Floating-point arithmetic (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Floating-point arithmetic" in English language version.

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24web.archive.org

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accu.org

Harris, Richard (October 2010). "You're Going To Have To Think!". Overload (99): 5–10. ISSN 1354-3172. Retrieved 2011-09-24. Far more worrying is cancellation error which can yield catastrophic loss of precision. [4]

acm.org

dl.acm.org

Randell, Brian. Digital Computers, History of Origins, (pdf), p. 545, Digital Computers: Origins, Encyclopedia of Computer Science, January 2003.

archive.org

Sterbenz, Pat H. (1974). Floating-Point Computation. Englewood Cliffs, NJ, United States: Prentice-Hall. ISBN 0-13-322495-3.

arm.com

infocenter.arm.com

"Procedure Call Standard for the ARM 64-bit Architecture (AArch64)" (PDF). 2013-05-22. Archived (PDF) from the original on 2013-07-31. Retrieved 2019-09-22.
"ARM Compiler toolchain Compiler Reference, Version 5.03" (PDF). 2013. Section 6.3 Basic data types. Archived (PDF) from the original on 2015-06-27. Retrieved 2019-11-08.

arxiv.org

Rojas, Raúl (2014-06-07). "The Z1: Architecture and Algorithms of Konrad Zuse's First Computer". arXiv:1406.1886 [cs.AR].
Micikevicius, Paulius; Stosic, Dusan; Burgess, Neil; Cornea, Marius; Dubey, Pradeep; Grisenthwaite, Richard; Ha, Sangwon; Heinecke, Alexander; Judd, Patrick; Kamalu, John; Mellempudi, Naveen; Oberman, Stuart; Shoeybi, Mohammad; Siu, Michael; Wu, Hao (2022-09-12). "FP8 Formats for Deep Learning". arXiv:2209.05433 [cs.LG].
Lemire, Daniel (2021-03-22). "Number parsing at a gigabyte per second". Software: Practice and Experience. 51 (8): 1700–1727. arXiv:2101.11408. doi:10.1002/spe.2984. S2CID 231718830.

berkeley.edu

people.eecs.berkeley.edu

Kahan, William Morton (1997-07-15). "The Baleful Effect of Computer Languages and Benchmarks upon Applied Mathematics, Physics and Chemistry. John von Neumann Lecture" (PDF). p. 3. Archived (PDF) from the original on 2008-09-05.
Severance, Charles (1998-02-20). "An Interview with the Old Man of Floating-Point".
Kahan, William Morton (2004-11-20). "On the Cost of Floating-Point Computation Without Extra-Precise Arithmetic" (PDF). Archived (PDF) from the original on 2006-05-25. Retrieved 2012-02-19.
Kahan, William Morton (2006-01-11). "How Futile are Mindless Assessments of Roundoff in Floating-Point Computation?" (PDF). Archived (PDF) from the original on 2004-12-21.
Kahan, William Morton (1997-10-01). "Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic" (PDF). p. 9. Archived (PDF) from the original on 2002-06-22.
Kahan, William Morton (2005-07-15). Floating-Point Arithmetic Besieged by "Business Decisions" (PDF). IEEE-sponsored ARITH 17, Symposium on Computer Arithmetic (Keynote Address). pp. 6, 18. Archived (PDF) from the original on 2006-03-17. Retrieved 2013-05-23. (NB. Kahan estimates that the incidence of excessively inaccurate results near singularities is reduced by a factor of approx. 1/2000 using the 11 extra bits of precision of double extended.)
Kahan, William Morton (2011-08-03). Desperately Needed Remedies for the Undebuggability of Large Floating-Point Computations in Science and Engineering (PDF). IFIP/SIAM/NIST Working Conference on Uncertainty Quantification in Scientific Computing, Boulder, CO. p. 33. Archived (PDF) from the original on 2013-06-20.
Kahan, William Morton; Darcy, Joseph (2001) [1998-03-01]. "How Java's floating-point hurts everyone everywhere" (PDF). Archived (PDF) from the original on 2000-08-16. Retrieved 2003-09-05.
Kahan, William Morton (2000-08-27). "Marketing versus Mathematics" (PDF). pp. 15, 35, 47. Archived (PDF) from the original on 2003-08-15.
Kahan, William Morton (1981-02-12). "Why do we need a floating-point arithmetic standard?" (PDF). p. 26. Archived (PDF) from the original on 2004-12-04.
Kahan, William Morton; Ivory, Melody Y. (1997-07-03). "Roundoff Degrades an Idealized Cantilever" (PDF). Archived (PDF) from the original on 2003-12-05.

betaarchive.com

"IEEE vs. Microsoft Binary Format; Rounding Issues (Complete)". Microsoft Support. Microsoft. 2006-11-21. Article ID KB35826, Q35826. Archived from the original on 2020-08-28. Retrieved 2010-02-24.

bitsavers.org

Lazarus, Roger B. (1957-01-30) [1956-10-01]. "MANIAC II" (PDF). Los Alamos, NM, USA: Los Alamos Scientific Laboratory of the University of California. p. 14. LA-2083. Archived (PDF) from the original on 2018-08-07. Retrieved 2018-08-07. […] the Maniac's floating base, which is 2¹⁶ = 65,536. […] The Maniac's large base permits a considerable increase in the speed of floating point arithmetic. Although such a large base implies the possibility of as many as 15 lead zeros, the large word size of 48 bits guarantees adequate significance. […]

books.google.com

Muller, Jean-Michel; Brisebarre, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Stehlé, Damien; Torres, Serge (2010). Handbook of Floating-Point Arithmetic (1st ed.). Birkhäuser. doi:10.1007/978-0-8176-4705-6. ISBN 978-0-8176-4704-9. LCCN 2009939668.
Parkinson, Roger (2000-12-07). "Chapter 2 - High resolution digital site survey systems - Chapter 2.1 - Digital field recording systems". High Resolution Site Surveys (1st ed.). CRC Press. p. 24. ISBN 978-0-20318604-6. Retrieved 2019-08-18. […] Systems such as the [Digital Field System] DFS IV and DFS V were quaternary floating-point systems and used gain steps of 12 dB. […] (256 pages)
Ronald T. Kneusel. Numbers and Computers, Springer, pp. 84–85, 2017. ISBN 978-3319505084
Wilkinson, James Hardy (2003-09-08). "Error Analysis". In Ralston, Anthony; Reilly, Edwin D.; Hemmendinger, David (eds.). Encyclopedia of Computer Science. Wiley. pp. 669–674. ISBN 978-0-470-86412-8. Retrieved 2013-05-14.
Einarsson, Bo (2005). Accuracy and reliability in scientific computing. Society for Industrial and Applied Mathematics (SIAM). pp. 50–. ISBN 978-0-89871-815-7. Retrieved 2013-05-14.
Higham, Nicholas John (2002). Accuracy and Stability of Numerical Algorithms (2nd ed.). Society for Industrial and Applied Mathematics (SIAM). pp. 27–28, 110–123, 493. ISBN 978-0-89871-521-7. 0-89871-355-2.
Oliveira, Suely; Stewart, David E. (2006-09-07). Writing Scientific Software: A Guide to Good Style. Cambridge University Press. pp. 10–. ISBN 978-1-139-45862-7.

christophervickery.com

"IEEE-754 Analysis". Retrieved 2024-08-29.

doi.org

Muller, Jean-Michel; Brisebarre, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Stehlé, Damien; Torres, Serge (2010). Handbook of Floating-Point Arithmetic (1st ed.). Birkhäuser. doi:10.1007/978-0-8176-4705-6. ISBN 978-0-8176-4704-9. LCCN 2009939668.
Beebe, Nelson H. F. (2017-08-22). "Chapter H. Historical floating-point architectures". The Mathematical-Function Computation Handbook - Programming Using the MathCW Portable Software Library (1st ed.). Salt Lake City, UT, USA: Springer International Publishing AG. p. 948. doi:10.1007/978-3-319-64110-2. ISBN 978-3-319-64109-6. LCCN 2017947446. S2CID 30244721.
Rojas, Raúl (April–June 1997). "Konrad Zuse's Legacy: The Architecture of the Z1 and Z3" (PDF). IEEE Annals of the History of Computing. 19 (2): 5–16. doi:10.1109/85.586067. Archived (PDF) from the original on 2022-07-03. Retrieved 2022-07-03. (12 pages)
Loitsch, Florian (2010). "Printing floating-point numbers quickly and accurately with integers" (PDF). Proceedings of the 31st ACM SIGPLAN Conference on Programming Language Design and Implementation. PLDI '10: ACM SIGPLAN Conference on Programming Language Design and Implementation. pp. 233–243. doi:10.1145/1806596.1806623. ISBN 978-1-45030019-3. S2CID 910409. Archived (PDF) from the original on 2014-07-29.
Adams, Ulf (2018-12-02). "Ryū: fast float-to-string conversion". ACM SIGPLAN Notices. 53 (4): 270–282. doi:10.1145/3296979.3192369. S2CID 218472153.
Lemire, Daniel (2021-03-22). "Number parsing at a gigabyte per second". Software: Practice and Experience. 51 (8): 1700–1727. arXiv:2101.11408. doi:10.1002/spe.2984. S2CID 231718830.
Goldberg, David (March 1991). "What Every Computer Scientist Should Know About Floating-Point Arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10.1145/103162.103163. S2CID 222008826. (With the addendum "Differences Among IEEE 754 Implementations": [2], [3])
Shewchuk, Jonathan Richard (1997). "Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates". Discrete & Computational Geometry. 18 (3): 305–363. doi:10.1007/PL00009321.
Becker, Heiko; Darulova, Eva; Myreen, Magnus O.; Tatlock, Zachary (2019). Icing: Supporting Fast-Math Style Optimizations in a Verified Compiler. CAV 2019: Computer Aided Verification. Vol. 11562. pp. 155–173. doi:10.1007/978-3-030-25543-5_10.

drive.google.com

Giulietti, Rafaello. "The Schubfach way to render doubles".

dspguide.com

Smith, Steven W. (1997). "Chapter 28, Fixed versus Floating Point". The Scientist and Engineer's Guide to Digital Signal Processing. California Technical Pub. p. 514. ISBN 978-0-9660176-3-2. Retrieved 2012-12-31.

ed-thelen.org

Rojas, Raúl (April–June 1997). "Konrad Zuse's Legacy: The Architecture of the Z1 and Z3" (PDF). IEEE Annals of the History of Computing. 19 (2): 5–16. doi:10.1109/85.586067. Archived (PDF) from the original on 2022-07-03. Retrieved 2022-07-03. (12 pages)

embarcadero.com

community.embarcadero.com

Borland staff (1998-07-02) [1994-03-10]. "Converting between Microsoft Binary and IEEE formats". Technical Information Database (TI1431C.txt). Embarcadero USA / Inprise (originally: Borland). ID 1400. Archived from the original on 2019-02-20. Retrieved 2016-05-30. […] _fmsbintoieee(float *src4, float *dest4) […] MS Binary Format […] byte order => m3 | m2 | m1 | exponent […] m1 is most significant byte => sbbb|bbbb […] m3 is the least significant byte […] m = mantissa byte […] s = sign bit […] b = bit […] MBF is bias 128 and IEEE is bias 127. […] MBF places the decimal point before the assumed bit, while IEEE places the decimal point after the assumed bit. […] ieee_exp = msbin[3] - 2; /* actually, msbin[3]-1-128+127 */ […] _dmsbintoieee(double *src8, double *dest8) […] MS Binary Format […] byte order => m7 | m6 | m5 | m4 | m3 | m2 | m1 | exponent […] m1 is most significant byte => smmm|mmmm […] m7 is the least significant byte […] MBF is bias 128 and IEEE is bias 1023. […] MBF places the decimal point before the assumed bit, while IEEE places the decimal point after the assumed bit. […] ieee_exp = msbin[7] - 128 - 1 + 1023; […]

espacenet.com

worldwide.espacenet.com

US patent 3037701A, Huberto M Sierra, "Floating decimal point arithmetic control means for calculator", issued 1962-06-05

gao.gov

"Patriot missile defense, Software problem led to system failure at Dharhan, Saudi Arabia". US Government Accounting Office. GAO report IMTEC 92-26.

github.com

"Added Grisu3 algorithm support for double.ToString(). by mazong1123 · Pull Request #14646 · dotnet/coreclr". GitHub.
"abolz/Drachennest". GitHub. 2022-11-10.
"google/double-conversion". GitHub. 2020-09-21.
"Bug in zheevd · Issue #43 · Reference-LAPACK/lapack". GitHub.

gnu.org

gcc.gnu.org

Using the GNU Compiler Collection, i386 and x86-64 Options Archived 2015-01-16 at the Wayback Machine.
"FloatingPointMath". GCC Wiki.
"55522 – -funsafe-math-optimizations is unexpectedly harmful, especially w/ -shared". gcc.gnu.org.
"Code Gen Options (The GNU Fortran Compiler)". gcc.gnu.org.

intel.com

"D.3.2.1". Intel 64 and IA-32 Architectures Software Developers' Manuals. Vol. 1.

llvm.org

"Auto-Vectorization in LLVM". LLVM 13 documentation. We support floating point reduction operations when -ffast-math is used.

loc.gov

lccn.loc.gov

Muller, Jean-Michel; Brisebarre, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Stehlé, Damien; Torres, Serge (2010). Handbook of Floating-Point Arithmetic (1st ed.). Birkhäuser. doi:10.1007/978-0-8176-4705-6. ISBN 978-0-8176-4704-9. LCCN 2009939668.
Beebe, Nelson H. F. (2017-08-22). "Chapter H. Historical floating-point architectures". The Mathematical-Function Computation Handbook - Programming Using the MathCW Portable Software Library (1st ed.). Salt Lake City, UT, USA: Springer International Publishing AG. p. 948. doi:10.1007/978-3-319-64110-2. ISBN 978-3-319-64109-6. LCCN 2017947446. S2CID 30244721.

microsoft.com

learn.microsoft.com

"IEEE Floating-Point Representation". 2021-08-03.

netlib.org

Gay, David M. (1990). Correctly Rounded Binary-Decimal and Decimal-Binary Conversions (Technical report). NUMERICAL ANALYSIS MANUSCRIPT 90-10, AT&T BELL LABORATORIES. CiteSeerX 10.1.1.31.4049. (dtoa.c in netlab)

nvidia.com

blogs.nvidia.com

Kharya, Paresh (2020-05-14). "TensorFloat-32 in the A100 GPU Accelerates AI Training, HPC up to 20x". Retrieved 2020-05-16.

developer.nvidia.com

"NVIDIA Hopper Architecture In-Depth". 2022-03-22.

nyu.edu

cims.nyu.edu

Kahan, William Morton (2001-06-04). Bindel, David (ed.). "Lecture notes of System Support for Scientific Computation" (PDF). Archived (PDF) from the original on 2013-05-17.

openexr.com

"openEXR". openEXR. Archived from the original on 2013-05-08. Retrieved 2012-04-25. Since the IEEE-754 floating-point specification does not define a 16-bit format, ILM created the "half" format. Half values have 1 sign bit, 5 exponent bits, and 10 mantissa bits.
"Technical Introduction to OpenEXR – The half Data Type". openEXR. Retrieved 2024-04-16.

oracle.com

docs.oracle.com

Goldberg, David (March 1991). "What Every Computer Scientist Should Know About Floating-Point Arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10.1145/103162.103163. S2CID 222008826. (With the addendum "Differences Among IEEE 754 Implementations": [2], [3])

pagetable.com

Steil, Michael (2008-10-20). "Create your own Version of Microsoft BASIC for 6502". pagetable.com. Archived from the original on 2016-05-30. Retrieved 2016-05-30.

perl.org

perldoc.perl.org

Christiansen, Tom; Torkington, Nathan; et al. (2006). "perlfaq4 / Why is int() broken?". perldoc.perl.org. Retrieved 2011-01-11.

psu.edu

citeseerx.ist.psu.edu

Gay, David M. (1990). Correctly Rounded Binary-Decimal and Decimal-Binary Conversions (Technical report). NUMERICAL ANALYSIS MANUSCRIPT 90-10, AT&T BELL LABORATORIES. CiteSeerX 10.1.1.31.4049. (dtoa.c in netlab)

python.org

Christopher Barker: PEP 485 -- A Function for testing approximate equality

quadibloc.com

Savard, John J. G. (2018) [2007], "The Decimal Floating-Point Standard", quadibloc, archived from the original on 2018-07-03, retrieved 2018-07-16

quickclick.es

Torres Quevedo, Leonardo. Automática: Complemento de la Teoría de las Máquinas, (pdf), pp. 575–583, Revista de Obras Públicas, 19 November 1914.

semanticscholar.org

api.semanticscholar.org

Beebe, Nelson H. F. (2017-08-22). "Chapter H. Historical floating-point architectures". The Mathematical-Function Computation Handbook - Programming Using the MathCW Portable Software Library (1st ed.). Salt Lake City, UT, USA: Springer International Publishing AG. p. 948. doi:10.1007/978-3-319-64110-2. ISBN 978-3-319-64109-6. LCCN 2017947446. S2CID 30244721.
Loitsch, Florian (2010). "Printing floating-point numbers quickly and accurately with integers" (PDF). Proceedings of the 31st ACM SIGPLAN Conference on Programming Language Design and Implementation. PLDI '10: ACM SIGPLAN Conference on Programming Language Design and Implementation. pp. 233–243. doi:10.1145/1806596.1806623. ISBN 978-1-45030019-3. S2CID 910409. Archived (PDF) from the original on 2014-07-29.
Adams, Ulf (2018-12-02). "Ryū: fast float-to-string conversion". ACM SIGPLAN Notices. 53 (4): 270–282. doi:10.1145/3296979.3192369. S2CID 218472153.
Lemire, Daniel (2021-03-22). "Number parsing at a gigabyte per second". Software: Practice and Experience. 51 (8): 1700–1727. arXiv:2101.11408. doi:10.1002/spe.2984. S2CID 231718830.
Goldberg, David (March 1991). "What Every Computer Scientist Should Know About Floating-Point Arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10.1145/103162.103163. S2CID 222008826. (With the addendum "Differences Among IEEE 754 Implementations": [2], [3])

speleotrove.com

"General Decimal Arithmetic". Speleotrove.com. Retrieved 2012-04-25.

stackoverflow.com

"long double (GCC specific) and __float128". StackOverflow.

tufts.edu

cs.tufts.edu

Loitsch, Florian (2010). "Printing floating-point numbers quickly and accurately with integers" (PDF). Proceedings of the 31st ACM SIGPLAN Conference on Programming Language Design and Implementation. PLDI '10: ACM SIGPLAN Conference on Programming Language Design and Implementation. pp. 233–243. doi:10.1145/1806596.1806623. ISBN 978-1-45030019-3. S2CID 910409. Archived (PDF) from the original on 2014-07-29.

umn.edu

www-users.cse.umn.edu

Skeel, Robert (July 1992), "Roundoff Error and the Patriot Missile" (PDF), SIAM News, 25 (4): 11, retrieved 2024-11-15

uni-jena.de

users.fmi.uni-jena.de

Zehendner, Eberhard (Summer 2008). "Rechnerarithmetik: Fest- und Gleitkommasysteme" (PDF) (Lecture script) (in German). Friedrich-Schiller-Universität Jena. p. 2. Archived (PDF) from the original on 2018-08-07. Retrieved 2018-08-07. [1] (NB. This reference incorrectly gives the MANIAC II's floating point base as 256, whereas it actually is 65536.)

web.archive.org

Zehendner, Eberhard (Summer 2008). "Rechnerarithmetik: Fest- und Gleitkommasysteme" (PDF) (Lecture script) (in German). Friedrich-Schiller-Universität Jena. p. 2. Archived (PDF) from the original on 2018-08-07. Retrieved 2018-08-07. [1] (NB. This reference incorrectly gives the MANIAC II's floating point base as 256, whereas it actually is 65536.)
Savard, John J. G. (2018) [2007], "The Decimal Floating-Point Standard", quadibloc, archived from the original on 2018-07-03, retrieved 2018-07-16
Lazarus, Roger B. (1957-01-30) [1956-10-01]. "MANIAC II" (PDF). Los Alamos, NM, USA: Los Alamos Scientific Laboratory of the University of California. p. 14. LA-2083. Archived (PDF) from the original on 2018-08-07. Retrieved 2018-08-07. […] the Maniac's floating base, which is 2¹⁶ = 65,536. […] The Maniac's large base permits a considerable increase in the speed of floating point arithmetic. Although such a large base implies the possibility of as many as 15 lead zeros, the large word size of 48 bits guarantees adequate significance. […]
Rojas, Raúl (April–June 1997). "Konrad Zuse's Legacy: The Architecture of the Z1 and Z3" (PDF). IEEE Annals of the History of Computing. 19 (2): 5–16. doi:10.1109/85.586067. Archived (PDF) from the original on 2022-07-03. Retrieved 2022-07-03. (12 pages)
Kahan, William Morton (1997-07-15). "The Baleful Effect of Computer Languages and Benchmarks upon Applied Mathematics, Physics and Chemistry. John von Neumann Lecture" (PDF). p. 3. Archived (PDF) from the original on 2008-09-05.
Using the GNU Compiler Collection, i386 and x86-64 Options Archived 2015-01-16 at the Wayback Machine.
"Procedure Call Standard for the ARM 64-bit Architecture (AArch64)" (PDF). 2013-05-22. Archived (PDF) from the original on 2013-07-31. Retrieved 2019-09-22.
"ARM Compiler toolchain Compiler Reference, Version 5.03" (PDF). 2013. Section 6.3 Basic data types. Archived (PDF) from the original on 2015-06-27. Retrieved 2019-11-08.
Kahan, William Morton (2004-11-20). "On the Cost of Floating-Point Computation Without Extra-Precise Arithmetic" (PDF). Archived (PDF) from the original on 2006-05-25. Retrieved 2012-02-19.
"openEXR". openEXR. Archived from the original on 2013-05-08. Retrieved 2012-04-25. Since the IEEE-754 floating-point specification does not define a 16-bit format, ILM created the "half" format. Half values have 1 sign bit, 5 exponent bits, and 10 mantissa bits.
Borland staff (1998-07-02) [1994-03-10]. "Converting between Microsoft Binary and IEEE formats". Technical Information Database (TI1431C.txt). Embarcadero USA / Inprise (originally: Borland). ID 1400. Archived from the original on 2019-02-20. Retrieved 2016-05-30. […] _fmsbintoieee(float *src4, float *dest4) […] MS Binary Format […] byte order => m3 | m2 | m1 | exponent […] m1 is most significant byte => sbbb|bbbb […] m3 is the least significant byte […] m = mantissa byte […] s = sign bit […] b = bit […] MBF is bias 128 and IEEE is bias 127. […] MBF places the decimal point before the assumed bit, while IEEE places the decimal point after the assumed bit. […] ieee_exp = msbin[3] - 2; /* actually, msbin[3]-1-128+127 */ […] _dmsbintoieee(double *src8, double *dest8) […] MS Binary Format […] byte order => m7 | m6 | m5 | m4 | m3 | m2 | m1 | exponent […] m1 is most significant byte => smmm|mmmm […] m7 is the least significant byte […] MBF is bias 128 and IEEE is bias 1023. […] MBF places the decimal point before the assumed bit, while IEEE places the decimal point after the assumed bit. […] ieee_exp = msbin[7] - 128 - 1 + 1023; […]
Steil, Michael (2008-10-20). "Create your own Version of Microsoft BASIC for 6502". pagetable.com. Archived from the original on 2016-05-30. Retrieved 2016-05-30.
"IEEE vs. Microsoft Binary Format; Rounding Issues (Complete)". Microsoft Support. Microsoft. 2006-11-21. Article ID KB35826, Q35826. Archived from the original on 2020-08-28. Retrieved 2010-02-24.
Kahan, William Morton (2006-01-11). "How Futile are Mindless Assessments of Roundoff in Floating-Point Computation?" (PDF). Archived (PDF) from the original on 2004-12-21.
Loitsch, Florian (2010). "Printing floating-point numbers quickly and accurately with integers" (PDF). Proceedings of the 31st ACM SIGPLAN Conference on Programming Language Design and Implementation. PLDI '10: ACM SIGPLAN Conference on Programming Language Design and Implementation. pp. 233–243. doi:10.1145/1806596.1806623. ISBN 978-1-45030019-3. S2CID 910409. Archived (PDF) from the original on 2014-07-29.
Goldberg, David (March 1991). "What Every Computer Scientist Should Know About Floating-Point Arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10.1145/103162.103163. S2CID 222008826. (With the addendum "Differences Among IEEE 754 Implementations": [2], [3])
Kahan, William Morton (1997-10-01). "Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic" (PDF). p. 9. Archived (PDF) from the original on 2002-06-22.
Kahan, William Morton (2005-07-15). Floating-Point Arithmetic Besieged by "Business Decisions" (PDF). IEEE-sponsored ARITH 17, Symposium on Computer Arithmetic (Keynote Address). pp. 6, 18. Archived (PDF) from the original on 2006-03-17. Retrieved 2013-05-23. (NB. Kahan estimates that the incidence of excessively inaccurate results near singularities is reduced by a factor of approx. 1/2000 using the 11 extra bits of precision of double extended.)
Kahan, William Morton (2011-08-03). Desperately Needed Remedies for the Undebuggability of Large Floating-Point Computations in Science and Engineering (PDF). IFIP/SIAM/NIST Working Conference on Uncertainty Quantification in Scientific Computing, Boulder, CO. p. 33. Archived (PDF) from the original on 2013-06-20.
Kahan, William Morton; Darcy, Joseph (2001) [1998-03-01]. "How Java's floating-point hurts everyone everywhere" (PDF). Archived (PDF) from the original on 2000-08-16. Retrieved 2003-09-05.
Kahan, William Morton (2000-08-27). "Marketing versus Mathematics" (PDF). pp. 15, 35, 47. Archived (PDF) from the original on 2003-08-15.
Kahan, William Morton (1981-02-12). "Why do we need a floating-point arithmetic standard?" (PDF). p. 26. Archived (PDF) from the original on 2004-12-04.
Kahan, William Morton (2001-06-04). Bindel, David (ed.). "Lecture notes of System Support for Scientific Computation" (PDF). Archived (PDF) from the original on 2013-05-17.
Kahan, William Morton; Ivory, Melody Y. (1997-07-03). "Roundoff Degrades an Idealized Cantilever" (PDF). Archived (PDF) from the original on 2003-12-05.

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Harris, Richard (October 2010). "You're Going To Have To Think!". Overload (99): 5–10. ISSN 1354-3172. Retrieved 2011-09-24. Far more worrying is cancellation error which can yield catastrophic loss of precision. [4]