Hardware Implementations of Fixed-Point Atan2

• Published in: Proceedings - Symposium on Computer Arithmetic pp. 34 - 41
• Main Authors: De Dinechin, Florent, Istoan, Matei
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.06.2015
• Subjects: Accuracy; Approximation methods; arctangent; atan2; Computer architecture; Context; Field programmable gate arrays; FPGA arithmetic; Hardware; Polynomials
• ISSN: 1063-6889
• DOI: 10.1109/ARITH.2015.23

The atan2 function computes the polar angle arctan(y/x) of a point given by its cartesian coordinates. It is widely used in digital signal processing to recover the phase of a signal. This article studies for this context the implementation of atan2 with fixed-point inputs and outputs. It compares the prevalent CORDIC shift-and-add algorithm to two multiplier-based techniques. The first one computes the bivariate atan2 function as the composition of two univariate functions: the reciprocal, and the arctangent, each evaluated using bipartite or polynomial approximation methods. The second technique directly uses piecewise bivariate polynomial approximations of degree 1 or 2. Each of these approaches requires a relevant argument reduction, which is also discussed. All the algorithms are last-bit accurate, and implemented with similar care in the open-source FloPoCo framework. Based on synthesis results on FPGAs, their relevance domains are discussed.