> You need to have _precise_ mapping between types in compiler and the language you implement.

No. You don't need that. You can treat your data however you want until you place it into the final binary. Before that, you can even treat all your numbers as strings if you really want to. If you need some constant expression evaluation, you just have to replicate the target machine's math operations in software - no magic involved here. As long as you get the right result, noone cares what you do internally.

If your compilation machine == target machine, you can even construct a function that calculates the expression and actually run it to get the result.