In the area of automatic parallelization of programs, analyzing and transforming loop nests with parametric aane loop bounds requires fundamental mathematical results. The most common geometrical model of iteration spaces, called the polytope model, is based on mathematics dealing with convex and discrete geometry, linear programming, combinatorics and… (More)
Algorithms speciied for parametrically sized problems are more general purpose and more reusable than algorithms for xed sized problems. For this reason, there is a need for representing and symbolically analyzing linearly parameterized algorithms. An important class of parallel algorithms can be described as systems of parameterized aane recurrence… (More)
Many compiler optimization techniques depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes. It is well known that the enumerator of such a set can be… (More)
A significant source for enhancing application performance and for reducing power consumption in embedded processor applications is to improve the usage of the memory hierarchy. In this paper, a temporal and spatial locality optimization framework of nested loops is proposed, driven by parameterized cost functions. The considered loops can be imperfectly… (More)
Many optimization techniques, including several targeted specifically at embedded systems, depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes. It… (More)
This paper deals with communication optimization which is a crucial issue in automatic parallelization. From a system of parameter-ized aane recurrence equations, we propose a heuristic which determines an eecient space-time transformation. It reduces rst the distant communications and then the local communications.
Optimizing parallel compilers need to be able to analyze nested loop programs with para-metric aane loop bounds, in order to derive eecient parallel programs. The iteration spaces of nested loop programs can be modeled by polyhedra and systems of linear constraints. Using this model, important program analyses such as computing the number of ops executed by… (More)
This paper presents the mathematical notions for the parallelization of DO-Loops used in the tool OPERA currently under development in our team. It aims at giving the user an environment to parallelize problems described by systems of parameterized aane recurrence equations which formalize single-assignment loop nests. The parallelization technique used in… (More)