Karatsuba Matrix Multiplication and Its Efficient Custom Hardware Implementations

IF 3.6 2区 计算机科学 Q2 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE
Trevor E. Pogue;Nicola Nicolici
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引用次数: 0

Abstract

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.
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来源期刊
IEEE Transactions on Computers
IEEE Transactions on Computers 工程技术-工程:电子与电气
CiteScore
6.60
自引率
5.40%
发文量
199
审稿时长
6.0 months
期刊介绍: The IEEE Transactions on Computers is a monthly publication with a wide distribution to researchers, developers, technical managers, and educators in the computer field. It publishes papers on research in areas of current interest to the readers. These areas include, but are not limited to, the following: a) computer organizations and architectures; b) operating systems, software systems, and communication protocols; c) real-time systems and embedded systems; d) digital devices, computer components, and interconnection networks; e) specification, design, prototyping, and testing methods and tools; f) performance, fault tolerance, reliability, security, and testability; g) case studies and experimental and theoretical evaluations; and h) new and important applications and trends.
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