Designing a scalable processor array for recurrent computations

In this paper, we study the design of a coprocessor (CoP) to execute efficiently recursive algorithms with uniform dependencies. Our design is based on two objectives: 1) fixed bandwidth to main memory (MM) and 2) scalability to higher performance without increasing MM bandwidth. Our CoP has an access unit (AU) organized as multiple queues, a processor array (PA) with regularly connected processing elements (PEs), and input/output networks for data routing. Our design is unique because it addresses input/output bottleneck and scalability, two of the most important issues in integrating processor arrays in current systems. To allow processor arrays to be widely usable, they must be scalable to high performance with little or no impact on the supporting memory system. The use of multiple queues in AU also eliminates the use of explicit data addresses, thereby simplifying the design of the control program. We present a mapping algorithm that partitions a data dependence graph (DG) of an application into regular blocks, sequences the blocks through AU, and schedules the execution of the blocks, one at a time, on PA. We show that our mapping procedure minimizes the amount of communication between blocks in the partitioned DG, and sequences the blocks through AU to reduce the communication between AU and MM. Using the matrix-product and transitive-closure applications, we study design trade-offs involving 1) division of a fixed chip area between PA and AU, and 2) improvements in speedup with respect to increases in chip area. Our results show, for a fixed chip area, 1) that there is little degradation in throughput in using a linear PA as compared to a PA organized as a square mesh, and 2) that the design is not sensitive to the division of chip area between PA and AU. We further show that, for a fixed throughput, there is an inverse square root relationship between speedup and total chip area. Our study demonstrates the feasibility of a low-cost, memory bandwidth-limited, and scalable coprocessor system for evaluating recurrent algorithms with uniform dependencies