Výsledky vyhledávání - "Jean-Michel Muller"

Autor: Sylvie Boldo, Claude-Pierre Jeannerod, Guillaume Melquiond, Jean-Michel Muller

Publikováno v: Acta Numerica
Acta Numerica, 2023, 32, pp.203-290. ⟨10.1017/S0962492922000101⟩

Floating-point numbers have an intuitive meaning when it comes to physics-based numerical computations, and they have thus become the most common way of approximating real numbers in computers. The IEEE-754 Standard has played a large part in making

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8a81db438afc25763b2ff59c578340f8
https://doi.org/10.1017/s0962492922000101

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Accurate calculation of Euclidean Norms using Double-word arithmetic

Autor: Vincent Lefèvre, Nicolas Louvet, Jean-Michel Muller, Joris Picot, Laurence Rideau

Publikováno v: ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software, 2023, 49 (1), pp.1-34. ⟨10.1145/3568672⟩

We consider the computation of the Euclidean (or L2) norm of an n -dimensional vector in floating-point arithmetic. We review the classical solutions used to avoid spurious overflow or underflow and/or to obtain very accurate results. We modify a rec

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0074f4c2d26fe700aebace2fd48b00a9
https://hal.science/hal-03482567

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Computer Arithmetic: Continuing a Long and Steady Emergence

Autor: Paolo Montuschi, Jean-Michel Muller, Florent de Dinechin

Publikováno v: Computer
Computer, 2022, 55 (10), pp.4-6. ⟨10.1109/MC.2022.3193206⟩

International audience

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https://hdl.handle.net/11583/2974400

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Algorithms for Triple-Word Arithmetic

Autor: Nicolas Fabiano, Jean-Michel Muller, Joris Picot

Publikováno v: IEEE Transactions on Computers
IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2019, 68 (11), pp.1573-1583. ⟨10.1109/TC.2019.2918451⟩
IEEE Transactions on Computers, 2019, 68 (11), pp.1573-1583. ⟨10.1109/TC.2019.2918451⟩

International audience; 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 vario

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1197ce1e82f2b0341e98453b2a63f381
https://doi.org/10.1109/tc.2019.2918451

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Elementary Functions and Approximate Computing

Autor: Jean-Michel Muller

Publikováno v: Proceedings of the IEEE
Proceedings of the IEEE, Institute of Electrical and Electronics Engineers, 2020, 108 (12), pp.1558-2256. ⟨10.1109/JPROC.2020.2991885⟩
Proceedings of the IEEE, 2020, 108 (12), pp.1558-2256. ⟨10.1109/JPROC.2020.2991885⟩

International audience; We review some of the classical methods used for quickly obtaining low-precision approximations to the elementary functions. Then, for each of the three main classes of elementary function algorithms (shift-and-add algorithms,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b7055c6f5296e8db7f8dc428ded68420
https://hal.archives-ouvertes.fr/hal-02517784v2/document

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An Architecture for Improving Variable Radix Real and Complex Division Using Recurrence Division

Autor: Milos D. Ercegovac, Jean-Michel Muller, James E. Stine

Publikováno v: ACSSC

This paper shows the details of an implementation of variable radix floating-point complex division based on previous implementations of the algorithm. This implementation takes advantage of the easier prescaling offered by low-radix division and rec

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::eafd1f13263ab8c7658fbeb90f2d6dba
https://doi.org/10.1109/ieeeconf51394.2020.9443498

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Error analysis of some operations involved in the Cooley-Tukey Fast Fourier Transform

Autor: Joris Picot, Mioara Joldes, Jean-Michel Muller, Nicolas Brisebarre, Ana-Maria Naneş

Publikováno v: ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software, 2020, 46 (2), pp.1-34. ⟨10.1145/3368619⟩
ACM Transactions on Mathematical Software, Association for Computing Machinery, 2020, 46 (2), pp.1-34. ⟨10.1145/3368619⟩

We are interested in obtaining error bounds for the classical Cooley-Tukey fast Fourier transform algorithm in floating-point arithmetic, for the 2-norm as well as for the infinity norm. For that purpose, we also give some results on the relative err

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b6b66bea36a9623aaf74b913a6f07526
https://hal.science/hal-01949458v2/document

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Emulating round-to-nearest ties-to-zero 'augmented' floating-point operations using round-to-nearest ties-to-even arithmetic

Autor: Jean-Michel Muller, Christoph Lauter, Sylvie Boldo

Publikováno v: IEEE Transactions on Computers
IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2021, 70 (7), pp.1046-1058. ⟨10.1109/TC.2020.3002702⟩
IEEE Transactions on Computers, 2021, 70 (7), pp.1046-1058. ⟨10.1109/TC.2020.3002702⟩

International audience; The 2019 version of the IEEE 754 Standard for Floating-Point Arithmetic recommends that new “augmented” operations should be provided for the binary formats. These operations use a new “rounding direction”: round to ne

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https://hal.archives-ouvertes.fr/hal-02137968

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Algorithms for manipulating quaternions in floating-point arithmetic

Autor: Mioara Joldes, Jean-Michel Muller

Publikováno v: Proceedings of ARITH-2020, IEEE 27th Symposium on Computer Arithmetic
ARITH-2020-IEEE 27th Symposium on Computer Arithmetic
ARITH-2020-IEEE 27th Symposium on Computer Arithmetic, Jun 2020, Portland, United States. pp.1-8, ⟨10.1109/ARITH48897.2020.00016⟩
ARITH

International audience; Quaternions form a set of four global but not unique parameters, which canrepresent three-dimensional rotations in a non-singular way. They arefrequently used in computer graphics, drone and aerospace vehiclecontrol. Floating-

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7956d57a1ce85d4c7d76a6996084dee9
https://hal.archives-ouvertes.fr/hal-02470766/file/quaternions-HAL.pdf

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Accurate Complex Multiplication in Floating-Point Arithmetic

Autor: Vincent Lefèvre, Jean-Michel Muller

Publikováno v: ARITH 2019-26th IEEE Symposium on Computer Arithmetic
ARITH 2019-26th IEEE Symposium on Computer Arithmetic, Jun 2019, Kyoto, Japan. pp.1-7
ARITH

International audience; We deal with accurate complex multiplication in binary floating-point arithmetic, with an emphasis on the case where one of the operands in a "double-word" number. We provide an algorithm that returns a complex product with no

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5d84cc2f1575052512c08804d00b3d55
https://hal.archives-ouvertes.fr/hal-02001080v2/document

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