Question

I know it’s ridiculous, but I need it for storage optimization. Is there any good way to implement it in C++?

It has to be flexible enough so that I can use it as a normal data type e.g Vector< int20 >, operator overloading, etc..

Answer 1

If storage is your main concern, I suspect you need quite a few 20-bit variables. How about storing them in pairs? You could create a class representing two such variables and store them in 2.5+2.5 = 5 bytes.

To access the variables conveniently you could override the []-operator so you could write:

int fst = pair[0];
int snd = pair[1];

Since you may want to allow for manipulations such as

pair[1] += 5;

you would not want to return a copy of the backing bytes, but a reference. However, you can’t return a direct reference to the backing bytes (since it would mess up it’s neighboring value), so you’d actually need to return a proxy for the backing bytes (which in turn has a reference to the backing bytes) and let the proxy overload the relevant operators.

As a metter of fact, as @Tony suggest, you could generalize this to have a general container holding N such 20-bit variables.

(I’ve done this myself in a specialization of a vector for efficient storage of booleans (as single bits).)