Comparison of 2-D FFT implementations on the Intel Paragon massively parallel supercomputer

We discuss the parallel implementation of multidimensional FFTs on distributed memory multiprocessor machines. We introduce a compact notation to describe four equivalent parallel algorithms and discuss their advantages and disadvantages. Two algorithms, suitable for the case when initial and final data are distributed either row- or column-wise, the traditional row-column (RC) and a variation of the vector radix (VR) that we call partial vector radix (PVR) are presented and their efficiency on the Paragon is compared. It is shown that the PVR, although it requires larger amount of interprocessor communication, results in more efficient implementations due to the regularity of local and distributed memory accesses. For the case in which data are partitioned along both dimensions, two suitable parallel algorithms, the collect-distribute (CD) and the general full vector-radix (FVR), are presented. Again, it is shown that regularity in memory accesses for the case of the FVR, results in more efficient implementations