), or use any other expressions as parameters to the greater() call. Note that in the function body parameters are always named as prm1, prm2, etc.

Multi-component vectors

Class template vex::multivector allows to store several equally sized device vectors and perform computations on all components synchronously. Operations are delegated to the underlying vectors. Expressions may include std::array<T,N> values, where N is equal to the number of multivector components. Each component gets corresponding element of std::array<> when expression is applied.

const size_t n = 1 << 20;
std::vector<double> host(n * 3);
std::generate(host.begin(), host.end(), rand);

vex::multivector<double,3> x(ctx.queue(), host);
vex::multivector<double,3> y(ctx.queue(), n);

std::array<int, 3> c = {4, 5, 6};

y = 2 * cos(x) - c;

std::array<double,3> v = y[42];
assert(fabs(v[1] - (2 * cos(host[n + 42]) - c[1])) < 1e-8);

Components of a multivector may be accessed with operator():

vex::vector<double> z = y(1);

Sometimes operations with multicomponent vector cannot be expressed with simple arithmetic operations. Imagine that you need to solve the following system of ordinary differential equations:

dx/dt = x + y;
dy/dx = x - y;

If the system state is represented as vex::multivector<double,2>, then the system function for this ODE could be implemented as

// vex::multivector<double,2> dxdt, x;
dxdt(0) = x(0) + x(1);
dxdt(1) = x(0) - x(1);

This results in two kernel launches. Instead, you can use the following form:

dxdt = std::make_tuple(x(0) + x(1), x(0) - x(1));

This expression would generate and launch single combined kernel, which would be more effective. Multi-expressions like these may also be used with ordinary vex::vectors with help of vex::tie() function:

// vex::vector<double> dx, dy, x, y;
vex::tie(dx,dy) = std::make_tuple(x + y, x - y);

Converting existing algorithms to kernels

VexCL kernel generator allows to transparently convert existing CPU algorithm to an OpenCL kernel. In order to do this you need to record sequence of arithmetic expressions made by an algorithm and convert the recorded sequence to a kernel. The recording part is done with help of vex::generator::symbolic<T> class. The class supports arithmetic expression templates and simply outputs to provided stream any expressions it is being subjected to.

To illustrate this, imagine that you have generic algorithm for a 4th order Runge-Kutta ODE stepper:

template <class state_type, class SysFunction>
void runge_kutta_4(SysFunction sys, state_type &x, double dt) {
    state_type xtmp, k1, k2, k3, k4;

    sys(x, k1, dt);

    xtmp = x + 0.5 * k1;
    sys(xtmp, k2, dt);

    xtmp = x + 0.5 * k2;
    sys(xtmp, k3, dt);

    xtmp = x + k3;
    sys(xtmp, k4, dt);

    x += (k1 + 2 * k2 + 2 * k3 + k4) / 6;

To model equation dx/dt = sin(x) we also provide the following system function:

template <class state_type>
void sys_func(const state_type &x, state_type &dx, double dt) {
    dx = dt * sin(x);

Now, to make a hundred of RK4 iterations for a double value on CPU, all that we need to do is

double x  = 1;
double dt = 0.01;
for(int i = 0; i < 100; i++)
    runge_kutta_4(sys_func<double>, x, dt);

Let us now generate the kernel for single RK4 step and apply the kernel to a vex::vector<double> (by doing this we essentially simpultaneously solve big number of same ODEs with different initial conditions).

// Set recorder for expression sequence.
std::ostringstream body;

// Create symbolic variable.
typedef vex::generator::symbolic<double> sym_state;
sym_state sym_x(sym_state::VectorParameter);

// Record expression sequience.
double dt = 0.01;
runge_kutta_4(sys_func<sym_state>, sym_x, dt);

// Build kernel.
auto kernel = vex::generator::build_kernel(ctx.queue(),
    "rk4_stepper", body.str(), sym_x);

// Create and initialize vector of states.
std::vector<double> xinit(n);
std::generate(xinit.begin(), xinit.end(), [](){
    return (double)rand() / RAND_MAX;
vex::vector<double> x(ctx.queue(), n);
vex::copy(xinit, x);

// Make 100 rk4 steps.
for(int i = 0; i < 100; i++) kernel(x);

This is much more effective than (for this to work correctly we would need to slightly change sys_func):

for(int i = 0; i < 100; i++)
    runge_kutta_4(sys_func<vex::vector<double>>, x, dt);

The generated kernel is more effective because temporary values used in sys_func are now represented not as full-blown vex::vectors, but as fast register variables inside the kernel body. We have seen upto tenfold performance improvement with this technique.

Using custom kernels

Custom kernels are of course possible as well. vector::operator(uint) returns cl::Buffer object for a specified device:

vex::Context ctx(Filter::Vendor("NVIDIA"));

const size_t n = 1 << 20;
vex::vector<float> x(ctx.queue(), n);

auto program = build_sources(context[0], std::string(
    "kernel void dummy(ulong size, global float *x)\n"
    "    size_t i = get_global_id(0);\n"
    "    if (i < size) x[i] = 4.2;\n"

for(uint d = 0; d < ctx.size(); d++) {
    auto dummy = cl::Kernel(program, "dummy").bind(ctx.queue()[d], alignup(n, 256), 256);
    dummy((cl_ulong)x.part_size(d), x(d));

Reductor<float,SUM> sum(ctx.queue());
std::cout << sum(x) << std::endl;


In the images below, scalability of the library with respect to number of compute devices is shown. Effective performance (GFLOPS) and bandwidth (GB/sec) were measured by launching big number of test kernels on one, two, or three Nvidia Tesla C2070 cards. Effect of adding fourth, slower, device (Intel Core i7) were tested as well. The results shown are averaged over 20 runs.

The details of the experiments may be found in benchmark.cpp. Basically, performance of the following code was measured:

// Vector arithmetic
a += b + c * d;

// Reduction
double s = sum(a * b);

// Stencil convolution
y = x * s;

// SpMV
y += A * x;


As you can see, performance and bandwidth for stencil convolution operation are much higher than for other primitives. This is due to the fact that much faster local (shared) memory is used in this algorithm, and formulas for effective performance and bandwidth do not take this into account.

Another thing worth noting is overall degradation of performance after Intel CPU is added to VexCL context. The only primitive gaining speed from this addition is vector arithmetic. This is probably because performance of vector arithmetic was used as a basis for problem partitioning.

Supported compilers

VexCL makes heavy use of C++11 features, so your compiler has to be modern enough. The compilers that have been tested and supported:

  • GCC v4.6 and above.
  • Clang v3.1 (and probably some earlier versions).
  • Microsoft Visual C++ 2010 manages to compile the project with some features disabled: since it does not support variadic templates, only one-argument builtin functions are enabled; user functions are not available at all.

This work is a joint effort of Supercomputer Center of Russian Academy of Sciences (Kazan branch) and Kazan Federal University. It is partially supported by RFBR grant No 12-07-0007.

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