Units is a compile-time enabled Modern C++ library that provides support for converting physical units and dimensions. The basic idea and design heavily bases on std::chrono::duration and extends it to work properly with many dimensions.

Here is a small example of possible operations:

static_assert(1000 / 1_s == 1_kHz);
static_assert(1_h == 3600_s);
static_assert(1_km + 1_m == 1001_m);
static_assert(10_km / 5_km == 2);
static_assert(10_km / 2 == 5_km);
static_assert(1_km / 1_s == 1000_mps);
static_assert(2_kmph * 2_h == 4_km);
static_assert(2_km / 2_kmph == 1_h);

Basic Concepts

`Dimensions`

units::dimension is a type-list like type that stores an ordered list of exponents of one or more base dimensions:

template<Exponent... Es>
struct dimension {
  using base_type = dimension<Es...>;
};

units::Dimension is a Concept that is satisfied by a type that is empty and publicly derived from units::dimension class template:

template<typename T>
concept Dimension =
    std::is_empty_v<T> &&
    detail::is_dimension<typename T::base_type> &&  // exposition only
    DerivedFrom<T, typename T::base_type>;

`Exponents`

units::exp provides an information about a single base dimension and its exponent in a derived dimension:

template<typename BaseDimension, int Value>
struct exp {
  using dimension = BaseDimension;
  static constexpr int value = Value;
};

where BaseDimension for now is:

template<int UniqueValue>
using dim_id = std::integral_constant<int, UniqueValue>;

but it is meant to be replaced with C++20 class constexpr values provided as non-type template parameters (when feature will be available in a compiler) so that for example base dimension for length will be expressed as dimension<exp<"length", 1>>.

units::Exponent concept is satisfied if provided type is an instantiation of units::exp class template:

template<typename T>
concept Exponent =
    detail::is_exp<T>;  // exposition only

`make_dimension`

Above design of dimensions is created with the ease of use for end users in mind. Compile-time errors should provide as short as possible template instantiations strings that should be easy to understand by every C++ programmer. Also types visible in a debugger should be easy to understand. That is why units::dimension type for derived dimensions always stores information about only those base dimensions that are used to form that derived dimension.

However, such an approach have some challenges:

constexpr Velocity auto v1 = 1_m / 1_s;
constexpr Velocity auto v2 = 2 / 2_s * 1_m;

static_assert(Same<decltype(v1), decltype(v2)>);
static_assert(v1 == v2);

Above code, no matter what is the order of the base dimensions in an expression forming our result, must produce the same Velocity type so that both values can be easily compared. In order to achieve that, dimension class templates should never be instantiated manually but through a make_dimension_t template metaprogramming factory function:

template<Exponent... Es>
struct make_dimension {
  using type = /* unspecified */;
};

template<Exponent... Es>
using make_dimension_t = typename make_dimension<Es...>::type;

So for example to create a dimension_velocity type we have to do:

struct dimension_velocity : make_dimension_t<exp<base_dim_length, 1>, exp<base_dim_time, -1>> {};

In order to make make_dimension_t work as expected it has to provide unique ordering for contained base dimensions. Beside providing ordering to base dimensions it also has to:

aggregate two arguments of the same base dimension but different exponents
eliminate two arguments of the same base dimension and with opposite equal exponents

Additionally, it would be good if the final type produced by make_dimension_t would be easy to understand for the user. For example we may decide to order base dimensions with decreasing order of their exponents. That is why second sorting of a type list may be required. For example:

template<Exponent... Es>
struct make_dimension {
  using type = mp::type_list_sort_t<detail::dim_consolidate_t<mp::type_list_sort_t<dimension<Es...>, exp_dim_id_less>>, exp_greater_equal>;
};

`merge_dimension`

units::merge_dimension is similar to make_dimension but instead of sorting the whole list of base dimensions from scratch it assumes that provided input dimension types are already sorted as a result of make_dimension.

Typical use case for merge_dimension is to produce final dimension return type of multiplying two different dimensions:

template<Dimension D1, Dimension D2>
struct dimension_multiply;

template<Exponent... E1, Exponent... E2>
struct dimension_multiply<dimension<E1...>, dimension<E2...>> {
  using type = upcasting_traits_t<merge_dimension_t<E1..., E2...>>;
};

template<Dimension D1, Dimension D2>
using dimension_multiply_t = typename dimension_multiply<typename D1::base_type, typename D2::base_type>::type;

Example implementation of merge_dimension may look like:

template<Exponent... Es>
struct merge_dimension {
  using type = mp::type_list_sort_t<detail::dim_consolidate_t<mp::type_list_merge_sorted_t<dimension<Es...>, exp_dim_id_less>>, exp_greater_equal>;
};

`Units`

units::unit is a class template that expresses the unit of a specific physical dimension:

template<Dimension D, Ratio R>
  requires (R::num > 0)
struct unit {
  using base_type = unit<D, R>;
  using dimension = D;
  using ratio = R;
};

units::Unit is a Concept that is satisfied by a type that is empty and publicly derived from units::unit class template:

template<typename T>
concept Unit =
    std::is_empty_v<T> &&
    detail::is_unit<typename T::base_type> &&  // exposition only
    DerivedFrom<T, typename T::base_type>;

`Quantities`

units::quantity is a class template that expresses the quantity/amount of a specific dimension expressed in a specific unit of that dimension:

template<Dimension D, Unit U, Number Rep>
  requires Same<D, typename U::dimension>
class quantity;

units::Quantity is a Concept that is satisfied by a type that is an instantiation of units::quantity class template:

template<typename T>
concept Quantity =
    detail::is_quantity<T>;  // exposition only

units::quantity provides the interface really similar to std::chrono::duration with additional member types and functions as below:

template<Dimension D, Unit U, Number Rep>
    requires Same<D, typename U::dimension>
class quantity {
public:
  using dimension = D;
  using unit = U;

  template<Dimension D1, Unit U1, Number Rep1, Dimension D2, Unit U2, Number Rep2>
      requires treat_as_floating_point<std::common_type_t<Rep1, Rep2>> || std::ratio_multiply<typename U1::ratio, typename U2::ratio>::den == 1
  quantity<dimension_multiply_t<D1, D2>, upcasting_traits_t<unit<dimension_multiply_t<D1, D2>, std::ratio_multiply<typename U1::ratio, typename U2::ratio>>>, std::common_type_t<Rep1, Rep2>>
  constexpr operator*(const quantity<D1, U1, Rep1>& lhs,
                      const quantity<D2, U2, Rep2>& rhs);

  template<Number Rep1, Dimension D, Unit U, Number Rep2>
  quantity<dim_invert_t<D>, upcasting_traits_t<unit<dim_invert_t<D>, std::ratio<U::ratio::den, U::ratio::num>>>, std::common_type_t<Rep1, Rep2>>
  constexpr operator/(const Rep1& v,
                      const quantity<D, U, Rep2>& q);

  template<Dimension D1, Unit U1, Number Rep1, Dimension D2, Unit U2, Number Rep2>
      requires treat_as_floating_point<std::common_type_t<Rep1, Rep2>> || std::ratio_divide<typename U1::ratio, typename U2::ratio>::den == 1
  quantity<dimension_divide_t<D1, D2>, upcasting_traits_t<unit<dimension_divide_t<D1, D2>, std::ratio_divide<typename U1::ratio, typename U2::ratio>>>, std::common_type_t<Rep1, Rep2>>
  constexpr operator/(const quantity<D1, U1, Rep1>& lhs,
                      const quantity<D2, U2, Rep2>& rhs);
};

Additional functions provide the support for operations that result in a different dimension type than those of their arguments.

`quantity_cast`

To explicitly force truncating conversions quantity_cast function is provided which is a direct counterpart of std::chrono::duration_cast.

Strong types instead of aliases, and type upcasting capability

Most of the important design decisions in the library are dictated by the requirement of providing the best user experience as possible.

For example with template aliases usage the following code:

const Velocity t = 20_s;

could generate a following compile time error:

C:\repos\units\example\example.cpp:39:22: error: deduced initializer does not satisfy placeholder constraints
   const Velocity t = 20_s;
                      ^~~~
In file included from C:\repos\units\example\example.cpp:23:
C:/repos/units/src/include/units/si/velocity.h:41:16: note: within 'template<class T> concept const bool units::Velocity<T> [with T = units::quantity<units::dimension<units::exp<units::base_dim_time, 1> >, units::unit<units::dimension<units::exp<units::base_dim_time, 1> >, std::ratio<1> >, long long int>]'
   concept Velocity = Quantity<T> && Same<typename T::dimension, dimension_velocity>;
           ^~~~~~~~
In file included from C:/repos/units/src/include/units/bits/tools.h:25,
                 from C:/repos/units/src/include/units/dimension.h:25,
                 from C:/repos/units/src/include/units/si/base_dimensions.h:25,
                 from C:/repos/units/src/include/units/si/velocity.h:25,
                 from C:\repos\units\example\example.cpp:23:
C:/repos/units/src/include/units/bits/stdconcepts.h:33:18: note: within 'template<class T, class U> concept const bool mp::std_concepts::Same<T, U> [with T = units::dimension<units::exp<units::base_dim_time, 1> >; U = units::dimension<units::exp<units::base_dim_length, 1>, units::exp<units::base_dim_time, -1> >]'
     concept Same = std::is_same_v<T, U>;
             ^~~~
C:/repos/units/src/include/units/bits/stdconcepts.h:33:18: note: 'std::is_same_v' evaluated to false

Time and velocity are not that complicated dimensions and there are much more complicated dimensions out there, but even for those dimensions

[with T = units::quantity<units::dimension<units::exp<units::base_dim_time, 1> >, units::unit<units::dimension<units::exp<units::base_dim_time, 1> >, std::ratio<1> >, long long int>]

and

[with T = units::dimension<units::exp<units::base_dim_time, 1> >; U = units::dimension<units::exp<units::base_dim_length, 1>, units::exp<units::base_dim_time, -1> >]

starts to be really hard to analyze or debug.

That is why it was decided to provide automated upcasting capability when possible. With that the same code will result with such an error:

C:\repos\units\example\example.cpp:40:22: error: deduced initializer does not satisfy placeholder constraints
   const Velocity t = 20_s;
                      ^~~~
In file included from C:\repos\units\example\example.cpp:23:
C:/repos/units/src/include/units/si/velocity.h:48:16: note: within 'template<class T> concept const bool units::Velocity<T> [with T = units::quantity<units::dimension_time, units::second, long long int>]'
   concept Velocity = Quantity<T> && Same<typename T::dimension, dimension_velocity>;
           ^~~~~~~~
In file included from C:/repos/units/src/include/units/bits/tools.h:25,
                 from C:/repos/units/src/include/units/dimension.h:25,
                 from C:/repos/units/src/include/units/si/base_dimensions.h:25,
                 from C:/repos/units/src/include/units/si/velocity.h:25,
                 from C:\repos\units\example\example.cpp:23:
C:/repos/units/src/include/units/bits/stdconcepts.h:33:18: note: within 'template<class T, class U> concept const bool mp::std_concepts::Same<T, U> [with T = units::dimension_time; U = units::dimension_velocity]'
     concept Same = std::is_same_v<T, U>;
             ^~~~
C:/repos/units/src/include/units/bits/stdconcepts.h:33:18: note: 'std::is_same_v' evaluated to false

Now

[with T = units::quantity<units::dimension_time, units::second, long long int>]

and

[with T = units::dimension_time; U = units::dimension_velocity]

are not arguably much easier to understand thus provide better user experience.

Upcasting capability is provided through dedicated upcasting_traits and by base_type member type in dimension and unit class templates.

template<typename T>
struct upcasting_traits : std::type_identity<T> {};

template<typename T>
using upcasting_traits_t = typename upcasting_traits<T>::type;

struct dimension_length : make_dimension_t<exp<base_dim_length, 1>> {};

template<>
struct upcasting_traits<typename dimension_length::base_type> :
    std::type_identity<dimension_length> {};

struct kilometer : unit<dimension_length, std::kilo> {};

template<>
struct upcasting_traits<typename kilometer::base_type> :
    std::type_identity<kilometer> {};

Adding new dimensions

In order to extend the library with custom dimensions the user has to:

Create a new dimension type and provide upcasting trait for it:

struct dimension_velocity : make_dimension_t<exp<base_dim_length, 1>, exp<base_dim_time, -1>> {};
template<> struct upcasting_traits<typename dimension_velocity::base_type> : std::type_identity<dimension_velocity> {};

Define the base unit (std::ratio<1>) and secondary ones and provide upcasting traits for them via:

struct meter_per_second : unit<dimension_velocity, std::ratio<1>> {};
template<> struct upcasting_traits<typename meter_per_second::base_type> : std::type_identity<meter_per_second> {};

Define a concept that will match a new dimension:

template<typename T>
concept Velocity = Quantity<T> && Same<typename T::dimension, dimension_velocity>;

Provide user-defined literals for the most important units:

namespace literals {
  constexpr auto operator""_mps(unsigned long long l) { return velocity<meter_per_second, std::int64_t>(l); }
  constexpr auto operator""_mps(long double l)        { return velocity<meter_per_second, long double>(l); }
}

Adding new base dimensions

For now base dimensions are defined in terms of std::integral_constant<int, ...> and the provided values must be unique. For example:

struct base_dim_length : dim_id<0> {};
struct base_dim_mass : dim_id<1> {};
struct base_dim_time : dim_id<2> {};
struct base_dim_electric_current : dim_id<3> {};
struct base_dim_temperature : dim_id<4> {};
struct base_dim_amount_of_substance : dim_id<5> {};
struct base_dim_luminous_intensity : dim_id<6> {};

However, as soon as C++20 class type values will be supported as non-type template parameters base dimensions will be just a text values. For example:

inline constexpr base_dim base_dim_length = "length";

With that it should be really easy to add support for any new non-standard base units to the library without the risk of collision with any dimension type defined by the library itself or by other users extending the library with their own dimension types.

Additionally, it should make the error logs even shorter thus easier to understand.

Open questions

Should we ensure that dimension is always a result of make_dimension? How to do it?
Should we provide strong types and upcasting_traits for quantity type?

In such a case all the operators have to be provided to a child class. Or maybe use CRTP?
What to do with time which is ambiguous?
What to do with std::chrono::duration?
What is the best way to add support for temperatures?

Temperatures require not only require std::ratio but also should adjusted/shifted by some constant values (i.e. [°C] = [K] − 273.15).
Should the "base dimension" be better expressed/isolated by the design?
seconds<int> or time<second, int>?
How to use CTAD?

CTAD for alias templates were already supported by EWG in San Diego 2018 so length(3.5) will work. However,deduction with partial argument lists was rejected so length<mile>(3) will not be supported for now.

README.md Unescape Escape

units - Physical Units Library for C++

Summary

Basic Concepts

Dimensions

Exponents

make_dimension

merge_dimension

Units

Quantities

quantity_cast