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1
November 2016
Numerical Algorithms: Volume 73 Issue 3, November 2016
Publisher: SpringerVerlag New York, Inc.
We study the accuracy of the classic algorithm for inverting a complex number given by its real and imaginary parts as floatingpoint numbers. Our analyses are done in binary floatingpoint 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, Floatingpoint arithmetic
2
April 2013
ARITH '13: Proceedings of the 2013 IEEE 21st Symposium on Computer Arithmetic
Publisher: IEEE Computer Society
This paper deals with the accuracy of complex division in radixtwo floatingpoint arithmetic. Assuming that a fused multiplyadd (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:
floatingpoint arithmetic, complex division, fused multiplyadd (FMA), rounding error analysis
3
March 2012
IEEE Transactions on Computers: Volume 61 Issue 3, March 2012
Publisher: IEEE Computer Society
This paper presents a study of some basic blocks needed in the design of floatingpoint summation algorithms. In particular, in radix2 floatingpoint arithmetic, we show that among the set of the algorithms with no comparisons performing only floatingpoint additions/subtractions, the 2Sum algorithm introduced by Knuth is minimal, both in terms ...
Keywords:
Floatingpoint 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
When implementing a function f in floatingpoint arithmetic, if we wish correct rounding and good performance, it is important to know if there are input floatingpoint values x such that f(x) is either the middle of two consecutive floatingpoint numbers (assuming roundedtonearest arithmetic), or a floatingpoint number (assuming rounded toward ...
Keywords:
algebraic function., Floatingpoint arithmetic, Floatingpoint arithmetic, correct rounding, algebraic function., correct rounding
5
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:
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We introduce several algorithms for accurately evaluating powers to a positive integer in floatingpoint arithmetic, assuming a fused multiplyadd (fma) instruction is available. For bounded, yet very large values of the exponent, we aim at obtaining correctly rounded results in roundtonearest mode, that is, our algorithms return the floatingpoint number ...
Keywords:
Correct rounding, floatingpoint arithmetic, integer power function
6
June 2009
ARITH '09: Proceedings of the 2009 19th IEEE Symposium on Computer Arithmetic
Publisher: IEEE Computer Society
This paper presents a study of some basic blocks needed in the design of floatingpoint summation algorithms. In particular, we show that among the set of the algorithms with no comparisons performing only floatingpoint additions/subtractions, the 2Sum algorithm introduced by Knuth is minimal, both in terms of number of operations ...
Keywords:
Floatingpoint 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
The compensated Horner algorithm improves the accuracy of polynomial evaluation in IEEE754 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
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:
PDF
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, IEEE754 floating point arithmetic, errorfree transformations

