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 Nicolas Louvet

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Average citations per article1.75
Citation Count14
Publication count8
Publication years2006-2016
Available for download2
Average downloads per article229.50
Downloads (cumulative)459
Downloads (12 Months)15
Downloads (6 Weeks)1
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8 results found Export Results: bibtexendnoteacmrefcsv

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1
November 2016 Numerical Algorithms: Volume 73 Issue 3, November 2016
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0

We study the accuracy of the classic algorithm for inverting a complex number given by its real and imaginary parts as floating-point numbers. Our analyses are done in binary floating-point arithmetic, with an unbounded exponent range and in precision p; we also assume that the basic arithmetic operations (+, ź, ...
Keywords: Rounding error analysis, Complex inversion, Floating-point arithmetic

2
April 2013 ARITH '13: Proceedings of the 2013 IEEE 21st Symposium on Computer Arithmetic
Publisher: IEEE Computer Society
Bibliometrics:
Citation Count: 0

This paper deals with the accuracy of complex division in radix-two floating-point arithmetic. Assuming that a fused multiply-add (FMA) instruction is available and that no underflow/overflow occurs, we study how to ensure high relative accuracy in the component wise sense. Since this essentially reduces to evaluating accurately three expressions of ...
Keywords: floating-point arithmetic, complex division, fused multiply-add (FMA), rounding error analysis

3
March 2012 IEEE Transactions on Computers: Volume 61 Issue 3, March 2012
Publisher: IEEE Computer Society
Bibliometrics:
Citation Count: 2

This paper presents a study of some basic blocks needed in the design of floating-point summation algorithms. In particular, in radix-2 floating-point arithmetic, we show that among the set of the algorithms with no comparisons performing only floating-point additions/subtractions, the 2Sum algorithm introduced by Knuth is minimal, both in terms ...
Keywords: Floating-point arithmetic, summation algorithms, correct rounding, 2Sum and Fast2Sum algorithms.

4
February 2011 IEEE Transactions on Computers: Volume 60 Issue 2, February 2011
Publisher: IEEE Computer Society
Bibliometrics:
Citation Count: 1

When implementing a function f in floating-point arithmetic, if we wish correct rounding and good performance, it is important to know if there are input floating-point values x such that f(x) is either the middle of two consecutive floating-point numbers (assuming rounded-to-nearest arithmetic), or a floating-point number (assuming rounded toward ...
Keywords: algebraic function., Floating-point arithmetic, Floating-point arithmetic, correct rounding, algebraic function., correct rounding

5 published by ACM
January 2010 ACM Transactions on Mathematical Software (TOMS): Volume 37 Issue 1, January 2010
Publisher: ACM
Bibliometrics:
Citation Count: 1
Downloads (6 Weeks): 1,   Downloads (12 Months): 11,   Downloads (Overall): 291

Full text available: PDFPDF
We introduce several algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. For bounded, yet very large values of the exponent, we aim at obtaining correctly rounded results in round-to-nearest mode, that is, our algorithms return the floating-point number ...
Keywords: Correct rounding, floating-point arithmetic, integer power function

6
June 2009 ARITH '09: Proceedings of the 2009 19th IEEE Symposium on Computer Arithmetic
Publisher: IEEE Computer Society
Bibliometrics:
Citation Count: 1

This paper presents a study of some basic blocks needed in the design of floating-point summation algorithms. In particular, we show that among the set of the algorithms with no comparisons performing only floating-point additions/subtractions, the 2Sum algorithm introduced by Knuth is minimal, both in terms of number of operations ...
Keywords: Floating-point arithmetic, summation algorithms, correct rounding, 2Sum and Fast2Sum algorithms

7
June 2007 ARITH '07: Proceedings of the 18th IEEE Symposium on Computer Arithmetic
Publisher: IEEE Computer Society
Bibliometrics:
Citation Count: 8

The compensated Horner algorithm improves the accuracy of polynomial evaluation in IEEE-754 floating point arithmetic: the computed result is as accurate as if it was computed with the classic Horner algorithm in twice the working precision. Since the condition number still governs the accuracy of this computation, it may return ...

8 published by ACM
April 2006 SAC '06: Proceedings of the 2006 ACM symposium on Applied computing
Publisher: ACM
Bibliometrics:
Citation Count: 1
Downloads (6 Weeks): 0,   Downloads (12 Months): 4,   Downloads (Overall): 168

Full text available: PDFPDF
Several different techniques and softwares intend to improve the accuracy of results computed in a fixed finite precision. Here we focus on a method to improve the accuracy of the polynomial evaluation. It is well known that the use of the Fused Multiply and Add operation available on some microprocessors ...
Keywords: fused multiply and add, horner scheme, polynomial evaluation, IEEE-754 floating point arithmetic, error-free transformations



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