Additive Symmetric: the Non-Negative Case

Marc Daumas 1 Philippe Langlois
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : An additive symmetric b of a with respect to c satisfies c = (a+b)/2. Existence and uniqueness of such $b$ are basic properties in exact arithmetic that fail when a and b are floating point numbers and the computation of $c$ performed in IEEE-754 like arithmetic. We exhibit and prove conditions on the existence, the uniqueness and the exact correspondence of an additive symmetric when b and c have the same sign.
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Submitted on : Wednesday, May 24, 2006 - 10:10:22 AM
Last modification on : Friday, April 19, 2019 - 3:24:32 PM
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Marc Daumas, Philippe Langlois. Additive Symmetric: the Non-Negative Case. Theoretical Computer Science, Elsevier, 2003, 291 (2), pp.143-157. ⟨10.1016/S0304-3975(02)00223-2⟩. ⟨inria-00072516⟩

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