>When reproducibility doesn't matter, If it doesn't matter, then high precision rarely matters either. Once you have results with unknown noise in them, and yo

>When reproducibility doesn't matter, If it doesn't matter, then high precision rarely matters either. Once you have results with unknown noise in them, and you do a few operations on those, the noise compounds, at approximately sqrt(N) bits for N steps of computation (rough estimate, it certainly depends on algorithm selection, compiler nuances, stability of problem, etc.). So high precision degrades quickly when doing any work without using a reproducible and understood rounding mode. >correct rounding is that it is the easiest mechanism to unlock reproducibility Any rounding method works works for reproducibility - truncate, round to zero, Bankers rounding, etc., all (roughly) equivalently hard/easy to implement. However, pretty much none of these are possible without the ability to do correcting rounding first as a result of the Table Makers' Dilemma. For example, Banker's rounding is generally better for doing computation than the usual correctly rounded. Knuth has some papers on this somewhere which are fascinating. Also note most of the non-reproducible issues in numerical computation are compiler added - compile code with GCC version X, get one result, compile with later version, and results may change. Or across compilers. Negative 0, denormals, rounding modes, all need carefully dealt with. It can be done, but is not trivial. Keeping floating point solid is very, very tricky over compilers and time.