# Adaptive CORDIC: using parallel angle recording to accelerate CORDIC rotations

 dc.contributor.advisor Swartzlander, Earl E. dc.creator Rodrigues, Terence Keith, 1974- dc.date.accessioned 2008-08-29T00:09:25Z dc.date.available 2008-08-29T00:09:25Z dc.date.created 2007-12 dc.date.issued 2008-08-29T00:09:25Z dc.identifier.uri http://hdl.handle.net/2152/3772 dc.description.abstract This dissertation presents the Parallel Angle Recoding algorithm which is used to accelerate the calculation of CORDIC rotations. The CORDIC algorithm is used in the evaluation of a wide variety of elementary functions such as Sin, Cos, Tan, Log, Exp, etc. It is a simple and versatile algorithm, but its characteristic linear convergence causes it to suffer from long latency. It can be sped up by using the angle recoding algorithm which skips over certain intermediate CORDIC iterations to deliver the same precision while requiring 50% or fewer iterations. However because the selection of the angle constants is quite complex and must be performed off-line, its use has been limited to applications where the rotation angle is static and known a priori. This dissertation extends the low-latency advantage of the angle recoding method to dynamic situations too, where the incoming angle of rotation is allowed to take on any arbitrary value. The proposed method is called Parallel Angle Recoding and it makes use of a much simpler angle selection scheme to identify the angle constants needed by angle recoding. Because of its simplicity, it can be easily implemented in hardware without having to increase the cycle time. All the angle constants for angle recoding can be found in parallel in a single preliminary step by testing just the initial incoming rotation angle using range comparators -- there is no need to perform successive CORDIC iterations in order to identify them. With increasing precision, (N= 8, 16, 24, 32, etc.) the number of comparators which are needed by this scheme increases rapidly. The parallel angle recoding method can be re-formulated to apply to smaller groups of consecutive angle constants known as 'sections.' This limits the number of comparators that are needed, to a reasonable amount. There is an attendant savings in area and power consumption, but at the same time the evaluation of multiple sections introduces additional overhead cycles which reduces some of the gains made in latency by the Parallel Angle Recoding method. By interleaving multiple rotations and making use of a small buffer to store intermediate results, the number of overhead cycles can be reduced drastically. The Parallel Angle Recoding technique is modelled using Verilog, synthesised and mapped to a 65 nm. cell library. The latency and area characteristics that are obtained show that the method can improve the performance of the rotation mode in CORDIC, by delivering a reduced iteration count with no increase in the cycle time, and only a modest increase in power and area. dc.format.medium electronic dc.language.iso eng dc.rights Copyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. dc.subject.lcsh Computer algorithms dc.title Adaptive CORDIC: using parallel angle recording to accelerate CORDIC rotations dc.title.alternative Using parallel angle recording to accelerate CORDIC rotations dc.description.department Electrical and Computer Engineering dc.identifier.oclc 213470775 dc.identifier.recnum b69831361 dc.type.genre Thesis dc.type.material text thesis.degree.department Electrical and Computer Engineering thesis.degree.discipline Electrical and Computer Engineering thesis.degree.grantor The University of Texas at Austin thesis.degree.level Doctoral thesis.degree.name Doctor of Philosophy

## Files in this work

Size: 840.5Kb
Format: application/pdf