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Here, we give the correctness proof of the verifiable equation (1) and (2).
3 contains the correctness proof for this implementation.
The model provides a foundation for precise problem specifications, detailed algorithm descriptions, and careful correctness proofs, as well as impossibility results.
This inspired us to derive the algorithm from its specification, so that anyone interested in a correctness proof can fill in the details easily.
It is worth emphasizing that, although total correctness proofs may be an overreaction, there is a sound motive behind them.
Another 23 papers cover arithmetic units, domain specific designs, verification and correctness proofs, modular arithmetic, floating-point error analysis, functional approximation, and arithmetic in cryptography.