Using Harmonized Parabolic Synthesis to Implement Sine and Cosine Functions

Unary function in integrated circuits (ICs) is the fundamental of mathematical calculations and complex algorithmic processing. However, the primary problem is the trade-off among accuracy, handling capacity, cost, and power consumption. The harmonized parabolic synthesis is a novel algorithm that has merits in many ways compared with the conventional approximation measures. It reduces computational complexity by introducing parallelism and has better hardware implementation efficiency. Despite this, parabolic synthesis approximation still remains immature and requires further optimization of functional constructions, circuit designs and practical verifications. This paper focuses on the implementation of sine and cosine functions by using harmonized parabolic synthesis. The major research contents of this paper consist of elucidation of principle analysis, the development of sub-functions and the algorithm implementation process. The comparison analysis of the efficacy of Polynomial Approximation, CORDIC, etc. and the parabolic synthesis have been discussed, and the advantages of calculation precision and computational efficiency are verified. This paper shows that using the harmonized parabolic synthesis methodology can yield performance improvement in both convergence and precision.