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 some multiprecision computation our novel techniques of recursive relaxation of the moduli and their variants enable us to carry out sign determination and comparisons by using only single precision Moreover to exploit modern day hardware we exclusively rely on oating point arithmetic which leads us to a hybrid symbolic numeric approach to exact arithmetic We show how our method can be used to generate robust and e cient implementations of real algebraic and geometric algo rithms including Sturm sequences algebraic representation of points and curves convex hull and Voronoi diagram computations and solid modeling This method is highly paralleliz able easy to implement and compares favorably with known multiprecision methods from a practical complexity point of view We substantiate these claims by experimental results and comparisons to other existing approaches