Out of Core FFTs in a Parallel Application Environment

A principle mission at the NAS facility is to establish highly parallel computer systems supporting full scale production use by 1996. In order to fulfill this objective, parallel systems must support high speed scalable I/O -suitable for handling output of large scale numerical aerodynamic simulation. Pursuant to this goal, we seek to execute an 'out of core' radix 2 Fast Fourier Transform (FFT) as rapidly as possible. By 'out of core' we mean that the size of the problem to be solved is too large to fit in normal memory. We implement out of core methods on each of two computer architectures: the CM5 with a scalable disk array (SDA), and the Intel iPSC/860 with a Concurrent File System (CFS). In the case of the out of core FFT, the most successful I/O approach known is to apply an intermediate transpose of the data when viewed as a two dimensional matrix [2]. We implement and evaluate three I/O methods for performing the required transpose. The first method (row/col) transposes by exchanging rows and columns of the data set, the second (diagonal) exchanges diagonals, and the third (recursive) applies a recursive divide and conquer approach. Only the recursive method can be feasibly implemented on the CM5 SDA because it does not support 'independent access' -the ability for each processor to maintain an independent pointer to a given file on disk. We discover that in absolute terms, the CM5 SDA, using the recursive method, outperforms the iPSC/860 CFS using any of the three methods in solving out of core FFTs. However, the recursive method shows a rapid decline in performance with problem size. The iPSC/860 CFS, using the diagonal method or the row/col method scales well with problem size. We conclude that if the CM5 SDA had the independent access provided by the iPSC/860 CFS, then the CM5 SDA would scale as well as the iPSC/860 CFS, but at a much higher level of absolute performance.