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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 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.

- Publication
- IEICE TRANSACTIONS on Information Vol.E93-D No.11 pp.2979-2988

- Publication Date
- 2010/11/01

- Publicized

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.E93.D.2979

- Type of Manuscript
- PAPER

- Category
- Fundamentals of Information Systems

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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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 -