The Domain of Parametric Hypercubes for Static Analysis of Computer Games Software

Computer Games Software deeply relies on physics simulations, which are particularly demanding to analyze because they manipulate a large amount of interleaving oating point variables. Therefore, this application domain is an interesting workbench to stress the trade-o between accuracy and e ciency of abstract domains for static analysis. In this paper, we introduce Parametric Hypercubes, a novel disjunctive non-relational abstract domain. Its main features are: (i) it combines the low computational cost of operations on (selected) multidimensional intervals with the accuracy provided by lifting to a power-set disjunctive domain, (ii) the compact representation of its elements allows to limit the space complexity of the analysis, and (iii) the parametric nature of the domain provides a way to tune the accuracy/e ciency of the analysis by just setting the widths of the hypercubes sides. The rst experimental results on a representative Computer Games case study outline both the e ciency and the precision of the proposal.