SpMV on large matrices is a heavily memory-bound kernel, a characteristic attributed to its extremely low computational intensity.To address this, research has mainly focused on compressing the matrix indices.Nevertheless, the values of a matrix usually occupy up to two thirds of the total size.Research on value compression, on the other hand, has been limited to specific matrix types.In this paper, we propose DIV, a combined index and value lossless compression scheme, based on variations of delta and run-length encoding, that achieves substantially improved SpMV performance for large matrices, i.e., those that exceed the CPU cache.We evaluate its performance against other state-of-the-art matrix formats, on an Intel Xeon and an AMD EPYC platform.Our format achieves 77% and 115% geometric mean speedup respectively versus the Intel MKL library.We finally demonstrate the applicability of DIV on a Biconjugate Gradient Stabilized solver, where we also achieve significant speedups.

The OPTIMA project aims to port and optimize industrial applications and a set of open-source libraries into two novel FPGA-populated HPC systems. Target applications are from the domains of robotics simulation, underground analysis and computational fluid dynamics (CFD), where data processing is based on differential equations, matrix-matrix and matrix-vector operations. Moreover, the OPTIMA OPen Source (OOPS) library will support basic linear algebraic operations, sparse matrix-vector arithmetic, as well as computer-aided engineering (CAE) solvers. The OPTIMA target platforms are JUMAX, an HPC system that couples an AMD Epyc Server with Maxeler FPGA-based Dataflow Engines (DFEs), and server class machines with Alveo FPGA cards installed. Experimental results show that performance on robotic simulation can be enhanced up to 1.2x, and CFD calculations up to 4.7x. Finally, BLAS L1 routines are improved up to 7x, with a performance-per-Watt ratio boost of more than 40x compared to multi-threaded software routines from the Intel Math Kernel Library (MKL) suite when executed on an Intel Xeon server-class machine.

OPTIMA is an SME-driven project (intermediate stage) that aims to port and optimize industrial applications and a set of open-source libraries into two novel FPGA-populated HPC systems. Target applications are from the domain of robotics simulation, underground analysis and computational fluid dy-namics (CFD), where data processing is based on differential equations, matrix-matrix and matrix-vector operations. Moreover, the OPTIMA OPen Source (OOPS) library will support basic linear algebraic operations, sparse matrix-vector arithmetic, as well as computer-aided engineering (CAE) solvers. The OPTIMA target platforms are JUMAX, an HPC system that couples an AMD Epyc Server with Maxeler FPGA-based Dataflow Engines (DFEs), and server-class machines with Alveo FPGA cards in-stalled. Experimental results on applications up to now, show that performance on robotic simulation can be enhanced up to 1.2x, CFD calculations up to 4.7x, and BLAS routines up to 7x compared to optimized software implementations from OpenBLAS.

The SpMV kernel is characterized by high performance variation per input matrix and computing platform. While GPUs were considered State-of-the-Art for SpMV, with the emergence of advanced multicore CPUs and low-power FPGA accelerators, we need to revisit its performance and energy efficiency. This paper provides a high-level SpMV performance analysis based on structural features of matrices related to common bottlenecks of memory-bandwidth intensity, low ILP, load imbalance and memory latency overheads. Towards this, we create a wide artificial matrix dataset that spans these features and study the performance of different storage formats in nine modern HPC platforms; five CPUs, three GPUs and an FPGA. After validating our proposed methodology using real-world matrices, we analyze our extensive experimental results and draw key insights on the competitiveness of different target architectures for SpMV and the impact of each feature/bottleneck on its performance.