arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2501.08889cs.ARcs.AIcs.PF
收藏

Karatsuba矩阵乘法及其高效的定制硬件实现

Karatsuba Matrix Multiplication and its Efficient Custom Hardware Implementations

McMaster University(麦克马斯特大学)

Trevor E. Pogue, Nicola Nicolici

AI总结:

本研究将标量Karatsuba算法扩展至矩阵乘法以降低额外加法复杂度,提出适配的定制硬件架构,经复杂度分析与多场景验证,可提升矩阵乘法硬件的单位面积性能。

摘要:

尽管Karatsuba算法降低了大整数乘法的复杂度,但对于更常用位宽的较小整数而言,其所需的额外加法运算削弱了该算法的优势。本研究将标量Karatsuba乘法算法扩展至矩阵乘法领域,证明了该扩展既保留了原始Karatsuba算法降低乘法复杂度的特性,又能降低额外加法运算的复杂度。此外,我们提出了新型矩阵乘法硬件架构,用于在定制硬件中高效利用Karatsuba算法的这一扩展。研究表明,与标量Karatsuba算法或传统矩阵乘法算法相比,所提算法与硬件架构能切实提升整数矩阵乘法的面积效率或执行速度,同时其核心可通过成熟的脉动阵列(systolic array)和传统乘法器架构实现。我们对算法和架构进行了复杂度分析,并将所提设计分别在独立场景和端到端深度学习加速器系统中,与基线设计及在同类计算平台上实现的现有最优研究成果进行了对比评估,证明了它们能够提升矩阵乘法硬件的单位面积性能。

英文摘要:

While the Karatsuba algorithm reduces the complexity of large integer multiplication, the extra additions required minimize its benefits for smaller integers of more commonly-used bitwidths. In this work, we propose the extension of the scalar Karatsuba multiplication algorithm to matrix multiplication, showing how this maintains the reduction in multiplication complexity of the original Karatsuba algorithm while reducing the complexity of the extra additions. Furthermore, we propose new matrix multiplication hardware architectures for efficiently exploiting this extension of the Karatsuba algorithm in custom hardware. We show that the proposed algorithm and hardware architectures can provide real area or execution time improvements for integer matrix multiplication compared to scalar Karatsuba or conventional matrix multiplication algorithms, while also supporting implementation through proven systolic array and conventional multiplier architectures at the core. We provide a complexity analysis of the algorithm and architectures and evaluate the proposed designs both in isolation and in an end-to-end deep learning accelerator system compared to baseline designs and prior state-of-the-art works implemented on the same type of compute platform, demonstrating their ability to increase the performance-per-area of matrix multiplication hardware.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑