Deferring Dag Construction by Storing Sums of Floats Speeds-Up Exact Decision Computations Based on Expression Dags

Abstract

Expression-dag-based number-types are a very general and user-friendly way to achieve exact geometric computation, a widely accepted approach to the reliable implementation of geometric algorithms. Such number-types record the computation history of a numerical value in an expression dag in order to allow for recomputing the value or an approximation of it at a later stage. We describe how to defer dag construction by using error-free transformations into sums of floating-point numbers. We store a limited number of summands in statically allocated memory in order to postpone or avoid dag creation which involves expensive dynamic memory allocations. Furthermore we report on experiments where we compare different implementation strategies of our new approach. The experiments show that for small polynomial expressions typically arising in geometric applications our approach is superior to existing expression-dag-based number-types in the presence of degenerate and nearly degenerate configurations and competitive otherwise.