Periodic Polyhedra

This paper presents a new method for computing the integer hull of a parameterized rational polyhedron by introducing the concept of periodic polyhedron. Besides concerning generally parametric combinatorial optimization, the method has many applications for the analysis, optimization and parallelization of loop nests, especially in compilers. 1 Motivation For many years, compiler writers have focused on parameterized loop nests, mainly because of their importance in scientific and multimedia programs. The polytope model [2] allows to manipulate loop nests whose bounds are affine functions with integer-valued parameters in the constant part by modeling them as parameterized rational polytopes P. As the considered loop indices are incremented by a constant integer value, the values taken by the n-vector of indices belong to a subset of Zn : an integer lattice L. So the values taken by the index vector I ∈ Zn , where n defines the number of nested loops, are given by the so-called Z-...

• Type: Conference
• Year: 2004
• Where: CC
• Authors: Benoît Meister
• Keywords: CC 2004, Loop Nests, Parameterized Loop Nests, Parameterized Rational Polyhedron, Programming Languages