Time: 9h30, Thursday,  October 22, 2015
Location: Room 201, Building A5, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Ha Noi
Abstract: On a computer, real numbers are usually represented by a finite set of numbers called floating-point numbers. When one performs an operation on these numbers, such as an evaluation by a function, one returns a floating-point number, close to the mathematical result of the operation. Ideally, this result should be the exact rounding of this mathematical value. One knows how to guarantee such a quality of results for arithmetical operations like +, -, x, / and square root but, as of today, it still remains a difficult issue when it comes to evaluate an elementary function such as cos, exp, cube root for instance. This problem, called Table Maker Dilemma, is actually a diophantine approximation problem, which has been tackled, in the last fifteen years, by V. Lefèvre, J.M. Muller, D. Stehlé, A. Tisserand and P. Zimmermann (LIP, ÉNS Lyon and LORIA, Nancy), using tools from algorithmic number theory. Their works made it possible to partially solve this question but it still remains an open problem. In this talk, I will present an ongoing joint work with Guillaume Hanrot (ÉNS Lyon, LIP, AriC), that improve the existing results.