IEEE Transactions on Software Engineering - Special issue on architecture-independent languages and software tools for parallel processing
Generation of Efficient Nested Loops from Polyhedra
International Journal of Parallel Programming - Special issue on instruction-level parallelism and parallelizing compilation, part 2
Translating Imperative Affine Nested Loop Programs into Process Networks
Embedded Processor Design Challenges: Systems, Architectures, Modeling, and Simulation - SAMOS
Translating imperative affine nested loop programs into process networks
Embedded processor design challenges
Static analysis of parameterized loop nests for energy efficient use of data caches
Compilers and operating systems for low power
Line Size Adaptivity Analysis of Parameterized Loop Nests for Direct Mapped Data Cache
IEEE Transactions on Computers
A geometric approach for partitioning n-dimensional non-rectangular iteration spaces
LCPC'04 Proceedings of the 17th international conference on Languages and Compilers for High Performance Computing
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In the area of automatic parallelization of programs, analyzing and transforming loop nests with parametric affine 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 geometry of numbers. In this paper, we present an automatic method for computing the number of integer points contained in a convex polytope or in a union of convex polytopes. The procedure consists of first, computing the parametric vertices of a polytope defined by a set of parametric linear constraints, and then computing the Ehrhart polynomial, i.e. a parametric expression of the number of integer points. The paper is illustrated with the computation of the maximum available parallelism of a given loop nest.