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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11berkeley.edu

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5semanticscholar.org

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4gnu.org

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accu.org (Global: low place; English: low place)

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 (Global: 1,185^th place; English: 840^th place)

dl.acm.org

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

archive.org (Global: 6^th place; English: 6^th place)

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

arm.com (Global: 4,773^rd place; English: 3,130^th place)

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 (Global: 69^th place; English: 59^th place)

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 (Global: 580^th place; English: 462^nd place)

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 (Global: low place; English: low place)

"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 (Global: 4,153^rd place; English: 2,291^st place)

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 (Global: 3^rd place; English: 3^rd place)

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 (Global: low place; English: low place)

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

doi.org (Global: 2^nd place; English: 2^nd place)

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)
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])
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.
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 (Global: 1,343^rd place; English: 1,354^th place)

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

dspguide.com (Global: low place; English: low place)

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 (Global: low place; English: 9,452^nd place)

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 (Global: low place; English: low place)

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 (Global: 800^th place; English: 676^th place)

worldwide.espacenet.com

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

gao.gov (Global: 2,954^th place; English: 1,848^th place)

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

github.com (Global: 383^rd place; English: 320^th place)

"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 (Global: 1,475^th place; English: 1,188^th place)

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 (Global: 1,118^th place; English: 825^th place)

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

llvm.org (Global: low place; English: 7,917^th place)

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

loc.gov (Global: 70^th place; English: 63^rd place)

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 (Global: 153^rd place; English: 151^st place)

learn.microsoft.com

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

netlib.org (Global: low place; English: low place)

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 (Global: 2,503^rd place; English: 1,760^th place)

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 (Global: 1,174^th place; English: 773^rd place)

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 (Global: low place; English: low place)

"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 (Global: 1,514^th place; English: 1,024^th place)

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])

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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.

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

psu.edu (Global: 207^th place; English: 136^th place)

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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 (Global: 2,232^nd place; English: 1,903^rd place)

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

quadibloc.com (Global: low place; English: low place)

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 (Global: low place; English: low place)

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

semanticscholar.org (Global: 11^th place; English: 8^th place)

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.
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])
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.

speleotrove.com (Global: low place; English: low place)

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tufts.edu (Global: 155^th place; English: 138^th place)

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 (Global: 1,266^th place; English: 860^th place)

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uni-jena.de (Global: 4,878^th place; English: 4,120^th place)

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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 (Global: 1^st place; English: 1^st place)

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.
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])
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.
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]

Floating-point arithmetic (English Wikipedia)

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