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Decimal Floating-Point Square Root Using Newton-Raphson Iteration

Liang-Kai Wang, M.J. Schulte
2005 IEEE International Conference on Application-Specific Systems, Architecture Processors (ASAP'05)  
This design uses an optimized piecewise linear approximation, a modified Newton-Raphson iteration, a specialized rounding technique, and a modified decimal multiplier.  ...  This paper presents an efficient arithmetic algorithm and hardware design for decimal floatingpoint square root.  ...  Decimal Square Root Algorithm Newton-Raphson iteration provides a high-speed method for computing square root of a number.  ... 
doi:10.1109/asap.2005.29 dblp:conf/asap/WangS05 fatcat:5qic6pqqrjcerexn225cpausgu

Implementation of an Algorithm to Calculate the Inverse Square Root Operation in a Microcontroller

L. Orozco, M. F. Rocha, C. A. Calva, M. R. Osnaya, M. I. Rocha, R. Navarrete, E. Andrade, C. Solis
2012 International Journal of Computer and Communication Engineering  
In this paper, an algorithm to calculate the inverse square root operation in Fixed-Point arithmetic is implemented in a microcontroller using Newton-Raphson Method and Least Squares Method.  ...  Index Terms-Firmware, fixed-point, inverse square root algorithm, microcontroller.  ...  The iterative function of Newton-Raphson Method is shown in equation 4.  ... 
doi:10.7763/ijcce.2012.v1.78 fatcat:x4buepdvprdz3kwdgrol7c44gi

Energy and Delay Improvement via Decimal Floating Point Units

Hossam A. H. Fahmy, Ramy Raafat, Amira M. Abdel-Majeed, Rodina Samy, Tarek ElDeeb, Yasmin Farouk
2009 2009 19th IEEE Symposium on Computer Arithmetic  
This paper presents new designs for decimal floating point (DFP) addition, multiplication, fused multiplyadd, division, and square root.  ...  It stresses the importance of energy savings achieved by hardware implementations of the IEEE standard for decimal floating point.  ...  Decimal divider and square root Our design for the divider and square root uses a modified Newton-Raphson method [11] , [13] to generate the initial approximation then iterate on the equation x i+1  ... 
doi:10.1109/arith.2009.21 dblp:conf/arith/FahmyRASEF09 fatcat:6klu3s6kgbbuxcbfw73q2tkthm

Decimal SRT Square Root: Algorithm and Architecture

Amir Kaivani, Seok-Bum Ko
2013 Circuits, systems, and signal processing  
Functional algorithms, entailing multiplication per iteration, seem inadequate to use for decimal square roots, given the high cost of decimal multipliers.  ...  Besides the four basic operations, the square root can be implemented as an instruction directly in the hardware, which improves the performance of the decimal floating-point unit in the processors.  ...  Decimal square rooters are usually implemented in hardware using functional algorithms such as Newton-Raphson [13, 17] and [12] . However, these methods require a multiplication per iteration.  ... 
doi:10.1007/s00034-013-9586-3 fatcat:gcxx4n4hkzduhmh4oaxshgjl3i

Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics

David H. Bailey, Jonathan M. Borwein
2012 The American mathematical monthly  
This article examines the computation of square roots in ancient India in the context of the discovery of positional decimal arithmetic.  ...  Acknowledgements The authors wish to thank useful comments and suggestions by Hemant Shukla, Shrikrishna G. Dani and three anonymous reviewers.  ...  Now let us compare the corresponding decimal values, together with the results of a Newton-Raphson-Heron iteration (starting with 316227), a Bakhshali iteration (starting with 316227), and the exact result  ... 
doi:10.4169/amer.math.monthly.119.08.646 fatcat:wbtvz3gn4rh5ddn2tryoicrmle

Ancient Indian Square Roots [chapter]

David H. Bailey, Jonathan M. Borwein
2014 Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures  
This article examines the computation of square roots in ancient India in the context of the discovery of positional decimal arithmetic.  ...  Acknowledgements The authors wish to thank useful comments and suggestions by Hemant Shukla, Shrikrishna G. Dani and three anonymous reviewers.  ...  Now let us compare the corresponding decimal values, together with the results of a Newton-Raphson-Heron iteration (starting with 316227), a Bakhshali iteration (starting with 316227), and the exact result  ... 
doi:10.1007/978-94-007-3934-5_10265-1 fatcat:dmzpqppjvfbkzp3r56hx6mdd2y

Implementation of Fixed and Floating Point Square Root Using Nonrestoring Algorithm on FPGA

Anuja Nanhe, Gaurav Gawali, Shashank Ahire, K. Sivasankaran
2013 International Journal of Computer and Electrical Engineering  
In this paper, we present pipelined architecture to implement 8 bit fixed and floating point square root in Field Programmable Gate Array (FPGA) using modified nonrestoring square root algorithm.  ...  Index Terms-Controlled subtract multiplex, fixed point, FPGA, nonrestoring, square root, verilog HDL.  ...  In case of floating point quotient, first four bits starting from MSB represent number before decimal point and the remaining bits represent number after decimal point.  ... 
doi:10.7763/ijcee.2013.v5.767 fatcat:l563sikxyveapfngirzqgstonu

A cost effective lighting processor for 3D graphics application

Cheng-Hsien Chen, Chen-Yi Lee
1999 Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348)  
These various light models are widely used in entertainment and game applications.  ...  Color accuracy is taken into account under fix-point simulation in MESA 3D graphics library.  ...  Taylor series or Newton-Raphson iteration is commonly used for hardware implementation.  ... 
doi:10.1109/icip.1999.823005 dblp:conf/icip/ChenL99 fatcat:vkkdlbfagng2rojskzyovycvum

Exponential Computing Digital Circuit Design Developed for FPGA-based Embedded Systems

Serkan Dereli, Mahmut Uç
2020 Academic Perspective Procedia  
In exponential expressions like square roots and cube roots, just like these circuits, it is found in many digital systems and performs tasks.  ...  In this study, a digital circuit design that computes both the integer and a floating point exponent of a 32-bit floating-point number has been realized.  ...  Guardia and Boemo were able to realize the cube root of floating point numbers in IEEE 754-2008 standard with Newton-Raphson method in only two iterations in their study [13] .  ... 
doi:10.33793/acperpro.03.01.59 fatcat:vpp6z6gqafh6xabhjedouwktdu

Floating-Point Division Operator based on CORDIC Algorithm

Pongyupinpanich Surapong, Faizal Arya Samman
1970 ECTI Transactions on Computer and Information Technology  
A hardware architecture of CORDIC algorithm capable of processing broader input ranges is implemented and presented in this paper by using a pre-processing and a post-processing stage.  ...  Oberman et al. for example [11] proposes a floating-point divider and square root for AMD-K7 by using Goldschmidt's algorithm.  ...  The work in [14] has presented for example a decimal floating-point divider using newtonraphson iteration, where an accurate piece-wise linear approximation is used to obtain an initial estimate of a  ... 
doi:10.37936/ecti-cit.201371.54356 fatcat:du2eftzcfzaxznqtecaxbltajm

Optimizing Secure Statistical Computations with PICCO [article]

Justin DeBenedetto, Marina Blanton
2016 arXiv   pre-print
using a general-purpose compiler.  ...  Here we assess performance of common statistical programs using PICCO.  ...  Next, we follow the Newton-Raphson method of iterations using the following formula for the kth iteration: b k = 1 2 b k−1 + a b k−1 .  ... 
arXiv:1612.08678v1 fatcat:eapdcmluknedtbhjmm5cmzcz44

Fast Computation of the Non-Central Chi Square PDF Outside the HDR Under a Requisite Precision Constraint

Paul Gendron
2015 Computation  
A computationally simple approximate solution to the location of the most significant terms as well as the exact solution based on a Newton-Raphson iteration is presented.  ...  Computationally efficient recursions are used over these improved intervals.  ...  Employing the more accurate starting point of Equation (12) requires a Newton-Raphson iteration and thus the evaluation of the information scale, I(n).  ... 
doi:10.3390/computation3020326 fatcat:usz7vegk2jdwtcchdwgrvp7ife

A Radix-10 Digit-Recurrence Division Unit: Algorithm and Architecture

Tomas Lang, Alberto Nannarelli
2007 IEEE Transactions on Computers  
Index Terms-Decimal arithmetic, digit-recurrence division, decimal division, algorithms and architectures for floating-point arithmetic.  ...  proposed radix-10 division unit show that its latency is close to that of radix-16 division units (comparable dynamic range of significands) and it has a shorter latency than a radix-10 unit based on the Newton-Raphson  ...  perform a decimal multiplication and m is the number of iterations needed for the approximation of 1=d (Newton-Raphson iterations).  ... 
doi:10.1109/tc.2007.1038 dblp:journals/tc/LangN06 fatcat:mzqt6jde4zccjh2cxtq6gohvjm


2020 Journal of Science and Technology - IUH  
However, floating-point division is slower than floating-point multiplication.  ...  The experimental results show that only 3 to 5 iterations are required to obtain the final quotient in a floating-point division computation.  ...  The Newton-Raphson-Base division is a technique, which uses iterative architecture to obtain roots [2] [19] . The CRO is proposed based on the GA method [20] .  ... 
doi:10.46242/jst-iuh.v38i02.284 fatcat:4k2nkavkq5g7vn3ydousesx76u

Fast Computation of the n-th Root in Quad-double Arithmetic Using a Fourth-order Iterative Scheme

Tsubasa Saito
2013 Journal of Information Processing  
We propose new algorithms for computing the n-th root of a quad-double number.  ...  We construct an iterative scheme that has quartic convergence and propose algorithms that require only about 50% to 60% of the doubleprecision arithmetic operations of the existing algorithms.  ...  Acknowledgments The author would like to thank the anonymous reviewers for their useful comments.  ... 
doi:10.2197/ipsjjip.21.315 fatcat:j46pyepgnfdwdkx2hksoljc3bq
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