Accelerating Fourier and Number Theoretic Transforms using Tensor Cores and Warp Shuffles

The discrete Fourier transform (DFT) and its specialized case, the number theoretic transform (NTT), are two important mathematical tools having applications in several areas of science and engineering. However, despite their usefulness and utility, their adoption continues to be a challenge as comp...

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Veröffentlicht in:2021 30th International Conference on Parallel Architectures and Compilation Techniques (PACT) S. 345 - 355
Hauptverfasser: Durrani, Sultan, Chughtai, Muhammad Saad, Hidayetoglu, Mert, Tahir, Rashid, Dakkak, Abdul, Rauchwerger, Lawrence, Zaffar, Fareed, Hwu, Wen-mei
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 01.09.2021
Schlagworte:
cyphertext
DFT
Discrete Fourier transforms
FFT
GPU
Graphics processing units
homomorphic encryption
Instruction sets
NTT
Parallel architectures
Tensor Cores
Tensors
Transforms
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Zusammenfassung:The discrete Fourier transform (DFT) and its specialized case, the number theoretic transform (NTT), are two important mathematical tools having applications in several areas of science and engineering. However, despite their usefulness and utility, their adoption continues to be a challenge as computing the DFT of a signal can be a time-consuming and expensive operation. To speed things up, fast Fourier transform (FFT) algorithms, which are reduced-complexity formulations for computing the DFT of a sequence, have been proposed and implemented for traditional processors and their corresponding instruction sets. With the rise of GPUs, NVIDIA introduced its own FFT computation library called cuFFT, which leverages the power of GPUs to compute the DFT. However, as this paper demonstrates, there is a lot of room for improvement to accelerate the FFT and NTT algorithms on modern GPUs by utilizing specialized operations and architectural advancements. In particular, we present four major types of optimizations that leverage tensor cores and the warp-shuffle instruction. Through extensive evaluations, we show that our approach consistently outperforms existing GPU-based implementations with a speedup of up to 4× for NTT and a speed of up to 1.5× for FFT.
DOI:10.1109/PACT52795.2021.00032