Kahan summation algorithm (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Kahan summation algorithm" in English language version.

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12doi.org

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8semanticscholar.org

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4github.com

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berkeley.edu

people.eecs.berkeley.edu

Richard Shewchuk, Jonathan (October 1997). "Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates" (PDF). Discrete & Computational Geometry. 18 (3): 305–363. doi:10.1007/PL00009321. S2CID 189937041.

books.google.com

Muller, Jean-Michel; Brunie, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge (2018) [2010]. Handbook of Floating-Point Arithmetic (2 ed.). Birkhäuser. p. 179. doi:10.1007/978-3-319-76526-6. ISBN 978-3-319-76525-9. LCCN 2018935254.

cnx.org

Johnson, S.G.; Frigo, M. C. Sidney Burns (ed.). "Fast Fourier Transforms: Implementing FFTs in Practice". Archived from the original on Dec 20, 2008.

doi.org

Higham, Nicholas J. (1993), "The accuracy of floating point summation", SIAM Journal on Scientific Computing, 14 (4): 783–799, Bibcode:1993SJSC...14..783H, CiteSeerX 10.1.1.43.3535, doi:10.1137/0914050, S2CID 14071038.
Kahan, William (January 1965), "Further remarks on reducing truncation errors" (PDF), Communications of the ACM, 8 (1): 40, doi:10.1145/363707.363723, S2CID 22584810, archived from the original (PDF) on 9 February 2018.
Bresenham, Jack E. (January 1965). "Algorithm for computer control of a digital plotter" (PDF). IBM Systems Journal. 4 (1): 25–30. doi:10.1147/sj.41.0025. S2CID 41898371.
Inose, H.; Yasuda, Y.; Murakami, J. (September 1962). "A Telemetering System by Code Manipulation – ΔΣ Modulation". IRE Transactions on Space Electronics and Telemetry. SET-8: 204–209. doi:10.1109/IRET-SET.1962.5008839. S2CID 51647729.
Muller, Jean-Michel; Brunie, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge (2018) [2010]. Handbook of Floating-Point Arithmetic (2 ed.). Birkhäuser. p. 179. doi:10.1007/978-3-319-76526-6. ISBN 978-3-319-76525-9. LCCN 2018935254.
Neumaier, A. (1974). "Rundungsfehleranalyse einiger Verfahren zur Summation endlicher Summen" [Rounding Error Analysis of Some Methods for Summing Finite Sums] (PDF). Zeitschrift für Angewandte Mathematik und Mechanik (in German). 54 (1): 39–51. Bibcode:1974ZaMM...54...39N. doi:10.1002/zamm.19740540106.
A., Klein (2006). "A generalized Kahan–Babuška-Summation-Algorithm". Computing. 76 (3–4). Springer-Verlag: 279–293. doi:10.1007/s00607-005-0139-x. S2CID 4561254.
Richard Shewchuk, Jonathan (October 1997). "Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates" (PDF). Discrete & Computational Geometry. 18 (3): 305–363. doi:10.1007/PL00009321. S2CID 189937041.
Kirchner, R.; Kulisch, U. (June 1988). "Accurate arithmetic for vector processors". Journal of Parallel and Distributed Computing. 5 (3): 250–270. doi:10.1016/0743-7315(88)90020-2.
Muller, M.; Rub, C.; Rulling, W. (1991). Exact accumulation of floating-point numbers. Proceedings 10th IEEE Symposium on Computer Arithmetic. pp. 64–69. doi:10.1109/ARITH.1991.145535.
Goldberg, David (March 1991), "What every computer scientist should know about floating-point arithmetic" (PDF), ACM Computing Surveys, 23 (1): 5–48, doi:10.1145/103162.103163, S2CID 222008826.
MacDonald, Tom (1991). "C for Numerical Computing". Journal of Supercomputing. 5 (1): 31–48. doi:10.1007/BF00155856. S2CID 27876900.

github.com

Hettinger, R. "Improve accuracy of builtin sum() for float inputs · Issue #100425 · python/cpython". GitHub - CPython v3.12 Added Features. Retrieved 7 October 2023.
RFC: use pairwise summation for sum, cumsum, and cumprod, github.com/JuliaLang/julia pull request #4039 (August 2013).
KahanSummation library in Julia.
HPCsharp nuget package of high performance algorithms.

gnu.org

gcc.gnu.org

GNU Compiler Collection manual, version 4.4.3: 3.10 Options That Control Optimization, -fassociative-math (Jan. 21, 2010).

harvard.edu

ui.adsabs.harvard.edu

Higham, Nicholas J. (1993), "The accuracy of floating point summation", SIAM Journal on Scientific Computing, 14 (4): 783–799, Bibcode:1993SJSC...14..783H, CiteSeerX 10.1.1.43.3535, doi:10.1137/0914050, S2CID 14071038.
Neumaier, A. (1974). "Rundungsfehleranalyse einiger Verfahren zur Summation endlicher Summen" [Rounding Error Analysis of Some Methods for Summing Finite Sums] (PDF). Zeitschrift für Angewandte Mathematik und Mechanik (in German). 54 (1): 39–51. Bibcode:1974ZaMM...54...39N. doi:10.1002/zamm.19740540106.

hp.com

h21007.www2.hp.com

Compaq Fortran User Manual for Tru64 UNIX and Linux Alpha Systems Archived 2011-06-07 at the Wayback Machine, section 5.9.7 Arithmetic Reordering Optimizations (retrieved March 2010).

ibm.com

research.ibm.com

Bresenham, Jack E. (January 1965). "Algorithm for computer control of a digital plotter" (PDF). IBM Systems Journal. 4 (1): 25–30. doi:10.1147/sj.41.0025. S2CID 41898371.

ieee.org

ieeexplore.ieee.org

Muller, M.; Rub, C.; Rulling, W. (1991). Exact accumulation of floating-point numbers. Proceedings 10th IEEE Symposium on Computer Arithmetic. pp. 64–69. doi:10.1109/ARITH.1991.145535.

intel.com

software.intel.com

Martyn J. Corden, "Consistency of floating-point results using the Intel compiler", Intel technical report (Sep. 18, 2009).

loc.gov

lccn.loc.gov

Muller, Jean-Michel; Brunie, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge (2018) [2010]. Handbook of Floating-Point Arithmetic (2 ed.). Birkhäuser. p. 179. doi:10.1007/978-3-319-76526-6. ISBN 978-3-319-76525-9. LCCN 2018935254.

mgnet.org

Kahan, William (January 1965), "Further remarks on reducing truncation errors" (PDF), Communications of the ACM, 8 (1): 40, doi:10.1145/363707.363723, S2CID 22584810, archived from the original (PDF) on 9 February 2018.

microsoft.com

msdn.microsoft.com

Eric Fleegal, "Microsoft Visual C++ Floating-Point Optimization", Microsoft Visual Studio Technical Articles (June 2004).

netlib.org

BLAS Technical Forum, section 2.7 (August 21, 2001), Archived on Wayback Machine.

psu.edu

citeseerx.ist.psu.edu

Higham, Nicholas J. (1993), "The accuracy of floating point summation", SIAM Journal on Scientific Computing, 14 (4): 783–799, Bibcode:1993SJSC...14..783H, CiteSeerX 10.1.1.43.3535, doi:10.1137/0914050, S2CID 14071038.

python.org

docs.python.org

What's New in Python 3.12.

sciencedirect.com

Kirchner, R.; Kulisch, U. (June 1988). "Accurate arithmetic for vector processors". Journal of Parallel and Distributed Computing. 5 (3): 250–270. doi:10.1016/0743-7315(88)90020-2.

semanticscholar.org

api.semanticscholar.org

Higham, Nicholas J. (1993), "The accuracy of floating point summation", SIAM Journal on Scientific Computing, 14 (4): 783–799, Bibcode:1993SJSC...14..783H, CiteSeerX 10.1.1.43.3535, doi:10.1137/0914050, S2CID 14071038.
Kahan, William (January 1965), "Further remarks on reducing truncation errors" (PDF), Communications of the ACM, 8 (1): 40, doi:10.1145/363707.363723, S2CID 22584810, archived from the original (PDF) on 9 February 2018.
Bresenham, Jack E. (January 1965). "Algorithm for computer control of a digital plotter" (PDF). IBM Systems Journal. 4 (1): 25–30. doi:10.1147/sj.41.0025. S2CID 41898371.
Inose, H.; Yasuda, Y.; Murakami, J. (September 1962). "A Telemetering System by Code Manipulation – ΔΣ Modulation". IRE Transactions on Space Electronics and Telemetry. SET-8: 204–209. doi:10.1109/IRET-SET.1962.5008839. S2CID 51647729.
A., Klein (2006). "A generalized Kahan–Babuška-Summation-Algorithm". Computing. 76 (3–4). Springer-Verlag: 279–293. doi:10.1007/s00607-005-0139-x. S2CID 4561254.
Richard Shewchuk, Jonathan (October 1997). "Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates" (PDF). Discrete & Computational Geometry. 18 (3): 305–363. doi:10.1007/PL00009321. S2CID 189937041.
Goldberg, David (March 1991), "What every computer scientist should know about floating-point arithmetic" (PDF), ACM Computing Surveys, 23 (1): 5–48, doi:10.1145/103162.103163, S2CID 222008826.
MacDonald, Tom (1991). "C for Numerical Computing". Journal of Supercomputing. 5 (1): 31–48. doi:10.1007/BF00155856. S2CID 27876900.

sun.com

Börje Lindh, Application Performance Optimization, Sun BluePrints OnLine (March 2002).

univie.ac.at

mat.univie.ac.at

Neumaier, A. (1974). "Rundungsfehleranalyse einiger Verfahren zur Summation endlicher Summen" [Rounding Error Analysis of Some Methods for Summing Finite Sums] (PDF). Zeitschrift für Angewandte Mathematik und Mechanik (in German). 54 (1): 39–51. Bibcode:1974ZaMM...54...39N. doi:10.1002/zamm.19740540106.

validlab.com

Goldberg, David (March 1991), "What every computer scientist should know about floating-point arithmetic" (PDF), ACM Computing Surveys, 23 (1): 5–48, doi:10.1145/103162.103163, S2CID 222008826.

web.archive.org

Kahan, William (January 1965), "Further remarks on reducing truncation errors" (PDF), Communications of the ACM, 8 (1): 40, doi:10.1145/363707.363723, S2CID 22584810, archived from the original (PDF) on 9 February 2018.
Johnson, S.G.; Frigo, M. C. Sidney Burns (ed.). "Fast Fourier Transforms: Implementing FFTs in Practice". Archived from the original on Dec 20, 2008.
Compaq Fortran User Manual for Tru64 UNIX and Linux Alpha Systems Archived 2011-06-07 at the Wayback Machine, section 5.9.7 Arithmetic Reordering Optimizations (retrieved March 2010).
BLAS Technical Forum, section 2.7 (August 21, 2001), Archived on Wayback Machine.