FFTs in external or hierarchical memory
The Journal of Supercomputing
Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
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Proceedings of the 19th ACM SIGPLAN symposium on Principles and practice of parallel programming
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We present novel algorithms for computing discrete Fourier transforms with high performance on GPUs. We present hierarchical, mixed radix FFT algorithms for both power-of-two and non-power-of-two sizes. Our hierarchical FFT algorithms efficiently exploit shared memory on GPUs using a Stockham formulation. We reduce the memory transpose overheads in hierarchical algorithms by combining the transposes into a block-based multi-FFT algorithm. For non-power-of-two sizes, we use a combination of mixed radix FFTs of small primes and Bluestein's algorithm. We use modular arithmetic in Bluestein's algorithm to improve the accuracy. We implemented our algorithms using the NVIDIA CUDA API and compared their performance with NVIDIA's CUFFT library and an optimized CPU-implementation (Intel's MKL) on a high-end quad-core CPU. On an NVIDIA GPU, we obtained performance of up to 300 GFlops, with typical performance improvements of 2--4x over CUFFT and 8--40x improvement over MKL for large sizes.