<p>The Walsh–Hadamard transform (WHT) is widely applied in numerous scientific fields, including logic design, system analysis, and signal and image processing. In image processing, WHT is commonly used for image compression, pattern recognition, sequence filtering, etc. Consequently, optimizing algorithms for efficient WHT computation remains an important research area. Many WHT computation algorithms are based on the fast Fourier transform (FFT), particularly the Cooley–Tukey approach. Over time, these methods have been improved to accommodate different representations of logical functions and to take advantage of diverse hardware architectures. Recent advancements in GPU technology, specifically the introduction of tensor cores, offer new possibilities for accelerating WHT computations. Tensor cores provide specialized hardware support for matrix–matrix multiplication, significantly enhancing the efficiency of arithmetically intensive operations. This paper presents an optimized implementation of WHT on GPUs equipped with tensor cores by adapting both the Cooley–Tukey and constant geometry algorithms. Performance is evaluated against traditional implementations on single-core and multi-core CPUs, as well as standard CUDA-based GPU approaches. The experimental results demonstrate that both tensor-core-optimized WHT algorithms outperform all conventional implementations. Furthermore, the reduction in computation time achieved by the proposed algorithms grows exponentially with an increasing number of input variables. When comparing these two tensor-core-optimized algorithms, the results indicate that the constant geometry approach achieves shorter execution time.</p>

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Walsh–Hadamard spectra computation on GPU with tensor cores by Cooley–Tukey and constant geometry algorithms

  • Ivica Marković,
  • Suzana Stojković,
  • Tatjana Nikolić

摘要

The Walsh–Hadamard transform (WHT) is widely applied in numerous scientific fields, including logic design, system analysis, and signal and image processing. In image processing, WHT is commonly used for image compression, pattern recognition, sequence filtering, etc. Consequently, optimizing algorithms for efficient WHT computation remains an important research area. Many WHT computation algorithms are based on the fast Fourier transform (FFT), particularly the Cooley–Tukey approach. Over time, these methods have been improved to accommodate different representations of logical functions and to take advantage of diverse hardware architectures. Recent advancements in GPU technology, specifically the introduction of tensor cores, offer new possibilities for accelerating WHT computations. Tensor cores provide specialized hardware support for matrix–matrix multiplication, significantly enhancing the efficiency of arithmetically intensive operations. This paper presents an optimized implementation of WHT on GPUs equipped with tensor cores by adapting both the Cooley–Tukey and constant geometry algorithms. Performance is evaluated against traditional implementations on single-core and multi-core CPUs, as well as standard CUDA-based GPU approaches. The experimental results demonstrate that both tensor-core-optimized WHT algorithms outperform all conventional implementations. Furthermore, the reduction in computation time achieved by the proposed algorithms grows exponentially with an increasing number of input variables. When comparing these two tensor-core-optimized algorithms, the results indicate that the constant geometry approach achieves shorter execution time.