Redundant Arithmetic CORDIC System with a Unit Scale Factor

Christopher T Clarke; G R Nudd

Redundant Arithmetic CORDIC System with a Unit Scale Factor

Christopher T Clarke, G R Nudd

Department of Electronic & Electrical Engineering

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

Abstract

The CORDIC algorithm for the calculation of trigonometric functions has traditionally suffered from two problems; speed, and the necessity to pre-scale the inputs. The speed problem is overcome to a large extent by the introduction of redundant number systems which have been shown by others. Here we show a new CORDIC system which has a unit scale factor that can be ignored. The unit scale factor is achieved by rotating the vector in 3 dimensional space in a manner which scales its projection onto the X-Y plane by the reciprocal of the overall scale factor. This new technique takes the same number of cycles as the standard CORDIC algorithm, with only marginally slower cycle times than the redundant system of Takagi. The system is shown to be entirely compatible with redundant number system implementations of the CORDIC algorithm.

Original language	English
Title of host publication	Mathematics in Signal Processing III
Editors	J G McWirter
Place of Publication	Oxford
Publisher	Oxford University Press
Pages	63-73
Number of pages	11
ISBN (Print)	0198534809
Publication status	Published - Aug 1994
Event	Mathematics in Signal Processing III - Warwick, UK United Kingdom Duration: 1 Aug 1994 → …

Conference

Conference	Mathematics in Signal Processing III
Country/Territory	UK United Kingdom
City	Warwick
Period	1/08/94 → …

Bibliographical note

Mathematics in signal processing III: based on the proceedings of the third conference organized by the Institute of Mathematics and Its Applications on mathematics in signal processing, held at the University of Warwick in December 1992

Cite this

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title = "Redundant Arithmetic CORDIC System with a Unit Scale Factor",

abstract = "The CORDIC algorithm for the calculation of trigonometric functions has traditionally suffered from two problems; speed, and the necessity to pre-scale the inputs. The speed problem is overcome to a large extent by the introduction of redundant number systems which have been shown by others. Here we show a new CORDIC system which has a unit scale factor that can be ignored. The unit scale factor is achieved by rotating the vector in 3 dimensional space in a manner which scales its projection onto the X-Y plane by the reciprocal of the overall scale factor. This new technique takes the same number of cycles as the standard CORDIC algorithm, with only marginally slower cycle times than the redundant system of Takagi. The system is shown to be entirely compatible with redundant number system implementations of the CORDIC algorithm.",

author = "Clarke, {Christopher T} and Nudd, {G R}",

note = "Mathematics in signal processing III: based on the proceedings of the third conference organized by the Institute of Mathematics and Its Applications on mathematics in signal processing, held at the University of Warwick in December 1992; Mathematics in Signal Processing III ; Conference date: 01-08-1994",

year = "1994",

month = aug,

language = "English",

isbn = "0198534809",

pages = "63--73",

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publisher = "Oxford University Press",

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AU - Nudd, G R

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PY - 1994/8

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N2 - The CORDIC algorithm for the calculation of trigonometric functions has traditionally suffered from two problems; speed, and the necessity to pre-scale the inputs. The speed problem is overcome to a large extent by the introduction of redundant number systems which have been shown by others. Here we show a new CORDIC system which has a unit scale factor that can be ignored. The unit scale factor is achieved by rotating the vector in 3 dimensional space in a manner which scales its projection onto the X-Y plane by the reciprocal of the overall scale factor. This new technique takes the same number of cycles as the standard CORDIC algorithm, with only marginally slower cycle times than the redundant system of Takagi. The system is shown to be entirely compatible with redundant number system implementations of the CORDIC algorithm.

AB - The CORDIC algorithm for the calculation of trigonometric functions has traditionally suffered from two problems; speed, and the necessity to pre-scale the inputs. The speed problem is overcome to a large extent by the introduction of redundant number systems which have been shown by others. Here we show a new CORDIC system which has a unit scale factor that can be ignored. The unit scale factor is achieved by rotating the vector in 3 dimensional space in a manner which scales its projection onto the X-Y plane by the reciprocal of the overall scale factor. This new technique takes the same number of cycles as the standard CORDIC algorithm, with only marginally slower cycle times than the redundant system of Takagi. The system is shown to be entirely compatible with redundant number system implementations of the CORDIC algorithm.

M3 - Chapter or section

SN - 0198534809

SP - 63

EP - 73

BT - Mathematics in Signal Processing III

A2 - McWirter, J G

PB - Oxford University Press

CY - Oxford

T2 - Mathematics in Signal Processing III

Y2 - 1 August 1994

ER -

Redundant Arithmetic CORDIC System with a Unit Scale Factor

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