IEEE Standard for Binary Floating-Point Arithmetic

May, John F.; Riganati, John P.; Sherr, Sava I.; Beall, J. H.; Buckley, Fletcher J.; Castenschiold, R.; Chelotti, Edward; Cohen, Edward J.; Cummings, Paul; Fleckenstein, Donald C.; Forster, Jay; Goldberg, Daniel L.; Hendrix, Kenneth D.; Howell, Irvin N.; Kinn, Jack; Koepfinger, Joseph L.; Kolodny, Irving; Lawrence, R. F.; McCall, Lawrence V.; Michael, Donald T.; Rose, Frank L.; Swanson, Clifford O.; Weger, J. Richard; Wilkens, W. B.; Wylie, Charles J.; Allison, Andrew; Ames, W.F.; Arya, Mike; Baron, Janis; Baumel, Steve; Bhandarkar, Dileep; Boney, Joel; Bristol, E. H.; Buchholz, Werner; Bunch, Jim; Burdick, Ed; Burke, Gary R.; Clemente, P. C. M.; Cody, W. J.; Coonen, Jerome T.; Crapuchettes, Jim; Davidesko, Itzhak; Davison, W.R.; Delp, R. H.; Demmel, James; Denman, Donn; Despain, Alvin M.; Dubrulle, Augustin A.; Eggers, Tom; Faillace, Philip J.; Fateman, Richard J.; Feign, David; Feinberg, Don; Feldman, Smart; Fisher, E. K.; Flanagan, Paul F.; Force, Gordon; Fosdick, Lloyd D.; Fraley, R. Chris; Fullmer, Howard; Gajski, Daniel D.; Gear, C. W.; Graham, M.; Gustavson, D.B.; Haas, Guy K.; Hanson, Kenton; Hastings, Chuck; Hough, David; Howe, J. E.; Hull, T. E.; Irukulla, Suren; Richard, Richard; Jensen, Paul S.; Kahan, W.; Kaikow, Howard; Karpinski, Richard; Klema, Virginia; Kohn, Les; Kuyper, Dan; Maples, M.; Martin, Roy J.; McAllister, William; McMaster, Colin; Miller, Dean; Miller, Webb; Nash, John C.; 'Dowd, Dan O; Olsen, Cash; Padegs, A.; Palmer, J.; Parlett, Beresford Ν.; Patterson, Dave; Payne, Mary; Pittman, Tom; Randall, Lew; Reid, Robert J.; Reinsch, C.; Ris, Frederic N.; Schmidt, Stan; Shahan, Van; Smith, Robert L.; Stafford, Roger; Stewart, G. W.; Stewart, Robert W.; Stone, Harold S.; Strecker, William D.; Swarz, Robert S.; Taylor, G. L.; Thomas, James W.; Tsien, Dar-Sun; Walker, Greg; Walther, John Stephen; Waser, Shlomo; Waterman, P. C.; White, Charles E.

doi:10.1109/ieeestd.1985.82928

Cited by 130 publications

(38 citation statements)

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“…The limited native precision is overcome by algorithms which implement multi-precision arithmetic using two native floatingpoint registers [20,21]. On hardware supporting the IEEE 754-1985 floating-point standard [22], proofs of numerical exactness have been given for multi-precision addition and multiplication [23]. For the GPU, which does not fully comply with IEEE 754-1985 in terms of rounding and division, these proofs have been adapted for double-single precision arithmetic using two native single precision floats [24].…”

Section: Double-single Precision Floating-point Arithmeticmentioning

confidence: 99%

Highly accelerated simulations of glassy dynamics using GPUs: Caveats on limited floating-point precision

Colberg

Höfling

2011

Computer Physics Communications

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Modern graphics processing units (GPUs) provide impressive computing resources, which can be accessed conveniently through the CUDA programming interface. We describe how GPUs can be used to considerably speed up molecular dynamics (MD) simulations for system sizes ranging up to about 1 million particles. Particular emphasis is put on the numerical long-time stability in terms of energy and momentum conservation, and caveats on limited floating-point precision are issued. Strict energy conservation over 10 8 MD steps is obtained by double-single emulation of the floating-point arithmetic in accuracy-critical parts of the algorithm. For the slow dynamics of a supercooled binary Lennard-Jones mixture, we demonstrate that the use of single-floating point precision may result in quantitatively and even physically wrong results. For simulations of a Lennard-Jones fluid, the described implementation shows speedup factors of up to 80 compared to a serial implementation for the CPU, and a single GPU was found to compare with a parallelised MD simulation using 64 distributed cores.

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Section: Double-single Precision Floating-point Arithmeticmentioning

confidence: 99%

Highly accelerated simulations of glassy dynamics using GPUs: Caveats on limited floating-point precision

Colberg

Höfling

2011

Computer Physics Communications

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“…For reference, Table 3 lists the maximum pattern orders that fit the primitive data types available on standard computer systems. Although ordinal patterns and their numerical representations are intrinsically integral, Table 3 also references two IEEE 754 floating point formats [36,37]. Those were included because computation environments like NumPy/Python, GNU Octave, and Matlab by default use the binary64 floating point data format.…”

Section: Memory Alignmentmentioning

confidence: 99%

Teaching Ordinal Patterns to a Computer: Efficient Encoding Algorithms Based on the Lehmer Code

Berger

Kravtsiv

Schneider

et al. 2019

Entropy

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Ordinal patterns are the common basis of various techniques used in the study of dynamical systems and nonlinear time series analysis. The present article focusses on the computational problem of turning time series into sequences of ordinal patterns. In a first step, a numerical encoding scheme for ordinal patterns is proposed. Utilising the classical Lehmer code, it enumerates ordinal patterns by consecutive non-negative integers, starting from zero. This compact representation considerably simplifies working with ordinal patterns in the digital domain. Subsequently, three algorithms for the efficient extraction of ordinal patterns from time series are discussed, including previously published approaches that can be adapted to the Lehmer code. The respective strengths and weaknesses of those algorithms are discussed, and further substantiated by benchmark results. One of the algorithms stands out in terms of scalability: its run-time increases linearly with both the pattern order and the sequence length, while its memory footprint is practically negligible. These properties enable the study of high-dimensional pattern spaces at low computational cost. In summary, the tools described herein may improve the efficiency of virtually any ordinal pattern-based analysis method, among them quantitative measures like permutation entropy and symbolic transfer entropy, but also techniques like forbidden pattern identification. Moreover, the concepts presented may allow for putting ideas into practice that up to now had been hindered by computational burden. To enable smooth evaluation, a function library written in the C programming language, as well as language bindings and native implementations for various numerical computation environments are provided in the supplements.

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“…Most modern large programs use two, or sometimes three of the real number precisions defined in the IEEE 754 Standard [1]. The analysis of large programs in aerospace technology and climate research has revealed very large numbers of inconsistencies in the precisions chosen.…”

Section: A) To Test the Adequacy Of The Choices Of Precision In Existmentioning

confidence: 99%

Testing the Numerical Precisions Required to Execute Real World Programs

Collins¹

2017

IJSEA

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IEEE Standard for Binary Floating-Point Arithmetic

Cited by 130 publications

References 0 publications

Highly accelerated simulations of glassy dynamics using GPUs: Caveats on limited floating-point precision

Highly accelerated simulations of glassy dynamics using GPUs: Caveats on limited floating-point precision

Teaching Ordinal Patterns to a Computer: Efficient Encoding Algorithms Based on the Lehmer Code

Testing the Numerical Precisions Required to Execute Real World Programs

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