Optimal Synthesis of Algorithm - Speci c Lower -

Processor arrays are frequently used to deliver high performance in many applications with computationally intensive operations. This paper presents the General Parameter Method (GP-M), a systematic parameter-based approach for synthesizing such algorithm-speciic architec-tures. GPM can synthesize processor arrays of any lower dimension from a uniform-recurrence description of the algorithm. The design objective is a general non-linear and non-monotonic user-speciied function, and depends on attributes such as computation time of the recurrence on the processor array, completion time, load time, and drain time. In addition, bounds on some or all of these attributes can be speciied. GPM performs an eecient search of polynomial complexity to nd the optimal design satisfying the user-speciied design constraints. As an illustration, we show how GPM can be used to nd optimal linear processor arrays for computing transitive closures. We consider design objectives that minimize computation time, or processor count, or completion time (including load and drain times), and user-speciied constraints on number of processing elements and/or computation/completion times. We show that GPM can be used to obtain optimal designs that trade between number of processing elements and completion time, thereby allowing the designer to choose a design that best meets the speciied design objectives. We also show the equivalence between the model assumed in GPM and that in the popular dependence-based methods 1, 2]. Consequently, GPM can be used to nd optimal designs for both models.