CORDIC

About: CORDIC is a research topic. Over the lifetime, 1765 publications have been published within this topic receiving 21185 citations.

The CORDIC Trigonometric Computing Technique

Abstract: The COordinate Rotation DIgital Computer(CORDIC) is a special-purpose digital computer for real-time airborne computation. In this computer, a unique computing technique is employed which is especially suitable for solving the trigonometric relationships involved in plane coordinate rotation and conversion from rectangular to polar coordinates. CORDIC is an entire-transfer computer; it contains a special serial arithmetic unit consisting of three shift registers, three adder-subtractors, and special interconnections. By use of a prescribed sequence of conditional additions or subtractions, the CORDIC arithmetic unit can be controlled to solve either set of the following equations: Y' = K(Y cos? + X sin?) X' = K(X cos? - Y sin?), or R = K?X2 + Y2 ? = tan-1 Y/X, where K is an invariable constant. This special arithmetic unit is also suitable for other computations such as multiplication, division, and the conversion between binary and mixed radix number systems. However, only the trigonometric algorithms used in this computer and the instrumentation of these algorithms are discussed in this paper.

A unified algorithm for elementary functions

Abstract: This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arctanh, In, exp and square-root The basis for the algorithm is coordinate rotation in a linear, circular, or hyperbolic coordinate system depending on which function is to be calculated The only operations required are shifting, adding, subtracting and the recall of prestored constants The limited domain of convergence of the algorithm is calculated, leading to a discussion of the modifications required to extend the domain for floating point calculations

A survey of CORDIC algorithms for FPGA based computers

Abstract: The current trend back toward hardware intensive signal processing has uncovered a relative lack of understanding of hardware signal processing architectures. Many hardware efficient algorithms exist, but these are generally not well known due to the dominance of software systems over the past quarter century. Among these algorithms is a set of shift-add algorithms collectively known as CORDIC for computing a wide range of functions including certain trigonometric, hyperbolic, linear and logarithmic functions. While there are numerous articles covering various aspects of CORDIC algorithms, very few survey more than one or two, and even fewer concentrate on implementation in FPGAs. This paper attempts to survey commonly used functions that may be accomplished using a CORDIC architecture, explain how the algorithms work, and explore implementation specific to FPGAs.

50 Years of CORDIC: Algorithms, Architectures, and Applications

Abstract: 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.

CORDIC-based VLSI architectures for digital signal processing

Abstract: The evolution of CORDIC, an iterative arithmetic computing algorithm capable of evaluating various elementary functions using a unified shift-and-add approach, and of CORDIC processors is reviewed. A method to utilize a CORDIC processor array to implement digital signal processing algorithms is presented. The approach is to reformulate existing DSP algorithms so that they are suitable for implementation with an array performing circular or hyperbolic rotation operations. Three categories of algorithm are surveyed: linear transformations, digital filters, and matrix-based DSP algorithms. >