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

TL;DR

This paper introduces an accelerated multiple precision floating-point direct method using AVX2 and applies it to mixed precision iterative refinement in Python, demonstrating improved efficiency on x86_64 systems.

Contribution

It presents a novel accelerated MPF direct method with AVX2 and integrates it with mixed precision iterative refinement in Python, enhancing computational efficiency.

Findings

Enhanced computational speed with AVX2 acceleration.

Effective implementation of mixed precision iterative refinement.

Demonstrated efficiency improvements on x86_64 platforms.

Abstract

Current Python programming environment does not have any reliable and efficient multiple precision floating-point (MPF) arithmetic except ``mpmath" and ``gmpy2" packages based on GNU MP(GMP) and MPFR libraries. Although it is well known that multi-component-type MPF library can be utilized for middle length precision arithmetic under 200 bits, they are not widely used on Python environment. In this paper, we describe our accelerated MPF direct method with AVX2 techniques and its application to mixed precision iterative refinement combined with mpmath, and demonstrate their efficiency on x86\_64 computational environments.