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Title:
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Redundant and Online CORDIC for Unitary Transformations |
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Author:
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Hemkumar, Nariankadu D.; Cavallaro, Joseph R.
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Type:
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Journal Paper |
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Keywords:
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CORDC; redudant arithmetic; online; unitary transformations; VLSI |
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Citation:
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N. D. Hemkumar and J. R. Cavallaro, "Redundant and Online CORDIC for Unitary Transformations," IEEE Transactions on Computers, vol. 43, no. 8, pp. 941-954, 1994. |
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Abstract:
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Two-sided unitary transformations of arbitrary 2 x 2 matrices are needed in parallel algorithms based on Jacobi-like methods for eigenvalue and singulare value decompositions of complex matrices. This paper presents a two-sided unitary transformation structured to facilitate the integrated evaluation of parameters and application of the typically required tranformations using only the primitives afforded by CORDIC; thus enabling significant speedup in the computation of these transformations on special-purpose processor array architectures implementing Jacobi-like algorithms. We discuss implementation in (nonredundant) CORDIC to motivate and lead up to implementation in the redundant and on-line enhancements to CORDIC. Both variable and constant scale factor redundant (CFR) CORDIC approaches are detailed and it is shown that the transformations may be computed in 10n+o time, where n is the data precision in bits and o is a constant accounting for accumulated on-line delays. A more area-intesive approach uisng a novel on-line CORDIC encode angle summation/difference scheme reduces computation time to 6n+o. The area/time complexities involved in the various approaches are detailed. |
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Date Published:
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1994-08-20 |
