Fixed-Point Error Analysis of CORDIC Arithmetic for Special-Purpose Signal Processors

Tze-Yun SUNG  Hsi-Chin HSIN  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.9   pp.2006-2013
Publication Date: 2007/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.9.2006
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
Keyword: 
CORDIC,  digital signal processing system,  convergence range,  approximation error,  truncation error,  

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Summary: 
CORDIC (COordinate Rotation DIgital Computer) is a well known algorithm using simple adders and shifters to evaluate various elementary functions. Thus, CORDIC is suitable for the design of high performance chips using VLSI technology. In this paper, a complete analysis of the computation error of both the (conventional) CORDIC algorithm and the CORDIC algorithm with expanded convergence range is derived to facilitate the design task. The resulting formulas regarding the relative and absolute approximation errors and the truncation error are summarized in the tabular form. As the numerical accuracy of CORDIC processors is determined by the word length of operands and the number of iterations, three reference tables are constructed for the optimal choice of these numbers. These tables can be used to facilitate the design of cost-effective CORDIC processors in terms of areas and performances. In addition, two design examples: singular value decomposition (SVD) and lattice filter for digital signal processing systems are given to demonstrate the goal and benefit of the derived numerical analysis of CORDIC.