Computation Error Analysis of CORDIC

• Main Author: 林國珍
• Other Authors: 宋志雲
• Format: Others
• Language: zh-TW
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/59559244300482804942

碩士 === 中華大學 === 電機工程研究所 === 85 === CORDIC(Coordinate Rotation Digital Computer), is an algorithm for performing a sequence of iteration computation using the coordinate rotation. It can generate some powerful elementary function only realized by a simple set of adder and shifter. As such, it is suitable to implement high performance chips which are applied in digital signal processing and image processing fields with high speed and massive function computation using VLSI technology. In the duration of the past thirty years, the CORDIC applications of implementation and algorithm had been discussed in different fields, but there were few papers proposed which were very important about computation error using CORDIC. As knowing where the errors are, we can design the hardware with the error consideration in order to get the best cost-performance and the desired outcomes. In this thesis, we had discussed the computation error of CORDIC. We split the error of CORDIC into different kinds in order to analyze and derive from it systematically. There were split into before and after expansion according to the expansion of input range, and then split into before and after iteration according to the compensation of scale factor which was applied or not. Every kind split into rotation and vector mode according to the characteristic of CORDIC, then split into approximation error and truncation error for kind of error. The truncation error split into fixed point and floating point. We had analyzed all errors to generate 108 formulas of error analysis or 72 formulas from overall view in three different coordinate system. We also revealed the reference error with functional base and some suggestions on design with the error tolerance in tables. In this thesis, we had got a far and wide and perfect error analysis of CORDIC. We had not only considered and promoted some neglected errors and formulas, but also revealed the outcomes of error analysis in the form which involved the iterative times and word-length only. We also had got some important discovery in the discussion of error analysis. Beside, we took examples to explain the CORDIC application for error computation. It was applied directly in the design and implementation of CORDIC from the outcomes of error analysis.