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Floating-point arithmetic (Q6047500)

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scientific article; zbMATH DE number 7736656

Language	Label	Description	Also known as
English	Floating-point arithmetic	scientific article; zbMATH DE number 7736656

Statements

scholarly article

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Floating-point arithmetic (English)

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Claude-Pierre Jeannerod

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Guillaume Melquiond

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Jean-Michel Muller

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publication date

12 September 2023

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1017/s0962492922000101

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Fast floating-point filters for robust predicates

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The Mathematical-Function Computation Handbook

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A Class of Fast and Accurate Summation Algorithms

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Pitfalls of a Full Floating-Point Proof: Example on the Formal Proof of the Veltkamp/Dekker Algorithms

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Kahan's Algorithm for a Correct Discriminant Computation at Last Formally Proven

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Emulation of a FMA and Correctly Rounded Sums: Proved Algorithms Using Rounding to Odd

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Exact and Approximated Error of the FMA

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On the Robustness of the 2Sum and Fast2Sum Algorithms

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Emulating Round-to-Nearest Ties-to-Zero “Augmented” Floating-Point Operations Using Round-to-Nearest Ties-to-Even Arithmetic

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On the Precision Attainable with Various Floating-Point Number Systems

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Error bounds on complex floating-point multiplication

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Correctly Rounded Multiplication by Arbitrary Precision Constants

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Exponential Sums and Correctly-Rounded Functions

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Error Analysis of Some Operations Involved in the Cooley-Tukey Fast Fourier Transform

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On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots

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Reducing Floating Point Error in Dot Product Using the Superblock Family of Algorithms

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The Early Computers of Konrad Zuse, 1935 to 1945

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Efficient and accurate computation of upper bounds of approximation errors

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Sollya: An Environment for the Development of Numerical Codes

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Probabilistic Rounding Error Analysis of Householder QR Factorization

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Stochastic Rounding and Its Probabilistic Backward Error Analysis

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Certifying the Floating-Point Implementation of an Elementary Function Using Gappa

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A floating-point technique for extending the available precision

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Underflow and the Reliability of Numerical Software

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Algorithms for Efficient Reproducible Floating Point Summation

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Fast and accurate floating point summation with application to computational geometry

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Parallel Reproducible Summation

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Algorithms for Triple-Word Arithmetic

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Reprint of a Note on Rounding-Off Errors

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How do you compute the midpoint of an interval?

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Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic

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Floating-point arithmetic with 84-bit numbers

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The Accuracy of Floating Point Summation

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Accuracy and Stability of Numerical Algorithms

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A New Approach to Probabilistic Rounding Error Analysis

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Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data

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Mixed precision algorithms in numerical linear algebra

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Simulating Low Precision Floating-Point Arithmetic

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Implementing complex elementary functions using exception handling

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Note on triple-precision floating-point arithmetic with 132-bit numbers

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Probabilistic Error Analysis for Inner Products

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A Radix-Independent Error Analysis of the Cornea-Harrison-Tang Method

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The relative accuracy of \(\mathtt{(x+y)*(x-y)}\)

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On relative errors of floating-point operations: Optimal bounds and applications

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Error bounds on complex floating-point multiplication with an FMA

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Further analysis of Kahan’s algorithm for the accurate computation of $2\times 2$ determinants

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Sharp error bounds for complex floating-point inversion

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Accurate, validated and fast evaluation of elementary symmetric functions and its application

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Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic

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CAMPARY: Cuda Multiple Precision Arithmetic Library and Applications

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On the Computation of Correctly Rounded Sums

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A statistical study of the accuracy of floating point number systems

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An axiomatic approach to rounded computations

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Computer arithmetic and validity. Theory, implementation, and applications

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Toward Accurate and Fast Summation

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A note on Dekker's FastTwoSum algorithm

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Error estimates for the summation of real numbers with application to floating-point summation

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Sharp estimates for perturbation errors in summations

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Faithfully Rounded Floating-point Computations

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Design, implementation and testing of extended and mixed precision BLAS

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On accurate floating-point summation

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In-and-out conversions

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Rounding error analysis of linear recurrences using generating series

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Quasi double-precision in floating point addition

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A mechanically checked proof of the AMD5/sub K/86/sup TM/ floating-point division program

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Introduction to Interval Analysis

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On the Error of Computing <i>ab</i> + <i>cd</i> using Cornea, Harrison and Tang's Method

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Elementary Functions

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Formalization of Double-Word Arithmetic, and Comments on “Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic”

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Handbook of Floating-Point Arithmetic

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Rundungsfehleranalyse einiger Verfahren zur Summation endlicher Summen

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Interval Methods for Systems of Equations

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Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit

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Accurate Sum and Dot Product

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Numerical Computing with IEEE Floating Point Arithmetic

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Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications

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Correction d'une somme en arithmétique à virgule flottante

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Efficient scaling for complex division

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Motivations for an arbitrary precision interval arithmetic and the MPFI library

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Innocuous Double Rounding of Basic Arithmetic Operations

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Ultimately Fast Accurate Summation

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Verification methods: Rigorous results using floating-point arithmetic

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Error estimation of floating-point summation and dot product

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IEEE754 Precision- <i>k</i> base-β Arithmetic Inherited by Precision- <i>m</i> Base-β Arithmetic for <i>k</i> < <i>m</i>

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Accurate Floating-Point Summation Part I: Faithful Rounding

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Computing predecessor and successor in rounding to nearest

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Adaptive precision floating-point arithmetic and fast robust geometric predicates

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A note on complex division

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On Taking the Square Root of a Complex Number

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Automated empirical optimizations of software and the ATLAS project

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Error analysis of floating-point computation

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Error Analysis of Direct Methods of Matrix Inversion

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Reducing truncation errors by programming

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Mixed-Precision Cholesky QR Factorization and Its Case Studies on Multicore CPU with Multiple GPUs

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Sharp ULP rounding error bound for the hypotenuse function

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Identifiers

10.1017/s0962492922000101

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6047500

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