research-article

High-Precision Floating-Point Arithmetic in Scientific Computation

Author:

David H. BaileyAuthors Info & Claims

Computing in Science and Engineering, Volume 7, Issue 3

Pages 54 - 61

https://doi.org/10.1109/MCSE.2005.52

Published: 01 May 2005 Publication History

Abstract

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: some of these applications require roughly twice this level; others require four times; while still others require hundreds or more digits to obtain numerically meaningful results. Such calculations have been facilitated by new high-precision software packages that include high-level language translation modules to minimize the conversion effort. These activities have yielded a number of interesting new scientific results in fields as diverse as quantum theory, climate modeling and experimental mathematics, a few of which are described in this article. Such developments suggest that in the future, the numeric precision used for a scientific computation may be as important to the program design as are the algorithms and data structures.

References

[1]

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer-Verlag, 2001.

[2]

R.P. Brent, "A Fortran Multiple-Precision Arithmetic Package," ACM Trans. Mathematical Software, vol. 4, no. 1, 1978, pp. 57–70.

Digital Library

[3]

D.H. Bailey and X.S. Li, "A Comparison of Three High-Precision Quadrature Schemes," Computational Research Division, Berkeley Lab Computing Sciences, 2004; http://crd.lbl.gov/~dhbailey/dhbpapers/quadrature.pdf.

[4]

D.H. Bailey and S. Robins, "Highly Parallel, High-Precision Numerical Integration," Computational Research Division, Berkeley Lab Computing Sciences, 2004; http://crd.lbl.gov/~dhbailey/dhbpapers/quadparallel.pdf.

[5]

Y. He and C. Ding, "Using Accurate Arithmetics to Improve Numerical Reproducibility and Stability in Parallel Applications," J. Supercomputing, vol. 18, no. 3, 2001, pp. 259–277.

Digital Library

[6]

P.H. Hauschildt and E. Baron, "The Numerical Solution of the Expanding Stellar Atmosphere Problem," J. Computational and Applied Mathematics, vol. 109, 1999, pp. 41–63.

[7]

D.H. Bailey and A.M. Frolov, "Universal Variational Expansion for High-Precision Bound-State Calculations in Three-Body Systems: Applications to Weakly-Bound, Adiabatic and Two-Shell Cluster Systems," J. Physics B, vol. 35, no. 20, 2002, pp. 4287–4298.

[8]

A.M. Frolov and D.H. Bailey, "Highly Accurate Evaluation of the Few-Body Auxiliary Functions and Four-Body Integrals," J. Physics B, vol. 36, no. 9, 2003, pp. 1857–1867.

[9]

Z.-C. Yan and G.W.F. Drake, "Bethe Logarithm and QED Shift for Lithium," Physical Rev. Letters, vol. 81, 12 Sept. 2003, pp. 774–777.

[10]

T. Zhang Z.-C. Yan and G.W.F. Drake, "QED Corrections of O(mc<sup>2</sup>α<sup>7</sup>lnα) to the Fine Structure Splittings of Helium and He-Like Ions," Physical Rev. Letters, vol. 77, no. 26, 1994, pp. 1715–1718.

[11]

B.E. Barrowes, et al., "Asymptotic Expansions of the Prolate Angular Spheroidal Wave Function for Complex Size Parameter," to appear in Studies in Applied Mathematics, 2005.

[12]

R.E. Caflisch, "Singularity Formation for Complex Solutions of the 3D Incompressible Euler Equations," Physica D, vol. 67, no. 1, 1993, pp. 1–18.

Digital Library

[13]

D.H. Bailey R. Krasny and R. Pelz, "Multiple Precision, Multiple Processor Vortex Sheet Roll-Up Computation," Proc. 6th SIAM Conf. Parallel Processing for Scientific Computing, SIAM Press, 1993, pp. 52–56.

[14]

W. Kahan and J. Darcy, "How Java's Floating-Point Hurts Everyone Everywhere," 1998; www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf.

[15]

D.H. Bailey, "Integer Relation Detection," Computing in Science & Eng., vol. 2, no. 1, 2000, pp. 24–28.

Digital Library

[16]

J.M. Borwein and D.H. Bailey, Mathematics by Experiment: Plausible Reasoning in the 21st Century, AK Peters, 2003.

[17]

D.H. Bailey and D. Broadhurst, "Parallel Integer Relation Detection: Techniques and Applications," Mathematics of Computation, vol. 70, no. 236, 2000, pp. 1719–1736.

Digital Library

[18]

D.H. Bailey and D.J. Broadhurst, "A Seventeenth-Order Polylogarithm Ladder," Computational Research Division, Berkeley Lab Computing Sciences, 1999; http://crd.lbl.gov/~dhbailey/dhbpapers/ladder.pdf.

[19]

D.H. Bailey P.B. Borwein and S. Plouffe, "On the Rapid Computation of Various Polylogarithmic Constants," Mathematics of Computation, vol. 66, no. 218, 1997, pp. 903–913.

Digital Library

[20]

D.H. Bailey and R.E. Crandall, "On the Random Character of Fundamental Constant Expansions," Experimental Mathematics, vol. 10, no. 2, 2001, pp. 175–190.

[21]

W. Gibbs, "A Digital Slice of Pi," Scientific Am., vol. 288, no. 5, 2003, pp. 23–24.

[22]

E. Klarreich, "Math Lab: How Computer Experiments Are Transforming Mathematics," Science News, vol. 165, 24 Apr. 2004, pp. 266–268.

[23]

D.H. Bailey and R.E. Crandall, "Random Generators and Normal Numbers," Experimental Mathematics, vol. 11, no. 4, 2004, pp. 527–546.

[24]

D.J. Broadhurst, "Massive Three-Loop Feynman Diagrams Reducible to SC* Primitives of Algebras of the Sixth Root of Unity," to appear in European Physical J. C, 2005; http://xxx.lanl.gov/abs/hep-th/9803091.

Cited By

Bommana ASiddamshetty SPudi DThumatti K. R. ABoppu SSabarimalai Manikandan MCenkeramaddi L(2023)Design of Synthesis-time Vectorized Arithmetic Hardware for Tapered Floating-point Addition and SubtractionACM Transactions on Design Automation of Electronic Systems10.1145/356742328:3(1-35)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1145/3567423
Feng BWang YChen GZhang WXie YDing YLee JPetrank E(2021)EGEMM-TCProceedings of the 26th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming10.1145/3437801.3441599(278-291)Online publication date: 17-Feb-2021
https://dl.acm.org/doi/10.1145/3437801.3441599
Mascagni MNeuman BDubois AMonroe LRobey R(2020)Fast, good, and repeatableInternational Journal of High Performance Computing Applications10.1177/109434202093842534:5(519-531)Online publication date: 1-Sep-2020
https://dl.acm.org/doi/10.1177/1094342020938425
Show More Cited By

Index Terms

High-Precision Floating-Point Arithmetic in Scientific Computation
1. Applied computing
  1. Physical sciences and engineering
    1. Chemistry
    2. Physics
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Arbitrary-precision arithmetic

Recommendations

Processor support for decimal floating-point arithmetic
Decimal Floating-Point Multiplication

Decimal multiplication is important in many commercial applications including financial analysis, banking, tax calculation, currency conversion, insurance, and accounting. This paper presents the design of two decimal floating-point multipliers: one ...
A binary floating-point adder with the signed-digit number arithmetic
CEA'07: Proceedings of the 2007 annual Conference on International Conference on Computer Engineering and Applications

In a conventional binary floating-point number arithmetic system, two's complement number representation is often used to perform addition/subtraction in a floating-point adder. Since the significand of an addition operand is usually expressed as a sign-...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Computing in Science and Engineering

Computing in Science and Engineering Volume 7, Issue 3

May 2005

89 pages

ISSN:1521-9615

Issue’s Table of Contents

Copyright © 2005.

Publisher

IEEE Educational Activities Department

United States

Publication History

Published: 01 May 2005

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

26
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 01 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Bommana ASiddamshetty SPudi DThumatti K. R. ABoppu SSabarimalai Manikandan MCenkeramaddi L(2023)Design of Synthesis-time Vectorized Arithmetic Hardware for Tapered Floating-point Addition and SubtractionACM Transactions on Design Automation of Electronic Systems10.1145/356742328:3(1-35)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1145/3567423
Feng BWang YChen GZhang WXie YDing YLee JPetrank E(2021)EGEMM-TCProceedings of the 26th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming10.1145/3437801.3441599(278-291)Online publication date: 17-Feb-2021
https://dl.acm.org/doi/10.1145/3437801.3441599
Mascagni MNeuman BDubois AMonroe LRobey R(2020)Fast, good, and repeatableInternational Journal of High Performance Computing Applications10.1177/109434202093842534:5(519-531)Online publication date: 1-Sep-2020
https://dl.acm.org/doi/10.1177/1094342020938425
Hanuman CKamala JAruna A(2020)Implementation of high precision/low latency FP divider using Urdhva–Tiryakbhyam multiplier for SoC applicationsDesign Automation for Embedded Systems10.1007/s10617-019-09225-224:2(111-125)Online publication date: 1-Jun-2020
https://dl.acm.org/doi/10.1007/s10617-019-09225-2
Ahmad KSundar HHall M(2019)Data-driven Mixed Precision Sparse Matrix Vector Multiplication for GPUsACM Transactions on Architecture and Code Optimization10.1145/337127516:4(1-24)Online publication date: 17-Dec-2019
https://dl.acm.org/doi/10.1145/3371275
Warr RWight C(2019)Error Bounds for Cumulative Distribution Functions of Convolutions via the Discrete Fourier TransformMethodology and Computing in Applied Probability10.1007/s11009-019-09739-z22:3(881-904)Online publication date: 30-Aug-2019
https://dl.acm.org/doi/10.1007/s11009-019-09739-z
Deelman EPeterka TAltintas ICarothers Cvan Dam KMoreland KParashar MRamakrishnan LTaufer MVetter J(2018)The future of scientific workflowsInternational Journal of High Performance Computing Applications10.5555/3195474.319547732:1(159-175)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.5555/3195474.3195477
Feinberg BVengalam UWhitehair NWang SIpek E(2018)Enabling scientific computing on memristive acceleratorsProceedings of the 45th Annual International Symposium on Computer Architecture10.1109/ISCA.2018.00039(367-382)Online publication date: 2-Jun-2018
https://dl.acm.org/doi/10.1109/ISCA.2018.00039
Nicponski JJung J(2018)A Note on High-Precision Approximation of Asymptotically Decaying Solution and Orthogonal DecompositionJournal of Scientific Computing10.1007/s10915-017-0619-076:1(189-215)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.1007/s10915-017-0619-0
Hamza RMuhammad KLv ZTitouna F(2017)Secure video summarization framework for personalized wireless capsule endoscopyPervasive and Mobile Computing10.1016/j.pmcj.2017.03.01141:C(436-450)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1016/j.pmcj.2017.03.011
Show More Cited By

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents