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Register a new userA Framework for General Sparse Matrix-Matrix Multiplication on GPUs and Heterogeneous Processors
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Weifeng Liu
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM implementation has to handle extra irregularity from three aspects: (1) the number of nonzero entries in the resulting sparse matrix is unknown in advance, (2) very expensive parallel insert operations at random positions in the resulting sparse matrix dominate the execution time, and (3) load balancing must account for sparse data in both input matrices. In this work we propose a framework for SpGEMM on GPUs and emerging CPU-GPU heterogeneous processors. This framework particularly focuses on the above three problems. Memory pre-allocation for the resulting matrix is organized by a hybrid method that saves a large amount of global memory space and efficiently utilizes the very limited on-chip scratchpad memory. Parallel insert operations of the nonzero entries are implemented through the GPU merge path algorithm that is experimentally found to be the fastest GPU merge approach. Load balancing builds on the number of necessary arithmetic operations on the nonzero entries and is guaranteed in all stages. Compared with the state-of-the-art CPU and GPU SpGEMM methods, our approach delivers excellent absolute performance and relative speedups on various benchmarks multiplying matrices with diverse sparsity structures. Furthermore, on heterogeneous processors, our SpGEMM approach achieves higher throughput by using re-allocatable shared virtual memory. The source code of this work is available at https://github.com/bhSPARSE/Benchmark_SpGEMM_using_CSR
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Sparse matrix-vector multiplication (SpMV) is a central building block for scientific software and graph applications. Recently, heterogeneous processors composed of different types of cores attracted much attention because of their flexible core configuration and high energy efficiency. In this paper, we propose a compressed sparse row (CSR) format based SpMV algorithm utilizing both types of cores in a CPU-GPU heterogeneous processor. We first speculatively execute segmented sum operations on the GPU part of a heterogeneous processor and generate a possibly incorrect results. Then the CPU part of the same chip is triggered to re-arrange the predicted partial sums for a correct resulting vector. On three heterogeneous processors from Intel, AMD and nVidia, using 20 sparse matrices as a benchmark suite, the experimental results show that our method obtains significant performance improvement over the best existing CSR-based SpMV algorithms. The source code of this work is downloadable at https://github.com/bhSPARSE/Benchmark_SpMV_using_CSR
Sparse matrix-vector multiplication (spMVM) is the most time-consuming kernel in many numerical algorithms and has been studied extensively on all modern processor and accelerator architectures. However, the optimal sparse matrix data storage format is highly hardware-specific, which could become an obstacle when using heterogeneous systems. Also, it is as yet unclear how the wide single instruction multiple data (SIMD) units in current multi- and many-core processors should be used most efficiently if there is no structure in the sparsity pattern of the matrix. We suggest SELL-C-sigma, a variant of Sliced ELLPACK, as a SIMD-friendly data format which combines long-standing ideas from General Purpose Graphics Processing Units (GPGPUs) and vector computer programming. We discuss the advantages of SELL-C-sigma compared to established formats like Compressed Row Storage (CRS) and ELLPACK and show its suitability on a variety of hardware platforms (Intel Sandy Bridge, Intel Xeon Phi and Nvidia Tesla K20) for a wide range of test matrices from different application areas. Using appropriate performance models we develop deep insight into the data transfer properties of the SELL-C-sigma spMVM kernel. SELL-C-sigma comes with two tuning parameters whose performance impact across the range of test matrices is studied and for which reasonable choices are proposed. This leads to a hardware-independent (catch-all) sparse matrix format, which achieves very high efficiency for all test matrices across all hardware platforms.
Sparse matrix-vector multiplication (SpMV) is a fundamental building block for numerous applications. In this paper, we propose CSR5 (Compressed Sparse Row 5), a new storage format, which offers high-throughput SpMV on various platforms including CPUs, GPUs and Xeon Phi. First, the CSR5 format is insensitive to the sparsity structure of the input matrix. Thus the single format can support an SpMV algorithm that is efficient both for regular matrices and for irregular matrices. Furthermore, we show that the overhead of the format conversion from the CSR to the CSR5 can be as low as the cost of a few SpMV operations. We compare the CSR5-based SpMV algorithm with 11 state-of-the-art formats and algorithms on four mainstream processors using 14 regular and 10 irregular matrices as a benchmark suite. For the 14 regular matrices in the suite, we achieve comparable or better performance over the previous work. For the 10 irregular matrices, the CSR5 obtains average performance improvement of 17.6%, 28.5%, 173.0% and 293.3% (up to 213.3%, 153.6%, 405.1% and 943.3%) over the best existing work on dual-socket Intel CPUs, an nVidia GPU, an AMD GPU and an Intel Xeon Phi, respectively. For real-world applications such as a solver with only tens of iterations, the CSR5 format can be more practical because of its low-overhead for format conversion. The source code of this work is downloadable at https://github.com/bhSPARSE/Benchmark_SpMV_using_CSR5
Although the matrix multiplication plays a vital role in computational linear algebra, there are few efficient solutions for matrix multiplication of the near-sparse matrices. The Sparse Approximate Matrix Multiply (SpAMM) is one of the algorithms to fill the performance gap neglected by traditional optimizations for dense/sparse matrix multiplication. However, existing SpAMM algorithms fail to exploit the performance potential of GPUs for acceleration. In this paper, we present cuSpAMM, the first parallel SpAMM algorithm optimized for multiple GPUs. Several performance optimizations have been proposed, including algorithm re-design to adapt to the thread parallelism, blocking strategies for memory access optimization, and the acceleration with the tensor core. In addition, we scale cuSpAMM to run on multiple GPUs with an effective load balance scheme. We evaluate cuSpAMM on both synthesized and real-world datasets on multiple GPUs. The experiment results show that cuSpAMM achieves significant performance speedup compared to vendor optimized cuBLAS and cuSPARSE libraries.
Sparse matrix vector multiplication (SpMV) is an important kernel in scientific and engineering applications. The previous optimizations are sparse matrix format specific and expose the choice of the best format to application programmers. In this work we develop an auto-tuning framework to bridge gap between the specific optimized kernels and their general-purpose use. We propose an SpMV auto-tuner (SMAT) that provides an unified interface based on compressed sparse row (CSR) to programmers by implicitly choosing the best format and the fastest implementation of any input sparse matrix in runtime. SMAT leverage a data mining model, which is formulated based on a set of performance parameters extracted from 2373 matrices in UF sparse matrix collection, to fast search the best combination. The experiments show that SMAT achieves the maximum performance of 75 GFLOP/s in single-precision and 33 GFLOP/s in double-precision on Intel, and 41 GFLOP/s in single-precision and 34 GFLOP/s in double-precision on AMD. Compared with the sparse functions in MKL library, SMAT runs faster by more than 3 times.
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