Modern Computer Arithmetic

Montuschi, Paolo; Muller, Jean-Michel

doi:10.1017/cbo9780511921698

Cited by 201 publications

(164 citation statements)

References 28 publications

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“…215-245], [26, pp. 299-318], [27,28,29], and [32]. Software packages implementing these schemes have been available since the early days of computing.…”

Section: High-precision Softwarementioning

confidence: 99%

High-precision computation: Mathematical physics and dynamics

Bailey

Barrio

Borwein

2012

Applied Mathematics and Computation

105

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At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort. This paper presents a survey of recent applications of these techniques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, studies of the fine structure constant, scattering amplitudes of quarks, gluons and bosons, nonlinear oscillator theory, experimental mathematics, evaluation of orthogonal polynomials, numerical integration of ODEs, computation of periodic orbits, studies of the splitting of separatrices, detection of strange nonchaotic attractors, Ising theory, quantum field theory, and discrete dynamical systems. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.

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“…215-245], [26, pp. 299-318], [27,28,29], and [32]. Software packages implementing these schemes have been available since the early days of computing.…”

Section: High-precision Softwarementioning

confidence: 99%

High-precision computation: Mathematical physics and dynamics

Bailey

Barrio

Borwein

2012

Applied Mathematics and Computation

105

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“…NewtonRaphson algorithm [22] can be used to compute functional inverse functions, such as reciprocal, division, reciprocal square root, and square root. A table lookup, which stores the approximate value, is always followed to reduce the number of Newton-Raphson iteration.…”

Section: Methods For Elementary Functionmentioning

confidence: 99%

“…[22] This iteration has quadratical convergence and the number of iterations is N n =log 2 (prec r /prec i ).…”

Section: Vp Division Algorithmmentioning

confidence: 99%

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FPGA-Specific Custom VLIW Architecture for Arbitrary Precision Floating-Point Arithmetic

Lei

Dou

Zhou

2011

IEICE Trans. Inf. & Syst.

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SUMMARYMany scientific applications require efficient variableprecision floating-point arithmetic. This paper presents a special-purpose Very Large Instruction Word (VLIW) architecture for variable precision floating-point arithmetic (VV-Processor) on FPGA. The proposed processor uses a unified hardware structure, equipped with multiple custom variable-precision arithmetic units, to implement various variable-precision algebraic and transcendental functions. The performance is improved through the explicitly parallel technology of VLIW instruction and by dynamically varying the precision of intermediate computation. We take division and exponential function as examples to illustrate the design of variable-precision elementary algorithms in VV-Processor. Finally, we create a prototype of VV-Processor unit on a Xilinx XC6VLX760-2FF1760 FPGA chip. The experimental results show that one VV-Processor unit, running at 253 MHz, outperforms the approach of a software-based library running on an Intel Core i3 530 CPU at 2.93 GHz by a factor of 5X-37X for basic variable-precision arithmetic operations and elementary functions.

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“…If n 0 is the threshold between classical multiplication and Karatsuba algorithm then up to threshold limit n 0 we can use Nikhilam multiply and beyond that limit we can use Karatsuba multiply. We can write the Karatsuba algorithm as given in [2], with the only modification that if n < n 0 NikhilamMultiplication is called. The corresponding pseudo code is given in Algorithm 3.…”

Section: Applicationsmentioning

confidence: 99%

An Efficient Multiplication Algorithm using Nikhilam Method

Dwivedi¹

2013

Fifth International Conference on Advances in Recent Technologies in Communication and Computing (ARTCom 2013)

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Abstract-Multiplication is one of the most important operation in computer arithmetic. Many integer operations such as squaring, division and computing reciprocal require same order of time as multiplication whereas some other operations such as computing GCD and residue operation require at most a factor of log n time more than multiplication. We propose an integer multiplication algorithm using Nikhilam method of Vedic mathematics which can be used to multiply two binary numbers efficiently.

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Modern Computer Arithmetic

Cited by 201 publications

References 28 publications

High-precision computation: Mathematical physics and dynamics

High-precision computation: Mathematical physics and dynamics

FPGA-Specific Custom VLIW Architecture for Arbitrary Precision Floating-Point Arithmetic

An Efficient Multiplication Algorithm using Nikhilam Method

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