Double/Single equality up to predefined error

Question

Is there a standard class for floating point numbers which implements <, == and > in a way that it ignores "small numerical errors" (where small has to be specified before)?

I know that I could implement something like that myself, but maybe I do not have to reinvent it.

you mean something like a tolerance limit for comparison, highly unlikely that something would be built in — V4Vendetta, Aug 08 '12 at 08:41
Maybe you could use [`Math.Round`](http://msdn.microsoft.com/en-us/library/75ks3aby.aspx) on both numbers then check if they are `==`, `<` or `>`. — matthewr, Aug 08 '12 at 08:42

score 2 · Accepted Answer · answered Aug 08 '12 at 13:27

2

In the MathNET.Numerics library there is a static Precision class that provides a lot of the requested functionality. There are no operator overloads, but perhaps the available methods can still prove sufficient.

answered Aug 08 '12 at 13:27

Anders Gustafsson

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score 1 · Answer 2 · answered Aug 08 '12 at 13:22

There is no widely used class or library for this because it is a poor programming technique, and, to the extent it provides any benefit, is not easily adaptable to different situations.

Accepting unequal numbers as equal reduces false negatives (results that are not accepted as equal due to rounding in floating-point operations but that would be equal if calculated exactly) but increases false positives (results that are accepted as equal but that are not equal if calculated exactly). There is no general principle that balances reduction of false negatives against increase of false positives or vice-versa, so there is no general solution for this problem.

Additionally, a number of different situations arise: The magnitude of floating-point errors may be relative to the magnitude of the results, so a tolerance for error would have to be proportional to the results. Or the magnitude may be largely absolute (with respect to the results, perhaps relative to some other aspect of the problem), so a tolerance for error would have to be a fixed number. Errors on one side of a threshold may be tolerable while errors on the other side might not be (as when taking an arcsine near one or a square root near zero).

If you do not care about false positives, then you can simply replace your test with true, and that will eliminate all false negatives. If that is not acceptable to you, then you need to determine what false positives are unacceptable.

This determination is highly dependent on the calculations you are performing and their purpose. It is important to determine what rounding errors may occur in your calculations, how they will affect your results, and whether the errors are tolerable in your application.

Double/Single equality up to predefined error

2 Answers2