# The C++ Units Library¶

The 2020 release of WPILib is coupled with a Units library for C++ teams. This library leverages the C++ type system to enforce proper dimensionality for method parameters, automatically perform unit conversions, and even allow users to define arbitrary defined unit types. Since the C++ type system is enforced at compile-time, the library has essentially no runtime cost.

## Using the Units Library¶

The units library is a header-only library. You must include the relevant header in your source files for the units you want to use. Here’s a list of available units.

```
#include <units/acceleration.h>
#include <units/angle.h>
#include <units/angular_acceleration.h>
#include <units/angular_velocity.h>
#include <units/area.h>
#include <units/capacitance.h>
#include <units/charge.h>
#include <units/concentration.h>
#include <units/conductance.h>
#include <units/current.h>
#include <units/curvature.h>
#include <units/data.h>
#include <units/data_transfer_rate.h>
#include <units/density.h>
#include <units/dimensionless.h>
#include <units/energy.h>
#include <units/force.h>
#include <units/frequency.h>
#include <units/illuminance.h>
#include <units/impedance.h>
#include <units/inductance.h>
#include <units/length.h>
#include <units/luminous_flux.h>
#include <units/luminous_intensity.h>
#include <units/magnetic_field_strength.h>
#include <units/magnetic_flux.h>
#include <units/mass.h>
#include <units/moment_of_inertia.h>
#include <units/power.h>
#include <units/pressure.h>
#include <units/radiation.h>
#include <units/solid_angle.h>
#include <units/substance.h>
#include <units/temperature.h>
#include <units/time.h>
#include <units/torque.h>
#include <units/velocity.h>
#include <units/voltage.h>
#include <units/volume.h>
```

The `units/math.h`

header provides unit-aware functions like `units::math::abs()`

.

### Unit Types and Container Types¶

The C++ units library is based around two sorts of type definitions: unit types and container types.

#### Unit Types¶

Unit types correspond to the abstract concept of a unit, without any actual stored value. Unit types are the fundamental “building block” of the units library - all unit types are defined constructively (using the `compound_unit`

template) from a small number of “basic” unit types (such as `meters`

, `seconds`

, etc).

While unit types cannot contain numerical values, their use in building other unit types means that when a type or method uses a template parameter to specify its dimensionality, that parameter will be a unit type.

#### Container Types¶

Container types correspond to an actual quantity dimensioned according to some unit - that is, they are what actually hold the numerical value. Container types are constructed from unit types with the `unit_t`

template. Most unit types have a corresponding container type that has the same name suffixed by `_t`

- for example, the unit type `units::meter`

corresponds to the container type `units::meter_t`

.

Whenever a specific quantity of a unit is used (as a variable or a method parameter), it will be an instance of the container type. By default, container types will store the actual value as a `double`

- advanced users may change this by calling the `unit_t`

template manually.

A full list of unit and container types can be found in the documentation.

### Creating Instances of Units¶

To create an instance of a specific unit, we create an instance of its container type:

```
// The variable speed has a value of 5 meters per second.
units::meter_per_second_t speed{5.0};
```

Alternatively, the units library has type literals defined for some of the more common container types. These can be used in conjunction with type inference via `auto`

to define a unit more succinctly:

```
// The variable speed has a value of 5 meters per second.
auto speed = 5_mps;
```

Units can also be initialized using a value of an another container type, as long as the types can be converted between one another. For example, a `meter_t`

value can be created from a `foot_t`

value.

```
auto feet = 6_ft;
units::meter_t meters{feet};
```

In fact, all container types representing convertible unit types are *implicitly convertible*. Thus, the following is perfectly legal:

```
units::meter_t distance = 6_ft;
```

In short, we can use *any* unit of length in place of *any other* unit of length, anywhere in our code; the units library will automatically perform the correct conversion for us.

### Performing Arithmetic with Units¶

Container types support all of the ordinary arithmetic operations of their underlying data type, with the added condition that the operation must be *dimensionally* sound. Thus, addition must always be performed on two compatible container types:

```
// Add two meter_t values together
auto sum = 5_m + 7_m; // sum is 12_m
// Adds meters to feet; both are length, so this is fine
auto sum = 5_m + 7_ft;
// Tries to add a meter_t to a second_t, will throw a compile-time error
auto sum = 5_m + 7_s;
```

Multiplication may be performed on any pair of container types, and yields the container type of a compound unit:

Note

When a calculation yields a compound unit type, this type will only be checked for validity at the point of operation if the result type is specified explicitly. If `auto`

is used, this check will not occur. For example, when we divide distance by time, we may want to ensure the result is, indeed, a velocity (i.e. `units::meter_per_second_t`

). If the return type is declared as `auto`

, this check will not be made.

```
// Multiply two meter_t values, result is square_meter_t
auto product = 5_m * 7_m; // product is 35_sq_m
```

```
// Divide a meter_t value by a second_t, result is a meter_per_second_t
units::meter_per_second_t speed = 6_m / 0.5_s; // speed is 12_mps
```

`<cmath>`

Functions¶

Some `std`

functions (such as `clamp`

) are templated to accept any type on which the arithmetic operations can be performed. Quantities stored as container types will work with these functions without issue.

However, other `std`

functions work only on ordinary numerical types (e.g. `double`

). The units library’s `units::math`

namespace contains wrappers for several of these functions that accept units. Examples of such functions include `sqrt`

, `pow`

, etc.

```
auto area = 36_sq_m;
units::meter_t sideLength = units::math::sqrt(area);
```

### Removing the Unit Wrapper¶

To convert a container type to a raw numeric value, the `to<..>()`

method can be used, where the template argument is the underlying type.

```
units::meter_t distance = 6.5_m;
double distanceMeters = distance.to<double>();
```

## Example of the Units Library in WPILib Code¶

Several arguments for methods in new features of WPILib (ex. kinematics) use the units library. Here is an example of sampling a trajectory.

```
// Sample the trajectory at 1.2 seconds. This represents where the robot
// should be after 1.2 seconds of traversal.
Trajectory::State point = trajectory.Sample(1.2_s);
// Since units of time are implicitly convertible, this is exactly equivalent to the above code
Trajectory::State point = trajectory.Sample(1200_ms);
```

Some WPILib classes represent objects that could naturally work with multiple choices of unit types - for example, a motion profile might operate on either linear distance (e.g. meters) or angular distance (e.g. radians). For such classes, the unit type is required as a template parameter:

```
// Creates a new set of trapezoidal motion profile constraints
// Max velocity of 10 meters per second
// Max acceleration of 20 meters per second squared
frc::TrapezoidProfile<units::meters>::Constraints{10_mps, 20_mps_sq};
// Creates a new set of trapezoidal motion profile constraints
// Max velocity of 10 radians per second
// Max acceleration of 20 radians per second squared
frc::TrapezoidProfile<units::radians>::Constraints{10_rad_per_s, 20__rad_per_s / 1_s};
```

For more detailed documentation, please visit the official GitHub page for the units library.