Square Root by Digit Recurrence

Ercegovac, M.D.; Lang, T.

doi:10.1016/b978-155860798-9/50008-7

Cited by 3 publications

(6 citation statements)

References 37 publications

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“…The literature comes tantalizingly close to deriving unified radix-4 selection constants but stops just short. The seminal textbooks on recurrence division and square root [6], [7] present a combined radix-2 algorithm but lack unified radix-4. The radix-4 division constants from Table 5.10 of [7] almost work for both but lack m-1(9/8) = -14 and m-1(12/8) = -18 needed for square root.…”

Section: Prior Artmentioning

confidence: 99%

“…Square root uses a closely-related approach and can share much of the hardware [5]. Ercegovac and Lang pioneered the unified approach to recurrence division and square root and wrote two authoritative books on the subject [6]- [7].…”

Section: Introductionmentioning

confidence: 99%

“…This paper presents the first complete derivation of selection constants for unified minimally redundant radix-4 recurrence division and square root. Compared to previous literature [6]- [7], this work also improves notation by moving the recurrence left shift after digit selection to avoid an unnecessary preshift, defining a thermometer code Cj for square root addend generation, and defining a selection interval Mk in place of the hats and stars. It concludes with verified hardware.…”

Section: Introductionmentioning

confidence: 99%

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Unified Digit Selection for Radix-4 Recurrence Division and Square Root

Harris,

Stine,

Ercegovac

et al. 2024

IEEE Trans. Comput.

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Division and square root are fundamental operations required by most computer systems. They are commonly implemented in hardware using radix-4 recurrence, which produces a 2-bit result digit on each step. Unified digit selection logic chooses the next quotient or square root digit based on a residual and divisor or square root approximation. This paper presents the first derivation of digit selection constants for unified radix-4 recurrence division and square root.

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Section: Prior Artmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Unified Digit Selection for Radix-4 Recurrence Division and Square Root

Harris,

Stine,

Ercegovac

et al. 2024

IEEE Trans. Comput.

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“…In order to have the capability to make a comparison of computing resources, an estimation of the area cost and time delay of the proposed architectures is presented here. The model we use for the estimations is taken from the references [33,34]. The unit τ a represents the area of a complex gate.…”

Section: Area Costs and Time Delay Estimationmentioning

confidence: 99%

Calculation Scheme Based on a Weighted Primitive: Application to Image Processing Transforms

Pont

García‐Chamizo

Mora

et al. 2007

EURASIP J. Adv. Signal Process.

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This paper presents a method to improve the calculation of functions which specially demand a great amount of computing resources. The method is based on the choice of a weighted primitive which enables the calculation of function values under the scope of a recursive operation. When tackling the design level, the method shows suitable for developing a processor which achieves a satisfying trade-off between time delay, area costs, and stability. The method is particularly suitable for the mathematical transforms used in signal processing applications. A generic calculation scheme is developed for the discrete fast Fourier transform (DFT) and then applied to other integral transforms such as the discrete Hartley transform (DHT), the discrete cosine transform (DCT), and the discrete sine transform (DST). Some comparisons with other well-known proposals are also provided.

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“…In this paper, we consider approximation and fast computation of the inverse square root function, which has numerous applications (see [ 8 , 10 , 14 , 15 , 16 , 17 ]), especially in 3D computer graphics, where it is needed for normalization of vectors [ 4 , 18 , 19 ]. The proposed algorithms are aimed primarily at floating-point platforms with limited hardware resources, such as microcontrollers, some field-programmable gate arrays (FPGAs), and graphics processing units (GPUs) that cannot use fast look-up table (LUT)-based hardware instructions, such as SSE (i.e., Streaming SIMD (single instruction, multiple data) Extensions) or Advanced Vector Extensions (AVX).…”

Section: Introductionmentioning

confidence: 99%

Improving the Accuracy of the Fast Inverse Square Root by Modifying Newton–Raphson Corrections

Walczyk

Moroz

Cieśliński

2021

Entropy

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Direct computation of functions using low-complexity algorithms can be applied both for hardware constraints and in systems where storage capacity is a challenge for processing a large volume of data. We present improved algorithms for fast calculation of the inverse square root function for single-precision and double-precision floating-point numbers. Higher precision is also discussed. Our approach consists in minimizing maximal errors by finding optimal magic constants and modifying the Newton–Raphson coefficients. The obtained algorithms are much more accurate than the original fast inverse square root algorithm and have similar very low computational costs.

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Square Root by Digit Recurrence

Cited by 3 publications

References 37 publications

Unified Digit Selection for Radix-4 Recurrence Division and Square Root

Unified Digit Selection for Radix-4 Recurrence Division and Square Root

Calculation Scheme Based on a Weighted Primitive: Application to Image Processing Transforms

Improving the Accuracy of the Fast Inverse Square Root by Modifying Newton–Raphson Corrections

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