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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A notable aspect of this paper, which is often cited as the “birth certificate of computer science”, is its position, expounded in Section 5.3, that floating-point arithmetic is generally a bad idea.
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Russinoff, D.M. (2019). Rounding. In: Formal Verification of Floating-Point Hardware Design. Springer, Cham. https://doi.org/10.1007/978-3-319-95513-1_6
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DOI: https://doi.org/10.1007/978-3-319-95513-1_6
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-95513-1
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