Is there a way to get a hashcode of a float with epsilon?

Question

It is well known that comparing floats by == is usually a mistake. In a 3D-vector class (with float components X, Y, Z) i wrote, two vectors are considered equa

Answer 1

I'm afraid it is not in the general case. A sketch of a proof goes like this:

Take any two numbers a and b. Let the difference between them be d. Then if you create the d/epsilon numbers with an epsilon step in between, each step must be "equal" to the step before, which by hashcode semantics have the same hashcode. So all numbers must have the same hashcode.

You can only solve this problem if you add some other constraint.

As an aside, you definition of Equals is wrong as well, as it can be true that a.Equals(b) and b.Equals(c) but not a.Equals(c), which is wrong for equals. This is known as breaking the Transitivity property.

What can I do then?

The solution depends on what you are using the hash for. One solution would be to introduce a conceptual grid. Change the equals and hashcode so two numbers are equal if in the same grid cube, by rounding to a constant number of decimal places, then taking equals and hashcode on the rounded number. If being close to zero is an important case, add a offset of epsilon/2 before rounding, so zero is the centre of the cube. This is correct, but you can have two numbers arbitrarily close together (under the limits of float) without being equal. So for some applications it will be ok, others it won't be. This is similar to an idea from mghie.