A New Acceleration Paradigm for Discrete CosineTransform and Other Fourier-Related Transforms

Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel computing systems. Public MD DCT implementations leverage a straightforward method that decomposes the computation into multiple 1D DCTs along every single dimension, which inevitably has non-optimal performance due to low computational efficiency, parallelism, and locality. In this paper, we propose a new acceleration paradigm for MD DCT. A three-stage procedure is proposed to factorize MD DCT into MD FFT and highly-optimized preprocessing/postprocessing with efficient computation and high arithmetic intensity. Our paradigm can be easily extended to other Fourier-related transforms and other parallel computing systems. Experimental results show that our 2D DCT/IDCT CUDA implementation has a stable, FFT-comparable execution time, which is $2\times$ faster than the previous row-column method. Several case studies demonstrate that a promising efficiency improvement can be achieved with our paradigm. The implementations are available at https://github.com/JeremieMelo/dct_cuda/tree/reconstruct.