Interval arithmetic is the arithmetic of quantities that lie within specified ranges (i.e., intervals) instead of having definite known values. Interval arithmetic can be especially useful when working with data that is subject to measurement errors or uncertainties. It can be considered a rigorous version of significance arithmetic (a.k.a., automatic precision control). It is powerful enough to provide rigorous mathematical proofs (de la Llave 1991, Hutchings et al. 2000, Tucker 2002, Gutowski 2003), but rigor comes at a price. In particular, interval arithmetic can be slow, and often gives overly pessimistic results for real-world computations.

floating-point arithmetic | interval | projectively extended real numbers