Performance Evaluation of Strassen Matrix Multiplication Supporting Triple-Double Precision Floating-Point Arithmetic

Abstract

The Strassen matrix multiplication can be categorized into divide-and-conquer algorithms, and they are known as the most efficient algorithms. We previously implemented them supporting multiple precision floating-point arithmetic using MPFR and Bailey’s QD libraries and have shown their effectiveness in our papers and open-source codes. In preparation for a future release, we have introduced an optimized triple-word floating-point arithmetic proposed by Fabiano et al., and we found its utility in our implementation of multiple precision matrix multiplication. In this paper, we demonstrate the effectiveness of the Strassen triple-double precision matrix multiplication through performance evaluation compared to those based on QD and MPFR libraries.

Accelerated Multiple Precision Direct Method and Mixed Precision Iterative Refinement on Python Programming Environment

“…), and also shows the results of 424 direct methods of mpmath. Stopping condition in process of iterations is set as (2), where x k is the k-th approximation and r It can be seen that the maximum relative errors are different for mixed precision iterative refinements with different computational precision, but normally accurate approximations are obtained for all precision. Mixed precision iterative refinements combined with multi-componenttype MPF direct methods are 49 to 139 times faster than 424bits direct method of mpmath.…”

“…We have already had BNCmatmul, accelerated MPF linear computation library based on DD, TD (Triple-double), and QD precision arithmetic [2]. It has been accelerated with AVX2 (Advanced Vector eXtension 2) available on x86 64 CPUs, and has had also SIMDized direct method including LU decomposition and forward and backward substitutions [3].…”