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Journal Articles Journal of Signal Processing Systems Year : 1998

Parametric Analysis of Polyhedral Iteration Spaces


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 automatic methods for computing the parametric vertices and the Ehrhart polynomial, i.e., a parametric expression of the number of integer points, of a polytope defined by a set of parametric linear constraints. These methods have many applications in analysis and transformations of nested loop programs. The paper is illustrated with exact symbolic array dataflow analysis, estimation of execution time, and with the computation of the maximum available parallelism of given loop nests.

Dates and versions

inria-00534840 , version 1 (10-11-2010)



Philippe Clauss, Vincent Loechner. Parametric Analysis of Polyhedral Iteration Spaces. Journal of Signal Processing Systems, 1998, 19 (2), pp.179-194. ⟨10.1023/A:1008069920230⟩. ⟨inria-00534840⟩


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