Perfomance Models for Blocked Sparse Matrix-Vector Multiplication Kernels

Abstract

Abstract-Sparse Matrix-Vector multiplication (SpMV) is a very challenging computational kernel, since its performance depends greatly on both the input matrix and the underlying architecture. The main problem of SpMV is its high demands on memory bandwidth, which cannot yet be abudantly offered from modern commodity architectures. One of the most promising optimization techniques for SpMV is blocking, which can reduce the indexing structures for storing a sparse matrix, and therefore alleviate the pressure to the memory subsystem. However, blocking methods can severely degrade performance if not used properly. In this paper, we study and evaluate a number of representative blocking storage formats and present a performance model that can accurately select the most suitable blocking storage format and the corresponding block shape and size for a specific sparse matrix. Our model considers both the memory and computational part of the kernel, which can be non-negligible when applying blocking, and also assumes an overlapping of memory accesses and computations that modern commodity architectures can offer through hardware prefetching mechanisms.

Optimization of Sparse Matrix-Vector Multiplication with Variant CSR on GPUs

“…Karakasis, et al, presented a BCSR-based performance model to accurately select the most suitable blocking storage format and the corresponding block shape and size [14], which could provide more accurate selections and predictions. Choi, et al, proposed variants on classical BCSR and Blocked ELLPACK (BELLPACK) storage formats with an autotuning model [15], which matched or exceeded state-of-the-art implements.…”

“…The experimented sparse matrices are from Tim Davis's sparse matrix collection [21]. The selected sparse matrices are described in Table II and are ofen used in other researches [11], [14], [15]. They represent different kind of real applications including economics, epidemiology, FEM based modeling, protein, webbase, and so on.…”

Sparse Matrix-Vector Multiplication on GPGPUs

“…Blocking storage techniques can be used to improve CSR compression and data reuse, especially of the input vector elements. BCSR is the classical blocked version of CSR, storing and indexing two-dimensional small dense blocks with at least one nonzero element and uses zero padding to construct full blocks [52]. Thus, BCSR reduces the indexing overhead for storing a sparse matrix but it needs zero fill-in in the blocks.…”

A segment‐based sparse matrix–vector multiplication on CUDA

“…The experimented sparse matrices are from Tim Davis' sparse matrix collection. The selected sparse matrices can represent different kinds of real applications including economics, epidemiology, FEM-based (Finite Element Method) modeling, protein, webbase, and so on, used in other researches [5,11,14], as described in Table IV. NVIDIA develops a library concerning SpMV computation. Several efficient implementation techniques are explored for SpMV in CUDA, as described in Section 3.…”

“…Buatois et al first investigated the performance of blocked-CSR (BCSR) on G80 series of NVIDIA graphic cards [13]. Karakasis et al presented a BCSR-based performance model to accurately select the most suitable blocking storage format and the corresponding block shape and size [14], which could provide more accurate selections and predictions. Choi et al proposed variants on classical BCSR and Blocked ELLPACK (BELL) storage formats with an autotuning model [5], which matched or exceeded state-of-the-art implements.…”