An E cient Allocation Strategy for MappingA ne Recurrences into

This paper adresses the problem of eecient mappings of nested loops, and more generally of systems of aane recurrence equations, into regular arrays. The presented technique is based on the transformation of an initial systolic mapping. By studying the processor element (PE) activity, a nearly space-optimal mapping is designed by serializing the computations of several initial PEs into a single one. A new approach of this technique is presented. It allows to map into regular arrays which may be nonplanar. Moreover, the solutions can be linearly time-optimal since this technique does not aaect the initial schedule. The methodology is illustrated by the LL T Cholesky factorization.