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CAMPARY: Cuda Multiple Precision Arithmetic Library and Applications
LAAS CNRS, 7 Ave Colonel Roche, F-31077 Toulouse, France..
ENS Lyon, LIP Lab, 46 Allee Italie, F-69364 Lyon 07, France..
ENS Lyon, LIP Lab, 46 Allee Italie, F-69364 Lyon 07, France..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2016 (English)In: Mathematical Software, ICMS 2016 / [ed] Greuel, GM; Koch, T; Paule, P; Sommese, A, 2016, p. 232-240Conference paper, Published paper (Refereed)
Abstract [en]

Many scientific computing applications demand massive numerical computations on parallel architectures such as Graphics Processing Units (GPUs). Usually, either floating-point single or double precision arithmetic is used. Higher precision is generally not available in hardware, and software extended precision libraries are much slower and rarely supported on GPUs. We develop CAMPARY: a multipleprecision arithmetic library, using the CUDA programming language for the NVidia GPU platform. In our approach, the precision is extended by representing real numbers as the unevaluated sum of several standard machine precision floating-point numbers. We make use of error-free transforms algorithms, which are based only on native precision operations, but keep track of all rounding errors that occur when performing a sequence of additions and multiplications. This offers the simplicity of using hardware highly optimized floating-point operations, while also allowing for rigorously proven rounding error bounds. This also allows for easy implementation of an interval arithmetic. Currently, all basic multiple-precision arithmetic operations are supported. Our target applications are in chaotic dynamical systems or automatic control.

Place, publisher, year, edition, pages
2016. p. 232-240
Series
Lecture Notes in Computer Science, ISSN 0302-9743 ; 9725
Keyword [en]
Floating-point arithmetic, Multiple precision library, GPGPU computing, Error-free transform, Floating-point expansions, Dynamical systems, Henon map, Semi-definite programming
National Category
Embedded Systems
Identifiers
URN: urn:nbn:se:uu:diva-311094DOI: 10.1007/978-3-319-42432-3_29ISI: 000387431800029ISBN: 9783319424323; 9783319424316 (print)OAI: oai:DiVA.org:uu-311094DiVA: diva2:1058565
Conference
5th International Congress on Mathematical Software (ICMS), JUL 11-14, 2016, Zuse Inst, Berlin, GERMANY
Available from: 2016-12-21 Created: 2016-12-21 Last updated: 2016-12-21Bibliographically approved

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Tucker, Warwick

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