Very-High Radix CORDIC Rotation Based on Selection by Rounding

Authors:
Elisardo Antelo;Tomás Lang;Javier D. Bruguera
Affiliations:
Department Electrónica y Computación, University of Santiago de Compostela, 15706-Santiago de Compostela, Spain;Department Electrical and Computer Eng., 408 Engineering Tower, University of California at Irvine, Irvine, CA 92697, USA;Department Electrónica y Computación, University of Santiago de Compostela, 15706-Santiago de Compostela, Spain
Venue:
Journal of VLSI Signal Processing Systems - special issue on CORDIC
Year:
2000

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Abstract

A very-high radix algorithm and implementation for CORDIC rotation in circular and hyperbolic coordinates is presented. The selection function consists of rounding the residual. It is shown that this assures convergence from the second iteration on. For the first iteration, the selection is done by table, using a lower radix than for the remaining iterations. The compensation of the variable scale factor is done by computing the logarithm of the scale factor and performing the compensation by an exponential. Estimations of the delay for 32-bit and 64-bit precision show a substantial speed up when compared to low radix implementations. The proposed algorithm is also compared with previously proposed very-high radix ones, and significant advantages are identified.