C++ vector expression template library for OpenCL/CUDA
VexCL is a vector expression template library for OpenCL/CUDA. It has been created for ease of GPGPU development with C++. VexCL strives to reduce amount of boilerplate code needed to develop GPGPU 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 talks:
Other talks may be found at speakerdeck.com.
VexCL provides two backends: OpenCL and CUDA. In order to choose either of those, user has to define
VEXCL_BACKEND_CUDA macros. In case neither of those are defined, OpenCL backend is chosen by default. One also has to link to either libOpenCL.so (OpenCL.dll) or libcuda.so (cuda.dll).
For the CUDA backend to work, CUDA Toolkit has to be installed, NVIDIA CUDA compiler driver
nvcc has to be in executable PATH and usable at runtime.
VexCL transparently works with multiple compute devices that are present in the system. A VexCL context is initialized with a device filter, which is just a functor that takes a reference to
vex::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 arithmetic are selected:
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.
vex::vector<T> class constructor accepts a const reference to
vex::Context instance may be conveniently converted to this type, but it is also possible to initialize the command queues elsewhere (e.g. with the OpenCL backend
vex::command_queue is typedefed to
cl::CommandQueue), 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. The 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 minimizes 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:
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:
vex::copy() allows one to copy data between host and device memory spaces. There are two forms of the function – a simple one and an STL-like one:
The STL-like variant can copy sub-ranges of the vectors, or copy data from/to raw host pointers.
Vectors also overload the array subscript operator,
operator, so that users may directly read or write individual vector elements. 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 block.
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. The method
vector::map(unsigned d) maps the d-th partition of the vector and returns the mapped array:
VexCL allows the use of convenient and intuitive notation for vector operations. In order to be used in the same expression, all vectors have to be compatible:
If these 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 command queues are used, then the queues of the vector that is being assigned to will be employed. Each vector expression results in the launch of a single compute kernel. The kernel is automatically generated and launched the first time the expression is encountered in the program. If the
VEXCL_SHOW_KERNELS macro is defined, then the sources of all generated kernels will be dumped to the standard output. For example, the expression:
will lead to the launch of the following compute kernel:
Here and in the rest of examples
Z are compatible instances of
vex::vector<double>; it is also assumed that OpenCL backend is selected.
VexCL is able to cache the compiled kernels offline. The compiled binaries are stored in
$HOME/.vexcl on Linux and MacOSX, and in
APPDATA%\vexcl on Windows systems. In order to enable this functionality for OpenCL backend, the user has to define the
VEXCL_CACHE_KERNELS macro. NVIDIA OpenCL implementation does the caching already, but on AMD or Intel platforms this may lead to dramatic decrease of program initialization time (e.g. VexCL tests take around 20 seconds to complete without kernel caches, and 2 seconds when caches are available). In case of the CUDA backend the offline caching is always enabled.
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.
As you have seen above,
2 in the expression
2 * Y - sin(Z) is passed to the generated compute kernel as an
int parameter (
prm_2). Sometimes this is desired behaviour, because the same kernel will be reused for the expressions
42 * Z - sin(Y) or
a * Y - sin(Y) (where
a is an integer variable). But this may lead to a slight overhead if an expression involves true constant that will always have same value. The macro
VEX_CONSTANT allows one to define such constants for use in vector expressions. Compare the generated kernel for the following example with the kernel above:
VexCL provides some predefined constants in the
vex::constants namespace that correspond to boost::math::constants (e.g.
vex::element_index(size_t offset = 0) allows one to use the index of each vector element inside vector expressions. The numbering is continuous across the compute devices and starts with an optional
Users may define custom functions for use in vector expressions. One has to define the function signature and the function body. The body may contain any number of lines of valid OpenCL or CUDA code, depending on the selected backend. The most convenient way to define a function is via the
The first macro parameter here defines the function return type, the second parameter is the function name, the third parameter defines function arguments in form of a preprocessor sequence. Each element of the sequence is a tuple of argument type and name. The rest of the macro is the function body (compare this with how functions are defined in C/C++). The resulting
squared_radius function object is stateless; only its type is used for kernel generation. Hence, it is safe to define commonly used functions at the global scope.
Note that any valid vector expression may be passed as a function parameter, including nested function calls:
Another version of the macro takes the function body directly as a string:
In case the function that is being defined calls other custom function inside its body, one can use the version of the
VEX_FUNCTION macro that takes sequence of parent function names as the fourth parameter:
VEX_FUNCTION_S, there is a version called
VEX_FUNCTION_SD) that takes the function body as a string parameter.
Custom functions may be used not only for convenience, but also for performance reasons. The example with
squared_radius could in principle be rewritten as:
The drawback of the latter variant is that
Y will be passed to the kernel and read twice (see next section for an explanation).
Note that prior to release 1.2 of VexCL the
VEX_FUNCTION macro had different interface. That version is considered deprecated but is still available as
The last example of the previous section is ineffective because the compiler cannot tell if any two terminals in an expression tree are actually referring to the same data. But programmers often have this information. VexCL allows one to pass this knowledge to compiler by tagging terminals with unique tags. By doing this, the programmer guarantees that any two terminals with matching tags are referencing same data.
Below is a more effective variant of the above example:
Here, the generated kernel will have one parameter for each of the vectors
Some expressions may have several occurences of the same subexpression. Unfortunately, VexCL is not able to determine these cases without the programmer's help. For example, let's look at the following expression:
log(X) would be computed twice. One could tag vector
X as in:
and hope that the backend compiler is smart enough to reuse result of
log(x) (e.g. NVIDIA's compiler is smart enough to do this). But it is also possible to explicitly ask VexCL to store result of a subexpression in a local variable and reuse it. The
vex::make_temp() function template serves this purpose:
Any valid vector or multivector expression (but not additive expressions, such as sparse matrix-vector products) may be wrapped into a
VexCL provides a 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, the generated values span the complete range; for floating point types, the generated values lie in the interval [0,1].
vex::element_index() here provides the random number generator with a sequence position N.
vex::permutation() allows the use of a permuted vector in a vector expression. The function accepts a vector expression that returns integral values (indices). The following example reverses
X and assigns it to
The drawback of the above approach is that you have to store and access an index vector. Sometimes this is a necessary evil, but in this simple example we can do better. In the following snippet a lightweight expression is used to construct the same permutation:
Note that any valid vector expression may be used as an index, including user-defined functions.
Permutation operations are only supported in single-device contexts.
An instance of the
vex::slicer<NDIM> class allows one 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 the dimensions of the array to be sliced. The following example extracts every other element from interval
[100, 200) of a one-dimensional vector X:
And the example below shows how to work with a two-dimensional matrix:
Slicing is only supported in single-device contexts.
vex::reduce() function allows one to reduce a multidimensional expression along one or more dimensions. The result is again a vector expression. The supported reduction operations are
MAX. The function takes three arguments: the shape of the expression to reduce (with the slowest changing dimension in the front), the expression to reduce, and the dimension(s) to reduce along. The latter are specified as indices into the shape array.
In the following example we find maximum absolute value of each row in a two-dimensional matrix and assign the result to a vector:
Expression reduction is only supported in single-device contexts.
vex::reshape(expr, dst_dims, src_dims) function is a powerful primitive that allows one to conveniently manipulate multidimensional data. It takes three arguments – an arbitrary vector expression
expr to reshape, the dimensions
dst_dims of the final result (with the slowest changing dimension in the front), and the dimensions
src_dims of the expression, which are specified as indices into
dst_dims. The function returns a vector expression that could be assigned to a vector or participate in a larger expression. The dimensions may be conveniently specified with help of
Here is an example of transposing a two-dimensional matrix of size NxM:
If the source expression lacks some of the destination dimensions, then those will be introduced by replicating the available data. For example, to make a two-dimensional matrix from a one-dimensional vector by copying the vector to each row of the matrix, one could do the following:
Here is a more realistic example of a dense matrix-matrix multiplication. Elements of a matrix product
C = A * B are defined as
C[i][j] = sum_k(A[i][k] * B[k][j]). Let's assume that matrix
A has shape
[N][L], and matrix
B is shaped as
[L][M]. Then matrix
C has dimensions
[N][M]. In order to implement the multiplication we extend matrices
B to the shape of
[N][L][M], multiply the resulting expressions, and reduce the product along the middle dimension
This of course would not be as efficient as a carefully crafted custom implementation or a call to a vendor BLAS function. Still, the fact that the result is a vector expression (and hence may be a part of a still larger expression) could be more important sometimes.
Reshaping is only supported in single-device contexts.
Given two tensors (arrays of dimension greater than or equal to one), A and B, and a list of axes pairs (where each pair represents corresponding axes from two tensors), the tensor product operation sums the products of A's and B's elements over the given axes. In VexCL this is implemented as
vex::tensordot() operation (compare with python's numpy.tensordot).
For example, the above matrix-matrix product may be implemented much more efficiently with
tensordot() is only available for single-device contexts._
VexCL provides an implementation of the MBA algorithm based on paper by Lee, Wolberg, and Shin ([S. Lee, G. Wolberg, and S. Y. Shin. Scattered data interpolation with multilevel B-Splines. IEEE Transactions on Visualization and Computer Graphics, 3:228–244, 1997][bsplines]). This is a fast algorithm for scattered N-dimensional data interpolation and approximation. Multilevel B-splines are used to compute a C2-continuously differentiable surface through a set of irregularly spaced points. The algorithm makes use of a coarse-to-fine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function. High-fidelity reconstruction is possible from a selected set of sparse and irregular samples.
The algorithm is first prepared on a CPU. After that, it may be used in vector expressions. Here is an example in 2D:
VexCL provides an implementation of the Fast Fourier Transform (FFT) that accepts arbitrary vector expressions as input, allows one to perform multidimensional transforms (of any number of dimensions), and supports arbitrary sized vectors:
The restriction of the FFT is that it currently only supports contexts with a single compute device.
An instance of
vex::Reductor<T, OP> allows one to reduce an arbitrary vector expression to a single value of type T. Supported reduction operations are
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:
And here is an easy way to compute an approximate value of π with Monte-Carlo method:
One of the most common operations in linear algebra is matrix-vector multiplication. An instance of
vex::SpMat class holds a representation of a sparse matrix. Its constructor accepts a sparse matrix in common CRS format. In the example below a
vex::SpMat is constructed from an Eigen sparse matrix:
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 the matrix representation may span several compute devices. Hence, a matrix-vector product operation may require several kernel launches and inter-device communication.
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 a normal vector expression with the help of
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 the moving average of a vector with a 5-point window:
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 the stencil operator constructor accepts a vector of command queues. The following example implements the nonlinear operator
y(i) = sin(x(i) - x(i - 1)) + sin(x(i+1) - sin(x(i)):
The current window is available inside the body of the operator through the
X array, which is indexed relative to the stencil center.
Stencil convolution operations, similar to the matrix-vector products, are only allowed in additive expressions.
Unfortunately, describing two dimensional stencils (e.g. discretization of the Laplace operator) would not be effective, because the stencil width would be too large. One can solve this problem by using a
raw_pointer(const vector<T>&) with a subscript operator. For the sake of simplicity, the example below implements a 3-point laplace operator for a one-dimensional vector; but this could be easily extended onto a two-dimensional case:
Similar approach could be used in order to implement an N-body problem with a user-defined function:
Note that the use of
raw_pointer() is limited to single-device contexts for obvious reasons.
VexCL provides several standalone parallel primitives that may not be used as part of a vector expression. These are
reduce_by_key. All of these functions take VexCL vectors as both input and output parameters.
Sorting and scan functions take an optional function object used for comparison and summing of elements. The functor should provide the same interface as, e.g.
std::less for sorting or
std::plus for summing; additionally, it should provide a VexCL function for device-side operations.
Here is an example of such an object comparing integer elements in such a way that even elements precede odd ones:
Same functor could be created with help of
VEX_DUAL_FUNCTOR macro, which takes return type, sequence of arguments (similar to
VEX_FUNCTION), and the body of the functor:
The need to provide both host-side and device-side parts of the functor comes from the fact that multidevice vectors are first sorted partially on each of the compute devices they are allocated on and then merged on the host.
Sorting algorithms may also take tuples of keys/values (in fact, any Boost.Fusion sequence will do). One will have to explicitly specify the comparison functor in this case. Both host and device variants of the comparison functor should take
2n arguments, where
n is the number of keys. The first
n arguments correspond to the left set of keys, and the second
n arguments correspond to the right set of keys. Here is an example that sorts values by a tuple of two keys:
The class template
vex::multivector<T,N> allows one 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 the corresponding element of
std::array<> when the expression is applied. Similarly, the 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 the overloaded
Some operations can not be expressed with simple multivector arithmetic. For example, an operation of two dimensional rotation mixes components in the right hand side expressions:
This may in principle be implemented as:
But this would result in two kernel launches. VexCL allows one to assign a tuple of expressions to a multivector, which will lead to the launch of a single fused kernel:
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 one to generate better optimized kernels for the problem at hand. VexCL exploits this possibility with help of its kernel generator mechanism. Moreover, VexCL's CUDA backend uses the same technique to generate and compile CUDA kernels at runtime.
An instance of
vex::symbolic<T> dumps to an output stream any arithmetic operations it is being subjected to. For example, this code snippet:
results in the following output:
The symbolic type allows one 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:
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:
The following code snippet makes one hundred RK4 iterations for a single
double value on a CPU:
Let's 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 a large number of identical ODEs with different initial conditions).
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 a substantial amount of both human and machine time when applicable.
VexCL also provides a user-defined function generator which takes a function signature and generic function object, and returns custom VexCL function ready to be used in vector expressions. Let's rewrite the above example using an autogenerated function for a Runge-Kutta stepper. First, we need to implement generic functor:
Now we can generate and apply the custom function:
Note that both
rk4_stepper may be reused for host-side computations.
It is very easy to generate a VexCL function from a Boost.Phoenix lambda expression (since Boost.Phoenix lambdas are themselves generic functors):
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 a
cl::Buffer that holds vector data on the k-th compute device. If the result depends on the neighboring 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 addressed manually.
The following example builds and launches a custom kernel for each device in the context:
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 the ViennaCL, Boost.compute and CLOGS libraries.
VexCL makes heavy use of C++11 features, so your compiler has to be modern enough. The compilers that have been tested and supported:
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.