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.
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]
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 (1ed.). Salt Lake City, Utah, USA: Springer International Publishing AG. p.966. doi:10.1007/978-3-319-64110-2. ISBN978-3-319-64109-6. LCCN2017947446. S2CID30244721. […] 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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