Area and Energy Efficient Approximate Square Rooters for Error Resilient Applications

Arya, Neelam; Soni, Teena; Pattanaik, Manisha; Sharma, Govind

doi:10.1109/vlsid49098.2020.00033

Cited by 8 publications

(3 citation statements)

References 14 publications

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“…The maximum relative error of this approximation is found to be 0.0607 and the approximated value is always larger than the exact square root value 48 . This relative error can be reduced to 0.03476 by replacing the quantity 127 × 2 22 = 532, 676, 608 in Eq. ( 12), by a smaller value that is equal to 532,369,100 48 .…”

Section: Methods By Dianov Et Almentioning

confidence: 99%

Novel seed generation and quadrature-based square rooting algorithms

Altamimi

Youssef

2022

Sci Rep

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The square root operation is indispensable in a myriad of computational science and engineering applications. Various computational techniques have been devised to approximate its value. In particular, convergence methods employed in this regard are highly affected by the initial approximation of the seed value. Research shows that the provision of an initial approximation with higher accuracy yields fewer additional iterations to calculate the square root. In this article, we propose two novel algorithms. The first one presents a seed generation technique that depends on bit manipulation and whose output is to be used as an initial value in the calculation of square roots. The second one describes a quadrature-based square rooting method that utilizes a rectangle as the plane figure for squaring. We provide error estimation of the former using the vertical parabola equation and employ a suitable lookup table, for the latter, to store needed cosine values. The seed generation approach produces a significant reduction in the number of iterations of up to 84.42% for selected convergence methods. The main advantages of our proposed square rooting algorithm lie in its high accuracy and in its requirement of just a single iteration. Our proposed algorithm also provides for lower computational latency, measured in the number of clock cycles, compared to Newton–Raphson’s and Bakhshali’s square rooting methods.

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Section: Methods By Dianov Et Almentioning

confidence: 99%

Novel seed generation and quadrature-based square rooting algorithms

Altamimi

Youssef

2022

Sci Rep

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“…In the recent 2020 survey of approximate arithmetic circuits by Jiang et al [3], there are only two references for square root circuits, and of those, only one [4] is for an approximate square root. However, another recent work by Arya et al [5] proposes an alternative approximate square root design, and the approximate subtractor cells proposed by Chen et al [6,7] can be appropriated for use in an approximate square root design. The approximate square root circuit proposed by Jiang et al [4] is based on removing the most significant bits of the radicand A down to the first nonzero bit, truncating the least significant bits of A so that 2k bits remain, with k used as an approximation degree parameter, and then using an exact circuit for the remaining 2k bits.…”

Section: Related Workmentioning

confidence: 99%

“…Recently, Arya et al have proposed alternative approximate square root circuits [5] based on square root arrays with cells designed for area reduction and least significant bit truncation. These are simple designs in which the approximation cell used is simple wire fall-through connections for the horizontal and vertical input wires in the square root array of Figure 1.…”

Section: Related Workmentioning

confidence: 99%

Approximate Square Root Circuits with Low Latency and Power Dissipation

Kim

Lee

2021

Electronics

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This paper proposes a series of approximate square root circuit designs with high accuracy, low latency, low area, and low power dissipation requirements. The proposed designs are constructed using an array of controlled add–subtract cell elements with both exact and approximate versions. The utility of the proposed designs are evaluated by utilizing them in an example image contrast enhancement application with demonstrably satisfactory results and large peak signal-to-noise ratios and structural similarity values. The accuracy and hardware characteristics of the proposed square root designs are also analyzed and compared with previously proposed state-of-the-art approximate square root designs. When applied to a 16-bit radicand (the number under the square root symbol), the proposed designs have the lowest error rates, normalized mean error distances, and mean relative error distances by at least 1.8x when compared to all previous methods using the same number of approximate cells. When the designs were synthesized using Synopsys Design Compiler with a 28 nm bulk CMOS process, the delay, area, power, and power-delay-product characteristics outperform all previous designs in all but a few cases. These results demonstrate that the proposed designs permit the use of a flexible range of approximate designs with varying accuracy and hardware overhead characteristics, and a suitable design can be selected based on the user design requirements.

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Generalized Exponentiation Using STT Magnetic Tunnel Junctions: Circuit Design, Performance, and Application to Neural Network Gradient Decay

Tatulian

DeMara

2022

SN COMPUT. SCI.

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Area and Energy Efficient Approximate Square Rooters for Error Resilient Applications

Cited by 8 publications

References 14 publications

Novel seed generation and quadrature-based square rooting algorithms

Novel seed generation and quadrature-based square rooting algorithms

Approximate Square Root Circuits with Low Latency and Power Dissipation

Generalized Exponentiation Using STT Magnetic Tunnel Junctions: Circuit Design, Performance, and Application to Neural Network Gradient Decay

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