[tomxor]

Indeed. The only way to accommodate numbers where the difference in order of magnitude exceeds the type's significand length is to not combine them, keep them separate and operate on them separately, combining them only for a sample.

One good common example is numerical integration. In any sufficient fine grained posteriori simulation, even with modest limits on position - delta velocity can be too small to preserve when adding to position, i.e when delta velocity is more than 2^52 smaller than position. Keeping a separate accumulator is the only way to handle this without arbitrarily increasing precision with software FP.