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Faster floating-point square root for integer processors

Claude-Pierre Jeannerod, Herve Knochel, Christophe Monat, Guillaume Revy
2007 2007 International Symposium on Industrial Embedded Systems  
This is illustrated with the square root function, whose implementation given here is faster by over 35% than the previously best one for such systems.  ...  We show how to use some key architectural features to design codes that achieve correct rounding-to-nearest without sacrificing for efficiency.  ...  Section II describes some features of the ST231 architecture and compiler that have been crucial for speeding up square root.  ... 
doi:10.1109/sies.2007.4297353 dblp:conf/sies/JeannerodKMR07 fatcat:sqzxcdgu6bdvzon2e3jkypozki

FAST DIFFERENTIABLE MATRIX SQUARE ROOT

Yue Song, Nicu Sebe, Wei Wang
2022 Zenodo  
Computing the matrix square root or its inverse in a differentiable manner is important in a variety of computer vision tasks.  ...  Both methods yield considerable speed-up compared with the SVD or the Newton-Schulz iteration.  ...  The principle square root A 1 2 and the inverse square root A − 1 2 (often derived by calculating the inverse of A 1 2 ) are mathematically of practical interests, mainly because some desired spectral  ... 
doi:10.5281/zenodo.6396092 fatcat:wbgkl2e5cbef3bwrngh3wzffai

Hardware Implementation of Single Iterated Multiplicative Inverse Square Root

Jun Luo, Qijun Huang, Hongwei Luo, Yue Zhi, Xiaoqiang Wang
2017 Elektronika ir Elektrotechnika  
This paper presents hardware implementation of fixed-point single iterated multiplicative inverse square root.  ...  Multiple piecewise linear approximation in softly nonlinear range is used to compute the initial value. Single iterated Newton-Raphson method is employed to obtain high precision.  ...  A high speed single precision floating point inverse square root was proposed in [7] , using special squaring unit and truncated multiplier.  ... 
doi:10.5755/j01.eie.23.4.18717 fatcat:loora7zgsjaizjtyy3dygljcau

Fast Differentiable Matrix Square Root and Inverse Square Root [article]

Yue Song, Nicu Sebe, Wei Wang
2022 arXiv   pre-print
A series of numerical tests show that both methods yield considerable speed-up compared with the SVD or the NS iteration.  ...  Computing the matrix square root and its inverse in a differentiable manner is important in a variety of computer vision tasks.  ...  The principle square root A 1 2 and the inverse square root A − 1 2 are mathematically of practical interests, mainly because some desired spectral properties can be obtained by such transformations.  ... 
arXiv:2201.12543v1 fatcat:pwycrp44knarhfww3pd7lzjyge

Fast Differentiable Matrix Square Root [article]

Yue Song, Nicu Sebe, Wei Wang
2022 arXiv   pre-print
Computing the matrix square root or its inverse in a differentiable manner is important in a variety of computer vision tasks.  ...  Both methods yield considerable speed-up compared with the SVD or the Newton-Schulz iteration.  ...  The principle square root A 1 2 and the inverse square root A − 1 2 (often derived by calculating the inverse of A 1 2 ) are mathematically of practical interests, mainly because some desired spectral  ... 
arXiv:2201.08663v1 fatcat:p4ax3yalejg6tmdknjiwr4fwvq

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

Leonid V. Moroz, Volodymyr V. Samotyy, Oleh Y. Horyachyy
2021 Computation  
In contrast, this article proposes a simple modification of the fast inverse square root method that has high accuracy and relatively low latency.  ...  root and/or reciprocal square root.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/computation9020021 fatcat:gdlehndewrft5l6ys3sdcsu64u

High-speed double-precision computation of reciprocal, division, square root, and inverse square root

J.-A. Pineiro, J.D. Bruguera
2002 IEEE transactions on computers  
A new method for the high-speed computation of double-precision floating-point reciprocal, division, square root, and inverse square root operations is presented in this paper.  ...  The high accuracy of the initial approximation allows us to obtain double-precision results by computing a single Goldschmidt iteration, significantly reducing the latency of the algorithm.  ...  Jean-Michel Muller for his fundamental contribution to the development of the second-degree minimax approximation method.  ... 
doi:10.1109/tc.2002.1146704 fatcat:uavk4w4ryja2dboij5ae7fwbhe

Reconfigurable HDL Library Development Platform for Arithmetic and Matrix Operations

Semih Aslan
2016 International Journal of Computer Applications  
The development tool improves design time and reduces the verification process, but the key point is to use a unified design that combines some of the basic operations with more complex operations to reduce  ...  Many design tools use predefined libraries and costly IPs during these design and verification cycles, and most of these libraries and IPs are static and difficult to modify.  ...  Some of these arithmetic building blocks are division, square root, inverse square root and CORDIC (used to design trigonometric, hyperbolic and exponential functions) and some matrix operations such as  ... 
doi:10.5120/ijca2016909618 fatcat:3yewzer7cjak3bw2ajhj65q5k4

Page 401 of Mathematical Reviews Vol. , Issue 92a [page]

1992 Mathematical Reviews  
Summary: “The problem of obtaining optimal starting values for the calculation of a square root using Newton-Raphson’s method is considered.  ...  (BG-AOS) On Halley-like algorithms with high order of convergence for simultaneous approximation of multiple roots of polynomials. C. R. Acad. Bulgare Sci. 43 (1990), no. 9, 29-32.  ... 

Finding polynomial roots by dynamical systems – A case study

Sergey Shemyakov, ,Institut de Mathématiques (UMR CNRS7373), Campus de Luminy 163 avenue de Luminy, Case 907 13288 Marseille 9, France, Roman Chernov, Dzmitry Rumiantsau, Dierk Schleicher, Simon Schmitt, Anton Shemyakov
2019 Discrete and Continuous Dynamical Systems. Series A  
We investigate two well known dynamical systems that are designed to find roots of univariate polynomials by iteration: the methods known by Newton and by Ehrlich-Aberth.  ...  It is clear that no continuous deterministic root finding system can converge to roots for every set of initial conditions: the domains of convergence to some set of roots is open, and the complement must  ...  This project has been inspired by several of our friends and colleagues.  ... 
doi:10.3934/dcds.2020261 fatcat:w3agxmyldnelbb3cv2uy4rrsoe

Study of the Magnetic Properties of Haematite Based on Spectroscopy and the IPSO-ELM Neural Network

Yachun Mao, Chongmin Liu, Dong Xiao, Jichun Wang, Ba Tuan Le
2018 Journal of Sensors  
Compared with traditional chemical analysis methods and manual methods, this method has great advantages in terms of economy, speed, and accuracy.  ...  The existing methods for measuring the magnetic properties of iron ore either have large errors or take a long time.  ...  There are two existing methods for detecting the magnetic property of existing iron ore. One method is to use a magnetometer to detect it. The speed of this method is relatively fast.  ... 
doi:10.1155/2018/6357905 fatcat:zzc2kjjijjbfti73vkrmncsk24

A review of optimisation and least-square problem methods on field programmable gate array-based orthogonal matching pursuit implementations

Muhammad Muzakkir Mohd Nadzri, Afandi Ahmad
2022 Indonesian Journal of Electrical Engineering and Computer Science  
OMP operates in an iteration-based nature, which involves optimisation and least-square problem (LSP) as the main processes.  ...  Orthogonal matching pursuit (OMP) is the most efficient algorithm used for the reconstruction of compressively sampled data signals in the implementation of compressive sensing.  ...  Communication of this research is made possible through monetary assistance by Universiti Tun Hussein Onn Malaysia and the UTHM Publisher's Office via Publication Fund E15216.  ... 
doi:10.11591/ijeecs.v25.i2.pp920-930 fatcat:thg2j4feuvf43gw3vms4htcr3m

High-speed function approximation using a minimax quadratic interpolator

J.-A. Pineiro, S.F. Oberman, J.-M. Muller, J.D. Bruguera
2005 IEEE transactions on computers  
A table-based method for high-speed function approximation in single-precision floating-point format is presented in this paper.  ...  Our focus is the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithms, trigonometric functions, powering (with a fixed exponent p), or special functions.  ...  14] , [26] , have led to the development of hardware-oriented methods for high-speed function approximation.  ... 
doi:10.1109/tc.2005.52 fatcat:kno2jv7nsnek3c2ivajlkxzuba

Hybrid Architecture for Data-Dependent Superimposed Training in Digital Receivers

Fernando Martín del Campo, René Cumplido, Roberto Perez-Andrade, A.G. Orozco-Lugo
2008 2008 International Conference on Reconfigurable Computing and FPGAs  
some of the most common operations encountered in the DSP field.  ...  The resulting system can be used partially or in its totality to implement many other algorithms with similar needs, and in fact it is an interesting source of information for implementing solutions for  ...  The high complexity of these operations comes not from the two multiplications required to obtain the squares of the real and imaginary parts of a complex number, but from the necessity to perform a square  ... 
doi:10.1109/reconfig.2008.52 dblp:conf/reconfig/CampoCPO08 fatcat:xqwqo5lx6nh6hepfeakzcx6cuy

Convergence of Newton Raphson Method and its Variants

Department of Mathematics, University Institute of Sciences, Chandigarh University, Gharuan, Mohali- 140413, Punjab, India.
2021 Journal of University of Shanghai for Science and Technology  
The derivation of the Newton Raphson formula, examples, uses, advantages, and downwards of the Newton Raphson Method has also been discussed during this dissertation.  ...  In Numerical Analysis and various uses, including operation testing and processing, Newton's method may be a fundamental technique.  ...  Example Remember the question of discovering a number's square root. One of the techniques for computing square roots is Newton's method.  ... 
doi:10.51201/jusst/21/07265 fatcat:c6vfxa7ecfcgtnii43wzqz6ccm
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