Acknowledgments We Thank

13 Tukey on zayante. The operating system may choose to run a ready thread on either processor, and so disk-server threads do not interfere with butterry computations as much as on zayante. Consequently, on adams it is always faster to use asynchronous I/O than to use synchronous I/O. 8 Conclusion We have examined both analytically and experimentally two classes of methods for computing large Fourier transforms. In-core FFT algorithms run slowly when they execute in a demand-paging environment. Of the three that we examined, Swarztrauber's method is by far the fastest and has the best locality of reference. The explicit out-of-core method that we developed for the PDM is asymptotically optimal in this model, and it has good empirical performance. On a DEC 2100 server with two processors, large memory, and eight data disks, our algorithm's normalized time is competitive with in-core methods, even when they run entirely in memory. Although it uses both processors, our current DEC 2100 implementation is essentially a unipro-cessor implementation. Our own breakdowns of running times on large problems show that computation time is a bottleneck. We plan to investigate true parallel out-of-core algorithms, using parallelized versions of the permutation methods described in this paper. for pointing us to applications of out-of-core FFTs, and also Dennis Healy and Eric Schwabe for their help in describing the mathematical structure of FFTs. Melissa Hirschl wrote the ViC* wrappers. David Kotz and Wayne Cripps advised us in sundry systems issues. The DEC 2100 server named adams was funded in part by an equipment allowance from Digital Equipment Corporation. References AV88] Alok Aggarwal and Jeerey Scott Vitter. The input/output complexity of sorting and related problems. 12 Problem Memory size (bytes) size 2 22 2 23 2 24 2 25 (points) sync async sync async sync async sync async 2 22 Table 2: Running times for the out-of-core algorithm on zayante with one disk, varying problem and memory sizes, and both synchronous and asynchronous I/O. Times are in seconds, and in italics are the normalized times (the running time divided by N lgN) in microseconds. Memory size (bytes) Problem size 2 26 2 27 (points) sync async sync async 2 23 Table 3: Running times for the out-of-core algorithm on adams with 8 disks, varying problem and memory sizes, and both synchronous and asynchronous I/O. Times are in seconds, and in italics are the normalized times (the running time divided …