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Comparing two floating point number by something like a_float == b_float is looking for trouble since a_float / 3.0 * 3.0 might not be equal to a_float due to round off error.
What one normally does is something like fabs(a_float - b_float) < tol.
How does one calculate tol?
Ideally tolerance should be just larger than the value of one or two of the least significant figures. So if the single precision floating point number is use tol = 10E-6 should be about right. However this does not work well for the general case where a_float might be very small or might be very large.
How does one calculate tol correctly for all general cases? I am interested in C or C++ cases specifically.
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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.
To compare two floating point 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.
Floating point values can be compared exactly by equals and compareTo, just using the "==" operator. If your application, uses floats that are a result of calculation, need to compare these values with the epsilon approach, it should do that only in that place where this is needed.
The compare() method of Float Class is a built-in method in Java that compares the two specified float values. The sign of the integer value returned is the same as that of the integer that would be returned by the function call. Parameters: The function accepts two parameters: f1: The first float value to be compared.
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.
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