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Journal Articles IEEE Transactions on Computers Year : 2017

Exponential sums and correctly-rounded functions


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 CRlibm, a library which offers correctly rounded evaluation in binary64 of some functions of the usual libm. 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.
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hal-01396027 , version 1 (13-11-2016)
hal-01396027 , version 2 (14-03-2017)
hal-01396027 , version 3 (17-04-2017)



Nicolas Brisebarre, Guillaume Hanrot, Olivier Robert. Exponential sums and correctly-rounded functions. IEEE Transactions on Computers, 2017, 66 (12), pp.2044-2057. ⟨10.1109/TC.2017.2690850⟩. ⟨hal-01396027v3⟩
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