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Multiplierless and Tableless Linear Approximation for SquareRelated Functions
InCheol PARK TaeHwan KIM
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E93D
No.11
pp.29792988 Publication Date: 2010/11/01 Online ISSN: 17451361
DOI: 10.1587/transinf.E93.D.2979 Print ISSN: 09168532 Type of Manuscript: PAPER Category: Fundamentals of Information Systems Keyword: square, squareroot, inverse square, inverse squareroot, computer arithmetic, approximation, linear interpolation,
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Summary:
Squarerelated functions such as square, inverse square, squareroot and inverse squareroot operations are widely used in digital signal processing and digital communication algorithms, and their efficient realizations are commonly required to reduce the hardware complexity. In the implementation point of view, approximate realizations are often desired if they do not degrade performance significantly. In this paper, we propose new linear approximations for the squarerelated functions. The traditional linear approximations need multipliers to calculate slope offsets and tables to store initial offset values and slope values, whereas the proposed approximations exploit the inherent properties of squarerelated functions to linearly interpolate with only simple operations, such as shift, concatenation and addition, which are usually supported in modern VLSI systems. Regardless of the bitwidth of the number system, more importantly, the maximum relative errors of the proposed approximations are bounded to 6.25% and 3.13% for square and squareroot functions, respectively. For inverse square and inverse squareroot functions, the maximum relative errors are bounded to 12.5% and 6.25% if the input operands are represented in 20 bits, respectively.


