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

Abstract: Current Python programming environment does not have any reliable and efficient multiple precision floating-point (MPF) arithmetic except mpmath" andgmpy2" 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.