portBLAS Implementation

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

portBLAS 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.

portBLAS 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

• portBLAS Implementation
  • Table of Contents
  • Motivation
  • Basic Concepts
    • Views
    • Operations
    • SB_Handle
    • Interface
  • API description
    • BLAS 1
    • BLAS 2
    • BLAS 3
    • Experimental Joint Matrix Support
  • Requirements
  • Setup
    • Compile with ComputeCpp
    • Compile with DPC++
    • Compile with hipSYCL
    • Instaling portBLAS
    • POWER_VR support (ComputeCpp Only)
    • Doxygen
    • CMake options
    • Cross-Compile (ComputeCpp Only)
  • Tests and benchmarks
  • Contributing to the project
    • Guides and Other Documents

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 portBLAS 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 portBLAS.

Basic Concepts

portBLAS 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.

portBLAS can be used

• either as a header-only framework by including portblas.hpp in an application and passing the src folder in the list of include directories
• or as a library by including portblas.h in an application.

All the relevant files can be found in the include directory.

There are four components in portBLAS, the View, the Operations, the SB_Handle and the Interface itself.

Views

The input data to all the operations in portBLAS 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 LegacyRandomAccessIterator 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 portBLAS 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).

SB_Handle

An SB_Handle traverses the Expression Tree to evaluate the operations that it defines. SB_Handle use different techniques to evaluate the expression tree. 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 portBLAS 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. The library follows the oneAPI MKL BLAS specification as reference for the api. We have support for both USM and Buffer api, however the group apis for USM are not supported. We don't support mixing USM and Buffer arguments together to compile the library, and instead stick to the aformentioned reference specification.

All operations take as their first argument a reference to the SB_Handle, a blas::SB_Handle created with a sycl::queue. The last argument for all operators is a vector of dependencies of type cl::sycl::event (empty by default). 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) can either be raw usm pointers or iterator buffers that can be created with a call to cl::sycl::malloc_device or make_sycl_iterator_buffer respectively.

The USM support in portBLAS is limited to device allocated memory only and we don't support shared or host allocations with USM.

We recommend checking the samples to get started with portBLAS. 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	sb_handle, N, alpha, vx, incx, vy, incy	Vector multiply-add: y = alpha * x + y
_copy	sb_handle, N, vx, incx, vy, incy	Copies a vector to another: y = x
_dot	sb_handle, N, vx, incx, vy, incy [, rs]	Dot product of two vectors x and y; written in rs if passed, else returned
_asum	sb_handle, N, vx, incx [, rs]	Absolute sum of the vector x; written in rs if passed, else returned
_iamax	sb_handle, 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	sb_handle, 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	sb_handle, N, vx, incx, vy, incy	Interchanges two vectors: y = x and x = y
_scal	sb_handle, N, alpha, vx, incx	Scalar product of a vector: x = alpha * x
_nrm2	sb_handle, N, vx, incx [, rs]	Euclidean norm of the vector x; written in rs if passed, else returned
_rot	sb_handle, N, vx, incx, vy, incy, c, s	Applies a plane rotation to x and y with a cosine c and a sine s
_rotg	sb_handle, a, b, c, s	Given the Cartesian coordinates (a, b) of a point, return the parameters c, s, r, and z associated with the Givens rotation.
_rotm	sb_handle, N, vx, incx, vy, incy, param	Applies a modified Givens rotation to x and y.
_rotmg	sb_handle, d1, d2, x1, y1 param	Given the Cartesian coordinates (x1, y1) of a point, return the components of a modified Givens transformation matrix that zeros the y-component of the resulting point.

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, transpose 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	sb_handle, 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)
_gbmv	sb_handle, trans, M, N, KL, KU, alpha, mA, lda, vx, incx, beta, vy, incy	Generalised band 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	sb_handle, uplo, trans, diag, N, alpha, mA, lda, vx, incx	Matrix-vector product for a triangular matrix: x = A * x
_symv	sb_handle, 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	sb_handle, M, N, alpha, vx, incx, vy, incy, mA, lda	Generalised vector-vector product followed by a matrix sum: A = alpha * x * yT + A
_syr	sb_handle, uplo, N, alpha, vx, incx, mA, lda	Generalised vector squaring followed by a sum with a symmetric matrix: A = alpha * x * xT + A
_syr2	sb_handle, 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
_spr	sb_handle, uplo, N, alpha, vx, incx, mPA	Symmetric vector-vector product followed by a matrix sum: mPA = alpha * x * xT + mPA
_spmv	sb_handle, uplo, N, alpha, mA, vx, incx, beta, vy, incy	Symmetric packed matrix-vector product: y = alpha * A * x + beta * y
_tpmv	sb_handle, uplo, trans, diag, N, mA, vx, incx	Triangular packed matrix-vector product: x = A * x

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.
• side is l for left or r for right.
• 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.

operation	arguments	description
_gemm	sb_handle, 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	sb_handle, transa, transb, M, N, K, alpha, A, lda, B, ldb, beta, C, ldc, batch_size, batch_type	Same as _gemm but the containers contain batch_size end-to-end matrices. GEMM operations are performed independently with matching matrices.
_gemm_strided_batched	sb_handle, transa, transb, M, N, K, alpha, A, lda, stridea, B, ldb, strideb, beta, C, ldc, stridec, batch_size	Same as _gemm but the containers contain batch_size end-to-end matrices. GEMM operations are performed independently with matching matrices.
_trsm	sb_handle, side, uplo, trans, diag, M, N, alpha, A, lda, B, ldb	Triangular solve with Multiple Right-Hand Sides.

EXTENSION

The following table sums up the interface that can be found in extension_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. In the case of in-place copy/transpose, the same matrix A is used with two different leading dimensions for input & output.
• stride_a, stride_b and stride_c are the striding size between consecutive matrices in a batched entry for inputs/outputs A, B and C.
• inc_a and inc_b are the distance between consecutive elements in A & B matrices.
• transa and transb are the transpose modes of the matrices A and B (cf BLAS 2).
• M and N are the dimensions of the matrices.
• alpha and beta are scaling scalars.
• batch_size is the number of batch matrices.
• inc_a and inc_b are integers. The distance between element in the same column.

operation	arguments	description
_omatcopy	sb_handle, transa, M, N, alpha, A, lda, B, ldb	Perform an out-of-place scaled matrix transpose or copy operation using a general dense matrix.
_omatcopy2	sb_handle, transa, M, N, alpha, A, lda, inc_a, B, ldb, inc_b	Computes two-strided scaling and out-of-place transposition or copying of general dense matrices.
_omatadd	sb_handle, transa, transb, M, N, alpha, A, lda, beta, B, ldb, C,ldc	Computes scaled general dense matrix addition with possibly transposed arguments.
_omatcopy_batch	sb_handle, transa, M, N, alpha, A, lda, stride_a, B, ldb, stride_b, batch_size	Perform an out-of-place scaled batched-strided matrix transpose or copy operation using a general dense matrix.
_imatcopy_batch	sb_handle, transa, M, N, alpha, A, lda, ldb, stride, batch_size	Perform an in-place scaled batched-strided matrix transpose* or copy operation using a general dense matrix. (*: Currently the transpose case is not supported).
_omatadd_batch	sb_handle, transa, transb, M, N, alpha, A, lda, stride_a, beta, B, ldb, stride_b, C,ldc, stride_c, batch_size	Computes a batch of scaled general dense matrix addition with optionally transposed arguments.

Other non-official extension operators :

operation	arguments	description
_transpose	sb_handle, M, N, A, lda, B, ldb	Computes an out-of-place matrix transpose operation using a general dense matrix.
_transpose*	sb_handle, M, N, A, lda, ldb	Computes an in-place matrix transpose operation using a general dense matrix, lda & ldb being input and output leading dimensions of A respectively (*Not implemented).

Experimental Joint Matrix Support

portBLAS now supports sub-group based collective GEMM operation using the experimental joint_matrix extension provided by DPC++. This support is only accessible for the latest NVIDIA Ampere GPUs and beyond. The requirements for using this experimental support are:

DPCPP_SYCL_TARGET = "nvptx64-nvidia-cuda"
DPCPP_SYCL_ARCH = "sm_80" | "sm_90"

To invoke the joint_matrix based GEMM, you need to set the following environment variable:

export SB_ENABLE_JOINT_MATRIX=1

The user should expect erroneous behaviour from the code if both of these requirements are not met.

Requirements

portBLAS 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.

A BLAS library, such as OpenBLAS, is also required to build and verify the test results. Instructions for building and installing OpenBLAS can be found on this page. Please note that although some distributions may provide packages for OpenBLAS these versions are typically quite old and may have issues with the TRMV implementation which can cause random test failures. Any version of OpenBLAS >= 0.3.0 will not suffer from these issues.

When using OpenBLAS or any other BLAS library the installation directory must be added to the CMAKE_PREFIX_PATH when building portBLAS (see below).

Setup

IMPORTANT NOTE: The TARGET CMake variable is no longer supported. It has been replaced by TUNING_TARGET, which accepts the same options. TUNING_TARGET affects only the tuning configuration and has no effect on the target triplet for DPC++ or the hipSYCL target. Please refer to the sections below for setting them.

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

Compile with ComputeCpp

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

Compile with DPC++

export CC=[path/to/intel/clang]
export CXX=[path/to/intel/clang++]
cd build
cmake -GNinja ../ -DSYCL_COMPILER=dpcpp
ninja

The target triplet can be set by adding -DDPCPP_SYCL_TARGET=<triplet>. If it is not set, the default values is spir64, which compiles for generic SPIR-V targets.

Other possible triplets are nvptx64-nvidia-cuda, and amdgcn-amd-amdhsa for compiling for NVIDIA and AMD GPUs. In this case, it is advisable for NVIDIA and mandatory for AMD to provide the specific device architecture through -DDPCPP_SYCL_ARCH=<arch>, e.g., <arch> can be sm_80 for NVIDIA or gfx908 for AMD.

Compile with hipSYCL

cd build
cmake -GNinja ../ -DhipSYCL_DIR=/path/to/hipSYCL/install/lib/cmake/hipSYCL -DSYCL_COMPILER=hipsycl
ninja

To build for other than the default devices (omp), set the HIPSYCL_TARGETS environment variable or specify -DHIPSYCL_TARGETS as documented.

Instaling portBLAS

To install the portBLAS library (see CMAKE_INSTALL_PREFIX below)

ninja install

POWER_VR support (ComputeCpp Only)

To enable the PowerVR target tuning, pass: -DTUNING_TARGET=POWER_VR

To use the neural network library from Imagination, pass: -DIMGDNN_DIR=path/to/library

Doxygen

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)
SYCL_COMPILER	name	Used to determine which SYCL implementation to use. By default, the first implementation found is used. Supported values are: computecpp, dpcpp and hipsycl.
TUNING_TARGET	name	By default, this flag is set to DEFAULT_CPU to restrict any device specific compiler optimizations. Use this flag to tune the code for a target (highly recommended for performance). The supported targets are: INTEL_GPU, NVIDIA_GPU, AMD_GPU
CMAKE_PREFIX_PATH	path	List of paths to check when searching for dependencies
CMAKE_INSTALL_PREFIX	path	Specify the install location, used when invoking ninja install
BUILD_SHARED_LIBS	ON/OFF	Build as shared library (ON 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
BLAS_ENABLE_CONST_INPUT	ON/OFF	Determines whether to enable kernel instantiation with const input buffer (ON by default)
BLAS_ENABLE_EXTENSIONS	ON/OFF	Determines whether to enable portBLAS extensions (ON by default)
BLAS_DATA_TYPES	half;float;double	Determines the floating-point types to instantiate BLAS operations for. Default is float
BLAS_INDEX_TYPES	int32_t;int64_t	Determines the type(s) to use for index_t and increment_t. Default is int
BLAS_ENABLE_COMPLEX	ON/OFF	Determines whether to enable Complex data type support (GEMM Kernels only) (ON by default)

Cross-Compile (ComputeCpp Only)

To cross-compile portBLAS 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"

Clone the ComputeCpp-SDK to retrieve the toolchain file. The following CMake command can be used to cross-compile portBLAS:

cmake  -GNinja                                                                         \
    ${SOURCE_ROOT}                                                                     \
   -DCMAKE_PREFIX_PATH="${OPENBLAS_PATH}"                                              \
   -DComputeCpp_DIR="${COMPUTECPP_DEVICE_PATH}"                                        \
   -DComputeCpp_HOST_DIR="${COMPUTECPP_X86_PATH}"                                      \
   -DCMAKE_TOOLCHAIN_FILE="/path/to/computecpp-sdk/cmake/toolchains/gcc-generic.cmake" \
   -DCMAKE_BUILD_TYPE='Release'                                                        \
   -DCMAKE_INSTALL_PREFIX=${CROSS_COMPILED_PORTBLAS_INSTALL}                           \
   -DOpenCL_INCLUDE_DIR="${OpenCL_Headers_PATH}"                                       \
   -DOpenCL_LIBRARY="${OpenCL_LIBRARY}"                                                \
   -DCOMPUTECPP_BITCODE="${DEVICE_BITCODE}"                                            \
   -DCMAKE_CXX_FLAGS='-O3'                                                             \
   -DTUNING_TARGET="${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

portBLAS 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.

Guides and Other Documents

• How to add a new operation
• Autotuner Developer Guide