Concepts

This chapter enumerates all the user-facing concepts in the mp-units library.

Dimension<T>

Dimension concept matches a dimension of either a base or derived quantity:

• Base dimensions are explicitly defined by the user by inheriting from the instantiation of a base_dimension class template. It should be instantiated with a unique symbol identifier describing this dimension in a specific system of quantities.
• Derived dimensions are implicitly created by the library's framework based on the quantity equation provided in the quantity specification.

All of the above dimensions have to be marked as final.

DimensionOf<T, V>

DimensionOf concept is satisfied when both arguments satisfy a Dimension concept and when they compare equal.

QuantitySpec<T>

QuantitySpec concept matches all the quantity specifications including:

• Base quantities defined by a user by inheriting from the quantity_spec class template instantiated with a base dimension argument.
• Derived named quantities defined by a user by inheriting from the quantity_spec class template instantiated with a result of a quantity equation passed as an argument.
• Other named quantities forming a hierarchy of quantities of the same kind defined by a user by inheriting from the quantity_spec class template instantiated with another "parent" quantity specification passed as an argument.
• Quantity kinds describing a family of mutually comparable quantities.
• Intermediate derived quantity specifications being a result of a quantity equations on other specifications.

All of the above quantity specifications have to be marked as final.

QuantitySpecOf<T, V>

QuantitySpecOf concept is satisfied when both arguments satisfy a QuantitySpec concept and when T is implicitly convertible to V.

More details

Additionally:

• T should not be a nested quantity specification of V
• either T is quantity kind or V should not be a nested quantity specification of T

Those additional conditions are required to make the following work:

static_assert(ReferenceOf<si::radian, isq::angular_measure>);
static_assert(!ReferenceOf<si::radian, dimensionless>);
static_assert(!ReferenceOf<isq::angular_measure[si::radian], dimensionless>);
static_assert(ReferenceOf<one, isq::angular_measure>);
static_assert(!ReferenceOf<dimensionless[one], isq::angular_measure>);

Unit<T>

Unit concept matches all the units in the library including:

• Base units defined by a user by inheriting from the named_unit class template instantiated with a unique symbol identifier describing this unit in a specific system of units.
• Named scaled units defined by a user by inheriting from the named_unit class template instantiated with a unique symbol identifier and a product of multiplying another unit with some magnitude.
• Prefixed units defined by a user by inheriting from the prefixed_unit class template instantiated with a prefix symbol, a magnitude, and a unit to be prefixed.
• Derived named units defined by a user by inheriting from the named_unit class template instantiated with a unique symbol identifier and a result of unit equation passed as an argument.
• Derived unnamed units being a result of a unit equations on other units.

All of the above units have to be marked as final.

Note

In the mp-units library, physical constants are also implemented as units.

AssociatedUnit<T>

AssociatedUnit concept describes a unit with an associated quantity and is satisfied by:

• All units derived from a named_unit class template instantiated with a unique symbol identifier and a QuantitySpec of a quantity kind.
• All units being a result of unit equations on other associated units.

Examples

All units in the SI have associated quantities. For example, si::second is specified to measure isq::time.

Natural units typically do not have an associated quantity. For example, if we assume c = 1, a natural::second unit can be used to measure both time and length. In such case, speed would have a unit of one.

PrefixableUnit<T>

PrefixableUnit concept is satisfied by all units derived from a named_unit class template for which a customization point unit_can_be_prefixed<T{}> was not explicitly set to false. Such units can be passed as an argument to a prefixed_unit class template.

Examples

All units in the SI can be prefixed with SI-defined prefixes.

Some off-system units like non_si::day can't be prefixed. To enforce that, the following has to be provided:

template<> inline constexpr bool unit_can_be_prefixed<non_si::day> = false;

UnitOf<T, V>

UnitOf concept is satisfied for all units T matching an AssociatedUnit concept with an associated quantity type implicitly convertible to V.

More details

Additionally, the kind of V and the kind of quantity type associated with T must be the same, or the quantity type associated with T may not be derived from the kind of V.

This condition is required to make dimensionless[si::radian] invalid as si::radian should be only used for isq::angular_measure, which is a nested quantity kind within the dimensionless quantities tree.

UnitCompatibleWith<T, V1, V2>

UnitCompatibleWith concept is satisfied for all units T when:

• V1 is a Unit,
• V2 is a QuantitySpec,
• T and V1 are defined in terms of the same reference unit,
• if T is an AssociatedUnit it should satisfy UnitOf<V2>.

Reference<T>

Reference concept is satisfied by all quantity reference types. Such types provide all the meta-information required to create a Quantity. A Reference can either be:

• An AssociatedUnit.
• The instantiation of a reference class template with a QuantitySpec passed as the first template argument and a Unit passed as the second one.

ReferenceOf<T, V>

ReferenceOf concept is satisfied by references T which have a quantity specification that satisfies QuantitySpecOf<V> concept. |

Representation<T>

Representation concept constraints a type of a number that stores the value of a quantity.

RepresentationOf<T, Ch>

RepresentationOf concept is satisfied by all Representation types that are of a specified quantity character Ch.

A user can declare a custom representation type to be of a specific character by providing the specialization with true for one or more of the following variable templates:

• is_scalar<T>
• is_vector<T>
• is_tensor<T>

Tip

If we want to use scalar types to also express vector quantities (e.g., ignoring the "direction" of the vector) the following definition can be provided to enable such a behavior:

template<class T>
  requires mp_units::is_scalar<T>
inline constexpr bool mp_units::is_vector<T> = true;

Quantity<T>

Quantity concept matches every quantity in the library and is satisfied by all types being or deriving from an instantiation of a quantity class template.

QuantityOf<T, V>

QuantityOf concept is satisfied by all the quantities for which a QuantitySpecOf<V> is true.

PointOrigin<T>

PointOrigin concept matches all quantity point origins in the library. It is satisfied by either:

• All types derived from an absolute_point_origin class template.
• All types derived from a relative_point_origin class template.

PointOriginFor<T, V>

PointOriginFor concept is satisfied by all PointOrigin types that have quantity type implicitly convertible from quantity specification V, which means that V must satisfy QuantitySpecOf<T::quantity_spec>.

Examples

si::ice_point can serve as a point origin for points of isq::Celsius_temperature because this quantity type implicitly converts to isq::thermodynamic_temperature.

However, if we define mean_sea_level in the following way:

inline constexpr struct mean_sea_level final : absolute_point_origin<isq::altitude> {} mean_sea_level;

then it can't be used as a point origin for points of isq::length or isq::width as none of them is implicitly convertible to isq::altitude:

• not every length is an altitude,
• width is not compatible with altitude.

QuantityPoint<T>

QuantityPoint concept is satisfied by all types being either a specialization or derived from quantity_point class template.

QuantityPointOf<T, V>

QuantityPointOf concept is satisfied by all the quantity points T that match the following value V:

V	Condition
QuantitySpec	The quantity point quantity specification satisfies QuantitySpecOf<V> concept.
PointOrigin	The point and V have the same absolute point origin.

QuantityLike<T>

QuantityLike concept provides interoperability with other libraries and is satisfied by a type T for which an instantiation of quantity_like_traits type trait yields a valid type that provides:

• Static data member reference that matches the Reference concept,
• rep type that matches RepresentationOf concept with the character provided in reference.
• to_numerical_value(T) static member function returning a raw value of the quantity packed in either convert_explicitly or convert_implicitly wrapper that enables implicit conversion in the latter case.
• from_numerical_value(rep) static member function returning T packed in either convert_explicitly or convert_implicitly wrapper that enables implicit conversion in the latter case.

Examples

This is how support for std::chrono::seconds can be provided:

template<>
struct mp_units::quantity_like_traits<std::chrono::seconds> {
  static constexpr auto reference = si::second;
  using rep = std::chrono::seconds::rep;

  [[nodiscard]] static constexpr convert_implicitly<rep> to_numerical_value(const std::chrono::seconds& q)
  {
    return q.count();
  }

  [[nodiscard]] static constexpr convert_implicitly<std::chrono::seconds> from_numerical_value(const rep& v)
  {
    return std::chrono::seconds(v);
  }
};

quantity q = 42s;
std::chrono::seconds dur = 42 * s;

QuantityPointLike<T>

QuantityPointLike concept provides interoperability with other libraries and is satisfied by a type T for which an instantiation of quantity_point_like_traits type trait yields a valid type that provides:

• Static data member reference that matches the Reference concept.
• Static data member point_origin that matches the PointOrigin concept.
• rep type that matches RepresentationOf concept with the character provided in reference.
• to_quantity(T) static member function returning the quantity being the offset of the point from the origin packed in either convert_explicitly or convert_implicitly wrapper that enables implicit conversion in the latter case.
• from_quantity(quantity<reference, rep>) static member function returning T packed in either convert_explicitly or convert_implicitly wrapper that enables implicit conversion in the latter case.

Examples

This is how support for a std::chrono::time_point of std::chrono::seconds can be provided:

template<typename C>
struct mp_units::quantity_point_like_traits<std::chrono::time_point<C, std::chrono::seconds>> {
  using T = std::chrono::time_point<C, std::chrono::seconds>;
  static constexpr auto reference = si::second;
  static constexpr struct point_origin final : absolute_point_origin<isq::time> {} point_origin{};
  using rep = std::chrono::seconds::rep;

  [[nodiscard]] static constexpr convert_implicitly<quantity<reference, rep>> to_quantity(const T& qp)
  {
    return quantity{qp.time_since_epoch()};
  }

  [[nodiscard]] static constexpr convert_implicitly<T> from_quantity(const quantity<reference, rep>& q)
  {
    return T(q);
  }
};

quantity_point qp = time_point_cast<std::chrono::seconds>(std::chrono::system_clock::now());
std::chrono::sys_seconds q = qp + 42 * s;