RCU- 2 m : A VLSI Radix- 2 m Cubic Unit
Eduardo Costa, Morgana Macedo Azevedo da Rosa · IEEE Transactions on Very Large Scale Integration (VLSI) Systems · 2024
Cubic operations are among the most used arithmetic operations in many applications that demand higher order simultaneous operand computation, such as cryptography and bicubic polynomial interpolation. This article proposes a novel VLSI radix-$2^{m}$cubic unit (RCU-$2^{m}$) capable of processing cubic operations at m bits simultaneously, with m values of 2 (RCU-4), 3 (RCU-8), and 4 (RCU-16). RCU-16 emerges as the most area-efficient configuration, surpassing RCU-8 and notably outperforming RCU-4. In the 8-bit scenario, RCU-16 achieves remarkable area savings, surpassing the literature’s proposed cubic unit by$11.58\times $. Across all configurations, RCU-$2^{m}$consistently outperforms the automatically selected cube unit, with energy savings ranging from$1.04\times $to$2\times $. In application specific integrated circuit (ASIC) and field-programmable gate array (FPGA)-based analyses, RCU-16 consistently exhibits superior performance in both area and energy savings compared with RCU-4, RCU-8, and solutions from the literature. These findings emphasize the importance of adopting radix-$2^{m}$configurations, particularly RCU-16, for optimal energy-constrained VLSI applications.