Design of 3D FFTs with FPGA clusters

Abstract

The three dimensional Fast Fourier Transform (3D FFT) is widely applied in various scientific applications. Distributed 3D FFTs require global communication: this becomes a serious concern when strong scaling is required as in long timescale molecular dynamics simulations. In this paper, we propose a parameterized 3D FFT design that targets at a 3D-torus FPGA-based network of various sizes. Characteristics include direct FPGA-FPGA communication links, support for various internal switch designs, and use of table-based routing which saves chip area and routing cycles. We find that even assuming extremely conservative parameters, we are able to run the 16 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> FFT in 3.9μs, 32 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> FFT in 5.46μs, 64 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> FFT in 9.52μs, and 128 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> FFT in 25.72μs. These results indicate that clusters based on commodity FPGAs are likely to be appropriate when strong scaling is needed in applications limited by the 3D FFT.