Hardware implementations of fixed-point Atan2

Florent De Dinechin 1 Matei Istoan 1
1 SOCRATE - Software and Cognitive radio for telecommunications
Inria Grenoble - Rhône-Alpes, CITI - CITI Centre of Innovation in Telecommunications and Integration of services
Abstract : —The atan2 function computes the polar angle arctan(x/y) 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 reduces the bivariate atan2 function to two functions of one variable: the reciprocal, and the arctangent. These two functions may be tabulated, or evaluated using bipartite or polynomial approximation methods. The second technique directly uses piecewise bivariate polynomial approximations, in degree 1 and degree 2. It requires larger tables but has the shortest latency. Each of these approaches requires a relevant argument reduction, which is also discussed. All the algorithms are described with the same accuracy target (faithful rounding) and implemented with similar care in an open-source library. Based on synthesis results on FPGAs, their relevance domains are discussed.
Type de document :
Communication dans un congrès
22nd IEEE Symposium on Computer Arithmetic, Jun 2015, Lyon, France. 2015
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Contributeur : Matei Istoan <>
Soumis le : jeudi 4 décembre 2014 - 16:51:40
Dernière modification le : samedi 27 octobre 2018 - 01:19:59
Document(s) archivé(s) le : lundi 9 mars 2015 - 05:59:46


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  • HAL Id : hal-01091138, version 1



Florent De Dinechin, Matei Istoan. Hardware implementations of fixed-point Atan2. 22nd IEEE Symposium on Computer Arithmetic, Jun 2015, Lyon, France. 2015. 〈hal-01091138〉



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