Re:Inexact floating point calculations... (Score 1)

Of course not all real numbers (or even rationals) can be represented as finite binary fractions -- let alone onex that fit into 53 bits! But floating point numbers are numbers, not fuzz. Add 0.5 and 0.5 in floating point, and you'll get 1.0 exactly -- not 1.0 plus or minus a unit in the last place.

Why does this matter if you can't represent your original data exactly? Because in intermediate computations, we rely on certain relationships holding. This is important in geometric computation, for example, since we'd like a consistent view of the world. Three ordered points on the plane should be listed clockwise or counterclockwise, or be colinear -- but not more than one of those. See the papers on robust geometric predicates by Jonathan Shewchuk, or papers on floating point computation by W. Kahan for details.