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Midpoints and Exact Points of Some Algebraic Functions in Floating-Point Arithmetic
February 2011 (vol. 60 no. 2)
pp. 228-241
ASCII Text
x 
 
Claude-Pierre Jeannerod, Nicolas Louvet, Jean-Michel Muller, Adrien Panhaleux, "Midpoints and Exact Points of Some Algebraic Functions in Floating-Point Arithmetic," IEEE Transactions on Computers, vol. 60, no. 2, pp. 228-241, February, 2011.
 
 
BibTex
x
 
@article{ 10.1109/TC.2010.144,
author = {Claude-Pierre Jeannerod and Nicolas Louvet and Jean-Michel Muller and Adrien Panhaleux},
title = {Midpoints and Exact Points of Some Algebraic Functions in Floating-Point Arithmetic},
journal ={IEEE Transactions on Computers},
volume = {60},
number = {2},
issn = {0018-9340},
year = {2011},
pages = {228-241},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2010.144},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Midpoints and Exact Points of Some Algebraic Functions in Floating-Point Arithmetic
IS - 2
SN - 0018-9340
SP228
EP241
EPD - 228-241
A1 - Claude-Pierre Jeannerod,
A1 - Nicolas Louvet,
A1 - Jean-Michel Muller,
A1 - Adrien Panhaleux,
PY - 2011
KW - Floating-point arithmetic
KW - correct rounding
KW - algebraic function.
VL - 60
JA - IEEE Transactions on Computers
ER -
 
Claude-Pierre Jeannerod, INRIA Grenoble - Rhône-Alpes, Universit de Lyon, Lyon
Nicolas Louvet, Université Claude Bernard Lyon 1, Universit de Lyon, Lyon
Jean-Michel Muller, CNRS, Universit de Lyon, Lyon
Adrien Panhaleux, École Normale Supérieure de Lyon, Universit de Lyon, Lyon
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 \pm \infty or toward 0 arithmetic). In the first case, we say that f(x) is a midpoint, and in the second case, we say that f(x) is an exact point. For some usual algebraic functions and various floating-point formats, we prove whether or not there exist midpoints or exact points. When there exist midpoints or exact points, we characterize them or list all of them (if there are not too many). The results and the techniques presented in this paper can be used in particular to deal with both the binary and the decimal formats defined in the IEEE 754-2008 standard for floating-point arithmetic.

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Index Terms:
Floating-point arithmetic, correct rounding, algebraic function.
Citation:
Claude-Pierre Jeannerod, Nicolas Louvet, Jean-Michel Muller, Adrien Panhaleux, "Midpoints and Exact Points of Some Algebraic Functions in Floating-Point Arithmetic," IEEE Transactions on Computers, vol. 60, no. 2, pp. 228-241, Feb. 2011, doi:10.1109/TC.2010.144
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