• Source: Tapered floating point

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.
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


The tapered floating-point scheme was first proposed by Robert Morris of Bell Laboratories in 1971, and refined with leveling by Masao Iri and Shouichi Matsui of University of Tokyo in 1981, and by Hozumi Hamada of Hitachi, Ltd.
Alan Feldstein of Arizona State University and Peter Turner of Clarkson University described a tapered scheme resembling a conventional floating-point system except for the overflow or underflow conditions.
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.




See also


Logarithmic number system (LNS)
Symmetric level-index arithmetic (SLI)




References






Further reading


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. 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) […]

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• Tapered floating point
• Double-precision floating-point format
• Single-precision floating-point format
• Floating-point arithmetic
• Half-precision floating-point format
• IEEE 754
• IBM hexadecimal floating-point
• Decimal floating point
• Octuple-precision floating-point format
• Quadruple-precision floating-point format