Exact memory size estimation for array computations

This paper presents a new algorithm for exact estimation of the minimum memory size required by programs dealing with array computations. Based on parametric partitioning of the iteration space and formalized live variable analysis, our algorithm transforms the minimum memory size estimation into an equivalent problem: integer point counting for intersection/union of mappings of parameterized polytopes. A heuristics was then proposed to solve the counting problem. Experimental results show that the algorithm achieves the exactness traditionally associated with totally unrolling loops while exploiting reduced computation complexity by preserving the original loop structure.