Hardware implementations of fixed-point Atan2 - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2015

Hardware implementations of fixed-point Atan2

Résumé

—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.
Fichier principal
Vignette du fichier
FixAtan2.pdf (322.69 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01091138 , version 1 (04-12-2014)

Licence

Identifiants

  • HAL Id : hal-01091138 , version 1

Citer

Florent de Dinechin, Matei Istoan. Hardware implementations of fixed-point Atan2. 22nd IEEE Symposium on Computer Arithmetic, Jun 2015, Lyon, France. ⟨hal-01091138⟩
317 Consultations
6485 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More