An Implementation of Parallel 1-D FFT on the K Computer

In this paper, we propose an implementation of a parallel one-dimensional fast Fourier transform (FFT) on the K computer. The proposed algorithm is based on the six-step FFT algorithm, which can be altered into the recursive six-step FFT algorithm to reduce the number of cache misses. The recursive six-step FFT algorithm improves performance by utilizing the cache memory effectively. We use the recursive six-step FFT algorithm to implement the parallel one-dimensional FFT algorithm. The performance results of one-dimensional FFTs on the K computer are reported. We successfully achieved a performance of over 18 TFlops on 8192 nodes of the K computer (82944 nodes, 128 GFlops/node, 10.6 PFlops peak performance) for a 2⁴¹-point FFT.