A geometrical coding to compile affine recurrence equations on regular arrays

The paper is devoted to the problem of mapping algorithms onto regular and synchronous processor arrays. The authors consider problems which are defined by Systems of Affine Recurrence Equations. From such statements, a geometrical coding is proposed to express the data dependencies in terms of two classes of vectors: the generating vectors and the inductive vectors. These vectors are used to implement constraints on the timing or the allocation functions. The authors differentiate two classes of constraints: the causal ones induced by the system of equations and the architecture-related ones. These constraints are taken into account to compile affine timing functions and allocations by projection. The authors illustrate these tools with the examples of the Gaussian elimination and the recursive convolution