# Rounding

Chapter

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## Abstract

The objective of floating-point rounding is the approximation of a real number by one that is representable in a given floating-point format. Thus, a *rounding mode* is a function that computes an *n*-exact value \(\mathcal {R}(x,n)\), given a real number *x* and precision *n*. In this chapter, we investigate the properties of a variety of rounding modes, including those that are prescribed by the IEEE standard as well as others that are commonly used in implementations of floating-point operations.

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