Optimal Synthesis of Processor Arrays withPipelined Arithmetic

Two-level pipelining in processor arrays (PAs) involves pipelining of operations across processing elements (PEs) and pipelining of operations in functional units in each PE. Although it is an attractive method for improving the throughput of PAs, existing methods for generating PAs with two-level pipelining are restricted and cannot systematically explore the entire space of feasible designs. In this paper, we extend a systematic design method, called General Parameter Method (GPM), we have developed earlier to nd optimal designs of PAs with two-level pipelines. The basic idea is to add new constraints on periods of data ows to include the eeect of internal functional pipelines in the PEs. As an illustration, we present pipelined PA designs for computing matrix products. For n-dimensional meshes and other symmetric problems, we provide an eecient scheme to obtain a pipelined PA from a non-pipelined PA using a reindexing transformation. This scheme is used in GPM as a pruning condition to arrive at optimal pipelined PAs eeciently. For pipelines with minimum initiation interval (MII) greater than unity, we show additional constraints that ensure correctness of the synthesized PAs.