fbpx
Wikipedia

Tapered floating point

January 01, 1970

In computing, tapered floating point (TFP) is a format similar to floating point, but with variable-sized entries for the significand and exponent instead of the fixed-length entries found in normal floating-point formats. In addition to this, tapered floating-point formats provide a fixed-size pointer entry indicating the number of digits in the exponent entry. The number of digits of the significand entry (including the sign) results from the difference of the fixed total length minus the length of the exponent and pointer entries.[1]

Thus numbers with a small exponent, i.e. whose order of magnitude is close to the one of 1, have a higher relative precision than those with a large exponent.

History edit

The tapered floating-point scheme was first proposed by Robert Morris of Bell Laboratories in 1971,[2] and refined with leveling by Masao Iri and Shouichi Matsui of University of Tokyo in 1981,[3][4][1] and by Hozumi Hamada of Hitachi, Ltd.[5][6][7]

Alan Feldstein of Arizona State University and Peter Turner[8] of Clarkson University described a tapered scheme resembling a conventional floating-point system except for the overflow or underflow conditions.[7]

In 2013, John Gustafson proposed the Unum number system, a variant of tapered floating-point arithmetic with an exact bit added to the representation and some interval interpretation to the non-exact values.[9][10]

See also edit

References edit

  1. ^ a b Zehendner, Eberhard (Summer 2008). "Rechnerarithmetik: Logarithmische Zahlensysteme" (PDF) (Lecture script) (in German). Friedrich-Schiller-Universität Jena. pp. 15–19. (PDF) from the original on 2018-07-09. Retrieved 2018-07-09.
  2. ^ Morris, Sr., Robert H. (December 1971). "Tapered Floating Point: A New Floating-Point Representation". IEEE Transactions on Computers. C-20 (12). IEEE: 1578–1579. doi:10.1109/T-C.1971.223174. ISSN 0018-9340. S2CID 206618406.
  3. ^ Matsui, Shourichi; Iri, Masao (1981-11-05) [January 1981]. "An Overflow/Underflow-Free Floating-Point Representation of Numbers". Journal of Information Processing. 4 (3). Information Processing Society of Japan (IPSJ): 123–133. ISSN 1882-6652. NAID 110002673298 NCID AA00700121. Retrieved 2018-07-09. [2]. Also reprinted in: Swartzlander, Jr., Earl E., ed. (1990). Computer Arithmetic. Vol. II. IEEE Computer Society Press. pp. 357–.
  4. ^ Higham, Nicholas John (2002). Accuracy and Stability of Numerical Algorithms (2 ed.). Society for Industrial and Applied Mathematics (SIAM). p. 49. ISBN 978-0-89871-521-7. 0-89871-355-2.
  5. ^ Hamada, Hozumi (June 1983). "URR: Universal representation of real numbers". New Generation Computing. 1 (2): 205–209. doi:10.1007/BF03037427. ISSN 0288-3635. S2CID 12806462. Retrieved 2018-07-09. (NB. The URR representation coincides with Elias delta (δ) coding.)
  6. ^ Hamada, Hozumi (1987-05-18). "A new real number representation and its operation". In Irwin, Mary Jane; Stefanelli, Renato (eds.). 1987 IEEE 8th Symposium on Computer Arithmetic (ARITH). Washington, D.C., USA: IEEE Computer Society Press. pp. 153–157. doi:10.1109/ARITH.1987.6158698. ISBN 0-8186-0774-2. S2CID 15189621. [3]
  7. ^ a b Hayes, Brian (September–October 2009). "The Higher Arithmetic". American Scientist. 97 (5): 364–368. doi:10.1511/2009.80.364. S2CID 121337883. [4]. Also reprinted in: Hayes, Brian (2017). "Chapter 8: Higher Arithmetic". Foolproof, and Other Mathematical Meditations (1 ed.). The MIT Press. pp. 113–126. ISBN 978-0-26203686-3.
  8. ^ Feldstein, Alan; Turner, Peter R. (March–April 2006). "Gradual and tapered overflow and underflow: A functional differential equation and its approximation". Journal of Applied Numerical Mathematics. 56 (3–4). Amsterdam, Netherlands: International Association for Mathematics and Computers in Simulation (IMACS) / Elsevier Science Publishers B. V.: 517–532. doi:10.1016/j.apnum.2005.04.018. ISSN 0168-9274. Retrieved 2018-07-09.
  9. ^ Gustafson, John Leroy (March 2013). "Right-Sizing Precision: Unleashed Computing: The need to right-size precision to save energy, bandwidth, storage, and electrical power" (PDF). (PDF) from the original on 2016-06-06. Retrieved 2016-06-06.
  10. ^ Muller, Jean-Michel (2016-12-12). "Chapter 2.2.6. The Future of Floating Point Arithmetic". Elementary Functions: Algorithms and Implementation (3 ed.). Boston, Massachusetts, USA: Birkhäuser. pp. 29–30. ISBN 978-1-4899-7981-0.

Further reading edit

  • Luk, Clement (1974-10-02) [1974-09-30]. "Microprogrammed significance arithmetic with tapered floating point representation". Conference record of the 7th annual workshop on Microprogramming - MICRO 7. Palo Alto, California, USA. pp. 248–252. doi:10.1145/800118.803869. ISBN 9781450374217.{{cite book}}: CS1 maint: location missing publisher (link)
  • Azmi, Aquil M.; Lombardi, Fabrizio (1989-09-06). "On a tapered floating point system" (PDF). Proceedings of 9th Symposium on Computer Arithmetic. Santa Monica, California, USA: IEEE. pp. 2–9. doi:10.1109/ARITH.1989.72803. ISBN 0-8186-8963-3. S2CID 38180269. (PDF) from the original on 2018-07-13. Retrieved 2018-07-13.
  • Yokoo, Hidetoshi (August 1992). "Overflow/Underflow-Free Floating-Point Number Representations with Self-Delimiting Variable-Length Exponent Field". IEEE Transactions on Computers. 41 (8). Washington, DC, USA: IEEE Computer Society: 1033–1039. doi:10.1109/12.156546. ISSN 0018-9340.. Previously published in: Yokoo, Hidetoshi (June 1991). Komerup, Peter; Matula, David W. (eds.). "Overflow/Underflow-Free Floating-Point Number Representations with Self-Delimiting Variable-Length Exponent Field". Proceedings of the 10th IEEE Symposium on Computer Arithmetic (ARITH 10). Washington, DC, USA: IEEE Computer Society: 110–117.
  • Anuta, Michael A.; Lozier, Daniel W.; Turner, Peter R. (March–April 1996) [1995-11-15]. "The MasPar MP-1 As a Computer Arithmetic Laboratory". Journal of Research of the National Institute of Standards and Technology. 101 (2): 165–174. doi:10.6028/jres.101.018. PMC 4907584. PMID 27805123.
  • Ray, Gary (2010-02-04). "Between Fixed and Floating Point". Electronic Systems Design Engineering incorporating Chip Design. from the original on 2018-07-10. Retrieved 2018-07-09.
  • Beebe, Nelson H. F. (2017-08-22). "Chapter H.8 - Unusual floating-point systems". The Mathematical-Function Computation Handbook - Programming Using the MathCW Portable Software Library (1 ed.). Salt Lake City, Utah, USA: Springer International Publishing AG. p. 966. doi:10.1007/978-3-319-64110-2. ISBN 978-3-319-64109-6. LCCN 2017947446. S2CID 30244721. […] representation with a moveable boundary between exponent and significand, sacrificing precision only when a larger range is needed (sometimes called tapered arithmetic) […]
 

This computer-engineering-related article is a stub. You can help Wikipedia by expanding it.

January 01, 1970
tapered, floating, point, computing, tapered, floating, point, format, similar, floating, point, with, variable, sized, entries, significand, exponent, instead, fixed, length, entries, found, normal, floating, point, formats, addition, this, tapered, floating,. In computing tapered floating point TFP is a format similar to floating point but with variable sized entries for the significand and exponent instead of the fixed length entries found in normal floating point formats In addition to this tapered floating point formats provide a fixed size pointer entry indicating the number of digits in the exponent entry The number of digits of the significand entry including the sign results from the difference of the fixed total length minus the length of the exponent and pointer entries 1 Thus numbers with a small exponent i e whose order of magnitude is close to the one of 1 have a higher relative precision than those with a large exponent Contents 1 History 2 See also 3 References 4 Further readingHistory editThe tapered floating point scheme was first proposed by Robert Morris of Bell Laboratories in 1971 2 and refined with leveling by Masao Iri and Shouichi Matsui of University of Tokyo in 1981 3 4 1 and by Hozumi Hamada of Hitachi Ltd 5 6 7 Alan Feldstein of Arizona State University and Peter Turner 8 of Clarkson University described a tapered scheme resembling a conventional floating point system except for the overflow or underflow conditions 7 In 2013 John Gustafson proposed the Unum number system a variant of tapered floating point arithmetic with an exact bit added to the representation and some interval interpretation to the non exact values 9 10 See also editLogarithmic number system LNS Symmetric level index arithmetic SLI References edit a b Zehendner Eberhard Summer 2008 Rechnerarithmetik Logarithmische Zahlensysteme PDF Lecture script in German Friedrich Schiller Universitat Jena pp 15 19 Archived PDF from the original on 2018 07 09 Retrieved 2018 07 09 1 Morris Sr Robert H December 1971 Tapered Floating Point A New Floating Point Representation IEEE Transactions on Computers C 20 12 IEEE 1578 1579 doi 10 1109 T C 1971 223174 ISSN 0018 9340 S2CID 206618406 Matsui Shourichi Iri Masao 1981 11 05 January 1981 An Overflow Underflow Free Floating Point Representation of Numbers Journal of Information Processing 4 3 Information Processing Society of Japan IPSJ 123 133 ISSN 1882 6652 NAID 110002673298 NCID AA00700121 Retrieved 2018 07 09 2 Also reprinted in Swartzlander Jr Earl E ed 1990 Computer Arithmetic Vol II IEEE Computer Society Press pp 357 Higham Nicholas John 2002 Accuracy and Stability of Numerical Algorithms 2 ed Society for Industrial and Applied Mathematics SIAM p 49 ISBN 978 0 89871 521 7 0 89871 355 2 Hamada Hozumi June 1983 URR Universal representation of real numbers New Generation Computing 1 2 205 209 doi 10 1007 BF03037427 ISSN 0288 3635 S2CID 12806462 Retrieved 2018 07 09 NB The URR representation coincides with Elias delta d coding Hamada Hozumi 1987 05 18 A new real number representation and its operation In Irwin Mary Jane Stefanelli Renato eds 1987 IEEE 8th Symposium on Computer Arithmetic ARITH Washington D C USA IEEE Computer Society Press pp 153 157 doi 10 1109 ARITH 1987 6158698 ISBN 0 8186 0774 2 S2CID 15189621 3 a b Hayes Brian September October 2009 The Higher Arithmetic American Scientist 97 5 364 368 doi 10 1511 2009 80 364 S2CID 121337883 4 Also reprinted in Hayes Brian 2017 Chapter 8 Higher Arithmetic Foolproof and Other Mathematical Meditations 1 ed The MIT Press pp 113 126 ISBN 978 0 26203686 3 Feldstein Alan Turner Peter R March April 2006 Gradual and tapered overflow and underflow A functional differential equation and its approximation Journal of Applied Numerical Mathematics 56 3 4 Amsterdam Netherlands International Association for Mathematics and Computers in Simulation IMACS Elsevier Science Publishers B V 517 532 doi 10 1016 j apnum 2005 04 018 ISSN 0168 9274 Retrieved 2018 07 09 Gustafson John Leroy March 2013 Right Sizing Precision Unleashed Computing The need to right size precision to save energy bandwidth storage and electrical power PDF Archived PDF from the original on 2016 06 06 Retrieved 2016 06 06 Muller Jean Michel 2016 12 12 Chapter 2 2 6 The Future of Floating Point Arithmetic Elementary Functions Algorithms and Implementation 3 ed Boston Massachusetts USA Birkhauser pp 29 30 ISBN 978 1 4899 7981 0 Further reading editLuk Clement 1974 10 02 1974 09 30 Microprogrammed significance arithmetic with tapered floating point representation Conference record of the 7th annual workshop on Microprogramming MICRO 7 Palo Alto California USA pp 248 252 doi 10 1145 800118 803869 ISBN 9781450374217 a href Template Cite book html title Template Cite book cite book a CS1 maint location missing publisher link Azmi Aquil M Lombardi Fabrizio 1989 09 06 On a tapered floating point system PDF Proceedings of 9th Symposium on Computer Arithmetic Santa Monica California USA IEEE pp 2 9 doi 10 1109 ARITH 1989 72803 ISBN 0 8186 8963 3 S2CID 38180269 Archived PDF from the original on 2018 07 13 Retrieved 2018 07 13 Yokoo Hidetoshi August 1992 Overflow Underflow Free Floating Point Number Representations with Self Delimiting Variable Length Exponent Field IEEE Transactions on Computers 41 8 Washington DC USA IEEE Computer Society 1033 1039 doi 10 1109 12 156546 ISSN 0018 9340 Previously published in Yokoo Hidetoshi June 1991 Komerup Peter Matula David W eds Overflow Underflow Free Floating Point Number Representations with Self Delimiting Variable Length Exponent Field Proceedings of the 10th IEEE Symposium on Computer Arithmetic ARITH 10 Washington DC USA IEEE Computer Society 110 117 Anuta Michael A Lozier Daniel W Turner Peter R March April 1996 1995 11 15 The MasPar MP 1 As a Computer Arithmetic Laboratory Journal of Research of the National Institute of Standards and Technology 101 2 165 174 doi 10 6028 jres 101 018 PMC 4907584 PMID 27805123 Ray Gary 2010 02 04 Between Fixed and Floating Point Electronic Systems Design Engineering incorporating Chip Design Archived from the original on 2018 07 10 Retrieved 2018 07 09 Beebe Nelson H F 2017 08 22 Chapter H 8 Unusual floating point systems The Mathematical Function Computation Handbook Programming Using the MathCW Portable Software Library 1 ed Salt Lake City Utah USA Springer International Publishing AG p 966 doi 10 1007 978 3 319 64110 2 ISBN 978 3 319 64109 6 LCCN 2017947446 S2CID 30244721 representation with a moveable boundary between exponent and significand sacrificing precision only when a larger range is needed sometimes called tapered arithmetic nbsp This computer engineering related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Tapered floating point amp oldid 1181919194 Leveling, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.