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I know we can't compare 2 floating point values using ==. We can only compare they are within some interval of each other. I know
if(val == 0.512) is wrong due to errors inherent in floating point calculations and conversion to binary and should be
if (val in (0.512-epsilon, 0.512+epsilon)) But is 0 special? Can we compare floats exactly to 0? Or even that is incorrect? Particularly in the context of C# and Java?
double val = 0; val = getVal(); if(val == 0) 
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To compare two floating point or double values, we have to consider the precision in to the comparison. For example, if two numbers are 3.1428 and 3.1415, then they are same up to the precision 0.01, but after that, like 0.001 they are not same.
In the case of floating-point numbers, the relational operator (==) does not produce correct output, this is due to the internal precision errors in rounding up floating-point numbers. In the above example, we can see the inaccuracy in comparing two floating-point numbers using “==” operator.
So as long your floats come from non decimal literals, the comparison with the equivalent integer will be the same, because the integer will be cast to the very same float before the comparison can be done.
Even though 0 has an exact representation, you can't rely on the result of a calculation using floats to be exactly 0. As you noted, this is due to floating point calculation and conversion issues.
So, you should test for 0 against your tolerance epsilon.
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