Power Efficient Strassen’s Algorithm using AVX512 and OpenMP in a Multi-core Architecture

Abstract

This paper presents an effective implementation of Strassen's algorithm for matrix-matrix multiplication on shared memory multi-core architecture. The proposed algorithm aims to augment the computation speed in terms of GFLOPS performance on average 4.5 and 4.1 times faster than Eigen and OpenBLAS, respectively while reducing the power consumption to as low as possible. Our algorithm relies on using AVX512 intrinsics, loop unrolling factor, and OpenMP directives. A new 2D blocking data allocation pattern is proposed for Strassen's algorithm to provide optimized cache temporal and spatial locality. The proposed implementation reduced not only the amount of main memory but also the burden of unnecessary memory allocation/deallocation and data transferring for each level of recursion in Strassen's algorithm. Moreover, the proposed algorithm consumed, on average, 4.25 and 3.67 times lower energy than the multiplication functions of the Eigen and OpenBLAS libraries, respectively. To measure the computational performance with the awareness of power consumption, GFLOPS per Watt (GFPW) is calculated, which out- performed on average 3.78 and 3.47 times higher than those of Eigen and OpenBLAS libraries, respectively.

Investigation of Energy and Power Characteristics of Various Matrix Multiplication Algorithms

“…Oo and Chaikan [21] optimized the Strassen-Winograd algorithm for arbitrary matrix sizes on a GPU using techniques such as empirical modeling, multi-kernel streaming, dynamic peeling, and two temporary matrices. They surpassed previous GPU implementations and showed Strassen's algorithm's practicality.…”

“…Oo and Chaikan [21] 2023 Enhanced Strassen's algorithm for power efficiency using AVX512 and OpenMP on multi-core architecture.…”