Hyperbolic CORDIC-Based Architecture for Computing Logarithm and Its Implementation
Hui Chen, Kaifeng Cheng, Zhonghai Lu, Yuxiang Fu, Li Li
Abstract
We present a CORDIC (Coordinate Rotation Digital Computer)-based method to compute the logarithm function with base 2 and validate this method by software simulation and hardware implementation. Technically, we overcome the limitation of traditional hyperbolic CORDIC and transform it based on the idea of generalized hyperbolic CORDIC so that it can be used to compute log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> x (x ε [1, 2)). The proposed method requires only simple shift-and-add operations and has a great tradeoff between precision (or speed) and area. In MATLAB, we provide different precisions corresponding to the iterations of the transformed CORDIC for user needs. Using a pipelined structure and setting the number of iterations to be 16 (the average relative error is 2.09×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> ), we implement an example hardware circuit. Synthesized under the SMIC 65nm CMOS technology, the circuit has an area of 24100 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and computation time of 11.1 ns, which can save 31.04% area and improve 6.92% computation speed averagely compared with existing methods.