Throughput-optimal systolic arrays from recurrence equations

Abstract: Many compute-bound software kernels have seen order-of-magnitude speedups on special-purpose accelerators built on specialized architectures such as field-programmable gate arrays (FPGAs). These architectures are particularly good at implementing dynamic programming algorithms that can be expressed as systems of recurrence equations, which in turn can be realized as systolic array designs. To efficiently find good realizations of an algorithm for a given hardware platform, we pursue software tools that can search the space of possible parallel array designs to optimize various design criteria. Most existing design tools in this area produce a design that is latency-space optimal. However, we instead wish to target applications that operate on a large collection of small inputs, e.g. a database of biological sequences. For such applications, overall throughput rather than latency per input is the most important measure of performance. In this work, we introduce a new procedure to optimize throughput of a systolic array subject to resource constraints, in this case the area and bandwidth constraints of an FPGA device. We show that the throughput of an array is dependent on the maximum number of lattice points executed by any processor in the array, which to a close approximation is determined solely by the array’s projection vector. We describe a bounded searc