Question: but how many different numbers can you fit in 64 bits using your encoding (sorry I understand the general approach but I have no idea how that fast hierarchy works). I guess it's still 2^64 different numbers?

So basically you have a very low density of representable numbers (2^64 / w218), I wonder how quickly it grows as you use more and more 1-bits, and is there even a correlation between the bit pattern and the corresponding number value?