Quantities in C++ and User Defined Literals

Some weeks ago one of my colleagues wrote about the use and implementation of physical quantities in C#. If you are writing an application in the technical or scientific domain chances are high that you should adhere to his advice and use a suitable representation of physical quantities instead of plain primitive values. Good news is that you can easily port/implement quantities to modern C++ or use existing libraries like Boost.Units.

With C++11 you can go one step further adding the so called User-defined literals. This feature allows definition of suffices for integer, floating-point, character and string literals to produce objects of the desired (quantity) type. While there is nothing wrong with using the multiplication operator to produce quantity instances user-defined literals provide just a little bit more syntactic sugar:

// Your quantity classes...
class Angle;

// operators for user-defined literals
constexpr Angle operator "" _deg(long double deg)
{
    return deg * degrees;
}

constexpr Angle operator "" _deg(unsigned long long int deg)
{
    return deg * degrees;
}

constexpr Angle operator "" _rad(long double rad)
{
    return (rad * 180 / M_PI) * degrees;
}

// add more if needed

This allows you to write code like:

Angle rightAngle = 90_deg;
Angle halfCircle = 3.141_rad;
Angle fullCircle = 4 * 90_deg;

In many cases this looks a tad simpler and cleaner than using the multiplication operator in conjunction with a unit especially in more complex formulas. There are a few things about quantities and user-defined literals in C++ I find noteworthy:

• These literals are only supported for the built-in literal types. If exact calculation and better than floating-point precision is needed, raw literals (instead of the explained cooked) and decimal libraries have to be used. For raw literals you have to parse the characters of the literal yourself.
• User-defined literals need to be prefixed with _ to avoid namespace clashes with current and future standard library literals. There are for example some nice literals for durations in the <chrono>-date and time standard library.
• If you implement your literal operators as constexpr they will be evaluated at compile time meaning slightly increased compile times and zero runtime overhead.

For some more in-depth discussion of user-defined literals have a look at the blog series from Andrzej Krzemieński.