Hardware architecture design and mapping of &amp;#x2018;Fast Inverse Square Root&amp;#x2019; algorithm

Zafar, Saad; Adapa, Raviteja

doi:10.1109/icaee.2014.6838433

Cited by 10 publications

(7 citation statements)

References 5 publications

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“…There are existing square root algorithm implementations in hardware, but they have not been applied to the field of image processing. We have studied two of these implementations-the non-restoring square root algorithm (Nanhe et al, 2013) and the FRSR (rsqrt) algorithm Lomont, 2003;Robertson, 2012;Zafar & Adapa, 2014;Kho et al, 2018). Because of the speed and efficiency of the FRSR algorithm, we have decided to use this in the design and implementation of the Sobel gradient computations.…”

Section: Background Theorymentioning

confidence: 99%

“…Furthermore, in most hardware-based square root computational systems (Li & Chu, 1997;Ercegovac et al, 2000;Ercegovac et al, 2005;Wang, 2007;Lachowicz, 2008;Sajid et al, 2010;Istoan & Pasca, 2015;Ananthalakshmi & Sudha, 2017), the non-restoring square root algorithm, or the sum of the absolute values of the gradients in the horizontal and vertical directions, is used to approximate the magnitude of the gradient vector. However, in this work, we are using the FRSR algorithm (Lomont, 2003;Robertson, 2012;Zafar & Adapa, 2014;Kho et al, 2018) to compute the square root in hardware.…”

Section: Sobel Using the Fast Reciprocal Square Root Algorithmmentioning

confidence: 99%

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Hardware-Based Sobel Gradient Computations for Sharpness Enhancement

Kho¹,

Fauzi²,

Sin³

2019

IJTech

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The majority of imaging systems are software based; they require some kind of microprocessor or microcontroller for the imaging algorithms to run. As the speed requirements of imaging and communications systems increase, the need for more hardware-based imaging systems arises. These fully hardware systems solve the fundamental problem inherent in software-based solutions, in which the speed of the algorithms depend on the instruction cycle speed of the processor. Once an algorithm is designed directly on hardware, the speed of the algorithm depends on the system clock frequency and the propagation delays of the logic cells (or standard cells) used in the design, usually measured in nanoseconds per cell. Therefore, such systems no longer depend on any instruction cycle delays, as there is no microprocessor involved. Most modern imaging and communications systems rely on digital signal processing (DSP) to compute complex mathematical operations. The emergence of powerful and low-cost field-programmable gate array (FPGA) devices with hundreds of arithmetic multipliers has enabled the development of many such DSP hardware applications, traditionally implemented only as software solutions.

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Section: Background Theorymentioning

confidence: 99%

Section: Sobel Using the Fast Reciprocal Square Root Algorithmmentioning

confidence: 99%

Hardware-Based Sobel Gradient Computations for Sharpness Enhancement

Kho¹,

Fauzi²,

Sin³

2019

IJTech

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“…Newton-Raphson iterations, which provide quadratic convergence of the iterative process. In the last formulas, 2 (16) As proven in [11][12], in order to know the behaviour of the relative error for 0 y in the whole range of normalized floating-point numbers, it suffices to consider the range…”

Section: Analytical Description Of Known Algorithmsmentioning

confidence: 99%

“…The best-known version of this algorithm called Fast Inverse Square Root (FISR) [8,[15][16][17][18], which was used in the computer game Quake III Arena [7], is given below: 2. float half = 0.5f * x; 3. int i = *(int*)&x; 4. i = 0x5F3759DF -(i>>1); 5. x = *(float*)&i; 6. x = x*(1.5f -half*x*x); 7. x = x*(1.5f -half*x*x); 8. return x; 9. } This InvSqrt1 code, written in the C/C++ language, implements a fast algorithm for inverse square root calculation.…”

Section: Introductionmentioning

confidence: 99%

Simple Effective Fast Inverse Square Root Algorithm With Two Magic Constants

Horyachyy¹,

Moroz²,

Otenko³

2019

IJC

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The purpose of this paper is to introduce a modification of Fast Inverse Square Root (FISR) approximation algorithm with reduced relative errors. The original algorithm uses a magic constant trick with input floating-point number to obtain a clever initial approximation and then utilizes the classical iterative Newton-Raphson formula. It was first used in the computer game Quake III Arena, causing widespread discussion among scientists and programmers, and now it can be frequently found in many scientific applications, although it has some drawbacks. The proposed algorithm has such parameters of the modified inverse square root algorithm that minimize the relative error and includes two magic constants in order to avoid one floating-point multiplication. In addition, we use the fused multiply-add function and iterative methods of higher order in the second iteration to improve the accuracy. Such algorithms do not require storage of large tables for initial approximation and can be effectively used on field-programmable gate arrays (FPGAs) and other platforms without hardware support for this function.

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“…Among the better-known methods of calculating the square root and reciprocal square root [1,2,15,20], the FISR method [20,[25][26][27][28][29] has recently gained increasing popularity in SW [8,20,27,[29][30][31][32] and HW [3,[33][34][35][36][37] applications. The algorithm was proposed for the first time in [24] but gained wider popularity through its use in the computer game Quake III Arena [27].…”

Section: Introductionmentioning

confidence: 99%

Modified Fast Inverse Square Root and Square Root Approximation Algorithms: The Method of Switching Magic Constants

2021

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Many low-cost platforms that support floating-point arithmetic, such as microcontrollers and field-programmable gate arrays, do not include fast hardware or software methods for calculating the square root and/or reciprocal square root. Typically, such functions are implemented using direct lookup tables or polynomial approximations, with a subsequent application of the Newton–Raphson method. Other, more complex solutions include high-radix digit-recurrence and bipartite or multipartite table-based methods. In contrast, this article proposes a simple modification of the fast inverse square root method that has high accuracy and relatively low latency. Algorithms are given in C/C++ for single- and double-precision numbers in the IEEE 754 format for both square root and reciprocal square root functions. These are based on the switching of magic constants in the initial approximation, depending on the input interval of the normalized floating-point numbers, in order to minimize the maximum relative error on each subinterval after the first iteration—giving 13 correct bits of the result. Our experimental results show that the proposed algorithms provide a fairly good trade-off between accuracy and latency after two iterations for numbers of type float, and after three iterations for numbers of type double when using fused multiply–add instructions—giving almost complete accuracy.

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Hardware architecture design and mapping of ‘Fast Inverse Square Root’ algorithm

Cited by 10 publications

References 5 publications

Hardware-Based Sobel Gradient Computations for Sharpness Enhancement

Hardware-Based Sobel Gradient Computations for Sharpness Enhancement

Simple Effective Fast Inverse Square Root Algorithm With Two Magic Constants

Modified Fast Inverse Square Root and Square Root Approximation Algorithms: The Method of Switching Magic Constants

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