New Fast Arctangent Approximation Algorithm for Generic Real-Time Embedded Applications - Benammar, Mohieddine; Alassi, Abdulrahman; Gastli, Adel; Ben-Brahim, Lazhar; Touati, Farid (Sensors (Basel, Switzerland), 2019)
Fast and accurate arctangent approximations are used in several contemporary applications, including embedded systems, signal processing, radar, and power systems. Three main approximation techniques are well-established in the literature, varying in their accuracy and resource utilization levels. Those are the iterative coordinate rotational digital computer (CORDIC), the lookup tables (LUTs)-based, and the rational formulae techniques. This paper presents a novel technique that combines the advantages of both rational formulae and LUT approximation methods. The new algorithm exploits the pseudo-linear region around the tangent function zero point to estimate a reduced input arctangent through a modified rational approximation before referring this estimate to its original value using miniature LUTs. A new 2nd order rational approximation formula is introduced for the first time in this work and benchmarked against existing alternatives as it improves the new algorithm performance. The eZDSP-F28335 platform has been used for practical implementation and results validation of the proposed technique. The contributions of this work are summarized as follows: (1) introducing a new approximation algorithm with high precision and application-based flexibility; (2) introducing a new rational approximation formula that outperforms literature alternatives with the algorithm at higher accuracy requirement; and (3) presenting a practical evaluation index for rational approximations in the literature.