Implementing data parallel rational multiple-residue arithmetic in Eden

Abstract

Residue systems present a well-known way to reduce computation cost for symbolic computation. However most residue systems are implemented for integers or polynomials. This work combines two known results in a novel manner. Firstly, it lifts an integral residue system to fractions. Secondly, it generalises a single-residue system to a multiple-residue one. Combined, a rational multi-residue system emerges. Due to the independent manner of single "parts" of the system, this work enables progress in parallel computing. We present a complete implementation of the arithmetic in the parallel extension e.g.. The parallelisation utilises algorithmic skeletons. A non-trivial example computation is also supplied. © 2010 Springer-Verlag Berlin Heidelberg.