Performance Analysis of the FFT Algorithm on a Shared-Memory Parallel Architecture

This paper presents a model for the performance prediction of FFT algorithms executed on a shared-memory parallel computer consisting of N processors an the same number of memory modules. The model applies a deterministic analysis to estimate the communication delay through the interconnection network by assuming that all requests arrive at the network in bursts. Our results indicate that the communication delay is significantly affected by the method applied to allocate data to memory modules. For the case in which all data items referenced by a processor during an iteration are allocated to a single memory module, the best-case communication time complexity grows as O[(log N) 2 /N]. The worst-case communication time complexity for this case, obtained by a different allocation of data to memory modules, is increased to O[(log N)/√N] due to high network contention. For the case in which the data items referenced by different processors during an iteration are allocated to the same memory module, the communication time complexity is further increased to O(log N) since all N requests generated by processors are serialized at a single memory module. The methods developed in this paper can be applied for the performance prediction of other well-structured parallel iterative algorithms.