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 consequence, CORDIC has been utilized for applications in diverse areas such as signal and image processing, communication systems, robotics and 3-D graphics apart from general scientific and technical computation. In this article, we present a brief overview of the key developments in the CORDIC algorithms and architectures along with their potential and upcoming applications.

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50 Years of CORDIC: Algorithms, Architectures, and Applications

The main characteristic of Reconfigurable Computing is the presence of hardware that can be reconfigured to implement specific functionality more suitable for specially tailored hardware than on a simple uniprocessor. Reconfigurable computing systems join microprocessors and programmable hardware in order to take advantage of the combined strengths of hardware and software and have been used in applications ranging from embedded systems to high performance computing. Many of the fundamental theories have been identified and used by the Hardware/Software Co-Design research field. Although the same background ideas are shared in both areas, they have different goals and use different approaches.This book is intended as an introduction to the entire range of issues important to reconfigurable computing, using FPGAs as the context, or "computing vehicles" to implement this powerful technology. It will take a reader with a background in the basics of digital design and software programming and provide them with the knowledge needed to be an effective designer or researcher in this rapidly evolving field.

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A unified algorithm for elementary functions

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Several methods for increasing the speed of the CORDIC algorithm are presented. First, an improved method which guarantees a constant scale factor when employing redundant addition schemes is developed. Then, an architecture with increased parallelism which considerably reduces the CORDIC latency time and the amount of hardware is described. >

Low latency time CORDIC algorithms

A new addition scheme and fast scaling factor compensation methods for CORDIC algorithms

One of the main problems of the CORDIC algorithm is the limited convergence domain, in which the functions can be calculated. Two different approaches can be employed to overcome this constraint: first, an argument reduction method and, second, an expansion of the CORDIC convergence domain. While the first approach requires significant processing overhead due to the need for divisions especially for tanh/sup -1/, the second technique achieves an increased but still limited convergence domain only. In this brief contribution, we present a unified division-free argument reduction method and a regular pipeline/array architecture for floating point or fixed point implementations which results in savings of computation time. In contrast to previous methods we avoid extra CORDIC arithmetic for realization of argument reduction. >

A unified and division-free CORDIC argument reduction method with unlimited convergence domain including inverse hyperbolic functions

A floating-point arithmetic unit based on the CORDIC algorithm is described. It computes a wide range of arithmetic, trigonometric, and hyperbolic functions and achieves a normalized peak performancle off 220 MFLOPs. The unit is implemented in 1.6pm double-metal CMOS technology and packaged in a 280 pin PGA.

A Cordic-based Floating-point Arithmetic Unit

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A new addition scheme and fast scaling factor compensation methods for CORDIC algorithms

A unified and division-free CORDIC argument reduction method with unlimited convergence domain including inverse hyperbolic functions

A Cordic-based Floating-point Arithmetic Unit