In computing, tapered floating point (TFP) is a format similar to

floating point In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be ...

, but with variable-sized entries for the

significand The significand (also mantissa or coefficient, sometimes also argument, or ambiguously fraction or characteristic) is part of a number in scientific notation or in floating-point representation, consisting of its significant digits. Depending on ...

and

exponent Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to re ...

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 An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic dis ...

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 Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...

in 1971, and refined with ''leveling'' by Masao Iri and Shouichi Matsui of

University of Tokyo , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...

in 1981, and by Hozumi Hamada of

Hitachi, Ltd. () is a Japanese multinational conglomerate corporation headquartered in Chiyoda, Tokyo, Japan. It is the parent company of the Hitachi Group (''Hitachi Gurūpu'') and had formed part of the Nissan ''zaibatsu'' and later DKB Group and Fuyo G ...

Alan Feldstein of

Arizona State University Arizona State University (Arizona State or ASU) is a public research university in the Phoenix metropolitan area. Founded in 1885 by the 13th Arizona Territorial Legislature, ASU is one of the largest public universities by enrollment in the ...

and Peter Turner of

Clarkson University Clarkson University is a private research university with its main campus in Potsdam, New York, and additional graduate program and research facilities in the New York Capital Region and Beacon, New York. It was founded in 1896 and has an enr ...

described a tapered scheme resembling a conventional floating-point system except for the overflow or underflow conditions. In 2013, John Gustafson proposed the

Unum Unum Group is an American insurance company headquartered in Chattanooga, Tennessee. Founded as Union Mutual in 1848 and known as UnumProvident from 1999-2007, the company is part of the Fortune 500. Unum Group was created by the 1999 merger of ...

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.

History

See also

References

Further reading