Sometimes it's one to big and sometimes one to small.

Right now, you are truncating the numbers. That means you are introducing an error as big as 1.0

$ perl -e'printf "%d\n", $_ for 4.9999999999, 5'
4
5
[download]

You need to round instead.

$ perl -e'printf "%.0f\n", $_ for 4.9999999999, 5'
5
5
[download]

But that's not good enough either.

$ perl -e'printf "%.0f\n", $_ for 5.4999999999, 5.5'
5
6
[download]

You need to round to your tolerance first.

$ perl -e'printf "%.0f\n", sprintf "%.8f", $_ for 5.4999999999, 5.5'
6
6
[download]

$ perl -e'printf "%.0f\n", $_ for 5.4999999999, 5.5'
5
6
[download]

I don't get what's the problem with the above. The output is what I would expect.

The point is that a infinitely small floating point error can change the result by 1.0