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- Kaveh R. Ghazi, Vincent Lefèvre, Philippe Théveny, Paul Zimmermann
- Computing in Science and Engineering
- 2010

Most nowadays floating-point computations are done in double precision, i.e., with a significand (or mantissa, see the “Glossary” sidebar) of 53 bits. However, some applications require more precision: double-extended (64 bits or more), quadruple precision (113 bits) or even more. In an article published in The Astronomical Journal in 2001, Toshio Fukushima… (More)

- Nathalie Revol, Philippe Théveny
- Reliable Computing
- 2013

Two main and not necessarily compatible objectives when implementing the product of two dense matrices with interval coefficients are accuracy and efficiency. In this work, we focus on an implementation on multicore architectures. One direction successfully explored to gain performance in execution time is the representation of intervals by their midpoints… (More)

- Nathalie Revol, Philippe Théveny
- IEEE Trans. Computers
- 2014

What is called numerical reproducibility is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different numbers of processing units, types, execution environments, computational loads etc. This problem is especially stringent for HPC numerical simulations.… (More)

We propose to join the research efforts of Richard Brent’s team at ANU (Australian National University, Canberra, Australia) with those of the CACAO team from the “Centre de Recherche INRIA Nancy-Grand Est” (Nancy, France) into an INRIA associate team called ANC (Algorithms, Numbers, Computers). We wish to extend in such a way a long-term and successful… (More)

Interval arithmetic is mathematically defined as set arithmetic. For implementation issues, it is necessary to detail the representation of intervals and to detail formulas for the arithmetic operations. Two main representations of intervals are considered here: inf-sup and midrad. Formulas for the arithmetic operations, using these representations, are… (More)

- Vincent Lefèvre, Philippe Théveny, +4 authors Nathalie Revol
- ACM Comm. Computer Algebra
- 2010

Generating certified and efficient numerical codes requires information ranging from the mathematical level to the representation of numbers. Even though the mathematical semantics can be expressed using the content part of MathML, this language does not encompass the implementation on computers. Indeed various arithmetics may be involved, like… (More)

- Philippe Théveny
- 2014

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