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## When (3x/3) and 3(x/3) are not equal to x

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Frédéric Goualard

#### Abstract

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.

#### Domains

Computer Science [cs] Computer Arithmetic

### Dates and versions

hal-01451457 , version 1 (01-02-2017)

### Identifiers

• HAL Id : hal-01451457 , version 1

### Cite

Frédéric Goualard. When (3x/3) and 3(x/3) are not equal to x. 2016. ⟨hal-01451457⟩

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