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Double-precision floating-point format

About: Double-precision floating-point format is a(n) research topic. Over the lifetime, 1204 publication(s) have been published within this topic receiving 20010 citation(s). The topic is also known as: binary64 & double.

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Open accessJournal ArticleDOI: 10.1021/CT200909J
Andreas W. Götz1, Mark J. Williamson1, Dong Xu1, Duncan Poole2  +2 moreInstitutions (2)
Abstract: We present an implementation of generalized Born implicit solvent all-atom classical molecular dynamics (MD) within the AMBER program package that runs entirely on CUDA enabled NVIDIA graphics processing units (GPUs). We discuss the algorithms that are used to exploit the processing power of the GPUs and show the performance that can be achieved in comparison to simulations on conventional CPU clusters. The implementation supports three different precision models in which the contributions to the forces are calculated in single precision floating point arithmetic but accumulated in double precision (SPDP), or everything is computed in single precision (SPSP) or double precision (DPDP). In addition to performance, we have focused on understanding the implications of the different precision models on the outcome of implicit solvent MD simulations. We show results for a range of tests including the accuracy of single point force evaluations and energy conservation as well as structural properties pertainining to protein dynamics. The numerical noise due to rounding errors within the SPSP precision model is sufficiently large to lead to an accumulation of errors which can result in unphysical trajectories for long time scale simulations. We recommend the use of the mixed-precision SPDP model since the numerical results obtained are comparable with those of the full double precision DPDP model and the reference double precision CPU implementation but at significantly reduced computational cost. Our implementation provides performance for GB simulations on a single desktop that is on par with, and in some cases exceeds, that of traditional supercomputers.

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1,282 Citations


Journal ArticleDOI: 10.1016/J.CPC.2012.09.022
Abstract: A new precision model is proposed for the acceleration of all-atom classical molecular dynamics (MD) simulations on graphics processing units (GPUs). This precision model replaces double precision arithmetic with fixed point integer arithmetic for the accumulation of force components as compared to a previously introduced model that uses mixed single/double precision arithmetic. This significantly boosts performance on modern GPU hardware without sacrificing numerical accuracy. We present an implementation for NVIDIA GPUs of both generalized Born implicit solvent simulations as well as explicit solvent simulations using the particle mesh Ewald (PME) algorithm for long-range electrostatics using this precision model. Tests demonstrate both the performance of this implementation as well as its numerical stability for constant energy and constant temperature biomolecular MD as compared to a double precision CPU implementation and double and mixed single/double precision GPU implementations.

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675 Citations


Open accessJournal ArticleDOI: 10.1007/PL00009321
Jonathan Richard Shewchuk1Institutions (1)
Abstract: Exact computer arithmetic has a variety of uses, including the robust implementation of geometric algorithms. This article has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive precision arithmetic that can often speed these algorithms when they are used to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to use these techniques to develop implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small.

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553 Citations


Open accessJournal ArticleDOI: 10.1007/BF01397083
Abstract: A technique is described for expressing multilength floating-point arithmetic in terms of singlelength floating point arithmetic, i.e. the arithmetic for an available (say: single or double precision) floating-point number system. The basic algorithms are exact addition and multiplication of two singlelength floating-point numbers, delivering the result as a doublelength floating-point number. A straight-forward application of the technique yields a set of algorithms for doublelength arithmetic which are given as ALGOL 60 procedures.

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444 Citations


Open accessJournal ArticleDOI: 10.1016/J.CPC.2010.05.002
Abstract: Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodynamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU ( 3 ) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson–Dirac sparse matrix–vector product that performs at up to 40, 135 and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

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334 Citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202123
202032
201923
201834
201726
201654

Top Attributes

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Topic's top 5 most impactful authors

James E. Stine

9 papers, 82 citations

Shawn D. Lundvall

8 papers, 96 citations

Guy Even

7 papers, 362 citations

George A. Constantinides

7 papers, 88 citations

Hossam A. H. Fahmy

7 papers, 90 citations

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