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Decimal Floating-Point Square Root Using Newton-Raphson Iteration

*
2005 IEEE International Conference on Application-Specific Systems, Architecture Processors (ASAP'05)
*

This design

doi:10.1109/asap.2005.29
dblp:conf/asap/WangS05
fatcat:5qic6pqqrjcerexn225cpausgu
*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. ...##
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Implementation of an Algorithm to Calculate the Inverse Square Root Operation in a Microcontroller

2012
*
International Journal of Computer and Communication Engineering
*

In this paper, an algorithm to calculate the inverse

doi:10.7763/ijcce.2012.v1.78
fatcat:x4buepdvprdz3kwdgrol7c44gi
*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. ...##
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Energy and Delay Improvement via Decimal Floating Point Units

2009
*
2009 19th IEEE Symposium on Computer Arithmetic
*

This paper presents new designs for

doi:10.1109/arith.2009.21
dblp:conf/arith/FahmyRASEF09
fatcat:6klu3s6kgbbuxcbfw73q2tkthm
*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 ...##
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Decimal SRT Square Root: Algorithm and Architecture

2013
*
Circuits, systems, and signal processing
*

Functional algorithms, entailing multiplication per

doi:10.1007/s00034-013-9586-3
fatcat:gcxx4n4hkzduhmh4oaxshgjl3i
*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*. ...##
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Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics

2012
*
The American mathematical monthly
*

This article examines the computation of

doi:10.4169/amer.math.monthly.119.08.646
fatcat:wbtvz3gn4rh5ddn2tryoicrmle
*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 ...##
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Ancient Indian Square Roots
[chapter]

2014
*
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures
*

This article examines the computation of

doi:10.1007/978-94-007-3934-5_10265-1
fatcat:dmzpqppjvfbkzp3r56hx6mdd2y
*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 ...##
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Implementation of Fixed and Floating Point Square Root Using Nonrestoring Algorithm on FPGA

2013
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International Journal of Computer and Electrical Engineering
*

In this paper, we present pipelined architecture to implement 8 bit fixed and

doi:10.7763/ijcee.2013.v5.767
fatcat:l563sikxyveapfngirzqgstonu
*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*. ...##
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A cost effective lighting processor for 3D graphics application

1999
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Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348)
*

These various light models are widely

doi:10.1109/icip.1999.823005
dblp:conf/icip/ChenL99
fatcat:vkkdlbfagng2rojskzyovycvum
*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. ...##
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Exponential Computing Digital Circuit Design Developed for FPGA-based Embedded Systems

2020
*
Academic Perspective Procedia
*

In exponential expressions like

doi:10.33793/acperpro.03.01.59
fatcat:vpp6z6gqafh6xabhjedouwktdu
*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] . ...##
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Floating-Point Division Operator based on CORDIC Algorithm

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

doi:10.37936/ecti-cit.201371.54356
fatcat:du2eftzcfzaxznqtecaxbltajm
*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 ...##
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Optimizing Secure Statistical Computations with PICCO
[article]

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 . ...

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

2015
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Computation
*

A computationally simple approximate solution to the location of the most significant terms as well as the exact solution based on a

doi:10.3390/computation3020326
fatcat:usz7vegk2jdwtcchdwgrvp7ife
*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). ...##
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A Radix-10 Digit-Recurrence Division Unit: Algorithm and Architecture

2007
*
IEEE Transactions on Computers
*

Index Terms-

doi:10.1109/tc.2007.1038
dblp:journals/tc/LangN06
fatcat:mzqt6jde4zccjh2cxtq6gohvjm
*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*). ...##
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A NOVEL QUOTIENT PREDICTION FOR FLOATING-POINT DIVISION

2020
*
Journal of Science and Technology - IUH
*

However,

doi:10.46242/jst-iuh.v38i02.284
fatcat:4k2nkavkq5g7vn3ydousesx76u
*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] . ...##
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Fast Computation of the n-th Root in Quad-double Arithmetic Using a Fourth-order Iterative Scheme

2013
*
Journal of Information Processing
*

We propose new algorithms for computing the n-th

doi:10.2197/ipsjjip.21.315
fatcat:j46pyepgnfdwdkx2hksoljc3bq
*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. ...
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