Philippe Théveny

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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(More)
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 mid-points(More)
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)
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)
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 mid-rad. Formulas for the arithmetic operations, using these representations, are(More)
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