[ntoronto]

I've monkeyed with a lot of numeric representations, and every one of them involves tough theoretical and practical trade-offs. Returning an exact rational as the result of division sounds reasonable.

My favorite representation so far pairs a signed float in [2^-512,2^512) with a signed integer to extend the exponent range. The idea is to avoid overflow and underflow, particularly when multiplying thousands of probabilities.

(On average, adding a few thousand log probabilities or densities and then exponentiating the sum yields a number with about 9 digits precision. Worst case for adding log probabilities and exponentiating is about 8 digits precision, and for adding log densities it's 0 digits. Multiplying the same number of probabilities or densities retains about 13 digits in the worst case.)