SYCL-BLAS Implementation

SYCL-BLAS implements BLAS - Basic Linear Algebra Subroutines - using SYCL 1.2, the Khronos abstraction layer for OpenCL.

SYCL-BLAS is a current work in progress research project from an ongoing collaboration with the High Performance Computing & Architectures (HPCA) group from the Universitat Jaume I UJI.

SYCL-BLAS is written using modern C++. The current implementation uses C++11 features. See Roadmap for details on the current status and plans for the project.

Table of Contents

• Motivation
• Basic Concepts
  • Views
  • Operations
  • Executors
  • Interface
• API description
  • BLAS 1
  • BLAS 2
  • BLAS 3
• Requirements
• Setup
  • How to compile
  • CMake options
  • Cross-Compile
• Tests and benchmarks
• Contributing to the project

Motivation

The same numerical operations are computed to solve many scientific problems and engineering applications, such as image and signal processing, telecommunication, computational finance, materials science simulations, structural biology, data mining, bio-informatics, fluid dynamics, and many other areas. Thus, it was identified that around the 90% percent of the computational cost is consumed on the 10% of the code, and therefore any improvement in this 10% of code would have a great impact in the performances of the applications. Numerical Linear Algebra is the science area in charge of identifying the most common operations and seeking their best implementation. To do this, the researchers should consider the numerical stability of the selected algorithm, and the platform on which the operation will be solved. The first analysis studies the accuracy of the solution while the second one compares the performances of the different implementations to select the best one.

Nowadays, all the numerical computations are based on a set of standard libraries on which the most common operations are implemented. These libraries are different for dense matrices (BLAS, LAPACK, ScaLAPACK, ...) and for sparse matrices (SparseBLAS, ...). Moreover, there are vendor implementations which are adjusted to the platform features:

• For multicores: ACML (AMD), ATLAS, Intel-MKL, OpenBLAS, ...
• For GPUs: cuBLAS (Nvidia), clBLAS, CLBlast, MAGMA, ...

But, in any case, BLAS is always the lowest level in the hierarchy of numerical libraries, such that a good BLAS implementation improves the performances of all the other libraries. The development of numerical libraries on SYCL is one of the most important objectives, because it will improve the performance of other SYCL applications. Obviously, it makes sense SYCL-BLAS was the first step in this task.

On GPUs, the data communication to/from the device and the grain of the kernels play an important rule on the performances of the developments. On one hand, to reduce the communication cost, the most of the data should be mapped on the device, even the scalars. On the other hand, growing the size of the kernels allows the CPU to complete other tasks while the GPU is computing or to enter an energy-efficient C-state, reducing the energy consumption.

To enlarge the grain of the kernels is a complex task, in which many aspects should be considered as the dependency between kernels, the grid topology, the grid sizes, etc. This complexity justifies that, usually, the fused kernels are manually written. An alternative to simplify this task could be to build a expression tree on which all the single operation which are required to solve a problem appears. This structure could be analysed by the compiler to decide how to merge the different kernel and the best grid topology to execute the fused kernel. The use of expression trees is one of most important features of SYCL-BLAS.

Basic Concepts

SYCL-BLAS uses C++ Expression Tree templates to generate SYCL Kernels via kernel composition. Expression Tree templates are a widely used technique to implement expressions on C++, that facilitate development and composition of operations. In particular, Kernel composition in SYCL has been used in various projects to create efficient domain-specific embedded languages that enable users to easily fuse GPU kernels.

SYCL-BLAS can be used

• either as a header-only framework by including sycl_blas.hpp in an application and passing src as pass to the application include directory.
• or as a library by including sycl_blas.h in an application.

All the relevant files can be found in the include directory. There are four components in SYCL-BLAS, the View, the Operations, the Executors and the Interface itself.

Views

The input data to all the operations in SYCL-BLAS is passed to the library using Views. A View represents data on top of a container, passed by reference. Views do not store data, they only map a visualization of the data on top of a container. This enables the library to implement the different indexing modes of the BLAS API, such as strides. Note than a view can be of a different size than a container.

All views derive from the base view class or the base matrix view class, which represents a view of a container as a vector or as a matrix. The container does not need to be multi-dimensional to store a matrix. The current restriction is that container must obey the RandomAccessIterator properties of the C++11 standard.

Operations

Operations among elements of vectors (or matrices) are expressed in the set of Operation Classes. Operations are templated classes that take templated types as input. Operations form the nodes of the SYCL-BLAS expression tree. Refer to the documentation of each node type for details.

Composing these is how the compile-time Expression tree is created: Given an operation node, the leaves of the node are other Operations. The leaf nodes of an Expression Tree are Views or Scalar types (data). The intermediate nodes of the Expression Tree are operations (e.g, binary operations, unary operations, etc).

Executors

An executor traverses the Expression Tree to evaluate the operations that it defines. Executors use different techniques to evaluate the expression tree. The basic C++ executor performs a for loop on the size of the data and calls the evaluation function on each item.

The SYCL evaluator transform the tree into a device tree (i.e, converting buffer to accessors) and then evaluates the Expression Tree on the device.

Interface

The different headers on the interface directory implement the traditional BLAS interface. Files are organised per BLAS level (1, 2, 3).

When the SYCL-BLAS BLAS interface is called, the Expression Tree for each operation is constructed, and then executed. Some API calls may execute several kernels (e.g, when a reduction is required). The expression trees in the API allow to compile-time fuse operations.

Note that, although this library features a BLAS interface, users are allowed to directly compose their own expression trees to compose multiple operations. The CG example shows an implementation of the Conjugate Gradient that uses various expression tree to demonstrate how to achieve compile-time kernel fusion of multiple BLAS operations.

API description

This section references all the supported operations and their interface.

All operations take as their first argument a reference to the executor, a blas::Executor created with a sycl::queue. The return value is usually an array of SYCL events (except for some operations that can return a scalar or a tuple). The containers for the vectors and matrices (and scalars written by the BLAS operations) are iterator buffers that can be created with make_sycl_iterator_buffer.

We recommend checking the samples to get started with SYCL-BLAS. It is better to be familiar with BLAS: Wikipedia ; Netlib reference.

BLAS 1

The following table sums up the interface that can be found in blas1_interface.h.

For all these operations:

• vx and vy are containers for vectors x and y.
• incx and incy are their increments (number of steps to jump to the next value, 1 for contiguous values).
• N, an integer, is the size of the vectors (less than or equal to the size of the containers).
• alpha is a scalar.
• rs is a container of size 1, containing either a scalar, an integer, or an index-value tuple.
• c and s for _rot are scalars (cosine and sine)

operation	arguments	description
_axpy	ex, N, alpha, vx, incx, vy, incy	Vector multiply-add: y = alpha * x + y
_copy	ex, N, vx, incx, vy, incy	Copies a vector to another: y = x
_dot	ex, N, vx, incx, vy, incy [, rs]	Dot product of two vectors x and y; written in rs if passed, else returned
_asum	ex, N, vx, incx [, rs]	Absolute sum of the vector x; written in rs if passed, else returned
_iamax	ex, N, vx, incx [, rs]	First index and value of the maximum element of x; written in rs if passed, else the index only is returned
_iamin	ex, N, vx, incx [, rs]	First index and value of the minimum element of x; written in rs if passed, else the index only is returned
_swap	ex, N, vx, incx, vy, incy	Interchanges two vectors: y = x and x = y
_scal	ex, N, alpha, vx, incx	Scalar product of a vector: x = alpha * x
_nrm2	ex, N, vx, incx [, rs]	Euclidean norm of the vector x; written in rs if passed, else returned
_rot	ex, N, vx, incx, vy, incy, c, s	Applies a plane rotation to x and y with a cosine c and a sine s

BLAS 2

The following table sums up the interface that can be found in blas2_interface.h.

For all these operations:

• trans is a char representing the transpose mode of the matrix: 'n', 't', or 'c'; respectively identity, tranpose and Hermitian transpose (note: the latter is not relevant yet as complex numbers are not supported).
• uplo is a char that provides information about triangular matrices: u for upper triangular and l for lower triangular matrices.
• diag is a char that provides information about the diagonal elements of a triangular matrix: u if the matrix is unit triangular (all diagonal elements are 1), else n.
• M and N are the numbers of rows and columns of the matrix. They also determine the sizes of the vectors so that dimensions match, depending on the BLAS operation. For operations on square matrices, only N is given.
• alpha and beta are scalars.
• mA is a container for a column-major matrix A.
• lda is the leading dimension of mA, i.e the step between an element and its neighbor in the next column and same row. lda must be at least M.
• vx and vy are containers for vectors x and y.
• incx and incy are their increments (cf BLAS 1).

operation	arguments	description
_gemv	ex, trans, M, N, alpha, mA, lda, vx, incx, beta, vy, incy	Generalised matrix-vector product followed by a vector sum: y = alpha * A * x + beta * y. Note: the dimensions of the vectors depend on the transpose mode (x: N and y: M for mode 'n' ; x: M and y: N otherwise)
_trmv	ex, uplo, trans, diag, N, alpha, mA, lda, vx, incx	Matrix-vector product for a triangular matrix: x = A * x
_symv	ex, uplo, N, alpha, mA, lda, vx, incx, beta, vy, incy	Variant of GEMV for a symmetric matrix (y = alpha * A * x + beta * y). Note: uplo specifies which side of the matrix will be read
_ger	ex, M, N, alpha, vx, incx, vy, incy, mA, lda	Generalised vector-vector product followed by a matrix sum: A = alpha * x * yT + A
_syr	ex, uplo, N, alpha, vx, incx, mA, lda	Generalised vector squaring followed by a sum with a symmetric matrix: A = alpha * x * xT + A
_syr2	ex, uplo, N, alpha, vx, incx, vy, incy, mA, lda	Generalised vector products followed by a sum with a symmetric matrix: A = alpha*x*yT + alpha*y*xT + A

BLAS 3

The following table sums up the interface that can be found in blas3_interface.h.

For all these operations:

• A, B and C are containers for the column-major matrices A, B and C.
• lda, ldb and ldc are the leading dimensions of the matrices A, B and C (cf BLAS 2). The leading dimension of a matrix must be greater than or equal to its number of rows.
• transa and transb are the transpose modes of the matrices A and B (cf BLAS 2).
• M, N and K are the dimensions of the matrices. The dimensions after transposition are A: MxK, B: KxN, C: MxN.
• alpha and beta are scalars.
• batch_size is an integer.

operation	arguments	description
_gemm	ex, transa, transb, M, N, K, alpha, A, lda, B, ldb, beta, C, ldc	Generalised matrix-matrix multiplication followed by matrix addition: C = alpha * A * B + beta * C
_gemm_batched	ex, transa, transb, M, N, K, alpha, A, lda, B, ldb, beta, C, ldc, batch_size	Same as _gemm but the containers contain batch_size end-to-end matrices. GEMM operations are performed independently with matching matrices.

Requirements

SYCL-BLAS is designed to work with any SYCL 1.2.1 implementation. We do not use any OpenCL interoperability, hence, the code is pure C++. The project is developed using ComputeCpp CE Edition using Ubuntu 16.04 on Intel OpenCL CPU and Intel GPU. In order to build the sources, GCC 5.4 or higher is required. The build system is CMake version 3.4.2 or higher. We rely on the FindComputeCpp.cmake imported from the Computecpp SDK to build the project.

A BLAS library, such as OpenBLAS, is also required to verify the test results. This can be installed on Ubuntu from the libopenblas-dev package.

Setup

How to compile

1. Clone the SYCL-BLAS repository, making sure to pass the --recursive option, in order to clone submodule(s), such as the computecpp-sdk.
2. Create a build directory
3. Run CMake from the build directory (see options in the section below):

cd build
cmake -GNinja ../ -DComputeCpp_DIR=/path/to/computecpp
ninja

To install the SYCL-BLAS library (see CMAKE_INSTALL_PREFIX below)

ninja install

Doxygen documentation can be generated by running:

doxygen doc/Doxyfile

CMake options

CMake options are given using -D immediately followed by the option name, the symbol = and a value (ON and OFF can be used for boolean options and are equivalent to 1 and 0). Example: -DBLAS_ENABLE_TESTING=OFF

Some of the supported options are:

name	value	description
BLAS_ENABLE_TESTING	ON/OFF	Set it to OFF to avoid building the tests (ON is the default value)
BLAS_ENABLE_BENCHMARK	ON/OFF	Set it to OFF to avoid building the benchmarks (ON is the default value)
TARGET	name	By default SYCL-BLAS library is built for CPU. Use that flag to compile it for a specific backend (highly recommended for performance). The supported targets are: INTEL_GPU, AMD_GPU, ARM_GPU, RCAR
SYSTEM_BLAS_ROOT	path	If tests or verified benchmarks are enabled, a reference BLAS implementation like OpenBLAS is required to be installed on the machine. Use this option to point to its root folder if it is installed in a custom location
CMAKE_INSTALL_PREFIX	path	Specify the install location, used when invoking ninja install
BLAS_ENABLE_STATIC_LIBRARY	ON/OFF	Build as a static library (OFF by default)
ENABLE_EXPRESSION_TESTS	ON/OFF	Build additional tests that use the header-only framework (e.g to test expression trees); OFF by default
BLAS_VERIFY_BENCHMARK	ON/OFF	Verify the results of the benchmarks instead of only measuring the performance. See the documentation of the benchmarks for more details. ON by default

Cross-Compile

To cross-compile SYCL-BLAS first the following environment variables must be set:

export COMPUTECPP_TOOLCHAIN_DIR="PATH TO TOOLCHAIN_DIR"
export COMPUTECPP_TARGET_TRIPLE="PATH TO TARGET_TRIPLE"
export COMPUTECPP_SYSROOT_DIR="$PATH TO SYSROOT_DIR"

The following CMake command can be used to cross-compile SYCL-BLAS:

cmake  -GNinja                                                                                           \
    ${SOURCE_ROOT}                                                                                       \
   -DSYSTEM_BLAS_ROOT="${OPENBLAS_PATH}"                                                                 \
   -DComputeCpp_DIR="${COMPUTECPP_DEVICE_PATH}"                                                          \
   -DComputeCpp_HOST_DIR="${COMPUTECPP_X86_PATH}"                                                        \
   -DCMAKE_TOOLCHAIN_FILE="${SYCL_BLAS_PATH}/external/computecpp-sdk/cmake/toolchains/gcc-generic.cmake" \
   -DCMAKE_BUILD_TYPE='Release'                                                                          \
   -DCMAKE_INSTALL_PREFIX=${CROSS_COMPILED_SYCLBLAS_INSTALL}                                             \
   -DOpenCL_INCLUDE_DIR="${OpenCL_Headers_PATH}"                                                         \
   -DOpenCL_LIBRARY="${OpenCL_LIBRARY}"                                                                  \
   -DCOMPUTECPP_BITCODE="${DEVICE_BITCODE}"                                                              \
   -DCMAKE_CXX_FLAGS='-O3'                                                                               \
   -DTARGET="${CHOSEN_TARGET}"

Tests and benchmarks

The tests and benchmarks have their own documentation:

• Documentation of the tests
• Documentation of the benchmarks

Contributing to the project

SYCL-BLAS is an Open Source project maintained by the HPCA group and Codeplay Software Ltd. Feel free to create an issue on the Github tracker to request features or report bugs.