Speeding Up Non-archimedean Numerical Computations Using AVX-512 SIMD Instructions

This work presents the acceleration of a Bounded Algorithmic Number (BAN) library exploiting vector instructions in general-purpose processors. With the use of this encoding, it is possible to represent non-Archimedean numbers that are not only finite (like real numbers) but also infinite or infinitesimal. The tremendous growth in non-Archimedean numerical computations over the past 20 years and the resulting applications spurred this study’s development. Enabling acceleration of BANs processing can significantly increase the throughput of non-Archimedean numerical computations, enlarging the spectrum of possible applications to industrial and real-time ones.