Type safe physics operations in C++

Solution 1:

Does it make sens in C++ to define physics units as separate types and define valid operations between those types?

Absolutely. The standard Chrono library already does this for time points and durations.

Is there any advantage in introducing a lot of types and a lot of operator overloading instead of using just plain floating point values to represent them?

Yes: you can use the type system to catch errors like adding a mass to a distance at compile time, without adding any runtime overhead.

If you don't feel like defining the types and operators yourself, Boost has a Units library for that.

Solution 2:

I would really recommend boost::units for this. It does all the conversion compile-time and also it gives you a compile time error if you're trying using erroneous dimensions psuedo code example:

length l1, l2, l3;
area a1 = l1 * l2; // Compiles
area a2 = l1 * l2 * l3; // Compile time error, an area can't be the product of three lengths.
volume v1 = l1 * l2 * l3; // Compiles

Solution 3:

I've gone down this road. The advantages are all the normal numerous and good advantages of type safety. The disadvantages I've run into:

• You'll want to save off intermediate values in calculations... such as seconds squared. Having these values be a type is somewhat meaningless (seconds^2 obviously isn't a type like velocity is).
• You'll want to do increasingly complex calculations which will require more and more overloads/operator defines to achieve.

At the end of the day, it's extremely clean for simple calculations and simple purposes. But when math gets complicated, it's hard to have a typed unit system play nice.