How do you decide how many bits distance should be encoded in? How many bits for mantissas, sign bits? I worked with half floats (FP16) and other weird partial

How do you decide how many bits distance should be encoded in? How many bits for mantissas, sign bits? I worked with half floats (FP16) and other weird partial word float formats ... I don't think it's trivial. I guess the most straightforward way is to convert to fixed point real numbers first, then it's essentially the same as integers. Or maybe just do it per block of each 128 floats?