Scaleable Sparse Matrix-Vector Multiplication with Functional Memory and GPUs

Abstract

Sparse matrix-vector multiplication on GPUs faces to a serious problem when the vector length is too large to be stored in GPU's device memory. To solve this problem, we propose a novel software-hardware hybrid method for a heterogeneous system with GPUs and functional memory modules connected by PCI express. The functional memory contains huge capacity of memory and provides scatter/gather operations. We perform some preliminary evaluation for the proposed method with using a sparse matrix benchmark collection. We observe that the proposed method for a GPU with converting indirect references to direct references without exhausting GPU's cache memory achieves 4.1 times speedup compared with conventional methods. The proposed method intrinsically has high scalability of the number of GPUs because intercommunication among GPUs is completely eliminated. Therefore we estimate the performance of our proposed method would be expressed as the single GPU execution performance, which may be suppressed by the burst-transfer bandwidth of PCI express, multiplied with the number of GPUs.

A memory accelerator with gather functions for bandwidth-bound irregular applications

“…Figure 7 shows the effective bandwidth of vector accesses during the execution of sparse matrices-vector double precision multiplication with two kinds of sparse matrix storage formats. The storage formats are the CRS and our format for GPUs [5]. As far as this experiment, we do not observe big difference in the two matrix storage formats.…”

“…For the evaluation of GPUs experiments, we use address trace data to which we apply the pre-processing algorithm [5] for the proposed extended memory and GPUs.…”

“…The address trace data for the multiplication is generated with the folding method [5], which is a pre-process for sparse matricesvector multiplication. In this experiment, we do not optimize the folding length.…”

“…In this experiment, we do not optimize the folding length. We also use the zero padding method [5] to fair the sparse matrices and the index file contains blocks of zero padding. However, the address trace file does not contain the zero padding accesses because registers or cache of the memory controller is available to access "zero" values without any memory references.…”

A portable OpenCL-based unstructured edge-based finite element Navier–Stokes solver on graphics hardware

“…This is more logical, as the data needed to solve the system of equation is generated and already resides in the GPU memory, and no transfer cost is to be needed. of SpMV kernels on graphics hardware has been the subject of many recent researches [23][24][25][26][27][28][29][30][31][32][33]. It has been shown that the naïve implementation of SpMV kernel is quite ineffective on such platforms [23].…”