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Exponential Sums and Correctly-Rounded Functions.
- Source :
-
IEEE Transactions on Computers . Dec2017, Vol. 66 Issue 12, p2044-2057. 14p. - Publication Year :
- 2017
-
Abstract
- The 2008 revision of the IEEE-754 standard, which governs floating-point arithmetic, recommends that a certain set of elementary functions should be correctly rounded. Successful attempts for solving the Table Maker's Dilemma in binary64 made it possible to design <monospace>CRlibm</monospace>, a library which offers correctly rounded evaluation in binary64 of some functions of the usual <monospace>libm</monospace>. It evaluates functions using a two step strategy, which relies on a folklore heuristic that is well spread in the community of mathematical functions designers. Under this heuristic, one can compute the distribution of the lengths of runs of zeros/ones after the rounding bit of the value of the function at a given floating-point number. The goal of this paper is to change, whenever possible, this heuristic into a rigorous statement. The underlying mathematical problem amounts to counting integer points in the neighborhood of a curve, which we tackle using so-called exponential sums techniques, a tool from analytic number theory. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189340
- Volume :
- 66
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Computers
- Publication Type :
- Academic Journal
- Accession number :
- 126112221
- Full Text :
- https://doi.org/10.1109/TC.2017.2690850