Literature Review: Progression of the Use of High-Performance Computing for Fast Fourier Transforms from 2005-2025

This paper covers two decades of FFT optimization across HPC hardware, including CPU cache autotuning, GPU shared-memory optimization, distributed multi-node scaling, Tensor Core reformulations, and mixed-precision communication compression. Key findings include that GPU acceleration shifts the FFT bottleneck from an arithmetic/computational issue to interconnect latency being dominant cost (97% of runtime on Summit). Additionally, slab decomposition was revived as the correct choice for dense GPU systems after a decade of pencil-decomposition dominance, and that numerical precision has evolved from a single compile-time setting to independently tunable parameters at the compute, communication, and accumulation layers.