Newton-Raphson Algorithms for Floating-Point Division Using an FMA

Nicolas Louvet 1 Jean-Michel Muller 1 Adrien Panhaleux 1, 2
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Since the introduction of the Fused Multiply and Add (FMA) in the IEEE-754-2008 standard [6] for floating-point arithmetic, division based on Newton-Raphson's iterations becomes a viable alternative to SRT-based divisions. The Newton-Raphson iterations were already used in some architecture prior to the revision of the IEEE-754 norm. For example, Itanium architecture already used this kind of iterations [8]. Unfortunately, the proofs of the correctness of binary algorithms do not extend to the case of decimal floating-point arithmetic. In this paper, we present general methods to prove the correct rounding of division algorithms using Newton-Raphson's iterations in software, for radix 2 and radix 10 floating-point arithmetic.
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Nicolas Louvet, Jean-Michel Muller, Adrien Panhaleux. Newton-Raphson Algorithms for Floating-Point Division Using an FMA. 21st IEEE International Conference on Application-specific Systems Architectures and Processors (ASAP), 2010, Jul 2010, Rennes, France. pp.200-207. ⟨ensl-00549027⟩

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