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ARENAIRE Research team

Computer arithmetic

  • Leader : Florent Dupont de dinechin
  • Research center(s) : CRI Grenoble - Rhône-Alpes
  • Field : Algorithmics, Programming, Software and Architecture
  • Theme : Algorithms, Certification, and Cryptography
  • Partner(s) : Université Claude Bernard (Lyon 1),Ecole normale supérieure de Lyon,CNRS
  • Collaborator(s) : U. LYON 1 (UCBL), ENS LYON, CNRS, INRIA

Team presentation

The ARENAIRE project-team works in the field of computer arithmetic. It consolidates existing knowledge and it explores new approaches in this area. Each study and each proposed solution relies on this scintifical basis and is furthermore developed while keeping in mind the peculiarities of the target problem. Our main research topics include the hardware implementation of arithmetic (integrated circuits or sc Fpga), numerical computations (floating-point arithmetic), very accurate or exact computations (multiple precision, interval arithmetic and arbitrary precision). The choice of a target often imposes the pint of view and the constraints. However, reliability, accuracy and speed are the main goals that underly every study of the ARENAIRE project-team.

Research themes

  • Hardware implementations of arithmetic: table-based methods, asynchronous arithmetic operators, low power consumption operators, design tools for arithmetic operators, arithmetic on FPGA, library of floating-point operators for FPGA.
  • Floating-point arithmetic: properties of this arithmetic, specifications and formal proofs, correct rounding of elementary functions, control and correction of rounding errors, tools for multiple precision computations.
  • Algorithms and arithmetics: algorithms for multiple-precision interval arithmetic, arithmetics and algorithms for exact linear algebra, libraries.

International and industrial relations

  • ST Microelectronics: division algorithm for DSP processors.
  • POSIC SA: interpolation algorithm for a position sensor, implemented on FPGA.
  • Xilinx: algorithms on FPGA.
  • HP-Intel: on IA-64, evaluation and improvement of the quality and performances on integer and floating-point computations.
  • LINBOX: NSF-CNRS contract for a library of linear algebra.
  • Cooperations with the Belgian university of Mons and the Morrocan universities of Rabat and Oujda.

Keywords: Computer arithmetic Acuracy Numerical reliability Operators Elementary functions Floating-point arithmetic Low power