Serialising Heterogeneous and Non-Factorisable Processor Arrays

This paper presents two classes of transformations for serialising an array of processors. The first serialises a heterogeneous array of size mk to one of size m . The second serialises an array from n to m components where m does not need to be a factor of n . Our transformations are expressed in the Ruby language, which provides a concise notation for capturing the serialised array and the boundary conditions; in particular many design constraints can be represented in the form of conjugate ( Q -1 ; R ; Q ) or transposed conjugate ([ Q ; P ] -1 ; R ; [ P ; Q ]) expressions. Design trade-offs in performance and resource requirements of various serialisation schemes are discussed.We illustrate our approach using several arithmetic and recursive filter designs, and their implementation using programmable hardware is outlined.