Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/TC.2010.144 | Computers, IEEE Transactions |
Keywords | Field | DocType |
input floating-point value,floating-point number,floating-point arithmetic,rounded-to-nearest arithmetic,consecutive floating-point number,correct rounding,good performance,algebraic functions,decimal format,exact points,various floating-point format,exact point,accuracy,functional analysis,floating point number,floating point arithmetic,algebraic function,tuning | Discrete mathematics,Midpoint,Floating point,Machine epsilon,Rounding,Algebraic function,Saturation arithmetic,Decimal,Mathematics,Binary number | Journal |
Volume | Issue | ISSN |
60 | 2 | 0018-9340 |
Citations | PageRank | References |
4 | 0.57 | 3 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Claude-Pierre Jeannerod | 1 | 224 | 22.05 |
| Nicolas Louvet | 2 | 37 | 6.61 |
| Jean-Michel Muller | 3 | 466 | 66.61 |
| Adrien Panhaleux | 4 | 6 | 1.80 |
| JeannerodClaude-Pierre | 5 | 4 | 0.57 |
| MullerJean-Michel | 6 | 4 | 0.57 |