933:
50:
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
810:
540:
170:
185:
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representation with a moveable boundary between exponent and significand, sacrificing precision only when a larger range is needed (sometimes called
254:
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263:
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166:
894:
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509:
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585:"Right-Sizing Precision: Unleashed Computing: The need to right-size precision to save energy, bandwidth, storage, and electrical power"
159:
719:
667:
544:
433:
412:
Hamada, Hozumi (1987-05-18). "A new real number representation and its operation". In Irwin, Mary Jane; Stefanelli, Renato (eds.).
355:
858:
134:
791:(eds.). "Overflow/Underflow-Free Floating-Point Number Representations with Self-Delimiting Variable-Length Exponent Field".
201:
100:
described a tapered scheme resembling a conventional floating-point system except for the overflow or underflow conditions.
196:
71:
993:
59:
967:
417:
306:
753:"Overflow/Underflow-Free Floating-Point Number Representations with Self-Delimiting Variable-Length Exponent Field"
104:
648:
Luk, Clement (1974-10-02) . "Microprogrammed significance arithmetic with tapered floating point representation".
128:
39:
93:
960:
796:
764:
584:
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The
Mathematical-Function Computation Handbook - Programming Using the MathCW Portable Software Library
527:"Gradual and tapered overflow and underflow: A functional differential equation and its approximation"
448:
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Muller, Jean-Michel (2016-12-12). "Chapter 2.2.6. The Future of
Floating Point Arithmetic".
548:
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51:
difference of the fixed total length minus the length of the exponent and pointer entries.
320:
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249:
234:
87:
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387:
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Beebe, Nelson H. F. (2017-08-22). "Chapter H.8 - Unusual floating-point systems".
495:
324:
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199:(December 1971). "Tapered Floating Point: A New Floating-Point Representation".
43:
425:
886:
780:
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379:
279:
271:
226:
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Anuta, Michael A.; Lozier, Daniel W.; Turner, Peter R. (March–April 1996) .
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218:
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841:
658:
650:
823:
811:
Journal of
Research of the National Institute of Standards and Technology
47:
793:
Proceedings of the 10th IEEE Symposium on
Computer Arithmetic (ARITH 10)
477:
286:
371:
772:
111:
number system, a variant of tapered floating-point arithmetic with an
541:
International
Association for Mathematics and Computers in Simulation
250:"An Overflow/Underflow-Free Floating-Point Representation of Numbers"
904:
703:
462:
Hayes, Brian (September–October 2009). "The Higher
Arithmetic".
210:
855:
Electronic
Systems Design Engineering incorporating Chip Design
70:
The tapered floating-point scheme was first proposed by
948:
525:
Feldstein, Alan; Turner, Peter R. (March–April 2006).
414:
1987 IEEE 8th
Symposium on Computer Arithmetic (ARITH)
806:"The MasPar MP-1 As a Computer Arithmetic Laboratory"
494:
Hayes, Brian (2017). "Chapter 8: Higher
Arithmetic".
700:
Proceedings of 9th Symposium on Computer Arithmetic
617:
Elementary Functions: Algorithms and Implementation
691:Azmi, Aquil M.; Lombardi, Fabrizio (1989-09-06).
160:"Rechnerarithmetik: Logarithmische Zahlensysteme"
652:. Palo Alto, California, USA. pp. 248–252.
153:
151:
356:"URR: Universal representation of real numbers"
54:Thus numbers with a small exponent, i.e. whose
787:Yokoo, Hidetoshi (June 1991). Komerup, Peter;
331:Society for Industrial and Applied Mathematics
326:Accuracy and Stability of Numerical Algorithms
27:Variant of floating-point numbers in computers
968:
497:Foolproof, and Other Mathematical Meditations
248:Matsui, Shourichi; Iri, Masao (1981-11-05) .
8:
457:
455:
398:(NB. The URR representation coincides with
975:
961:
682:: CS1 maint: location missing publisher (
619:(3 ed.). Boston, Massachusetts, USA:
42:, but with variable-sized entries for the
877:(1 ed.). Salt Lake City, Utah, USA:
831:
657:
115:bit added to the representation and some
532:Journal of Applied Numerical Mathematics
301:Swartzlander, Jr., Earl E., ed. (1990).
119:interpretation to the non-exact values.
58:is close to the one of 1, have a higher
264:Information Processing Society of Japan
147:
675:
18:Tapered floating-point representation
7:
929:
927:
879:Springer International Publishing AG
693:"On a tapered floating point system"
82:by Masao Iri and Shouichi Matsui of
167:Friedrich-Schiller-Universität Jena
158:Zehendner, Eberhard (Summer 2008).
947:. You can help Knowledge (XXG) by
851:"Between Fixed and Floating Point"
62:than those with a large exponent.
25:
702:. Santa Monica, California, USA:
545:Elsevier Science Publishers B. V.
255:Journal of Information Processing
86:in 1981, and by Hozumi Hamada of
931:
751:Yokoo, Hidetoshi (August 1992).
135:Symmetric level-index arithmetic
861:from the original on 2018-07-10
739:from the original on 2018-07-13
597:from the original on 2016-06-06
539:(3–4). Amsterdam, Netherlands:
176:from the original on 2018-07-09
757:IEEE Transactions on Computers
202:IEEE Transactions on Computers
165:(Lecture script) (in German).
1:
354:Hamada, Hozumi (June 1983).
785:. Previously published in:
553:10.1016/j.apnum.2005.04.018
418:IEEE Computer Society Press
307:IEEE Computer Society Press
1015:
999:Computer engineering stubs
926:
763:(8). Washington, DC, USA:
426:10.1109/ARITH.1987.6158698
78:in 1971, and refined with
887:10.1007/978-3-319-64110-2
416:. Washington, D.C., USA:
129:Logarithmic number system
38:) is a format similar to
849:Ray, Gary (2010-02-04).
712:10.1109/ARITH.1989.72803
360:New Generation Computing
94:Arizona State University
795:. Washington, DC, USA:
219:10.1109/T-C.1971.223174
943:-related article is a
400:Elias delta (δ) coding
197:Morris, Sr., Robert H.
32:tapered floating point
797:IEEE Computer Society
765:IEEE Computer Society
659:10.1145/800118.803869
581:Gustafson, John Leroy
492:. Also reprinted in:
321:Higham, Nicholas John
299:. Also reprinted in:
941:computer-engineering
824:10.6028/jres.101.018
504:. pp. 113–126.
420:. pp. 153–157.
333:(SIAM). p. 49.
96:and Peter Turner of
994:Computer arithmetic
478:10.1511/2009.80.364
303:Computer Arithmetic
98:Clarkson University
84:University of Tokyo
919:tapered arithmetic
623:. pp. 29–30.
465:American Scientist
372:10.1007/BF03037427
169:. pp. 15–19.
92:Alan Feldstein of
60:relative precision
56:order of magnitude
956:
955:
896:978-3-319-64109-6
773:10.1109/12.156546
630:978-1-4899-7981-0
340:978-0-89871-521-7
266:(IPSJ): 123–133.
76:Bell Laboratories
16:(Redirected from
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30:In computing,
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949:expanding it
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547:: 517–532.
44:significand
988:Categories
905:2017947446
865:2018-07-09
799:: 110–117.
743:2018-07-13
621:Birkhäuser
601:2016-06-06
566:2018-07-09
543:(IMACS) /
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292:2018-07-09
287:AA00700121
180:2018-07-09
142:References
781:0018-9340
678:cite book
561:0168-9274
486:121337883
380:0288-3635
272:1882-6652
235:206618406
227:0018-9340
103:In 2013,
913:30244721
859:Archived
842:27805123
734:Archived
730:38180269
592:Archived
444:15189621
388:12806462
323:(2002).
171:Archived
123:See also
117:interval
80:leveling
48:exponent
833:4907584
66:History
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909:S2CID
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482:S2CID
440:S2CID
384:S2CID
262:(3).
231:S2CID
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137:(SLI)
131:(LNS)
113:exact
945:stub
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211:IEEE
207:C-20
109:Unum
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74:of
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