Fault Tolerant Systolic Evaluation of Polynomials and Exponentials of Polynomials for equispaced Arguments Using Time Redundancy

Abstract

Many applications which require high speed evaluation of polynomials and exponentials of polynomials can now be implemented in the hardware very efficiently because of the advances in VLSI technology. Several fast algorithms have been proposed in the recent past for the efficient evaluation of polynomials and exponentials of polynomials for equispaced arguments on uniprocessor systems. In this paper, we consider the problem of organizing this evaluation on VLSI chips in the form of systolic arrays. We present linear fault tolerant systolic arrays which can evaluate the polynomials and exponentials of polynomials of any degree for a large number of equispaced points. These organizations have the main advantage that the interconnections between the processing elements are very regular and simple, and hence are very appropriate for VLSI implementation.