3D FFTs on a Single FPGA

The 3D FFT is critical in many physical simulations and image processing applications. On FPGAs, however, the 3D FFT was thought to be inefficient relative to other methods such as convolution-based implementations of multi-grid. We find the opposite: a simple design, operating at a conservative frequency, takes 4μs for 16³, 21μs for 32³, and 215μs for 64³ single precision data points. The first two of these compare favorably with the 25μs and 29μs obtained running on a current Nvidia GPU. Some broader significance is that this is a critical piece in implementing a large scale FPGA-based MD engine: even a single FPGA is capable of keeping the FFT off of the critical path for a large fraction of possible MD simulations.