Corresponding Quantity¶

Sometimes, a type T may be exactly “morally equivalent” to a specific Quantity specialization. If T stores a value in an underlying type, Rep, and that value represents a quantity whose units are quantity-equivalent to Unit, then there’s no danger in converting between T and Quantity<Unit, Rep>, and it would be convenient to make this as easy as possible.

The CorrespondingQuantity<T> type trait makes this possible. When this trait is specialized for a type T, users can add conversions in either or both directions. These conversions will allow T to participate in the usual Quantity-to-Quantity implicit conversions as if it were its corresponding quantity type.

How to specialize¶

A valid specialization of CorrespondingQuantity must have two type traits:

Unit is the unit type for the units of T.
Rep is the underlying storage type in T.

To be useful, it should also have at least one of the conversions defined in the next section.

Conversions¶

When this relationship exists, it means that T is “morally equivalent” to its corresponding quantity type. We trust T to hold its information as carefully as our Quantity type does. Therefore, we enable implicit conversions.

From `T` to `Quantity`¶

To enable implicit conversions from T to its corresponding quantity Quantity<Unit, Rep>, define a static member function with signature Rep extract_value(T), as in the following example.

Example of setting up implicit conversion from T to Quantity

Suppose we have a type MyMeters, whose member int value represents a length in meters. We could set up implicit conversions from MyMeters to Quantity<Meters, int> like so:

template<>
struct CorrespondingQuantity<MyMeters> {
    using Unit = Meters;
    using Rep = int;

    static Rep extract_value(MyMeters x) { return x.value; }
};

Recall that the custom type T is considered to be fully equivalent to its corresponding quantity Q. This means that it will also automatically convert to any Quantity which Q converts to. See the following example.

Example of ‘two-hop’ conversion, continued from above

QuantityD<Milli<Meters>> x = MyMeters{3};

Here we have a “two-hop” conversion. MyMeters{3} is treated as equivalent to a Quantity<Meters, int> holding a 3. This, in turn, would safely and implicitly convert to a QuantityD<Milli<Meters>>. Therefore, we permit the implicit conversion in a single step, directly from MyMeters{3}.

The final result would be milli(meters)(3000.0).

From `Quantity` to `T`¶

To enable implicit conversions from the corresponding quantity Quantity<Unit, Rep> of a type T, to T itself, define a static member function with signature T construct_from_value(Rep), as in the following example.

Example of setting up implicit conversion from Quantity to T

Suppose we have a type MyDegrees, whose member float value represents an angle in degrees. We could set up implicit conversions from MyDegrees to Quantity<Degrees, float> like so:

template<>
struct CorrespondingQuantity<MyDegrees> {
    using Unit = Degrees;
    using Rep = float;

    static MyDegrees construct_from_value(float x) { return MyDegrees{x}; }
};

Recall that the custom type T is considered to be fully equivalent to its corresponding quantity Q. This means that any Quantity which converts to Q will also convert to T. See the following example.

Example of ‘two-hop’ conversion, continued from above

MyDegrees angle = radians(get_value<double>(Magnitude<Pi>{} / mag<2>()));

Here we have a “two-hop” conversion. The corresponding quantity for MyDegrees is Quantity<Degrees, float>. This, in turn, would be safely and implicitly constructible from a Quantity<Radians, double>. Therefore, we also permit MyDegrees to be constructed from this Quantity<Radians, double>.

The final result would be MyDegrees{90.0f}, within floating point rounding error.

`as_quantity()`¶

The as_quantity() function converts any type to an instance of its corresponding Quantity, as long as this direction of conversion has been set up. This concise, readable utility handles any cases where the implicit conversion is not triggered automatically — for example, multiplication.

Multiplying an Au speed by a chrono duration

Imagine we have a third-party API which measures durations, and returns its results using the venerable std::chrono library.

namespace third_party {
std::chrono::nanoseconds measure_duration();
}

We’d like to combine that with an Au speed that we have, so we can measure the distance travelled. Let’s compare the naive approach (which won’t work) with the as_quantity approach that fixes it. (Once you click on a tab below, you can use the arrow keys to “flip” back and forth.)

Naive approach (broken)as_quantity() (fixed)

const auto speed = (miles / hour)(65.0);
const QuantityD<Meters> dist = speed * measure_duration();
// Compiler error! ------------------^

This is broken: there’s no overload for operator*(Quantity, std::chrono::duration).

const auto speed = (miles / hour)(65.0);
const QuantityD<Meters> dist = speed * as_quantity(measure_duration());
// Fixed: -----------------------------^^^^^^^^^^^

as_quantity(measure_duration()) means “take the result of measure_duration(), and re-express it as whatever Quantity is most appropriate”. At this point, Au’s machinery takes over. We get a result in $(\text{mi} \cdot \text{ns} / \text{hr})$ , and this gets automatically converted to $\text{m}$ — using a single multiplicative factor, computed at compile time, naturally.

as_quantity() is SFINAE-friendly. If you have a template on a type T, you can use delctype(as_quantity(T{})) in a SFINAE context — such as std::enable_if_t, or a trailing return type — to constrain the template. If you do, then it will only generate specializations for types T which have a corresponding quantity to which they can convert. There are some examples in the library itself.

Built-in corresponding quantities¶

Au strives to minimize dependencies, but we do depend on C++14. Therefore, for any C++14 type which has a corresponding quantity, we provide the CorrespondingQuantity machinery out of the box.

Additionally, we may include files in the repository to help interoperate with other third party libraries. Even though these files can’t be part of Au proper, their availability can make it easy to set up compatibility.

Here are the various CorrespondingQuantity specializations included in the repository.

`std::chrono::duration`¶

std::chrono::duration has two template parameters: Rep, and Period. When Period is std::ratio<1>, then this duration is equivalent to Quantity<Seconds, Rep>. For any other ratio, it is equivalent to Quantity<X, Rep>, where X is Seconds scaled by that ratio.

We include this correspondence out of the box. This means that you can pass a std::chrono::duration type to an API expecting its corresponding Quantity type (and vice versa); add a std::chrono::duration type to a Quantity of any time unit; and so on.

nholthaus/units library¶

We include a file that sets up a correspondence between the quantity types in the popular nholthaus/units library, and those in Au.

This file is not “active” by default. You will need to set it up in your project, following our detailed how-to guide.

Corresponding Quantity¶

How to specialize¶

Conversions¶

From T to Quantity¶

From Quantity to T¶

as_quantity()¶