Definition
In affine arithmetic, each input or computed quantity x is represented by a formula where are known floating-point numbers, and are symbolic variables whose values are only known to lie in the range .
Thus, for example, a quantity X which is known to lie in the range can be represented by the affine form, for some k. Conversely, the form implies that the corresponding quantity X lies in the range .
The sharing of a symbol among two affine forms, implies that the corresponding quantities X, Y are partially dependent, in the sense that their joint range is smaller than the Cartesian product of their separate ranges. For example, if and, then the individual ranges of X and Y are and, but the joint range of the pair (X,Y) is the hexagon with corners (2,27), (6,27), (18,19), (18,13), (14,13), (2,21) — which is a proper subset of the rectangle ×.
Read more about this topic: Affine Arithmetic
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