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FFTs with Near-Optimal Memory Access Through Block Data Layouts: Algorithm, Architecture and Design Automation

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Abstract

Fast Fourier transform algorithms on large data sets achieve poor performance on various platforms because of the inefficient strided memory access patterns. These inefficient access patterns need to be reshaped to achieve high performance implementations. In this paper we formally restructure 1D, 2D and 3D FFTs targeting a generic machine model with a two-level memory hierarchy requiring block data transfers, and derive memory access pattern efficient algorithms using custom block data layouts. These algorithms need to be carefully mapped to the targeted platform’s architecture, particularly the memory subsystem, to fully utilize performance and energy efficiency potentials. Using the Kronecker product formalism, we integrate our optimizations into Spiral framework and evaluate a family of DRAM-optimized FFT algorithms and their hardware implementation design space via automated techniques. In our evaluations, we demonstrate DRAM-optimized accelerator designs over a large tradeoff space given various problem (single/double precision 1D, 2D and 3D FFTs) and hardware platform (off-chip DRAM, 3D-stacked DRAM, ASIC, FPGA, etc.) parameters. We show that Spiral generated pareto optimal designs can achieve close to theoretical peak performance of the targeted platform offering 6x and 6.5x system performance and power efficiency improvements respectively over conventional row-column FFT algorithms.

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Notes

  1. Calculated as 5n log2(n)/t for DFT n where t is the total runtime.

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Acknowledgments

The work was sponsored by Defense Advanced Research Projects Agency (DARPA) under agreement no. HR0011-13-2-0007. The content, views and conclusions presented in this document do not necessarily reflect the position or the policy of DARPA or the U.S. Government. No official endorsement should be inferred.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA

    Berkin Akin, Franz Franchetti & James C. Hoe

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  1. Berkin Akin
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  2. Franz Franchetti
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  3. James C. Hoe
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Correspondence to Berkin Akin.

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Akin, B., Franchetti, F. & Hoe, J.C. FFTs with Near-Optimal Memory Access Through Block Data Layouts: Algorithm, Architecture and Design Automation. J Sign Process Syst 85, 67–82 (2016). https://doi.org/10.1007/s11265-015-1018-0

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  • DOI: https://doi.org/10.1007/s11265-015-1018-0

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