# 50 Years of CORDIC: Algorithms, Architectures, and Applications

@article{Meher200950YO, title={50 Years of CORDIC: Algorithms, Architectures, and Applications}, author={Pramod Kumar Meher and Javier Valls-Coquillat and Tso-Bing Juang and Krishnamurthy Sridharan and Koushik Maharatna}, journal={IEEE Transactions on Circuits and Systems I: Regular Papers}, year={2009}, volume={56}, pages={1893-1907} }

Year 2009 marks the completion of 50 years of the invention of CORDIC (coordinate rotation digital computer) by Jack E. Volder. The beauty of CORDIC lies in the fact that by simple shift-add operations, it can perform several computing tasks such as the calculation of trigonometric, hyperbolic and logarithmic functions, real and complex multiplications, division, square-root, solution of linear systems, eigenvalue estimation, singular value decomposition, QR factorization and many others. As a…

## 523 Citations

### An efficient mathematically correct scale free CORDIC

- Computer ScienceArXiv
- 2016

An overview of the CORDIC algorithm for the computation of the circular functions is presented, essentially the scaling free version, and a substential improvement to the commonly used one is given.

### Technology Roadmap of CORDIC Algorithm

- Computer Science
- 2012

This paper presents evolution of CORDIC along with its architecture and applications, and also covers some comparative result analysis of CordIC core implementation.

### Hyperbolic CORDIC-Based Architecture for Computing Logarithm and Its Implementation

- Computer ScienceIEEE Transactions on Circuits and Systems II: Express Briefs
- 2020

A CORDIC (Coordinate Rotation Digital Computer)-based method to compute the logarithm function with base 2 is presented and validated by software simulation and hardware implementation.

### Hardware-Oriented Algorithm for

- Computer Science
- 2011

A novel highly parallel efficient hardware- oriented 8-D octonion CORDIC algorithm for quaternion-valued matrix decomposition is designed and presented, and a successful sequence of iterations with guaranteed convergence is determined.

### A study and comparison of COordinate Rotation DIgital Computer (CORDIC) architectures

- Computer ScienceArXiv
- 2022

This paper gives a brief overview of various existing CORDIC architectures, their working principle, application domain and a comparison of these architectures.

### Implementation of trigonometric function using CORDIC algorithms

- Computer Science
- 2018

The CORDIC technique is used in order to generating the output angle between range 0o to 90o and error analysis is concern and the result showed that the average percentage error is about 0.042% at angles between ranges 00 to 900.

### Efficient fault diagnosis for CORDIC Algorithm by using Hamming Codes

- Computer Science
- 2020

The proposed design is achieved by integrating the Hamming codes to the CORDIC algorithm and hence achieving the error-free CORDic algorithm and the reliability constraints be achieved.

### Low latency & high precision CORDIC architecture using improved parallel angle recoding

- Computer Science2011 International Conference on Signal Processing, Communication, Computing and Networking Technologies
- 2011

A improved PAR of CORDIC is presented with reduced latency from 10 cycles to 7 cycles and error of the CORDic is reduced 15% without any significant penalty on the power and area.

### Implementation of a Fast Hybrid CORDIC Architecture

- Computer Science2016 Second International Conference on Computational Intelligence & Communication Technology (CICT)
- 2016

Verilog Hardware Description Language (HDL) implementation of CORDIC hybrid architecture is presented and it is compared with parallel architecture using Xilinx ISE Webpack and Synopsys Design Vision.

### Generic-Precision algorithm for DCT-Cordic architectures

- Computer ScienceArXiv
- 2016

A generic algorithm is proposed to calculate the rotation parameters of CORDIC angles required for the Discrete Cosine Transform algorithm (DCT), and a hardware implementation of the novel transformation is proposed, and a substantial improvement in PSNR quality is found.

## References

SHOWING 1-10 OF 113 REFERENCES

### Householder CORDIC Algorithms

- Computer ScienceIEEE Trans. Computers
- 1995

VLSI implementations of Householder CORDIC processors are presented and their speed and area are estimated, and the method employed to prove the convergence of these multidimensional algorithms differs from the one used in the 2D case.

### The Differential CORDIC Algorithm: Constant Scale Factor Redundant Implementation without Correcting Iterations

- Computer ScienceIEEE Trans. Computers
- 1996

It is proved that, due to the lack of additional operations, DCORDIC compares favorably with the previously known redundant methods in terms of latency and computational complexity.

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

- Computer ScienceIEEE Trans. Computers
- 1990

The application of the modified CORDIC method to matrix triangularization by Givens' rotations and to the computation of the singular value decomposition (SVD) are discussed.

### Implementation of unidirectional CORDIC algorithm using precomputed rotation bits

- Computer ScienceThe 2002 45th Midwest Symposium on Circuits and Systems, 2002. MWSCAS-2002.
- 2002

A new technique to compute various trigonometric, logarithmic and transcendental functions fast with a high degree of accuracy with significant reduction in the number of iterations, and power savings is proposed.

### The CORDIC Trigonometric Computing Technique

- Computer ScienceIRE Trans. Electron. Comput.
- 1959

The trigonometric algorithms used in this computer and the instrumentation of these algorithms are discussed in this paper.

### CORDIC-based VLSI architectures for digital signal processing

- Computer ScienceIEEE Signal Processing Magazine
- 1992

A method to utilize a CORDIC processor array to implement digital signal processing algorithms is presented, to reformulate existing DSP algorithms so that they are suitable for implementation with an array performing circular or hyperbolic rotation operations.

### Redundant and On-Line CORDIC for Unitary Transformations

- Computer ScienceIEEE Trans. Computers
- 1994

A two-sided unitary transformation structured to facilitate the integrated evaluation of parameters and application of the typically required transformations using only the primitives afforded by CORDIC is presented, enabling significant speedup in the computation of these transformations on special-purpose processor array architectures implementing Jacobi-like algorithms.

### Para-CORDIC: parallel CORDIC rotation algorithm

- Computer ScienceIEEE Trans. Circuits Syst. I Regul. Pap.
- 2004

The parallel COrdinate Rotation DIgital Computer (CORDIC) rotation algorithm in circular and hyperbolic coordinate is proposed and the critical path delay is reduced since the concurrently predicted rotations can be combined using multioperand carry-save addition structures.

### A maximum pipelined CORDIC architecture for inverse kinematic position computation

- Computer ScienceIEEE Journal on Robotics and Automation
- 1987

A cost-effective coordinate rotation digital computer (CORDIC) architecture is described for the computation of inverse kinematic position solution based on a functional decomposition of the…

### An Angle Recoding Method for CORDIC Algorithm Implementation

- Computer ScienceIEEE Trans. Computers
- 1993

A greedy algorithm which takes only O(n/sup 2/) operations is developed to perform CORDIC angle recoding, and it is proven that this algorithm is able to reduce the total number of required elementary rotation angles by at least 50% without affecting the computational accuracy.