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 desired 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 offsets 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.
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In-Cheol PARK, Tae-Hwan KIM, "Multiplier-less and Table-less Linear Approximation for Square-Related Functions" in IEICE TRANSACTIONS on Information,
vol. E93-D, no. 11, pp. 2979-2988, November 2010, doi: 10.1587/transinf.E93.D.2979.
Abstract: 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 desired 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 offsets 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.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E93.D.2979/_p
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@ARTICLE{e93-d_11_2979,
author={In-Cheol PARK, Tae-Hwan KIM, },
journal={IEICE TRANSACTIONS on Information},
title={Multiplier-less and Table-less Linear Approximation for Square-Related Functions},
year={2010},
volume={E93-D},
number={11},
pages={2979-2988},
abstract={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 desired 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 offsets 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.},
keywords={},
doi={10.1587/transinf.E93.D.2979},
ISSN={1745-1361},
month={November},}
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TY - JOUR
TI - Multiplier-less and Table-less Linear Approximation for Square-Related Functions
T2 - IEICE TRANSACTIONS on Information
SP - 2979
EP - 2988
AU - In-Cheol PARK
AU - Tae-Hwan KIM
PY - 2010
DO - 10.1587/transinf.E93.D.2979
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E93-D
IS - 11
JA - IEICE TRANSACTIONS on Information
Y1 - November 2010
AB - 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 desired 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 offsets 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.
ER -