default output validator error margin

[RagnarGrootKoerkamp]

In the default output validator, when the float (absolute/relative) error is given as epsilon, we should probably use epsilon * (1 + 0.01) or so in practice, to avoid rejecting submissions that are only just below epsilon away from the correct answer.

We should also check what the DOMjudge/Kattis default output validators do and make this consistent maybe.

[mzuenni]

right now we should be identical to domjudge

[mpsijm]

For reference: that's this file, but it looks like this has been updated since we last synced:

https://github.com/DOMjudge/domjudge/blob/main/sql/files/defaultdata/compare/compare.cc

DOMjudge also does not have an extra "error on top of the allowed error". I think it's fine if we keep it like this, because typical submissions should not get close to the error that we permit anyway – this only matters for the jury submissions that very crudely add a constant 10¯⁶ on top of the actual answer for the purpose of testing the validator.

[mzuenni]

The current behavior should be identical to DOMjudge and I also think its the "correct" behavior. With perfect precision the math is just correct and the kind of calculations we do is quite robust. The larger problem would be that we already read values as long doubles which could be an issue but fixing that is... not feasible.