Coordinate Rotation Digital Computer Units Research Articles

CORDIC Designs for Fixed Angle of Rotation

Rotation of vectors through fixed and known angles has wide applications in robotics, digital signal processing, graphics, games, and animation. But, we do not find any optimized coordinate rotation digital computer (CORDIC) design for vector-rotation through specific angles. Therefore, in this paper, we present optimization schemes and CORDIC circuits for fixed and known rotations with different levels of accuracy. For reducing the area- and time-complexities, we have proposed a hardwired pre-shifting scheme in barrel-shifters of the proposed circuits. Two dedicated CORDIC cells are proposed for the fixed-angle rotations. In one of those cells, micro-rotations and scaling are interleaved, and in the other they are implemented in two separate stages. Pipelined schemes are suggested further for cascading dedicated single-rotation units and bi-rotation CORDIC units for high-throughput and reduced latency implementations. We have obtained the optimized set of micro-rotations for fixed and known angles. The optimized scale-factors are also derived and dedicated shift-add circuits are designed to implement the scaling. The fixed-point mean-squared-error of the proposed CORDIC circuit is analyzed statistically, and strategies for reducing the error are given. We have synthesized the proposed CORDIC cells by Synopsys Design Compiler using TSMC 90-nm library, and shown that the proposed designs offer higher throughput, less latency and less area-delay product than the reference CORDIC design for fixed and known angles of rotation. We find similar results of synthesis for different Xilinx field-programmable gate-array platforms.

Application of Reconfigurable CORDIC Architectures

Reconfiguration enables the adaption of Coordinate Rotation DIgital Computer (CORDIC) units to the specific needs of sets of applications, hence creating application specific CORDIC-style implementations. Reconfiguration can be implemented at a high level, taking the entire CORDIC unit as a basic cell (CORDIC-cells) implemented in VLSI, or at a low level such as Field-Programmable Gate Arrays (FPGAs). We suggest a design methodology and analyze area/time results for coarse (VLSI) and fine-grain (FPGA) reconfigurable CORDIC units. For FPGAs we implement CORDIC units in Verilog HDL and our object-oriented design environment, PAM-Blox. For CORDIC-cells, multiple reconfigurable CORDIC modules are synthesized with state-of-the-art CAD tools. At the algorithm level we present a case study combining multiple CORDICs based on a geometrical interpretation of a normalized ladder algorithm for adaptive filtering to reduce latency and area of a fully pipelined CORDIC implementation. Ultimately, the goal is to create automatic tools to map applications directly to reconfigurable high-level arithmetic units such as CORDICs.

A CORDIC processor for FFT computation and its implementation using gallium arsenide technology

In this paper, the architecture and the implementation of a complex fast Fourier transform (CFFT) processor using 0.6 /spl mu/m gallium arsenide (GaAs) technology are presented. This processor computes a 1024-point FFT of 16 bit complex data in less than 8 /spl mu/s, working at a frequency beyond 700 MHz, with a power consumption of 12.5 W. The architecture of the processor is based on the COordinate Rotation DIgital Computer (CORDIC) algorithm, which avoids the use of conventional multiplication-and-accumulation (MAC) units, but evaluates the trigonometric functions using only add and shift operations, Improvements to the basic CORDIC architecture are introduced in order to reduce the area and power of the processor. This together with the use of pipelining and carry save adders produces a very regular and fast processor, The CORDIC units were fabricated and tested in order to anticipate the final performance of the processor. This work also demonstrates the maturity of GaAs technology for implementing ultrahigh-performance signal processors.

Numerical accuracy and hardware tradeoffs for CORDIC arithmetic for special-purpose processors

The coordinate rotation digital computer (CORDIC) algorithm is used in numerous special-purpose systems for real-time signal processing applications. An analysis of fixed-point CORDIC in the Y-reduction mode, which allows computation of the inverse tangent function, shows that unnormalized input values can result in large numerical errors. The authors describe two approaches for tackling the numerical accuracy problem. The first approach builds on a fixed-point CORDIC unit and eliminates the problem by including additional hardware for normalization. A method for integrating the normalization operation with the CORDIC iterations for efficient implementation in O(n/sup 1.5/) hardware is provided. The second solution to the accuracy problem is to use a floating-point CORDIC unit but reduce the implementation complexity by using a hybrid architecture. Arguments to support the use of such an architecture in certain special-purpose arrays are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>