Algorithms for triple-word arithmetic

Nicolas Fabiano 1 Jean-Michel Muller 2 Joris Picot 2
2 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Triple-word arithmetic consists in representing high-precision numbers as the unevaluated sum of three floating-point numbers (with "nonoverlapping"' constraints that are explicited in the paper). We introduce and analyze various algorithms for manipulating triple-word numbers: rounding a triple-word number to a floating-point number, adding, multiplying, dividing, and computing square-roots of triple-word numbers, etc. We compare our algorithms, implemented in the Campary library, with other solutions of comparable accuracy. It turns out that our new algorithms are significantly faster than what one would obtain by just using the usual floating-point expansion algorithms in the special case of expansions of length 3.
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Contributor : Jean-Michel Muller <>
Submitted on : Monday, May 20, 2019 - 10:03:47 AM
Last modification on : Tuesday, May 21, 2019 - 9:41:01 AM


  • HAL Id : hal-01869009, version 2



Nicolas Fabiano, Jean-Michel Muller, Joris Picot. Algorithms for triple-word arithmetic. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, In press, pp.1-11. ⟨hal-01869009v2⟩



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