Performance Analysis and Optimization of Sparse Matrix-Vector Multiplication on Modern Multi- and Many-Core Processors

This paper presents a low-overhead optimizer for the ubiquitous sparse matrix-vector multiplication (SpMV) kernel. Architectural diversity among different processors together with structural diversity among different sparse matrices lead to bottleneck diversity. This justifies an SpMV optimizer that is both matrix- and architecture-adaptive through runtime specialization. To this direction, we present an approach that first identifies the performance bottlenecks of SpMV for a given sparse matrix on the target platform either through profiling or by matrix property inspection, and then selects suitable optimizations to tackle those bottlenecks. Our optimization pool is based on the widely used Compressed Sparse Row (CSR) sparse matrix storage format and has low preprocessing overheads, making our overall approach practical even in cases where fast decision making and optimization setup is required. We evaluate our optimizer on three x86-based computing platforms and demonstrate that it is able to distinguish and appropriately optimize SpMV for the majority of matrices in a representative test suite, leading to significant speedups over the CSR and Inspector-Executor CSR SpMV kernels available in the latest release of the Intel MKL library.Comment: 10 pages, 7 figures, ICPP 201

Automatically Harnessing Sparse Acceleration

Sparse linear algebra is central to many scientific programs, yet compilers fail to optimize it well. High-performance libraries are available, but adoption costs are significant. Moreover, libraries tie programs into vendor-specific software and hardware ecosystems, creating non-portable code. In this paper, we develop a new approach based on our specification Language for implementers of Linear Algebra Computations (LiLAC). Rather than requiring the application developer to (re)write every program for a given library, the burden is shifted to a one-off description by the library implementer. The LiLAC-enabled compiler uses this to insert appropriate library routines without source code changes. LiLAC provides automatic data marshaling, maintaining state between calls and minimizing data transfers. Appropriate places for library insertion are detected in compiler intermediate representation, independent of source languages. We evaluated on large-scale scientific applications written in FORTRAN; standard C/C++ and FORTRAN benchmarks; and C++ graph analytics kernels. Across heterogeneous platforms, applications and data sets we show speedups of 1.1$\times$ to over 10$\times$ without user intervention.Comment: Accepted to CC 202