Tapered floating point explained
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
Further reading
- Book: Clement . Luk . Conference record of the 7th annual workshop on Microprogramming - MICRO 7 . Microprogrammed significance arithmetic with tapered floating point representation . 248–252 . Palo Alto, California, USA . 1974-09-30 . 1974-10-02 . 10.1145/800118.803869 . 9781450374217 . free .
- Book: Aquil M. . Azmi . Fabrizio . Lombardi . Proceedings of 9th Symposium on Computer Arithmetic . On a tapered floating point system . 1989-09-06 . 0-8186-8963-3 . 10.1109/ARITH.1989.72803 . . Santa Monica, California, USA . 2–9 . 38180269 . http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Azmi.pdf . 2018-07-13 . live . https://web.archive.org/web/20180713190341/http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Azmi.pdf . 2018-07-13.
- Hidetoshi . Yokoo . Overflow/Underflow-Free Floating-Point Number Representations with Self-Delimiting Variable-Length Exponent Field . IEEE Transactions on Computers. 41 . 8 . August 1992 . 0018-9340 . 1033–1039 . . Washington, DC, USA . 10.1109/12.156546 . . Previously published in: Hidetoshi . Yokoo . 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) . Peter . Komerup . David W. . Matula . David Matula. June 1991 . . Washington, DC, USA . 110–117.
- The MasPar MP-1 As a Computer Arithmetic Laboratory . Michael A. . Anuta . Daniel W. . Lozier . Peter R. . Turner . . 101 . 165–174 . 2 . March–April 1996 . 1995-11-15 . 10.6028/jres.101.018 . 27805123 . 4907584.
- Web site: Between Fixed and Floating Point . Gary . Ray . 2010-02-04 . Electronic Systems Design Engineering incorporating Chip Design . 2018-07-09 . live . https://web.archive.org/web/20180710035319/http://chipdesignmag.com/display.php?articleId=3921 . 2018-07-10.
- Book: Nelson H. F. . Beebe . The Mathematical-Function Computation Handbook - Programming Using the MathCW Portable Software Library . Chapter H.8 - Unusual floating-point systems . 2017-08-22 . Salt Lake City, Utah, USA . . 1 . 2017947446 . 978-3-319-64109-6 . 10.1007/978-3-319-64110-2 . 966 . 30244721 . […] representation with a moveable boundary between exponent and significand, sacrificing precision only when a larger range is needed (sometimes called tapered arithmetic) […].