Storing very small numbers - but only order of magnitude
I want to store a very small number - too small for even a long double. However, I don't need the number to be stored very precisely - in fact, all I really need is the order of magnitude of the number. For example, the number 5.205849034425 X 10^-381 can just be stored as an integer of -381 for my purposes. I don't really care about the precision of the 5.205849034425 part.
The reason I get this very small number, is because I am multiplying together thousands of numbers, all of which are around 0.0001 in value. So, one way to do this would be to store all these individual values as simply their order of magnitude (e.g. -4) and then instead of multiplying the numbers, I would just add up their orders of magnitude. However, I am wondering whether there is a way in C++ to do this without me having to change the way I store my data - I still would like to keep the original values if possible.