Petri - Net Model for Loop

Most scientiic computations spend a signiicant part of their time in the execution of loops. As a result, compiler designers for high-performance computer architectures have been focusing their attention on the eeective and eecient exploitation of parallelism within loops. In this paper, we use dataaow graphs as our program representation for a class of loops, and we develop a timed Petri-net model to model these loops. The behavior graph of the Petri net is used to determine, at compile time, a repetitive execution pattern. Such a pattern, once detected, can be used to generate parallel instructions schedule during code generation. We show that, for an ideal model, after the earliest ring schedule is relaxed to satisfy an initial token-distribution constraint, the repetitive pattern of a loop can be detected in O(n 2) iterations. This improves considerably the polynomial bound reported earlier 17]. Furthermore, we show that our results apply to all nodes on or oo any critical cycles. We have examined the application of the behavior graph approach to a target pipelined architecture with multiple clean execution pipelines. A number of typical benchmarks (loops) in scientiic programs have been simulated, and we nd that the repetitive patterns can be reached very fast. This veriies the feasibility of employing the proposed method in a compiler.