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Tools for a gentle slope transition From floating point arithmetic to exact real arithmetic

Valérie Ménissier-Morain 1 
1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : Floating point arithmetic (FPA) is one century old and is effectively used commonly since 60 years. Exact real arithmetic (ERA) appears 40 years ago and has been developed essentially since the end of the 80's resulting both of the dissatisfaction about FPA results and the sharp increase of material computing power that allows computation ambition. FPA is essentially a fixed precision arithmetic while ERA adapts the precision of each operation to ensure the desired accuracy of the result. However for a long time, we have had to choose between fast computed, completely wrong, FPA results on the one hand and accurate ERA results obtained too late to be useful on the other hand. Alternative to FPA such as interval arithmetic (IA) have been designed by mathematicians since the 50's and during the last three decades numerous tools have been designed by computer scientists to reduce the gap between FPA and ERA with two principle directions: evaluate the inaccuracy of the result and try to produce a more accurate result. We present here a survey of these tools.
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  • HAL Id : hal-01526031, version 1


Valérie Ménissier-Morain. Tools for a gentle slope transition From floating point arithmetic to exact real arithmetic. Eleventh International Conference on Computability and Complexity in Analysis (CCA 2014), Jul 2014, Darmstadt, Germany. ⟨hal-01526031⟩



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