Sparse matrix-vector multiply on the HICAMP architecture

Abstract

Sparse matrix-vector multiply (SpMV) is a critical task in the inner loop of modern iterative linear system solvers and exhibits very little data reuse. This low reuse means that its performance is bounded by main-memory bandwidth. Moreover, the random patterns of indirection make it difficult to achieve this bound. We present sparse matrix storage formats based on deduplicated memory. These formats reduce memory traffic during SpMV and thus show significantly improved performance bounds: 90x better in the best case. Additionally, we introduce a matrix format that inherently exploits any amount of matrix symmetry and is at the same time fully compatible with non-symmetric matrix code. Because of this, our method can concurrently operate on a symmetric matrix without complicated work partitioning schemes and without any thread synchronization or locking. This approach takes advantage of growing processor caches, but incurs an instruction count overhead. It is feasible to overcome this issue by using specialized hardware as shown by the recently proposed Hierarchical Immutable ContentAddressable Memory Processor, or HICAMP architecture.

A 3D-stacked logic-in-memory accelerator for application-specific data intensive computing

“…WWW graph, social networks) [16]. These problems are important enough to support architecture investments to surpass the traditional computing which has reached the limit for increasing performance without an increase in power [25], [19]. It is widely accepted to exploit the duality between sparse matrix and graph to solve graph algorithms [7].…”

Smat

“…This idea is reflected in previous work. By far, more than ten storage formats [7,21,25,28,29,31] have been proposed, most of which are either application-specific or architecture-specific so that their applicable domains are limited. Recently, several hybrid storage formats have been developed.…”

“…For example, the algebraic multigrid (AMG) solver [13], an iterative algorithm widely used in both laser fusion and climate modeling, reports above 90% SpMV operation of its overall iterations. Since 1970s, plenty of researches have been dedicated to optimizing SpMV performance for its fundamental importance, which are generally separated into two paths, one for developing new application-specific storage formats [7,21,[29][30][31][32]36], and the other for tuning on emerging processor architectures [10,11,16,22,27,28,34,35]. This separation leads to low performance and low productivity in SpMV solvers and applications:…”

Accelerating sparse matrix-matrix multiplication with 3D-stacked logic-in-memory hardware

“…WWW graph, social networks) [14]. These problems are important enough to support architecture investments to surpass the traditional computing which has reached the limit for increasing performance without an increase in power [25], [17]. It is widely accepted to exploit the duality between sparse matrix and graph to solve graph algorithms.…”