Redundant CORDIC Methods with a Constant Scale Factor for Sine and Cosine Computation
IEEE Transactions on Computers
Constant-Factor Redundant CORDIC for Angle Calculation and Rotation
IEEE Transactions on Computers - Special issue on computer arithmetic
Elementary functions: algorithms and implementation
Elementary functions: algorithms and implementation
Radix-4 Vectoring CORDIC Algorithm and Architectures
Journal of VLSI Signal Processing Systems - Special issue on application specific systems, architectures and processors
Very High Radix Square Root with Prescaling and Rounding and a Combined Division/Square Root Unit
IEEE Transactions on Computers
Very-High Radix CORDIC Rotation Based on Selection by Rounding
Journal of VLSI Signal Processing Systems - special issue on CORDIC
Fast Hardware-Based Algorithms for Elementary Function Computations Using Rectangular Multipliers
IEEE Transactions on Computers
Very-High Radix Division with Prescaling and Selection by Rounding
IEEE Transactions on Computers
BKM: A New Hardware Algorithm for Complex Elementary Functions
IEEE Transactions on Computers
High Radix Cordic Rotation Based on Selection by Rounding
Euro-Par '96 Proceedings of the Second International Euro-Par Conference on Parallel Processing-Volume II
Complex Logarithmic Number System Arithmetic Using High-Radix Redundant CORDIC Algorithms
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Very-High Radix CORDIC Vectoring with Scalings and Selection by Rounding
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Fast CORDIC Algorithm Based on a New Recoding Scheme for Rotation Angles and Variable Scale Factors
Journal of VLSI Signal Processing Systems
50 years of CORDIC: algorithms, architectures, and applications
IEEE Transactions on Circuits and Systems Part I: Regular Papers
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A very-high radix algorithm and implementation for circular CORDIC is presented. We first present in depth the algorithm for the vectoring mode in which the selection of the digits is performed by rounding of the control variable. To assure convergence with this kind of selection, the operands are prescaled. However, in the CORDIC algorithm, the coordinate $x$ varies during the execution so several scalings might be needed; we show that two scalings are sufficient. Moreover, the compensation of the variable scale factor (including the CORDIC scale factor and the prescaling factors) is done by computing the logarithm of the scale factor and performing the compensation by an exponential. Then, we combine, in a unified unit, the proposed vectoring algorithm and the very-high radix rotation algorithm, which was previously proposed by the authors. We compare with low-radix implementations in terms of latency and hardware complexity. Estimations of the delay for 32-bit precision show a speedup of about two with respect to the radix-4 case with redundant addition. This speedup is obtained at the cost of an increase in the hardware complexity, which is moderate for the pipelined implementation. We also compare at the algorithmic level with other very-high radix proposals, demonstrating the advantages of our algorithms.