Reliable computing with GNU MPFR Paul Zimmermann ´ LORIA/INRIA Nancy-Grand Est, Equipe CARAMEL - bˆ atiment A,

Source URL: www.loria.fr

• Computer arithmetic
• GNU MPFR
• Rounding
• Paul Zimmermann
• GNU Multiple Precision Arithmetic Library
• SageMath
• Extended precision
• Floating point
• Interval arithmetic
• GNU Compiler Collection
• Precision
• IEEE floating point

Introduction Bounds Rounding Errors Conclusion De l’arithm´etique d’intervalles `a la certification de programmes Guillaume Melquiond Sous la direction de Marc Daumas

Source URL: www.lri.fr

• Computer arithmetic
• Numerical analysis
• Arithmetic
• Floating point
• Arithmetic underflow
• Rounding
• Interval arithmetic
• Precision
• Round-off error
• Significant figures

INDEX Funktionsbeschreibungen Mathematical Procedures ________________________________________________________ 3 ABS (return absolute value) _____________________________________________________________ 4 INRANGE (check

Source URL: www.schoeffler.biz

• Logarithms
• Computing
• Software engineering
• Computer programming
• Rounding
• Bc
• Common logarithm
• Subroutine
• Parameter
• Natural logarithm
• C mathematical functions
• Module:GliderMaven/converttest

Motivations for an arbitrary precision interval arithmetic and the MPFI library N. Revol ()∗ ´ INRIA, Project Arenaire, LIP (CNRS/ENSL/INRIA/UCBL), Ecole Normale

Source URL: perso.ens-lyon.fr

• Computer arithmetic
• GNU MPFR
• Interval arithmetic
• Floating point
• Rounding
• GNU Multiple Precision Arithmetic Library
• Precision
• Machine epsilon
• Arbitrary-precision arithmetic
• IEEE floating point
• Significant figures
• Interval

GNU MPFR The Multiple Precision Floating-Point Reliable Library EditionJuneThe MPFR team

Source URL: www.mpfr.org

• Software
• Computer arithmetic
• Compiling tools
• C
• GNU MPFR
• GNU Multiple Precision Arithmetic Library
• Configure script
• SageMath
• Rounding
• GNU Compiler Collection
• C standard library
• GNU

A Formally-Verified C Compiler Supporting Floating-Point Arithmetic Sylvie Boldo∗ , Jacques-Henri Jourdan† , Xavier Leroy† , and Guillaume Melquiond∗ ∗ Inria Saclay–ˆIle-de-France & LRI, CNRS UMR 8623, Univ

Source URL: www.lri.fr

• Computer arithmetic
• Computing
• Software engineering
• Computer architecture
• IEEE floating point
• Double-precision floating-point format
• Extended precision
• Processor register
• Compiler correctness
• Rounding
• Fortran
• Single-precision floating-point format

Noname manuscript No. (will be inserted by the editor) Some issues related to double rounding Érik Martin-Dorel · Guillaume Melquiond · Jean-Michel Muller

Source URL: www.lri.fr

• Computer arithmetic
• Mathematics
• Theoretical computer science
• Computing
• Rounding
• IEEE floating point
• Double-precision floating-point format
• Normal number
• Arithmetic underflow
• Division algorithm
• Q
• Denormal number

11. A PPROXIMATION A LGORITHMS ‣ load balancing ‣ center selection ‣ pricing method: vertex cover ‣ LP rounding: vertex cover ‣ generalized load balancing

Source URL: vigna.di.unimi.it

• Scheduling
• Operations research
• NP-complete problems
• Complexity classes
• Combinatorial optimization
• Makespan
• Knapsack problem
• NP
• Algorithm
• Vertex cover
• Approximation algorithm
• Job shop scheduling

Accurate Evaluation of Arithmetic Expressions Matthieu Martel DALI - Universite´ de Perpignan Via Domitia LIRMM - CNRS: UMRUniversite´ Montpellier 2, France

Source URL: nsad2012.ucombinator.org

• Computer arithmetic
• Floating point
• Abstract interpretation
• Rounding
• IEEE floating point
• Double-precision floating-point format
• Precision
• NaN
• Expression

Treveri® Cellars Sparkling Syrah Treveri Cellars Sparkling Syrah Rounding out the Core Tier, this one-of-a-kind wine combines rich flavors of blackberry, pepper, cherries, and a hint of tobacco for a dark and delicious

Source URL: www.trevericellars.com