High-Radix Generalized Hyperbolic CORDIC and Its Hardware Implementation

• Published in: IEEE transactions on computers Vol. 74; no. 3; pp. 983 - 995
• Main Authors: Chen, Hui, Quan, Lianghua, Chen, Ke, Liu, Weiqiang
• Format: Journal Article
• Language: English
• Published: IEEE 01.03.2025
• Subjects: Accuracy; Computer architecture; Computers; Convergence; exponential; generalized; Hardware; hardware implementation; High-radix; hyperbolic CORDIC; logarithmic; Mathematical models; Real-time systems; Software; Software algorithms; Vectors
• ISSN: 0018-9340; 1557-9956
• DOI: 10.1109/TC.2024.3512183

In this paper, we propose a high-radix generalized hyperbolic coordinate rotation digital computer (HGH-CORDIC). This algorithm not only computes logarithmic and exponential functions with any fixed base but also significantly reduces the number of iterations required compared to traditional CORDIC methods. Initially, we present the general iteration formulas for HGH-CORDIC. Subsequently, we discuss its pivotal convergence properties and selection criteria, exemplifying these with commonly used cases. Through extensive software simulations, we validate the theoretical foundations of our approach. Finally, we explore efficient hardware implementation strategies. Our analysis indicates that, relative to state-of-the-art radix-2 GH-CORDIC, the proposed HGH-CORDIC can decrease the number of iterations by more than <inline-formula><tex-math notation="LaTeX">50\%</tex-math> <mml:math><mml:mn>50</mml:mn><mml:mi mathvariant="normal">%</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq1-3512183.gif"/> </inline-formula> while maintaining comparable accuracy. Synthesized under the 28nm CMOS technology, the reports show that the reference circuit can save about <inline-formula><tex-math notation="LaTeX">40\%</tex-math> <mml:math><mml:mn>40</mml:mn><mml:mi mathvariant="normal">%</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq2-3512183.gif"/> </inline-formula> area and power consumption averagely for <inline-formula><tex-math notation="LaTeX">2^{x}</tex-math> <mml:math><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msup></mml:math><inline-graphic xlink:href="chen-ieq3-3512183.gif"/> </inline-formula> and <inline-formula><tex-math notation="LaTeX">log_{2}x</tex-math> <mml:math><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>x</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq4-3512183.gif"/> </inline-formula> calculations compared with the latest CORDIC method.