Modified Parabolic Synthesis for Hardware-Oriented Approximation of Unary Functions

The approximation of unary functions such as sine and arctangent is an essential part of many digital signal processing applications, often requiring significant computational power and resources. Traditionally, trigonometric functions are computed using software approximations or dedicated hardware accelerators like CORDIC. This paper presents a novel methodology to efficiently compute unary functions in VLSI designs, based on parabolic synthesis by E. Hertz et al. In contrast to traditional parabolic synthesis, all parabolic sub-functions are combined using adders instead of costly multipliers. A corresponding hardware architecture is developed, demonstrating its effectiveness. Taking the sine function as a reference, approximation accuracy is characterized over a wide range of configurations and compared with alternative approaches. Finally, area and critical path is evaluated using the Skywater 130 nm technology node, demonstrating its strength against traditional parabolic synthesis and CORDIC. The results show significant improvements in both critical path and area across the full range of configurations, achieving more than 2× reduction in area while simultaneously doubling frequency compared to traditional parabolic synthesis having similar approximation accuracy.