Bringing High-Performance Reconfigurable Computing to Exact Computations

Abstract

Numerical non-robustness is a recurring phenomenon in scientific computing. It is primarily caused by numerical errors arising because of fixed-precision arithmetic in integer and/or floating-point computations. Exact computation, based on arbitrary-precision arithmetic, has been developed over the last decade as an emerging numerical computation paradigm in response to this problem of numerical non-robustness. Exact arithmetic, specifically arbitrary-precision arithmetic, has been traditionally implemented using efficient software libraries such as GNU Multi-Precision (GMP). However, this results in a slower arithmetic performance when compared to fixed-precision arithmetic. In this paper we present a first effort, to the best of our knowledge, of reconfigurable hardware support for arbitrary-precision arithmetic. The proposed hardware architectures are based on virtual convolution sche <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> duling which is derived from a formal representation of the problem. Targeting high performance and efficiency, dynamic (non-linear) pipelines techniques were exploited to eliminate the effects of deeply-pipelined operators. Referenced to GMP, our experiments showed promising results.