When (3x/3) and 3(x/3) are not equal to x
Résumé
Rounding Error Analysis is routinely used to compute a worst-case
error bound on the result of algorithms that use floating-point
arithmetic. However, for some applications (e.g., when it is necessary to
prove some inclusion of the result in a domain), the knowledge of
both an upper-bound of the magnitude of the error and of its sign
is paramount. Using standard rounding error analysis together with a
simple systematic approach, we compute such information for the
expressions $3x$, $x/3$, $3(x/3)$, and $3x/3$, which can be used, e.g., in the proof
of interval arithmetic operators.
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