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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..
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int is always 32 bits wide. sizeof(T) represents the number of 8-bit bytes (octets) needed to store a variable of type T .
So the reason why you are seeing an int as 4 bytes (32 bits), is because the code is compiled to be executed efficiently by a 32-bit CPU. If the same code were compiled for a 16-bit CPU the int may be 16 bits, and on a 64-bit CPU it may be 64 bits.
Most of the textbooks say integer variables occupy 2 bytes.
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).)
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