Towards Robustness in Residue Number Systems

Sign Detection in Residue Number Systems

Sign Determination in Residue Number Systems

Sign determination is a fundamental problem in algebraic as well as geometric computing. It is the critical operation when using real algebraic numbers and exact geometric predicates. We propose an exact and eecient method that determines the sign of a multivariate polynomial expression with rational coeecients. Exactness is achieved by using modular computation. Although this usually requires ...

Integer Division in Residue Number Systems

This contribution to the ongoing discussion of division algorithms for residue number systems (RNS) is based on Newton iteration for computing the reciprocal. An extended RNS with twice the number of moduli provides the range required for multiplication and scaling. Separation of the algorithm description from its RNS implementation achieves a high level of modularity, and makes the complexity ...

High Speed Convolution Using Residue Number Systems

This thesis investigates architectures for high speed signal convolution using residue number system techniques. The focus is on VLSI implementations, a choice that gives two parameters by which judge different architectures: speed and hardware size. Although the focus is on the standard residue number system, the same concepts can be directly applied to quadratic residue number system architec...

Towards Distributed Robustness in Embedded Systems

Recently, we witness a significant amount of effort being put into a research of robustness of complex computer systems. Computer scientists noticed that, despite decades of investigations into dependability, computer systems still lack the degree of resilience which can be seen in biological systems. In the biological context, one of the main aspects that stand behind a system’s robustness is ...