Sign determination 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 ...

Sign Determination in Residue Number Systems Herv Br nnimann

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 predi cates We propose an exact and e cient method that determines the sign of a multivariate polynomial expression with rational coe cients Exactness is achieved by using modular computation Although this usually requires som...

Sign Detection in Residue Number Systems

New distributed algorithms for fast sign detection in residue number systems (RNS)

We identify a canonical parameter in the Chinese Remainder Theorem (CRT) and call it the ‘‘Reconstruction Coefficient’’, (denoted by ‘‘RC ’’); and introduce the notions of ‘‘Partial’’ and ‘‘Full’’ Reconstruction. If the RC can be determined efficiently, then arithmetic operations that are (relatively) harder to realize in RNS; including Sign Detection, Base change/extension and Scaling or divis...

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 ...