Multiplier-less and Table-less Linear Approximation for Square-Related Functions

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Square related functions such as square inverse square square root and Inverse square root 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 de sired if they do not degrade performance significantly In this paper we propose new linear approximations for the square related functions The traditional linear approximations need multipliers to calculate slope off sets and tables to store initial offset values and slope values whereas the proposed approximations exploit the inherent properties of square related 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 bit width 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 square root functions respectively For inverse square and inverse square root functions the maximum relative errors are bounded to 12 5% and 6 25% if the input operands are represented in 20 bits respectively
Publisher
IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS E
Issue Date
2010-11
Language
English
Article Type
Article
Keywords

EUCLIDEAN NORM; COMPLEXITY; ALGORITHM; DESIGN

Citation

IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS, v.E93D, no.11, pp.2979 - 2988

ISSN
0916-8532
DOI
10.1587/transinf.E93.D.2979
URI
http://hdl.handle.net/10203/99710
Appears in Collection
EE-Journal Papers(저널논문)
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