Floating point equality and tolerances

This blogpost contains an example, fairly foolproof implementation, and detailed theory behind it http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ it is also one of a series, so you can always read more. In short: use ULP for most numbers, use epsilon for numbers near zero, but there are still caveats. If you want to be sure about your floating point math i recommend reading whole series.

As far as I know, one doesn't.

There is no general "right answer", since it can depend on the application's requirement for precision.

For instance, a 2D physics simulation working in screen-pixels might decide that 1/4 of a pixel is good enough, while a 3D CAD system used to design nuclear plant internals might not.

I can't see a way to programmatically decide this from the outside.