VexCL is a vector expression template library for OpenCL. It has been created for ease of OpenCL development 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, sparse matrix-vector products, etc. Multi-device and even multi-platform computations are supported. The source code of the library is distributed under very permissive MIT license.

The code is available at https://github.com/ddemidov/vexcl.

Doxygen-generated documentation: http://ddemidov.github.io/vexcl.

Slides from VexCL-related talks:

• Meeting C++ 2012, Dusseldorf
• SIAM CSE 2013, Boston
• FOSDEM 2013, Brussels

The paper Programming CUDA and OpenCL: A Case Study Using Modern C++ Libraries compares both convenience and performance of several GPGPU libraries, including VexCL.

• Context initialization
• Memory allocation
• Copies between host and devices
• Vector expressions
  • Builtin operations
  • Element indices
  • User-defined functions
  • Tagged terminals
  • Random number generation
  • Permutations
  • Slicing
• Reductions
• Sparse matrix-vector products
• Stencil convolutions
• Fast Fourier Transform
• Multivectors
• Converting generic C++ algorithms to OpenCL
  • Kernel generator
  • Function generator
• Custom kernels
• Interoperability with other libraries
• Supported compilers

VexCL can transparently work with multiple compute devices that are present in the system. VexCL context is initialized with a device filter, which is just a functor that takes a reference to cl::Device and returns a bool. Several standard filters are provided, but one can easily add a custom functor. Filters may be combined with logical operators. All compute devices that satisfy the provided filter are added to the created context. In the example below all GPU devices that support double precision arithmetics are selected:

#include <iostream>
#include <stdexcept>
#include <vexcl/vexcl.hpp>

int main() {
    vex::Context ctx( vex::Filter::Type(CL_DEVICE_TYPE_GPU) && vex::Filter::DoublePrecision );

    if (!ctx) throw std::runtime_error("No devices available.");

    // Print out list of selected devices:
    std::cout << ctx << std::endl;
}

One of the most convenient filters is vex::Filter::Env which selects compute devices based on environment variables. It allows to switch compute device without need to recompile the program.

The vex::vector<T> class constructor accepts a const reference to std::vector<cl::CommandQueue>. A vex::Context instance may be conveniently converted to the type, but it is also possible to initialize the command queues elsewhere, thus completely eliminating the need to create a vex::Context. Each command queue in the list should uniquely identify a single compute device.

The contents of the created vector will be partitioned across all devices that were present in the queue list. Size of each partition will be proportional to the device bandwidth, which is measured the first time the device is used. All vectors of the same size are guaranteed to be partitioned consistently, which allows to minimize inter-device communication.

In the example below, three device vectors of the same size are allocated. Vector A is copied from host vector a, and the other vectors are created uninitialized:

const size_t n = 1024 * 1024;
vex::Context ctx( vex::Filter::All );

std::vector<double> a(n, 1.0);

vex::vector<double> A(ctx, a);
vex::vector<double> B(ctx, n);
vex::vector<double> C(ctx, n);

Assuming that the current system has an NVIDIA and an AMD GPUs along with an Intel CPU installed, possible partitioning may look as in the following figure:

Function vex::copy() allows to copy data between host and device memories. There are two forms of the function -- simple one and an STL-like:

std::vector<double> h(n);       // Host vector.
vex::vector<double> d(ctx, n);  // Device vector.

// Simple form:
vex::copy(h, d);    // Copy data from host to device.
vex::copy(d, h);    // Copy data from device to host.

// STL-like form:
vex::copy(h.begin(), h.end(), d.begin()); // Copy data from host to device.
vex::copy(d.begin(), d.end(), h.begin()); // Copy data from device to host.

The STL-like variant allows to copy sub-ranges of the vectors, or copy data from/to raw host pointers.

Vectors also overload array subscript operator, so that users may have direct read or write access to individual vector elements. But this operation is highly ineffective and should be used with caution. Iterators allow for element access as well, so that STL algorithms may in principle be used with device vectors. This would be very slow but may be used as a temporary building blocks.

Another option for host-device data transfer is mapping device memory buffer to a host array. The mapped array then may be transparently read or written. Method vector::map(unsigned d) maps d-th partition of the vector and returns the mapped array:

vex::vector<double> X(ctx, N);
auto mapped_ptr = X.map(0); // Unmapped automatically when goes out of scope
for(size_t i = 0; i < X.part_size(0); ++i)
    mapped_ptr[i] = host_function(i);

VexCL allows to use convenient and intuitive notation for vector operations. In order to be used in the same expression, all vectors have to be compatible:

• Have same size;
• Span same set of compute devices.

If the conditions are satisfied, then vectors may be combined with rich set of available expressions. Vector expressions are processed in parallel across all devices they were allocated on. One should keep in mind that in case several OpenCL command queues are used, then the queues of the vector that is being assigned to will be employed. Each vector expression results in launch of a single OpenCL kernel. The kernel is automatically generated and launched the first time the expression is encountered in the program. If VEXCL_SHOW_KERNELS macro is defined, then the sources of all generated kernels will be dumped to the standard output. For example, the expression:

X = 2 * Y - sin(Z);

will lead to the launch of the following OpenCL kernel:

kernel void minus_multiplies_term_term_sin_term_(
    ulong n,
    global double *res,
    int prm_1,
    global double *prm_2,
    global double *prm_3
)
{
    for(size_t idx = get_global_id(0); idx < n; idx += get_global_size(0)) {
        res[idx] = ( ( prm_1 * prm_2[idx] ) - sin( prm_3[idx] ) );
    }
}

Here and in the rest of examples X, Y, and Z are compatible instances of vex::vector<double>.

VexCL expressions may combine device vectors and scalars with arithmetic, logic, or bitwise operators as well as with builtin OpenCL functions. If some builtin operator or function is unavailable, it should be considered a bug. Please do not hesitate to open an issue in this case.

Z = sqrt(2 * X) + pow(cos(Y), 2.0);

Function vex::element_index(size_t offset = 0) allows to use an index of each vector element inside vector expressions. The numbering is continuous across the compute devices and starts with an optional offset.

// Linear function:
double x0 = 0.0, dx = 1.0 / (X.size() - 1);
X = x0 + dx * vex::element_index();

// Single period of sine function:
Y = sin(2 * M_PI * vex::element_index() / Y.size());

Users may define custom functions to use in vector expressions. One has to define function signature and function body. The body may contain any number of lines of valid OpenCL code. Function parameters are named prm1, prm2, etc. The most convenient way to define a function is VEX_FUNCTION macro:

VEX_FUNCTION(squared_radius, double(double, double), "return prm1 * prm1 + prm2 * prm2;");
Z = sqrt(squared_radius(X, Y));

The resulting squared_radius function object is stateless; only its type is used for kernel generation. Hence, it is safe to put commonly used functions in global scope.

Note that any valid vector expression may be passed as a function parameter:

Z = squared_radius(sin(X + Y), cos(X - Y));

Custom functions may be used not only for convenience, but also for performance reasons. The above example could in principle be rewritten as:

Z = sqrt(X * X + Y * Y);

The drawback of the latter variant is that X and Y will be read twice.

Code snippet from the last paragraph is ineffective because compiler can not tell if any two terminals in an expression tree are actually referring to the same data. But programmers often have this information. VexCL allows to pass this knowledge to compiler by tagging terminals with unique tags. Programmer guarantees that any two terminals with matching tags are referencing same data.

Below is more effective variant of the above example:

using vex::tag;
Z = sqrt(tag<1>(X) * tag<1>(X) + tag<2>(Y) * tag<2>(Y));

Here, the generated kernel will have one parameter per vectors X and Y.

VexCL provides counter-based random number generators from Random123 suite, in which Nth random number is obtained by applying a stateless mixing function to N instead of the conventional approach of using N iterations of a stateful transformation. This technique is easily parallelizable and is well suited for use in GPGPU applications.

For integral types, generated values span the complete range; for floating point types, generated values are in [0,1] interval.

In order to use a random number sequence in a vector expression, user has to declare an instance of either vex::Random or vex::RandomNormal class template as in the following example:

vex::Random<double, vex::random::threefry> rnd;

// X will contain random numbers from [-1, 1]:
X = 2 * rnd(vex::element_index(), std::rand()) - 1;

Note that vex::element_index() here provides the random number generator with a sequence position N.

vex::permutation allows to use permuted vector in a vector expression. The class constructor accepts vex::vector<size_t> of indices. The following example assigns reversed vector X to Y:

vex::vector<size_t> I(ctx, N);
I = N - 1 - vex::element_index();

vex::permutation reverse(I);

Y = reverse(X);

Permutation operation is only supported in single-device contexts.

An instance of vex::slicer<NDIM> class allows to conveniently access sub-blocks of multi-dimensional arrays that are stored in vex::vector in row-major order. The constructor of the class accepts dimensions of an array to be sliced. The following example extracts every other element from interval [100, 200) of one-dimensional vector X:

vex::vector<double> X(ctx, n);
vex::vector<double> Y(ctx, 50);

vex::slicer<1> slice({n});

Y = slice[vex::range(100, 2, 200)](X);

And the example below shows how to work with two-dimensional matrix:

using vex::range;

vex::vector<double> X(ctx, n * n); // n-by-n matrix stored in row-major order.
vex::vector<double> Y(ctx, n);

// vex::extents is a helper object similar to boost::multi_array::extents
vex::slicer<2> slice(vex::extents[n][n]);

Y = slice[42](X);          // Put 42-nd row of X into Y.
Y = slice[range()][42](X); // Put 42-nd column of X into Y.

slice[range()][10](X) = Y; // Put Y into 10-th column of X.

// Assign sub-block [10,20)x[30,40) of X to Z:
vex::vector<double> Z = slice[range(10, 20)][range(30, 40)](X);
assert(Z.size() == 100);

Slicing is only supported in single-device contexts.

An instance of vex::Reductor<T, OP> allows to reduce an arbitrary vector expression to a single value of type T. Supported reduction operations are SUM, MIN, and MAX. Reductor objects receive a list of command queues at construction and should only be applied to vectors residing on the same compute devices.

In the following example an inner product of two vectors is computed:

vex::Reductor<double, vex::SUM> sum(ctx);

double s = sum(x * y);

And here is an easy way to compute an approximate value of π with Monte-Carlo method:

VEX_FUNCTION(squared_radius, double(double, double), "return prm1 * prm1 + prm2 * prm2;");

vex::Reductor<size_t, vex::SUM> sum(ctx);
vex::Random<double, vex::random::threefry> rnd;

X = 2 * rnd(vex::element_index(), std::rand()) - 1;
Y = 2 * rnd(vex::element_index(), std::rand()) - 1;

double pi = 4.0 * sum(squared_radius(X, Y) < 1) / X.size();

One of the most common operations in linear algebra is matrix-vector multiplication. An instance of vex::SpMat class holds representation of a sparse matrix. Its constructor accepts sparse matrix in common CRS format. In the example below a vex::SpMat is constructed from an Eigen sparse matrix:

Eigen::SparseMatrix<double, Eigen::RowMajor, int> E;

vex::SpMat<double, int> A(ctx, E.rows(), E.cols(),
    E.outerIndexPtr(), E.innerIndexPtr(), E.valuesPtr());

The matrix-vector products may be used in vector expressions. The only restriction is that the expressions have to be additive. This is due to the fact that matrix representation may span several compute devices. Hence, a matrix-vector product operation may require several kernel launches and inter-device communication.

// Compute residual value for a system of linear equations:
Z = Y - A * X;

This restriction may be lifted for single-device contexts. In this case VexCL does not need to worry about inter-device communication. Hence, it is possible to inline matrix-vector product into normal vector expression with help of vex::make_inline() function:

residual = sum(Y - vex::make_inline(A * X));
Z = sin(vex::make_inline(A * X));

Stencil convolution is another common operation that may be used, for example, to represent a signal filter, or a (one-dimensional) differential operator. VexCL implements two stencil kinds. The first one is a simple linear stencil that holds linear combination coefficients. The example below computes moving average of a vector with a 5-point window:

vex::stencil<double> S(ctx, /*coefficients:*/{0.2, 0.2, 0.2, 0.2, 0.2}, /*center:*/2);

Y = X * S;

Users may also define custom stencil operators. This may be of use if, for example, the operator is nonlinear. The definition of a stencil operator looks very similar to a definition of a custom function. The only difference is that stencil operator constructor accepts vector of OpenCL command queues. The following example implements non-linear operator y(i) = sin(x(i) - x(i - 1)) + sin(x(i+1) - sin(x(i)):

VEX_STENCIL_OPERATOR(S, /*return type:*/double, /*window width:*/3, /*center:*/1,
    "return sin(X[0] - X[-1]) + sin(X[1] - X[0]);", ctx);

Z = S(Y);

The current window is available inside the body of the operator through the X array that is indexed relatively to the stencil center.

Stencil convolution operations, similar to the matrix-vector products, are only allowed in additive expressions.

VexCL provides implementation of Fast Fourier Transform (FFT) that accepts arbitrary vector expressions as input, allows to perform multidimensional transforms (of any number of dimensions), and supports arbitrary sized vectors:

vex::FFT<double, cl_double2> fft(ctx, n);
vex::FFT<cl_double2, double> ifft(ctx, n, vex::fft::inverse);

vex::vector<double> in(ctx, n), back(ctx, n);
vex::vector<cl_double2> out(ctx, n);

// ...

out  = fft (in);
back = ifft(out);

Z = fft(sin(X) + cos(Y));

FFT is another example of operation that is only available in additive expressions. Another restriction is that FFT currently only supports contexts with a single compute device.

Class template vex::multivector<T,N> allows to store several equally sized device vectors and perform computations on all components synchronously. Each operation is delegated to the underlying vectors, but usually results in the launch of a single fused kernel. Expressions may include values of std::array<T,N> type, where N is equal to the number of multivector components. Each component gets corresponding element of std::array<> when expression is applied. Similarly, array subscript operator or reduction of a multivector returns an std::array<T,N>. In order to access k-th component of a multivector, one can use overloaded operator():

VEX_FUNCTION(between, bool(double, double, double), "return prm1 <= prm2 && prm2 <= prm3;");

vex::Reductor<double, vex::SUM> sum(ctx);
vex::SpMat<double> A(ctx, ... );
std::array<double, 2> v = {6.0, 7.0};

vex::multivector<double, 2> X(ctx, N), Y(ctx, N);

// ...

X = sin(v * Y + 1);             // X(k) = sin(v[k] * Y(k) + 1);
v = sum( between(0, X, Y) );    // v[k] = sum( between( 0, X(k), Y(k) ) );
X = A * Y;                      // X(k) = A * Y(k);

Some operations can not be expressed with simple multivector arithmetics. For example, an operation of two dimensional rotation mixes components in the right hand side expressions:

y0 = x0 * cos(alpha) - x1 * sin(alpha);
y1 = x0 * sin(alpha) + x1 * cos(alpha);

This may in principle be implemented as:

double alpha;
vex::multivector<double, 2> X(ctx, N), Y(ctx, N);

Y(0) = X(0) * cos(alpha) - X(1) * sin(alpha);
Y(1) = X(0) * sin(alpha) + X(1) * cos(alpha);

But this would result in two kernel launches. VexCL allows to assign a tuple of expressions to a multivector, which will lead to the launch of a single fused kernel:

Y = std::tie( X(0) * cos(alpha) - X(1) * sin(alpha),
              X(0) * sin(alpha) + X(1) * cos(alpha) );

CUDA and OpenCL differ in their handling of compute kernels compilation. In NVIDIA's framework the compute kernels are compiled to PTX code together with the host program. In OpenCL the compute kernels are compiled at runtime from high-level C-like sources, adding an overhead which is particularly noticeable for smaller sized problems. This distinction leads to higher initialization cost of OpenCL programs, but at the same time it allows to generate better optimized kernels for the problem at hand. VexCL allows to exploit the possibility with help of its kernel generator mechanism.

An instance of vex::symbolic<T> dumps to output stream any arithmetic operations it is being subjected to. For example, this code snippet:

vex::symbolic<double> x = 6, y = 7;
x = sin(x * y);

results in the following output:

double var1 = 6;
double var2 = 7;
var1 = sin( ( var1 * var2 ) );

The symbolic type allows to record a sequence of arithmetic operations made by a generic C++ algorithm. To illustrate the idea, consider the generic implementation of 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 k1 = dt * sys(x);
    state_type k2 = dt * sys(x + 0.5 * k1);
    state_type k3 = dt * sys(x + 0.5 * k2);
    state_type k4 = dt * sys(x + k3);

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

This function takes a system function sys, state variable x, and advances x by time step dt. For example, to model the equation dx/dt = sin(x), one has to provide the following system function:

template <class state_type>
state_type sys_func(const state_type &x) {
    return sin(x);
}

The following code snippet makes a hundred of RK4 iterations for a single double value on a CPU:

double x = 1, dt = 0.01;

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

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

// Set recorder for expression sequence.
std::ostringstream body;
vex::generator::set_recorder(body);

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

// Record expression sequience for a single RK4 step.
double dt = 0.01;
runge_kutta_4(sys_func<sym_state>, sym_x, dt);

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

// Create initial state.
const size_t n = 1024 * 1024;
vex::vector<double> x(ctx, n);
x = 10.0 * vex::element_index() / n;

// Make 100 RK4 steps.
for(int i = 0; i < 100; i++) kernel(x);

This approach has some obvious restrictions. Namely, the C++ code has to be embarrassingly parallel and is not allowed to contain any branching or data-dependent loops. Nevertheless, the kernel generation facility may save substantial amount of both human and machine time when applicable.

VexCL also provides a user-defined function generator which takes function signature and generic function object, and returns custom OpenCL function ready to be used in vector expressions. Lets rewrite the above example using autogenerated function for a Runge-Kutta stepper. First, we need to implement generic functor:

struct rk4_stepper {
    double dt;

    rk4_stepper(double dt) : dt(dt) {}

    template <class state_type>
    state_type operator()(const state_type &x) const {
        state_type new_x = x;
        runge_kutta_4(sys_func<state_type>, new_x, dt);
        return new_x;
    }
};

Now we can generate and apply the custom function:

double dt = 0.01;
rk4_stepper stepper(dt);

// Generate custom OpenCL function:
auto rk4 = vex::generator::make_function<double(double)>(stepper);

// Create initial state.
const size_t n = 1024 * 1024;
vex::vector<double> x(ctx, n);
x = 10.0 * vex::element_index() / n;

// Use the function to advance initial state:
for(int i = 0; i < 100; i++) x = rk4(x);

Note that both runge_kutta_4() function and rk4_stepper function object may be reused for host-side computations.

It is very easy to generate an OpenCL function from a Boost.Phoenix lambda expression (since Boost.Phoenix lambdas are themselves generic functors):

using namespace boost::phoenix::arg_names;
using vex::generator::make_function;

auto squared_radius = make_function<double(double, double)>(arg1 * arg1 + arg2 * arg2);

Z = squared_radius(X, Y);

As Kozma Prutkov repeatedly said, "One cannot embrace the unembraceable". So in order to be usable, VexCL has to support custom kernels. vex::vector::operator()(uint k) returns cl::Buffer that holds vector data on k-th compute device. If the result depends on the neighbor points, one has to keep in mind that these points are possibly located on a different compute device. In this case the exchange of these halo points has to be arranged manually.

The following example builds and launches a custom kernel for each device in the context:

std::vector<cl::Kernel> kernel(ctx.size());

// Compile and store the kernels for later use.
for(uint d = 0; d < ctx.size(); d++) {
    cl::Program program = vex::build_sources(ctx.context(d),
        "kernel void dummy(ulong size, global float *x)\n"
        "{\n"
        "    size_t i = get_global_id(0);\n"
        "    if (i < size) x[i] = 4.2;\n"
        "}\n"
        );
    kernel[d] = cl::Kernel(program, "dummy");
}

// Apply the kernels to the vector partitions on each device.
for(uint d = 0; d < ctx.size(); d++) {
    cl_ulong n = x.part_size();
    kernel[d].setArg(0, n);
    kernel[d].setArg(1, x(d));
    ctx.queue(d).enqueueNDRangeKernel(kernel[d], cl::NullRange, n, cl::NullRange);
}

Since VexCL is built upon standard Khronos OpenCL C++ bindings, it is easily interoperable with other OpenCL libraries. In particular, VexCL provides some glue code for ViennaCL and for Boost.compute libraries.

ViennaCL (The Vienna Computing Library) is a scientific computing library written in C++. It provides OpenCL, CUDA, and OpenMP compute backends. The programming interface is compatible with Boost.uBLAS and allows for simple, high-level access to the vast computing resources available on parallel architectures such as GPUs. The library's primary focus is on common linear algebra operations (BLAS levels 1, 2 and 3) and the solution of large sparse systems of equations by means of iterative methods with optional preconditioners.

It is possible to use generic ViennaCL's solvers with VexCL types. See examples/viennacl/solvers.cpp for an example.

Boost.compute is a GPU/parallel-computing library for C++ based on OpenCL. The core library is a thin C++ wrapper over the OpenCL C API and provides access to compute devices, contexts, command queues and memory buffers. On top of the core library is a generic, STL-like interface providing common algorithms (e.g. transform(), accumulate(), sort()) along with common containers (e.g. vector<T>, flat_set<T>). It also features a number of extensions including parallel-computing algorithms (e.g. exclusive_scan(), scatter(), reduce()) and a number of fancy iterators (e.g. transform_iterator<>, permutation_iterator<>, zip_iterator<>).

vexcl/external/boost_compute.hpp provides an example of using Boost.compute algorithms with VexCL vectors. Namely, it implements parallel sort and inclusive scan primitives on top of the corresponding Boost.compute algorithms.

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 higher.
• Clang v3.1 and higher.
• Microsoft Visual C++ 2010 and higher.

VexCL uses standard OpenCL bindings for C++ from Khronos group. The cl.hpp file should be included with the OpenCL implementation on your system, but it is also provided with the library.

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 grants No 12-07-0007 and 12-01-00033.