A new approach for sparse matrix vector product on NVIDIA GPUs

Abstract

SUMMARYThe sparse matrix vector product (SpMV) is a key operation in engineering and scientific computing and, hence, it has been subjected to intense research for a long time. The irregular computations involved in SpMV make its optimization challenging. Therefore, enormous effort has been devoted to devise data formats to store the sparse matrix with the ultimate aim of maximizing the performance. Graphics Processing Units (GPUs) have recently emerged as platforms that yield outstanding acceleration factors. SpMV implementations for NVIDIA GPUs have already appeared on the scene. This work proposes and evaluates a new implementation of SpMV for NVIDIA GPUs based on a new format, ELLPACK-R, that allows storage of the sparse matrix in a regular manner. A comparative evaluation against a variety of storage formats previously proposed has been carried out based on a representative set of test matrices. The results show that, although the performance strongly depends on the specific pattern of the matrix, the implementation based on ELLPACK-R achieves higher overall performance. Moreover, a comparison with standard state-of-the-art superscalar processors reveals that significant speedup factors are achieved with GPUs.

Towards Ad-Hoc GPU Acceleration Of Parallel Eigensystem Computations

“…The challenges of achieving efficient performance on a GPU architecture may justify the extended effort of custom algorithms developed specifically for the strengths of the platform (Vzquez et al, 2010). However, we maintain the original algorithms of the legacy EISPACK implementation for several reasons:…”

Consumo energético de métodos iterativos para sistemas dispersos en procesadores gráficos

“…Both schemes aim to reduce the memory footprint by explicitly storing only the non-zero elements, though the ELLPACK format may store some zero elements for padding all rows to the same length; see Figure 3.3 and Table 3.3 for the evoked overhead. While in general this incurs some additional storage cost, the aligned structure allows for more efficient hardware use when targeting streaming processors like the GPUs [108,130].…”

“…In those cases, the associated memory and computational overheads may result in poor performance, despite that coalesced memory access is highly beneficial for streaming processors like the GPUs. ELLR-T [130,131] is a subtle variant of ELLPACK that addresses this problem while maintaining the coalesced memory access pattern of the original layout. In particular, it reduces useless computations with zeros and improves thread load balancing, often resulting in superior performance.…”

“…, en el que se incorporan versiones optimizadas del CG, principalmente centradas en la operación SpMV sobre las mismas arquitecturas. En concreto, para las arquitecturas multinúcleo se utilizaron los formatos CSR, BCSR y CSB [192,193,194,195,196], mientras que para las GPUs se utilizaron los formatos ELLPACK, ELLR_T y SELL-P [197,198,199,200,201], y también se incluyó el "fusionado de kernels CUDA". Además, en el estudio se utilizó aritmética de DP, aunque como complemento final, también se comprobó el uso de SP para la GPU (Kepler) y un procesador de propósito general (Intel Bridge).…”

“…Section 4.4 offers a short introduction to two GPU implementations of the sparse matrixvector product, using the popular compressed storage row (CSR) format [144], and describes our initial GPU code for the CG method built on top of this operation and NVIDIA's CUBLAS library [150]. While there exist alternative algorithms and storage layouts for the sparse matrix-vector product that, in general, render higher performance on the GPU [141,155], we note here that our energy-saving techniques are orthogonal to the actual implementation of the matrix-vector product kernel. Indeed, we expect that a more efficient implementation of this operation will shift part of the relative cost towards other kernels of the CG method, so that by Amdahl's law, the gains could be even higher.…”