Hardware Assists for High Performance Computing Using a Mathematics of Arrays

Work in progress at the University of Missouri - Rolla on hardware assists for high performance computing and communication is presented. This research consists of a field programmable gate array based rapid prototyping environment (Chameleon) being used to evaluate hardware architectures for speedup of array partitioning and routing algorithms. These algorithms have been developed using a Mathematics of Arrays (MOA) and are optimal in the sense that they reduce normal array indexing operations to a series of primitive additions based on array shape. The method is simple yet powerful, produces algorithms which are provably correct, and are independent of dimensionality. Software implementations have been used to provide speedups on the order of 100% to the solution of heat transfer equations on a uniprocessor. 2. An Introduction to MOA This section presents a brief introduction to the main operators used in a Mathematics of Arrays. The complete reference for MOA can be found in [1]. ..