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http://dx.doi.org/10.6109/JKIICE.2007.11.1.46

An Improved Newton-Raphson's Reciprocal and Inverse Square Root Algorithm  

Cho, Gyeong-Yeon (부경대학교 전자컴퓨터정보통신공학부)
Publication Information
Journal of the Korea Institute of Information and Communication Engineering / v.11, no.1, 2007 , pp. 46-55 More about this Journal
Abstract
The Newton-Raphson's algorithm for finding a floating point reciprocal and inverse square root calculates the result by performing a fixed number of multiplications. In this paper, an improved Newton-Raphson's algorithm is proposed, that performs multiplications a variable number. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal and inverse square tables with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal and inverse square root unit. Also, it can be used to construct optimized approximate tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.
Keywords
Floating point; Newton-Raphson; Reciprocal; Divide; Inverse square root;
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Times Cited By KSCI : 1  (Citation Analysis)
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