I do see floating point as like automatically compressed integers, but unlike simulations such as, Conway's game of life, the operations in a physics simulation

I do see floating point as like automatically compressed integers, but unlike simulations such as, Conway's game of life, the operations in a physics simulation produce real number values even if we begin with integer state, due to square roots and divisions mainly. I think whatever strength of integer or floated precision used to store results, it will never be possible to tell whether a certain parameter was eg. 328480284374964325 or 328480284374964326. And we need to be able to tell exactly what the input state for any output state must be, in order to have reversibility.