I’m sure that you are aware of the fact that floats representation in any programming language is limited by the precision of the internal binary representations. In other words, you can never have an exact float representation – there will always be some precision associated with the float you are working with. The simplest example is the difference in precision between the float and double types in C.

Suppose I have the following code fragment:
[C] if ( result.score >= input->raw_cut_off ) [/C]

Both result.score and input->raw_cut_off are of type float, and can have positive and negative values. When compared with the greater than or equal ( >= ) operator, it is not always that condition is true – for the precision reasons shortly mentioned above.

As I already said, there is no precision specification for equality operators in C. But it is quite simple to “invent” precision specification; e.g. if I wanted to test for equality only, I could write
[C] if ( fabsf( result.score – input->raw_cut_off ) < 0.000001 )[/C] In this example, I'm effectively asking for 6-digit precision for the equality comparison of floating-point values. Note, that if you replace that 0.000001 with the actual precision limit of the floating type you are using, you will be "exactly" comparing floating-point numbers - up to that type's precision, of course .

The first-most example with the >= operator can be rewritten as
[C] if ( result.score > ( input->raw_cut_off – precision) ) [/C]
where precision is exactly what it is named, e.g. precision = 0.000001.

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• comment by Randy A. Ynchausti
• scientific programming