A radix-2 FFT on connection machine

We describe a radix-2 FFT implementation on the Connection Machine. The FFT implementation pipelines successive FFT stages to make full use of the communication capability of the network interconnecting processors, when there are multiple elements assigned to each processor. Of particular interest in distributed memory architectures such as the Connection Machine is the allocation of twiddle factors to processors. We show that with a consecutive data allocation scheme and normal order input a decimation-in-time FFT results in a factor of log2N less storage for twiddle factors than a decimation-in-frequency FFT for N processors. Similarly, with consecutive storage and bit-reversed input a decimation-in-frequency FFT requires a factor of log2N less storage than a decimation-in-time FFT. The performance of the local FFT has a peak of about 3 Gflops/s. The “global” FFT has a peak performance of about 1.7 Gflops/s.