Proceedings Article10.1145/1176760.1176771
Memory optimization by counting points in integer transformations of parametric polytopes
Rachid Seghir,Vincent Loechner +1 more
- 22 Oct 2006
- pp 74-82
TL;DR: A novel algorithm is proposed to solve the Presburger formula whose solution is a union of parametric Z-polytopes and an algorithm to count points in such a union is proposed, which is compared to other existing methods.
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Abstract: Memory size reduction and memory accesses optimization are crucial issues for embedded systems. In the context of affine programs, these two challenges are classically tackled by array linearization, cache access optimization and memory size computation. Their formalization in the polyhedral model reduce to solving the following problem: count the number of solutions of a Presburger formula.In this paper we propose a novel algorithm that answers this question. We solve the Presburger formula whose solution is a union of parametric Z-polytopes and we propose an algorithm to count points in such a union of parametric Z-polytopes. These algorithms were implemented and we compare them to other existing methods.
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