Radix-4 Vectoring CORDIC Algorithm and Architectures

Authors:
J. Villalba;E. L. Zapata;E. Antelo;J. D. Bruguera
Affiliations:
Dept. of Computer Architecture, University of Málaga, Málaga, Spain;Dept. of Computer Architecture, University of Málaga, Málaga, Spain;Dept. Electrónica, y Computación, University of Santiago de Compostela, Spain;Dept. Electrónica, y Computación, University of Santiago de Compostela, Spain
Venue:
Journal of VLSI Signal Processing Systems - Special issue on application specific systems, architectures and processors
Year:
1998

Citing 8
Cited 3

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Redundant and On-Line CORDIC: Application to Matrix Triangularization and SVD

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Constant-Factor Redundant CORDIC for Angle Calculation and Rotation

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High Performance Rotation Architectures Based on the Radix-4 CORDIC Algorithm

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Division and Square Root: Digit-Recurrence Algorithms and Implementations

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Reducing Iteration Time When Result Digit is Zero for Radix 2 SRT Division and Square Root with Redundant Remainders

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Redundant and On-Line CORDIC for Unitary Transformations

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Redundant CORDIC Rotator Based on Parallel Prediction

ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic

Very-High Radix Circular CORDIC: Vectoring and Unified Rotation/Vectoring

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CORDIC Processor for Variable-Precision Interval Arithmetic

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Fine-grained vs. coarse-grained shift-and-add arithmetic in FPGAs (abstract only)

Proceedings of the 18th annual ACM/SIGDA international symposium on Field programmable gate arrays

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Abstract

In this work we extend the radix-4 CORDIC algorithm to the vectoringmode (the radix-4 CORDIC algorithm was proposed recently by the authors forthe rotation mode). The extension to the vectoring mode is notstraightforward, since the digit selection function is more complex in thevectoring case than in the rotation case; as in the rotation mode, the scalefactor is not constant. Although the radix-4 CORDIC algorithm in vectoringmode has a similar recurrence as the radix-4 division algorithm, there arespecific issues concerning the vectoring algorithm that demand dedicatedstudy. We present the digit selection for nonredundant and redundantarithmetic (following two different approaches: arithmetic comparisons andtable look-up), the computation and compensation of the scale factor, andthe implementation of the algorithm (with both types of digit selection) ina word-serial architecture. When compared with conventional radix-2(redundant and non-redundant) architectures, the radix-4 algorithms presenta significant speed up for angle calculation. For the computation of themagnitude the speed up is very slight, due to the nonconstant scale factorin the radix-4 algorithm.