Mathematics-Online lexicon: Rounding

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	Mathematics-Online lexicon:
	Rounding

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overview

Standard rounding approximates a real number with the nearest even floating point number R. If $\vert x\vert$ lies within the admissible floating point range, then

R $\displaystyle x - x = \delta x,\quad \vert\delta\vert \le$ eps $\displaystyle = \beta^{1-p}/2,$

where $\beta$ is the base and the number of digits of the floating point representation. The constant eps is called the machine precision and equals

$\displaystyle 2^{1-53}/2=2^{-53}$

for double precision.

Annotation:

Proof: Rounding

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automatically generated 3/ 8/2007