Computing the exact sign of sums of products with floating point arithmetic (2109.07838v2)

Abstract: IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed for the exact solution of linear programming problems and systems of linear inequalities. Computing these signs exactly with inexact floating point arithmetic is challenging, and we present yet another algorithm for this task. Our algorithm is efficient and uses only of floating point arithmetic, which is much faster than exact arithmetic. We prove that the algorithm is correct and provide efficient and tested \texttt{C++} code for it.