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Briefly read, it looks like an idea and not an 'apparatus'. Yes, carrying error bound information along with the number is interesting. How is that implemented in real time? How is accumulated error calculated (how do we know the floating values we are calculating with are not perfectly precise e.g. 3.0000... and not 3.000...1)?

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> Briefly read, it looks like an idea and not an 'apparatus'.

It's patent law lingo. The patent covers both the idea (the "system") and subsequent implementations (the "apparatus") that are direct implementations of the idea.

That's easy, always round down and also carry max possible error (calculated by rounding up and subtracting the rounded down value). For example, 1/3 can be represented as 0.333 with error 0.001. Multiply it by 3 and get 0.999 with error 0.003.

You won't need many bits for the error, and operations can be made reasonably fast as only several lowest bits are affected.

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