Why does floating point modulus exactness matters?
Note that inexact floating point implementation affect the weather.

There have been tests running weather predictions with the same inputs on different hardware and the predictions diverged. If you are running iterative algorithm then a small rounding difference here or there can result in a butterfly effect changing sunshine into rain.

The rounding rules in standards (IEEE 754, ISO/IEC 10967) have been carefully thought out so numeric algorithms behave predictable with the most accuracy and reproduce the same result every time. By not following the standard numerical algorithms designed for those rounding rules will break and iterative algorithms like weather predictions can even give a random result.

(and doesn't that say something about weather predictions? :)