CAMPARY: Cuda multiple precision arithmetic library and applications

Mioara Joldes, Jean Michel Muller, Valentina Popescu, Warwick Tucker

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearch

13 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationMathematical Software – ICMS 2016
Subtitle of host publication5th International Conference on Mathematical Software, ICMS 2016; Berlin; Germany; 11 July 2016 through 14 July 2016
EditorsGert-Martin Greuel, Andrew Sommese, Thorsten Koch, Peter Paule
Place of PublicationCham Switzerland
PublisherSpringer-Verlag London Ltd.
Pages232-240
Number of pages9
Volume9725
ISBN (Electronic)9783319424323
ISBN (Print)9783319424316
DOIs
Publication statusPublished - 1 Jan 2016
Externally publishedYes
Event5th International Conference on Mathematical Software, ICMS 2016 - Berlin, Germany
Duration: 11 Jul 201614 Jul 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9725
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Conference on Mathematical Software, ICMS 2016
CountryGermany
CityBerlin
Period11/07/1614/07/16

Keywords

  • Dynamical systems
  • Error-free transform
  • Floating-point arithmetic
  • Floating-point expansions
  • GPGPU computing
  • Hénon map, semi-definite programming
  • Multiple precision library

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