refactor: 💥 basic_concepts, quantity and quantity_cast refactored

BREAKING CHANGE:  ScalableNumber renamed to QuantityValue

Resolves #107

CHANGELOG.md

@@ -1 +0,0 @@
-docs/CHANGELOG.md

docs/design/quantity.rst

@@ -11,7 +11,7 @@ Interface
 The difference is that it uses ``double`` as a default representation and has
 a few additional member types and functions::
 
-    template<Dimension D, UnitOf<D> U, ScalableNumber Rep = double>
+    template<Dimension D, UnitOf<D> U, QuantityValue Rep = double>
     class quantity {
     public:
       using dimension = D;
@@ -27,7 +27,7 @@ a few additional member types and functions::
     [[nodiscard]] constexpr Quantity auto operator*(const quantity<D1, U1, Rep1>& lhs,
                                                     const quantity<D2, U2, Rep2>& rhs);
 
-    template<ScalableNumber Value, typename D, typename U, typename Rep>
+    template<QuantityValue Value, typename D, typename U, typename Rep>
       requires std::magma<std::ranges::divided_by, Value, Rep>
     [[nodiscard]] constexpr Quantity auto operator/(const Value& v,
                                                     const quantity<D, U, Rep>& q);

docs/framework/constants.rst

@@ -18,7 +18,7 @@ For example the speed of light constant in :term:`SI` is defined as::
 
     namespace si::si2019 {
 
-    template<ScalableNumber Rep = double>
+    template<QuantityValue Rep = double>
     inline constexpr auto speed_of_light = speed<metre_per_second, Rep>(299792458);
 
     }
@@ -27,7 +27,7 @@ The same constant defined for natural units may be provided as::
 
     namespace natural {
 
-    template<ScalableNumber Rep = double>
+    template<QuantityValue Rep = double>
     inline constexpr auto speed_of_light = speed<one, Rep>(1);
 
     }

docs/framework/dimensions.rst

@@ -58,8 +58,8 @@ dimension, than we will end up with just a scalable number type:
     Time auto dur1 = 10_q_s;
     Time auto dur2 = 2_q_s;
     Frequency auto fr1 = 5_q_Hz;
-    ScalableNumber auto v1 = dur1 / dur2;    // 5
+    QuantityValue auto v1 = dur1 / dur2;    // 5
-    ScalableNumber auto v2 = dur1 * fr1;     // 50
+    QuantityValue auto v2 = dur1 * fr1;     // 50
 
 Quantity points have a more restricted set of operations.
 Quantity points can't be added together,

docs/framework/quantities.rst

@@ -34,7 +34,7 @@ type to ``double`` by default::
 
     namespace si {
 
-    template<Unit U, ScalableNumber Rep = double>
+    template<Unit U, QuantityValue Rep = double>
     using length = quantity<dim_length, U, Rep>;
 
     }
@@ -75,7 +75,7 @@ be used::
     All instances of `quantity` class always match the `Quantity` concept.
     All other regular types that are not quantities are called
     :term:`scalable numbers <scalable number>` by the library and match the
-    `ScalableNumber` concept.
+    `QuantityValue` concept.
 
 However, the above is not the most important usage of those concepts. Let's
 assume that the user wants to implement an ``avg_speed`` function that will
@@ -185,7 +185,7 @@ are provided::
     template<typename T>
     concept Dimensionless = QuantityOf<T, dim_one>;
 
-    template<Unit U, ScalableNumber Rep = double>
+    template<Unit U, QuantityValue Rep = double>
     using dimensionless = quantity<dim_one, U, Rep>;
 
 There are two special units provided for usage with such a quantity:

docs/reference/core/concepts.rst

@@ -63,7 +63,7 @@ Concepts
     satisfy :expr:`Quantity<typename T::value_type>` recursively
     (i.e. ``std::optional<si::length<si::metre>>``).
 
-.. concept:: template<typename T> ScalableNumber
+.. concept:: template<typename T> QuantityValue
 
     A concept matching non-Quantity types. Satisfied by types that match
     :expr:`(!Quantity<T>) && (!WrappedQuantity<T>) && std::regular<T>` and satisfy one of the

docs/use_cases/custom_representation_types.rst

@@ -9,11 +9,11 @@ its own custom logic for it (i.e. use a complex number or a measurement class th
 not only a value but also a measurement error).
 
 
-A `ScalableNumber` concept
+A `QuantityValue` concept
 --------------------------
 
 To support a minimum set of `quantity` operations all custom representation types have to
-satisfy at least the `ScalableNumber` concept. Which means that they:
+satisfy at least the `QuantityValue` concept. Which means that they:
 
 - cannot be quantities by themselves,
 - cannot be wrappers over the `quantity` type (i.e. ``std::optional<si::length<si::metre>>``),
@@ -101,7 +101,7 @@ The only difference here is that in this case we have to explicitly cast the `qu
 Additional Requirements
 -----------------------
 
-As noted in the previous chapter, the `ScalableNumber` concept guarantees us the possibility
+As noted in the previous chapter, the `QuantityValue` concept guarantees us the possibility
 to construct quantities, convert between the units of the same dimension, and compare them
 for equality. To provide additional `quantity` operations the custom representation type
 have to satisfy more requirements.
@@ -200,7 +200,7 @@ The `quantity` class template has a few static member functions: `quantity::zero
 representation type. The default implementation is provided through the `quantity_values` class
 template::
 
-    template<ScalableNumber Rep>
+    template<QuantityValue Rep>
     struct quantity_values {
       static constexpr Rep zero() noexcept { return Rep(0); }
       static constexpr Rep one() noexcept { return Rep(1); }
@@ -220,7 +220,7 @@ library's framework treat floating-point representation types differently than t
 ones. This behavior can also be extended to the custom representation types with
 `treat_as_floating_point` customization point which default definition is::
 
-    template<ScalableNumber Rep>
+    template<QuantityValue Rep>
     inline constexpr bool treat_as_floating_point = std::is_floating_point_v<Rep>;
 
 If our representation type should have a floating-point semantics or if it is a class

docs/use_cases/extensions.rst

@@ -121,7 +121,7 @@ coherent unit::
     struct desk_per_hour : deduced_unit<desk_per_hour, dim_desk_rate, desk, si::hour> {};
 
     // a quantity of our dimension
-    template<Unit U, ScalableNumber Rep = double>
+    template<UnitOf<dim_desk_rate> U, QuantityValue Rep = double>
     using desk_rate = quantity<dim_desk_rate, U, Rep>;
 
     // a concept matching the above quantity
@@ -150,7 +150,7 @@ define a new base dimension, its units, quantity helper, concept, and UDLs::
     struct person : named_unit<person, "person", no_prefix> {};
     struct dim_people : base_dimension<"people", person> {};
 
-    template<Unit U, ScalableNumber Rep = double>
+    template<UnitOf<dim_people> U, QuantityValue Rep = double>
     using people = quantity<dim_people, U, Rep>;
 
     template<typename T>
@@ -169,7 +169,7 @@ With the above we can now define a new derived dimension::
 
     struct person_per_desk : deduced_unit<person_per_desk, dim_occupancy_rate, person, desk> {};
 
-    template<Unit U, ScalableNumber Rep = double>
+    template<UnitOf<dim_occupancy_rate> U, QuantityValue Rep = double>
     using occupancy_rate = quantity<dim_occupancy_rate, U, Rep>;
 
     template<typename T>
@@ -216,7 +216,7 @@ Such units do not share their references with base units of other systems:
 
     struct dim_length : base_dimension<"L", foot> {};
 
-    template<Unit U, ScalableNumber Rep = double>
+    template<UnitOf<dim_length> U, QuantityValue Rep = double>
     using length = quantity<dim_length, U, Rep>;
 
     }  // namespace fps
@@ -236,7 +236,7 @@ different systems:
 
     struct dim_length : base_dimension<"L", metre> {};
 
-    template<Unit U, ScalableNumber Rep = double>
+    template<UnitOf<dim_length> U, QuantityValue Rep = double>
     using length = quantity<dim_length, U, Rep>;
 
     namespace fps {
@@ -246,7 +246,7 @@ different systems:
 
     struct dim_length : base_dimension<"L", foot> {};
 
-    template<Unit U, ScalableNumber Rep = double>
+    template<UnitOf<dim_length> U, QuantityValue Rep = double>
     using length = quantity<dim_length, U, Rep>;
 
     }  // namespace fps

example/custom_systems.cpp

@@ -33,7 +33,7 @@ struct yard : named_scaled_unit<yard, "yd", no_prefix, ratio(3), foot> {};
 
 struct dim_length : base_dimension<"L", foot> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_length> U, QuantityValue Rep = double>
 using length = quantity<dim_length, U, Rep>;
 
 }  // namespace fps
@@ -45,7 +45,7 @@ struct kilometre : prefixed_unit<kilometre, units::physical::si::kilo, metre> {}
 
 struct dim_length : base_dimension<"L", metre> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_length> U, QuantityValue Rep = double>
 using length = quantity<dim_length, U, Rep>;
 
 namespace fps {
@@ -55,7 +55,7 @@ struct yard : named_scaled_unit<yard, "yd", no_prefix, ratio(3), foot> {};
 
 struct dim_length : base_dimension<"L", foot> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_length> U, QuantityValue Rep = double>
 using length = quantity<dim_length, U, Rep>;
 
 }  // namespace fps

example/glide_computer.cpp

@@ -87,7 +87,7 @@ public:
   }
 
   template<typename V>
-    requires (ScalableNumber<V> || Dimensionless<V>)
+    requires (QuantityValue<V> || Dimensionless<V>)
   [[nodiscard]] friend constexpr auto operator*(const vector& lhs, const V& value)
     requires requires { lhs.magnitude() * value; }
   {
@@ -95,7 +95,7 @@ public:
   }
 
   template<typename V>
-    requires (ScalableNumber<V> || Dimensionless<V>)
+    requires (QuantityValue<V> || Dimensionless<V>)
   [[nodiscard]] friend constexpr auto operator*(const V& value, const vector& rhs)
     requires requires { value * rhs.magnitude(); }
   {

example/linear_algebra.cpp

@@ -200,10 +200,10 @@ void matrix_of_quantity_tests()
   matrix_of_quantity_divide_by_scalar();
 }
 
-template<units::Unit U = si::metre, units::ScalableNumber Rep = double>
+template<units::Unit U = si::metre, units::QuantityValue Rep = double>
 using length_v = si::length<U, vector<Rep>>;
 
-template<units::Unit U = si::newton, units::ScalableNumber Rep = double>
+template<units::Unit U = si::newton, units::QuantityValue Rep = double>
 using force_v = si::force<U, vector<Rep>>;
 
 void quantity_of_vector_add()
@@ -273,7 +273,7 @@ void quantity_of_vector_tests()
   quantity_of_vector_divide_by_scalar();
 }
 
-template<units::Unit U = si::metre, units::ScalableNumber Rep = double>
+template<units::Unit U = si::metre, units::QuantityValue Rep = double>
 using length_m = si::length<U, matrix<Rep>>;
 
 void quantity_of_matrix_add()

example/measurement.cpp

@@ -114,15 +114,13 @@ private:
   value_type uncertainty_{};
 };
 
-static_assert(units::ScalableNumber<measurement<double>>);
-
 }  // namespace
 
-template<typename T>
-inline constexpr bool units::treat_as_floating_point<measurement<T>> = std::is_floating_point_v<T>;
 
 namespace {
 
+static_assert(units::QuantityValue<measurement<double>>);
+
 void example()
 {
   using namespace units::physical;

src/include/units/bits/basic_concepts.h

@@ -25,6 +25,7 @@
 #include <units/bits/external/downcasting.h>
 #include <units/bits/external/fixed_string.h>
 #include <units/bits/external/hacks.h>
+#include <units/customization_points.h>
 #include <units/ratio.h>
 #include <units/bits/external/type_traits.h>
 #include <functional>
@@ -229,6 +230,34 @@ template<typename T>
 concept QuantityPoint = detail::is_quantity_point<T>;
 
 
+// QuantityValue
+
+template<typename T, typename U>
+concept common_type_with_ =
+  std::same_as<std::common_type_t<T, U>, std::common_type_t<U, T>> &&
+  std::constructible_from<std::common_type_t<T, U>, T> &&
+  std::constructible_from<std::common_type_t<T, U>, U>;
+
+template<typename T, typename U = T>
+concept scalable_number_ = // exposition only
+  std::regular_invocable<std::multiplies<>, T, U> &&
+  std::regular_invocable<std::divides<>, T, U>;
+
+template<typename T>
+concept castable_number_ = // exposition only
+  common_type_with_<T, std::intmax_t> &&
+  scalable_number_<std::common_type_t<T, std::intmax_t>>;
+
+template<typename T> 
+concept scalable_ = // exposition only
+  castable_number_<T> ||
+  (requires { typename T::value_type; } && castable_number_<typename T::value_type> && scalable_number_<T, std::common_type_t<typename T::value_type, std::intmax_t>>);
+
+template<typename From, typename To> 
+concept scalable_with_ = // exposition only
+  common_type_with_<From, To> &&
+  scalable_<std::common_type_t<From, To>>;
+
 // WrappedQuantity
 namespace detail {
 
@@ -248,31 +277,8 @@ inline constexpr bool is_wrapped_quantity<T> = Quantity<typename T::value_type>
  * recursively (i.e. `std::optional<si::length<si::metre>>`).
  */
 template<typename T>
-concept WrappedQuantity = detail::is_wrapped_quantity<T>;
+concept wrapped_quantity_ = // exposition only
-
+  detail::is_wrapped_quantity<T>;
-// ScalableNumber
-
-namespace detail {
-
-template<typename T>
-concept constructible_from_integral =
-  // construction from an integral type
-  std::constructible_from<T, std::int64_t> &&
-  // unit scaling
-  std::regular_invocable<std::multiplies<>, T, T> &&
-  std::regular_invocable<std::divides<>, T, T>;
-
-template<typename T>
-concept not_constructible_from_integral =
-  // not construction from an integral type
-  (!std::constructible_from<T, std::int64_t>) &&
-
-  // scaling by the value from ratio
-  std::regular_invocable<std::multiplies<>, T, std::int64_t> &&
-  std::regular_invocable<std::multiplies<>, std::int64_t, T>; // &&
-  // std::regular_invocable<std::divides<>, T, std::int64_t>;  // TODO Uncomment when a bug in LA is fixed
-
-}  // namespace detail
 
 /**
  * @brief A concept matching non-Quantity types.
@@ -280,10 +286,10 @@ concept not_constructible_from_integral =
  * Satisfied by types that satisfy `(!Quantity<T>) && (!WrappedQuantity<T>) && std::regular<T>`.
  */
 template<typename T>
-concept ScalableNumber =
+concept QuantityValue =
   (!Quantity<T>) &&
-  (!WrappedQuantity<T>) &&
+  (!wrapped_quantity_<T>) &&
   std::regular<T> &&
-  (detail::constructible_from_integral<T> || detail::not_constructible_from_integral<T>);
+  scalable_<T>;
 
 }  // namespace units

src/include/units/bits/common_quantity.h

@@ -28,10 +28,10 @@
 
 namespace units {
 
-template<Dimension D, UnitOf<D> U, ScalableNumber Rep>
+template<Dimension D, UnitOf<D> U, QuantityValue Rep>
 class quantity;
 
-template<Dimension D, UnitOf<D> U, ScalableNumber Rep>
+template<Dimension D, UnitOf<D> U, QuantityValue Rep>
 class quantity_point;
 
 namespace detail {
@@ -70,8 +70,7 @@ quantity_point<D, U, Rep> common_quantity_point_impl(quantity<D, U, Rep>);
 
 }  // namespace detail
 
-template<Quantity Q1, Quantity Q2, ScalableNumber Rep = std::common_type_t<typename Q1::rep, typename Q2::rep>>
+template<Quantity Q1, QuantityEquivalentTo<Q1> Q2, QuantityValue Rep = std::common_type_t<typename Q1::rep, typename Q2::rep>>
-  requires equivalent<typename Q1::dimension, typename Q2::dimension>
 using common_quantity = TYPENAME detail::common_quantity_impl<Q1, Q2, Rep>::type;
 
 template<QuantityPoint QP1, QuantityPoint QP2>

src/include/units/bits/quantity_of.h

@@ -73,7 +73,10 @@ concept QuantityOfT = Quantity<Q> && DimensionOfT<typename Q::dimension, DimTemp
  * Satisfied by all quantities with a dimension being the instantiation derived from
  * the provided dimension type.
  */
-template<typename T, typename Dim>
+template<typename Q, typename Dim>
-concept QuantityOf = Quantity<T> && Dimension<Dim> && equivalent<typename T::dimension, Dim>;
+concept QuantityOf = Quantity<Q> && Dimension<Dim> && equivalent<typename Q::dimension, Dim>;
+
+template<typename Q1, typename Q2>
+concept QuantityEquivalentTo = Quantity<Q1> && QuantityOf<Q2, typename Q1::dimension>;
 
 }  // namespace units

src/include/units/customization_points.h

@@ -22,7 +22,6 @@
 
 #pragma once
 
-#include <units/concepts.h>
 #include <limits>
 #include <type_traits>
 
@@ -37,9 +36,13 @@ namespace units {
  * 
  * @tparam Rep a representation type for which a type trait is defined
  */
-template<ScalableNumber Rep>
+template<typename Rep>
 inline constexpr bool treat_as_floating_point = std::is_floating_point_v<Rep>;
 
+template<typename T>
+  requires requires { typename T::value_type; }
+inline constexpr bool treat_as_floating_point<T> = treat_as_floating_point<typename T::value_type>;
+
 /**
  * @brief A type trait that defines zero, one, min, and max for a representation type
  * 
@@ -49,7 +52,7 @@ inline constexpr bool treat_as_floating_point = std::is_floating_point_v<Rep>;
  * 
  * @tparam Rep a representation type for which a type trait is defined
  */
-template<ScalableNumber Rep>
+template<typename Rep>
 struct quantity_values {
   static constexpr Rep zero() noexcept { return Rep(0); }
   static constexpr Rep one() noexcept { return Rep(1); }

src/include/units/data/base/information.h

@@ -48,7 +48,7 @@ struct dim_information : base_dimension<"information", bit> {};
 template<typename T>
 concept Information = QuantityOf<T, dim_information>;
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_information> U, QuantityValue Rep = double>
 using information = quantity<dim_information, U, Rep>;
 
 inline namespace literals {

src/include/units/data/derived/bitrate.h

@@ -41,7 +41,7 @@ struct pebibit_per_second : deduced_unit<pebibit_per_second, dim_bitrate, pebibi
 template<typename T>
 concept Bitrate = QuantityOf<T, dim_bitrate>;
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_bitrate> U, QuantityValue Rep = double>
 using bitrate = quantity<dim_bitrate, U, Rep>;
 
 inline namespace literals {

src/include/units/generic/angle.h

@@ -35,7 +35,7 @@ struct dim_angle : base_dimension<"A", U> {};
 template<typename T>
 concept Angle = QuantityOfT<T, dim_angle>;
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_angle<>> U, QuantityValue Rep = double>
 using angle = quantity<dim_angle<>, U, Rep>;
 
 inline namespace literals {

src/include/units/generic/dimensionless.h

@@ -40,7 +40,7 @@ struct dim_one : derived_dimension<dim_one, one> {};
 template<typename T>
 concept Dimensionless = QuantityOf<T, dim_one>;
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_one> U, QuantityValue Rep = double>
 using dimensionless = quantity<dim_one, U, Rep>;
 
 }  // namespace units

src/include/units/physical/natural/bits/dimensions.h

@@ -29,35 +29,35 @@
 namespace units::physical::natural {
 
 struct dim_length : physical::dim_length<inverted_gigaelectronvolt> {};
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_length> U, QuantityValue Rep = double>
 using length = quantity<dim_length, U, Rep>;
 
 struct dim_time : physical::dim_time<inverted_gigaelectronvolt> {};
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_time> U, QuantityValue Rep = double>
 using time = quantity<dim_time, U, Rep>;
 
 struct dim_mass : physical::dim_mass<gigaelectronvolt> {};
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_mass> U, QuantityValue Rep = double>
 using mass = quantity<dim_mass, U, Rep>;
 
 struct dim_speed : physical::dim_speed<dim_speed, one, dim_length, dim_time> {};
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_speed> U, QuantityValue Rep = double>
 using speed = quantity<dim_speed, U, Rep>;
 
 struct dim_acceleration : physical::dim_acceleration<dim_acceleration, gigaelectronvolt, dim_length, dim_time> {};
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_acceleration> U, QuantityValue Rep = double>
 using acceleration = quantity<dim_acceleration, U, Rep>;
 
 struct dim_force : physical::dim_force<dim_force, square_gigaelectronvolt, dim_mass, dim_acceleration> {};
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_force> U, QuantityValue Rep = double>
 using force = quantity<dim_force, U, Rep>;
 
 struct dim_momentum : physical::dim_momentum<dim_momentum, gigaelectronvolt, dim_mass, dim_speed> {};
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_momentum> U, QuantityValue Rep = double>
 using momentum = quantity<dim_momentum, U, Rep>;
 
 struct dim_energy : physical::dim_energy<dim_energy, gigaelectronvolt, dim_force, dim_length> {};
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_force> U, QuantityValue Rep = double>
 using energy = quantity<dim_force, U, Rep>;
 
 // Typical UDLs will not work here as the same units are reused by many quantities.

src/include/units/physical/natural/constants.h

@@ -26,7 +26,7 @@
 
 namespace units::physical::natural {
 
-template<ScalableNumber Rep = double>
+template<QuantityValue Rep = double>
 inline constexpr auto speed_of_light = speed<one, Rep>(1);
 
 }  // namespace units::physical::natural

src/include/units/physical/si/base/amount_of_substance.h

@@ -32,7 +32,7 @@ struct mole : named_unit<mole, "mol", prefix> {};
 
 struct dim_amount_of_substance : physical::dim_amount_of_substance<mole> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_amount_of_substance> U, QuantityValue Rep = double>
 using amount_of_substance = quantity<dim_amount_of_substance, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/base/electric_current.h

@@ -52,7 +52,7 @@ struct yottaampere : prefixed_unit<yottaampere, yotta, ampere> {};
 
 struct dim_electric_current : physical::dim_electric_current<ampere> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_electric_current> U, QuantityValue Rep = double>
 using electric_current = quantity<dim_electric_current, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/base/length.h

@@ -54,7 +54,7 @@ struct astronomical_unit : named_scaled_unit<astronomical_unit, "au", no_prefix,
 
 struct dim_length : physical::dim_length<metre> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_length> U, QuantityValue Rep = double>
 using length = quantity<dim_length, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/base/luminous_intensity.h

@@ -52,7 +52,7 @@ struct yottacandela : prefixed_unit<yottacandela, yotta, candela> {};
 
 struct dim_luminous_intensity : physical::dim_luminous_intensity<candela> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_luminous_intensity> U, QuantityValue Rep = double>
 using luminous_intensity = quantity<dim_luminous_intensity, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/base/mass.h

@@ -76,7 +76,7 @@ struct dalton : named_scaled_unit<dalton, "Da", no_prefix, ratio(16'605'390'666'
 
 struct dim_mass : physical::dim_mass<kilogram> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_mass> U, QuantityValue Rep = double>
 using mass = quantity<dim_mass, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/base/thermodynamic_temperature.h

@@ -31,7 +31,7 @@ struct kelvin : named_unit<kelvin, "K", no_prefix> {};
 
 struct dim_thermodynamic_temperature : physical::dim_thermodynamic_temperature<kelvin> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_thermodynamic_temperature> U, QuantityValue Rep = double>
 using thermodynamic_temperature = quantity<dim_thermodynamic_temperature, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/base/time.h

@@ -43,7 +43,7 @@ struct day : named_scaled_unit<day, "d", no_prefix, ratio(24), hour> {};
 
 struct dim_time : physical::dim_time<second> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_time> U, QuantityValue Rep = double>
 using time = quantity<dim_time, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/cgs/base/length.h

@@ -31,7 +31,7 @@ using si::centimetre;
 
 struct dim_length : physical::dim_length<centimetre> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_length> U, QuantityValue Rep = double>
 using length = quantity<dim_length, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/cgs/base/mass.h

@@ -31,7 +31,7 @@ using si::gram;
 
 struct dim_mass : physical::dim_mass<gram> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_mass> U, QuantityValue Rep = double>
 using mass = quantity<dim_mass, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/cgs/derived/acceleration.h

@@ -31,7 +31,7 @@ namespace units::physical::si::cgs {
 struct gal : named_unit<gal, "Gal", si::prefix> {};
 struct dim_acceleration : physical::dim_acceleration<dim_acceleration, gal, dim_length, dim_time> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_acceleration> U, QuantityValue Rep = double>
 using acceleration = quantity<dim_acceleration, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/cgs/derived/area.h

@@ -32,7 +32,7 @@ using si::square_centimetre;
 
 struct dim_area : physical::dim_area<dim_area, square_centimetre, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_area> U, QuantityValue Rep = double>
 using area = quantity<dim_area, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/cgs/derived/energy.h

@@ -33,7 +33,7 @@ struct erg : named_unit<erg, "erg", si::prefix> {};
 
 struct dim_energy : physical::dim_energy<dim_energy, erg, dim_force, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_energy> U, QuantityValue Rep = double>
 using energy = quantity<dim_energy, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/cgs/derived/force.h

@@ -34,7 +34,7 @@ struct dyne : named_unit<dyne, "dyn", si::prefix> {};
 
 struct dim_force : physical::dim_force<dim_force, dyne, dim_mass, dim_acceleration> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_force> U, QuantityValue Rep = double>
 using force = quantity<dim_force, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/cgs/derived/power.h

@@ -33,7 +33,7 @@ struct erg_per_second : unit<erg_per_second> {};
 
 struct dim_power : physical::dim_power<dim_power, erg_per_second, dim_energy, dim_time> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_power> U, QuantityValue Rep = double>
 using power = quantity<dim_power, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/cgs/derived/pressure.h

@@ -34,7 +34,7 @@ struct barye : named_unit<barye, "Ba", si::prefix> {};
 
 struct dim_pressure : physical::dim_pressure<dim_pressure, barye, dim_force, dim_area> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_pressure> U, QuantityValue Rep = double>
 using pressure = quantity<dim_pressure, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/cgs/derived/speed.h

@@ -32,7 +32,7 @@ namespace units::physical::si::cgs {
 struct centimetre_per_second : unit<centimetre_per_second> {};
 struct dim_speed : physical::dim_speed<dim_speed, centimetre_per_second, dim_length, dim_time> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_speed> U, QuantityValue Rep = double>
 using speed = quantity<dim_speed, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/constants.h

@@ -32,31 +32,31 @@
 
 namespace units::physical::si::si2019 {
 
-template<ScalableNumber Rep = double>
+template<QuantityValue Rep = double>
 inline constexpr auto planck_constant = energy<joule, Rep>(6.62607015e-34) * time<second, Rep>(1);
 
-template<ScalableNumber Rep = double>
+template<QuantityValue Rep = double>
 inline constexpr auto reduced_planck_constant = energy<gigaelectronvolt, Rep>(6.582119569e-10) * time<second, Rep>(1);
 
-template<ScalableNumber Rep = double>
+template<QuantityValue Rep = double>
 inline constexpr auto elementary_charge = electric_charge<coulomb, Rep>(1.602176634e-19);
 
-template<ScalableNumber Rep = double>
+template<QuantityValue Rep = double>
 inline constexpr auto boltzmann_constant = energy<joule, Rep>(1.380649e-23) / temperature<kelvin, Rep>(1);
 
-template<ScalableNumber Rep = double>
+template<QuantityValue Rep = double>
 inline constexpr auto avogadro_constant = Rep(6.02214076e23) / substance<mole, Rep>(1);
 
-template<ScalableNumber Rep = double>
+template<QuantityValue Rep = double>
 inline constexpr auto speed_of_light = speed<metre_per_second, Rep>(299'792'458);
 
-template<ScalableNumber Rep = double>
+template<QuantityValue Rep = double>
 inline constexpr auto hyperfine_structure_transition_frequency = frequency<hertz, Rep>(9'192'631'770);
 
-// template<ScalableNumber Rep = double>
+// template<QuantityValue Rep = double>
 // inline constexpr auto luminous_efficacy = 683_q_lm / 1_q_W;
 
-template<ScalableNumber Rep = double>
+template<QuantityValue Rep = double>
 inline constexpr auto standard_gravity = acceleration<metre_per_second_sq, Rep>(9.80665);
 
 }  // namespace units::physical::si::si2019

src/include/units/physical/si/derived/absorbed_dose.h

@@ -53,7 +53,7 @@ struct yottagray : prefixed_unit<yottagray, yotta, gray> {};
 
 struct dim_absorbed_dose : physical::dim_absorbed_dose<dim_absorbed_dose, gray, dim_energy, dim_mass> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_absorbed_dose> U, QuantityValue Rep = double>
 using absorbed_dose = quantity<dim_absorbed_dose, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/acceleration.h

@@ -31,7 +31,7 @@ namespace units::physical::si {
 struct metre_per_second_sq : unit<metre_per_second_sq> {};
 struct dim_acceleration : physical::dim_acceleration<dim_acceleration, metre_per_second_sq, dim_length, dim_time> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_acceleration> U, QuantityValue Rep = double>
 using acceleration = quantity<dim_acceleration, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/angular_velocity.h

@@ -34,7 +34,7 @@ struct radian_per_second : named_unit<radian_per_second, basic_symbol_text{"ω",
 
 struct dim_angular_velocity : physical::dim_angular_velocity<dim_angular_velocity, radian_per_second, dim_angle<>, dim_time> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_angular_velocity> U, QuantityValue Rep = double>
 using angular_velocity = quantity<dim_angular_velocity, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/area.h

@@ -54,7 +54,7 @@ struct square_yottametre : deduced_unit<square_yottametre, dim_area, yottametre>
 
 struct hectare : alias_unit<square_hectometre, "ha", no_prefix> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_area> U, QuantityValue Rep = double>
 using area = quantity<dim_area, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/capacitance.h

@@ -54,7 +54,7 @@ struct yottafarad : prefixed_unit<yottafarad, yotta, farad> {};
 
 struct dim_capacitance : physical::dim_capacitance<dim_capacitance, farad, dim_electric_charge, dim_voltage> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_capacitance> U, QuantityValue Rep = double>
 using capacitance = quantity<dim_capacitance, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/catalytic_activity.h

@@ -56,7 +56,7 @@ struct enzyme_unit : named_scaled_unit<enzyme_unit, "U", prefix, ratio(1, 60, -6
 
 struct dim_catalytic_activity : physical::dim_catalytic_activity<dim_catalytic_activity, katal, dim_time, dim_amount_of_substance> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_catalytic_activity> U, QuantityValue Rep = double>
 using catalytic_activity = quantity<dim_catalytic_activity, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/charge_density.h

@@ -36,10 +36,10 @@ struct coulomb_per_metre_sq : unit<coulomb_per_metre_sq> {};
 struct dim_charge_density : physical::dim_charge_density<dim_charge_density, coulomb_per_metre_cub, dim_electric_charge, dim_length> {};
 struct dim_surface_charge_density : physical::dim_surface_charge_density<dim_surface_charge_density, coulomb_per_metre_sq, dim_electric_charge, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_charge_density> U, QuantityValue Rep = double>
 using charge_density = quantity<dim_charge_density, U, Rep>;
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_surface_charge_density> U, QuantityValue Rep = double>
 using surface_charge_density = quantity<dim_surface_charge_density, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/concentration.h

@@ -32,7 +32,7 @@ namespace units::physical::si {
 struct mol_per_metre_cub : unit<mol_per_metre_cub> {};
 struct dim_concentration : physical::dim_concentration<dim_concentration, mol_per_metre_cub, dim_amount_of_substance, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_concentration> U, QuantityValue Rep = double>
 using concentration = quantity<dim_concentration, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/conductance.h

@@ -49,7 +49,7 @@ struct yottasiemens : prefixed_unit<yottasiemens, yotta, siemens> {};
 
 struct dim_conductance : physical::dim_conductance<dim_conductance, siemens, dim_resistance> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_conductance> U, QuantityValue Rep = double>
 using conductance = quantity<dim_conductance, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/current_density.h

@@ -34,7 +34,7 @@ struct ampere_per_metre_sq : unit<ampere_per_metre_sq> {};
 
 struct dim_current_density : physical::dim_current_density<dim_current_density, ampere_per_metre_sq, dim_electric_current, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_current_density> U, QuantityValue Rep = double>
 using current_density = quantity<dim_current_density, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/density.h

@@ -34,7 +34,7 @@ struct kilogram_per_metre_cub : unit<kilogram_per_metre_cub> {};
 
 struct dim_density : physical::dim_density<dim_density, kilogram_per_metre_cub, dim_mass, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_density> U, QuantityValue Rep = double>
 using density = quantity<dim_density, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/dynamic_viscosity.h

@@ -32,7 +32,7 @@ namespace units::physical::si {
 struct pascal_second : unit<pascal_second> {};
 struct dim_dynamic_viscosity : physical::dim_dynamic_viscosity<dim_dynamic_viscosity, pascal_second, dim_pressure, dim_time> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_dynamic_viscosity> U, QuantityValue Rep = double>
 using dynamic_viscosity = quantity<dim_dynamic_viscosity, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/electric_charge.h

@@ -33,7 +33,7 @@ struct coulomb : named_unit<coulomb, "C", prefix> {};
 
 struct dim_electric_charge : physical::dim_electric_charge<dim_electric_charge, coulomb, dim_time, dim_electric_current> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_electric_charge> U, QuantityValue Rep = double>
 using electric_charge = quantity<dim_electric_charge, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/electric_field_strength.h

@@ -31,7 +31,7 @@ namespace units::physical::si {
 struct volt_per_metre : unit<volt_per_metre> {};
 struct dim_electric_field_strength : physical::dim_electric_field_strength<dim_electric_field_strength, volt_per_metre, dim_voltage, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_electric_field_strength> U, QuantityValue Rep = double>
 using electric_field_strength = quantity<dim_electric_field_strength, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/energy.h

@@ -52,7 +52,7 @@ struct gigaelectronvolt : prefixed_unit<gigaelectronvolt, giga, electronvolt> {}
 
 struct dim_energy : physical::dim_energy<dim_energy, joule, dim_force, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_energy> U, QuantityValue Rep = double>
 using energy = quantity<dim_energy, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/force.h

@@ -54,7 +54,7 @@ struct yottanewton : prefixed_unit<yottanewton, yotta, newton> {};
 
 struct dim_force : physical::dim_force<dim_force, newton, dim_mass, dim_acceleration> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_force> U, QuantityValue Rep = double>
 using force = quantity<dim_force, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/frequency.h

@@ -48,7 +48,7 @@ struct yottahertz : prefixed_unit<yottahertz, yotta, hertz> {};
 
 struct dim_frequency : physical::dim_frequency<dim_frequency, hertz, dim_time> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_frequency> U, QuantityValue Rep = double>
 using frequency = quantity<dim_frequency, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/heat_capacity.h

@@ -39,13 +39,13 @@ struct dim_heat_capacity : physical::dim_heat_capacity<dim_heat_capacity, joule_
 struct dim_specific_heat_capacity : physical::dim_specific_heat_capacity<dim_specific_heat_capacity, joule_per_kilogram_kelvin, dim_heat_capacity, dim_mass> {};
 struct dim_molar_heat_capacity : physical::dim_molar_heat_capacity<dim_molar_heat_capacity, joule_per_mole_kelvin, dim_heat_capacity, dim_amount_of_substance> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_heat_capacity> U, QuantityValue Rep = double>
 using heat_capacity = quantity<dim_heat_capacity, U, Rep>;
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_specific_heat_capacity> U, QuantityValue Rep = double>
 using specific_heat_capacity = quantity<dim_specific_heat_capacity, U, Rep>;
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_molar_heat_capacity> U, QuantityValue Rep = double>
 using molar_heat_capacity = quantity<dim_molar_heat_capacity, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/inductance.h

@@ -50,7 +50,7 @@ struct yottahenry : prefixed_unit<yottahenry, yotta, henry> {};
 
 struct dim_inductance : physical::dim_inductance<dim_inductance, henry, dim_magnetic_flux, dim_electric_current> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_inductance> U, QuantityValue Rep = double>
 using inductance = quantity<dim_inductance, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/luminance.h

@@ -32,7 +32,7 @@ namespace units::physical::si {
 struct candela_per_metre_sq : unit<candela_per_metre_sq> {};
 struct dim_luminance : physical::dim_luminance<dim_luminance, candela_per_metre_sq, dim_luminous_intensity, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_luminance> U, QuantityValue Rep = double>
 using luminance = quantity<dim_luminance, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/magnetic_flux.h

@@ -50,7 +50,7 @@ struct yottaweber : prefixed_unit<yottaweber, yotta, weber> {};
 
 struct dim_magnetic_flux : physical::dim_magnetic_flux<dim_magnetic_flux, weber, dim_magnetic_induction, dim_area> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_magnetic_flux> U, QuantityValue Rep = double>
 using magnetic_flux = quantity<dim_magnetic_flux, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/magnetic_induction.h

@@ -54,7 +54,7 @@ struct gauss : named_scaled_unit<gauss, "G", prefix, ratio(1, 10'000), tesla> {}
 
 struct dim_magnetic_induction : physical::dim_magnetic_induction<dim_magnetic_induction, tesla, dim_voltage, dim_time, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_magnetic_induction> U, QuantityValue Rep = double>
 using magnetic_induction = quantity<dim_magnetic_induction, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/molar_energy.h

@@ -34,7 +34,7 @@ struct joule_per_mole : unit<joule_per_mole> {};
 
 struct dim_molar_energy : physical::dim_molar_energy<dim_molar_energy, joule_per_mole, dim_energy, dim_amount_of_substance> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_molar_energy> U, QuantityValue Rep = double>
 using molar_energy = quantity<dim_molar_energy, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/momentum.h

@@ -32,7 +32,7 @@ namespace units::physical::si {
 struct kilogram_metre_per_second : unit<kilogram_metre_per_second> {};
 struct dim_momentum : physical::dim_momentum<dim_momentum, kilogram_metre_per_second, dim_mass, dim_speed> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_momentum> U, QuantityValue Rep = double>
 using momentum = quantity<dim_momentum, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/permeability.h

@@ -33,7 +33,7 @@ struct henry_per_metre : unit<henry_per_metre> {};
 
 struct dim_permeability : physical::dim_permeability<dim_permeability, henry_per_metre, dim_inductance, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_permeability> U, QuantityValue Rep = double>
 using permeability = quantity<dim_permeability, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/permittivity.h

@@ -33,7 +33,7 @@ struct farad_per_metre : unit<farad_per_metre> {};
 
 struct dim_permittivity : physical::dim_permittivity<dim_permittivity, farad_per_metre, dim_capacitance, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_permittivity> U, QuantityValue Rep = double>
 using permittivity = quantity<dim_permittivity, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/power.h

@@ -49,7 +49,7 @@ struct yottawatt : prefixed_unit<yottawatt, yotta, watt> {};
 
 struct dim_power : physical::dim_power<dim_power, watt, dim_energy, dim_time> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_power> U, QuantityValue Rep = double>
 using power = quantity<dim_power, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/pressure.h

@@ -54,7 +54,7 @@ struct yottapascal : prefixed_unit<yottapascal, yotta, pascal> {};
 
 struct dim_pressure : physical::dim_pressure<dim_pressure, pascal, dim_force, dim_area> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_pressure> U, QuantityValue Rep = double>
 using pressure = quantity<dim_pressure, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/resistance.h

@@ -50,7 +50,7 @@ struct yottaohm : prefixed_unit<yottaohm, yotta, ohm> {};
 
 struct dim_resistance : physical::dim_resistance<dim_resistance, ohm, dim_voltage, dim_electric_current> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_resistance> U, QuantityValue Rep = double>
 using resistance = quantity<dim_resistance, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/speed.h

@@ -34,7 +34,7 @@ struct dim_speed : physical::dim_speed<dim_speed, metre_per_second, dim_length,
 
 struct kilometre_per_hour : deduced_unit<kilometre_per_hour, dim_speed, kilometre, hour> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_speed> U, QuantityValue Rep = double>
 using speed = quantity<dim_speed, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/surface_tension.h

@@ -32,7 +32,7 @@ struct newton_per_metre : unit<newton_per_metre> {};
 
 struct dim_surface_tension : physical::dim_surface_tension<dim_surface_tension, newton_per_metre, dim_force, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_surface_tension> U, QuantityValue Rep = double>
 using surface_tension = quantity<dim_surface_tension, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/thermal_conductivity.h

@@ -33,7 +33,7 @@ struct watt_per_metre_kelvin : unit<watt_per_metre_kelvin> {};
 
 struct dim_thermal_conductivity : physical::dim_thermal_conductivity<dim_thermal_conductivity, watt_per_metre_kelvin, dim_power, dim_length, dim_thermodynamic_temperature> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_thermal_conductivity> U, QuantityValue Rep = double>
 using thermal_conductivity = quantity<dim_thermal_conductivity, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/torque.h

@@ -34,7 +34,7 @@ struct newton_metre : named_unit<newton_metre, "Nm", prefix> {};
 
 struct dim_torque : physical::dim_torque<dim_torque, newton_metre, dim_energy, dim_angle<>> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_torque> U, QuantityValue Rep = double>
 using torque = quantity<dim_torque, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/voltage.h

@@ -54,7 +54,7 @@ struct yottavolt : prefixed_unit<yottavolt, yotta, volt> {};
 
 struct dim_voltage : physical::dim_voltage<dim_voltage, volt, dim_power, dim_electric_current> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_voltage> U, QuantityValue Rep = double>
 using voltage = quantity<dim_voltage, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/derived/volume.h

@@ -74,7 +74,7 @@ struct exalitre : prefixed_unit<petalitre, exa, litre> {};
 struct zettalitre : prefixed_alias_unit<cubic_megametre, zetta, litre> {};
 struct yottalitre : prefixed_unit<yottalitre, yotta, litre> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_volume> U, QuantityValue Rep = double>
 using volume = quantity<dim_volume, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/fps/base/length.h

@@ -51,7 +51,7 @@ struct nautical_mile : named_scaled_unit<nautical_mile, "mi(naut)", no_prefix, r
 
 struct dim_length : physical::dim_length<foot> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_length> U, QuantityValue Rep = double>
 using length = quantity<dim_length, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/fps/base/mass.h

@@ -32,7 +32,7 @@ struct pound : named_scaled_unit<pound, "lb", no_prefix, ratio(45'359'237, 100'0
 
 struct dim_mass : physical::dim_mass<pound> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_mass> U, QuantityValue Rep = double>
 using mass = quantity<dim_mass, U, Rep>;
 
 struct grain : named_scaled_unit<grain, "gr", no_prefix, ratio(1, 7000), pound>{};

src/include/units/physical/si/fps/derived/acceleration.h

@@ -31,7 +31,7 @@ namespace units::physical::si::fps {
 struct foot_per_second_sq : unit<foot_per_second_sq> {};
 struct dim_acceleration : physical::dim_acceleration<dim_acceleration, foot_per_second_sq, dim_length, dim_time> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_acceleration> U, QuantityValue Rep = double>
 using acceleration = quantity<dim_acceleration, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/fps/derived/area.h

@@ -32,7 +32,7 @@ struct square_foot : unit<square_foot> {};
 struct dim_area : physical::dim_area<dim_area, square_foot, dim_length> {};
 
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_area> U, QuantityValue Rep = double>
 using area = quantity<dim_area, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/fps/derived/density.h

@@ -33,7 +33,7 @@ struct pound_per_foot_cub : unit<pound_per_foot_cub> {};
 
 struct dim_density : physical::dim_density<dim_density, pound_per_foot_cub, dim_mass, dim_length> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_density> U, QuantityValue Rep = double>
 using density = quantity<dim_density, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/fps/derived/energy.h

@@ -39,7 +39,7 @@ struct foot_pound_force : noble_deduced_unit<foot_pound_force, dim_energy, pound
 
 
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_energy> U, QuantityValue Rep = double>
 using energy = quantity<dim_energy, U, Rep>;
 
 

src/include/units/physical/si/fps/derived/force.h

@@ -43,7 +43,7 @@ struct kip : alias_unit<kilopound_force, "klbf", no_prefix> {};
 
 struct dim_force : physical::dim_force<dim_force, poundal, dim_mass, dim_acceleration> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_force> U, QuantityValue Rep = double>
 using force = quantity<dim_force, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/fps/derived/power.h

@@ -37,7 +37,7 @@ struct foot_pound_force_per_second : deduced_unit<foot_pound_force_per_second, d
 
 struct horse_power : named_scaled_unit<horse_power, "hp", no_prefix, ratio(550), foot_pound_force_per_second> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_power> U, QuantityValue Rep = double>
 using power = quantity<dim_power, U, Rep>;
 
 inline namespace literals {

src/include/units/physical/si/fps/derived/pressure.h

@@ -34,7 +34,7 @@ struct poundal_per_foot_sq : unit<poundal_per_foot_sq> {};
 
 struct dim_pressure : physical::dim_pressure<dim_pressure, poundal_per_foot_sq, dim_force, dim_area> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_pressure> U, QuantityValue Rep = double>
 using pressure = quantity<dim_pressure, U, Rep>;
 
 struct pound_force_per_foot_sq : named_scaled_unit<pound_force_per_foot_sq, "lbf ft2", si::prefix, ratio(32'174'049, 1'000'000), poundal_per_foot_sq> {};

src/include/units/physical/si/fps/derived/speed.h

@@ -32,7 +32,7 @@ namespace units::physical::si::fps {
 struct foot_per_second : unit<foot_per_second> {};
 struct dim_speed : physical::dim_speed<dim_speed, foot_per_second, dim_length, dim_time> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_speed> U, QuantityValue Rep = double>
 using speed = quantity<dim_speed, U, Rep>;
 
 struct mile_per_hour : deduced_unit<mile_per_hour, dim_speed, mile, hour>{};

src/include/units/physical/si/fps/derived/volume.h

@@ -33,7 +33,7 @@ struct dim_volume : physical::dim_volume<dim_volume, cubic_foot, dim_length> {};
 
 struct cubic_yard : deduced_unit<cubic_yard, dim_volume, yard> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_volume> U, QuantityValue Rep = double>
 using volume = quantity<dim_volume, U, Rep>;
 
 inline namespace literals {

src/include/units/quantity.h

@@ -34,19 +34,52 @@
 
 namespace units {
 
-namespace detail {
+template<typename T>
+concept floating_point_ = // exposition only
+  (Quantity<T> && treat_as_floating_point<typename T::rep>) ||
+  (!Quantity<T> && treat_as_floating_point<T>);
 
 template<typename From, typename To>
-concept safe_convertible = // exposition only
+concept safe_convertible_to_ = // exposition only
+    !(Quantity<From>) &&
+    !(Quantity<To>) &&
     std::convertible_to<From, To> &&
-    (treat_as_floating_point<To> || (!treat_as_floating_point<From>));
+    (floating_point_<To> || (!floating_point_<From>));
 
-template<typename Rep, typename QuantityFrom, typename QuantityTo>
+// QFrom ratio is an exact multiple of QTo
-concept safe_divisible = // exposition only
+template<typename QFrom, typename QTo>
-    treat_as_floating_point<Rep> ||
+concept harmonic_ = // exposition only
-    is_integral(quantity_ratio(QuantityFrom{}) / quantity_ratio(QuantityTo{}));
+    Quantity<QFrom> &&
+    Quantity<QTo> &&
+    requires(QFrom from, QTo to) { requires is_integral(detail::quantity_ratio(from) / detail::quantity_ratio(to)); };
 
-} // namespace detail
+template<typename QFrom, typename QTo>
+concept safe_castable_to_ = // exposition only
+    Quantity<QFrom> &&
+    QuantityOf<QTo, typename QFrom::dimension> &&
+    scalable_with_<typename QFrom::rep, typename QTo::rep> &&
+    (floating_point_<QTo> || (!floating_point_<QFrom> && harmonic_<QFrom, QTo>));
+
+template<typename Func, typename T, typename U>
+concept quantity_value_for_ =
+  std::regular_invocable<Func, T, U> &&
+  QuantityValue<std::invoke_result_t<Func, T, U>>;
+
+template<typename T, typename Func, typename U, typename V>
+concept invoke_result_convertible_to_ =
+  QuantityValue<T> &&
+  quantity_value_for_<Func, U, V> &&
+  safe_convertible_to_<T, std::invoke_result_t<Func, U, V>>;
+
+template<typename Func, typename Q, typename V>
+concept have_quantity_for_ =
+  Quantity<Q> &&
+  (!Quantity<V>) &&
+  quantity_value_for_<Func, typename Q::rep, V>;
+
+template<typename Func, Quantity Q1, QuantityEquivalentTo<Q1> Q2>
+  requires quantity_value_for_<Func, typename Q1::rep, typename Q2::rep>
+using common_quantity_for = common_quantity<Q1, Q2, std::invoke_result_t<Func, typename Q1::rep, typename Q2::rep>>;
 
 /**
  * @brief A quantity
@@ -58,63 +91,69 @@ concept safe_divisible = // exposition only
  * @tparam U a measurement unit of the quantity
  * @tparam Rep a type to be used to represent values of a quantity
  */
-template<Dimension D, UnitOf<D> U, ScalableNumber Rep = double>
+template<Dimension D, UnitOf<D> U, QuantityValue Rep = double>
 class quantity {
   Rep value_;
 public:
+  // member types
   using dimension = D;
   using unit = U;
   using rep = Rep;
 
+  // static member functions
+  [[nodiscard]] static constexpr quantity zero() noexcept
+    requires requires { quantity_values<rep>::zero(); }
+  {
+    return quantity(quantity_values<rep>::zero());
+  }
+
+  [[nodiscard]] static constexpr quantity one() noexcept
+    requires requires { quantity_values<rep>::one(); }
+  {
+    return quantity(quantity_values<rep>::one());
+  }
+
+  [[nodiscard]] static constexpr quantity min() noexcept
+    requires requires { quantity_values<rep>::min(); }
+  {
+    return quantity(quantity_values<rep>::min());
+  }
+
+  [[nodiscard]] static constexpr quantity max() noexcept
+    requires requires { quantity_values<rep>::max(); }
+  {
+    return quantity(quantity_values<rep>::max());
+  }
+
+  // construction, assignment, destruction
   quantity() = default;
   quantity(const quantity&) = default;
   quantity(quantity&&) = default;
 
-  template<ScalableNumber Value>
+  template<safe_convertible_to_<rep> Value>
-    requires detail::safe_convertible<Value, rep>
+  explicit(!(equivalent<quantity, dimensionless<::units::one, rep>>)) constexpr quantity(const Value& v) : value_(static_cast<rep>(v)) {}
-  constexpr explicit(!(equivalent<quantity, dimensionless<one, Rep>>)) quantity(const Value& v) : value_{static_cast<rep>(v)} {}
 
-  template<Quantity Q2>
+  template<safe_castable_to_<quantity> Q2>
-    requires equivalent<D, typename Q2::dimension> &&
+  constexpr quantity(const Q2& q) : value_(quantity_cast<quantity>(q).count()) {}
-             detail::safe_convertible<typename Q2::rep, rep> &&
-             detail::safe_divisible<rep, Q2, quantity>
-  constexpr quantity(const Q2& q) : value_{quantity_cast<quantity>(q).count()} {}
 
   quantity& operator=(const quantity&) = default;
   quantity& operator=(quantity&&) = default;
 
+  // data access
   [[nodiscard]] constexpr rep count() const noexcept { return value_; }
 
-  [[nodiscard]] static constexpr quantity zero() noexcept
+  // member unary operators
-    requires requires { quantity_values<Rep>::zero(); }
+  [[nodiscard]] constexpr quantity operator+() const
+    requires requires(rep v) { { +v } -> std::same_as<rep>; }
   {
-    return quantity(quantity_values<Rep>::zero());
+    return *this;
   }
 
-  [[nodiscard]] static constexpr quantity one() noexcept
+  [[nodiscard]] constexpr Quantity auto operator-() const
-    requires requires { quantity_values<Rep>::one(); }
-  {
-    return quantity(quantity_values<Rep>::one());
-  }
-
-  [[nodiscard]] static constexpr quantity min() noexcept
-    requires requires { quantity_values<Rep>::min(); }
-  {
-    return quantity(quantity_values<Rep>::min());
-  }
-
-  [[nodiscard]] static constexpr quantity max() noexcept
-    requires requires { quantity_values<Rep>::max(); }
-  {
-    return quantity(quantity_values<Rep>::max());
-  }
-
-  [[nodiscard]] constexpr quantity operator+() const { return *this; }
-
-  [[nodiscard]] constexpr quantity operator-() const
     requires std::regular_invocable<std::negate<>, rep>
   {
-    return quantity(-count());
+    using ret = quantity<D, U, decltype(-count())>;
+    return ret(-count());
   }
 
   constexpr quantity& operator++()
@@ -143,51 +182,45 @@ public:
     return quantity(value_--);
   }
 
-  template<typename Rep2>
+  constexpr quantity& operator+=(const quantity& q)
-    requires detail::safe_convertible<Rep2, rep>
+    requires requires(rep a, rep b) { { a += b } -> std::same_as<rep&>; }
-  constexpr quantity& operator+=(const quantity<D, U, Rep2>& q)
   {
     value_ += q.count();
     return *this;
   }
 
-  template<typename Rep2>
+  constexpr quantity& operator-=(const quantity& q)
-    requires detail::safe_convertible<Rep2, rep>
+    requires requires(rep a, rep b) { { a -= b } -> std::same_as<rep&>; }
-  constexpr quantity& operator-=(const quantity<D, U, Rep2>& q)
   {
     value_ -= q.count();
     return *this;
   }
 
-  template<typename Rep2>
+  constexpr quantity& operator*=(const rep& rhs)
-    requires detail::safe_convertible<Rep2, rep>
+    requires requires(rep a, rep b) { { a *= b } -> std::same_as<rep&>; }
-  constexpr quantity& operator*=(const Rep2& rhs)
   {
     value_ *= rhs;
     return *this;
   }
 
-  template<typename Rep2>
+  constexpr quantity& operator/=(const rep& rhs)
-    requires detail::safe_convertible<Rep2, rep>
+    requires requires(rep a, rep b) { { a /= b } -> std::same_as<rep&>; }
-  constexpr quantity& operator/=(const Rep2& rhs)
   {
     value_ /= rhs;
     return *this;
   }
 
-  template<ScalableNumber Value>
+  constexpr quantity& operator%=(const rep& rhs)
-    requires (!treat_as_floating_point<rep>) &&
+    requires (!floating_point_<rep>) &&
-             (!treat_as_floating_point<Value>)
+             requires(rep a, rep b) { { a %= b } -> std::same_as<rep&>; }
-  constexpr quantity& operator%=(const Value& rhs)
-    requires requires(rep v1, Value v2) { { v1 %= v2 } -> std::same_as<rep&>; }
   {
     value_ %= rhs;
     return *this;
   }
 
   constexpr quantity& operator%=(const quantity& q)
-    requires (!treat_as_floating_point<rep>) &&
+    requires (!floating_point_<rep>) &&
-             requires(rep v1, rep v2) { { v1 %= v2 } -> std::same_as<rep&>; }
+             requires(rep a, rep b) { { a %= b } -> std::same_as<rep&>; }
   {
     value_ %= q.count();
     return *this;
@@ -195,143 +228,88 @@ public:
 
   // Hidden Friends
   // Below friend functions are to be found via argument-dependent lookup only
-
   [[nodiscard]] friend constexpr quantity operator+(const quantity& lhs, const quantity& rhs)
-    requires std::regular_invocable<std::plus<>, Rep, Rep>
+    requires invoke_result_convertible_to_<rep, std::plus<>, rep, rep>
   {
     return quantity(lhs.count() + rhs.count());
   }
 
-  template<typename D2, typename U2, typename Rep2>
-    requires std::regular_invocable<std::plus<>, Rep, Rep2> && equivalent<D, D2>
-  [[nodiscard]] friend constexpr Quantity auto operator+(const quantity& lhs, const quantity<D2, U2, Rep2>& rhs)
-  {
-    using common_rep = decltype(lhs.count() + rhs.count());
-    using ret = common_quantity<quantity, quantity<D2, U2, Rep2>, common_rep>;
-    return ret(ret(lhs).count() + ret(rhs).count());
-  }
-
   [[nodiscard]] friend constexpr quantity operator-(const quantity& lhs, const quantity& rhs)
-    requires std::regular_invocable<std::minus<>, Rep, Rep>
+    requires invoke_result_convertible_to_<rep, std::minus<>, rep, rep>
   {
     return quantity(lhs.count() - rhs.count());
   }
 
-  template<typename D2, typename U2, typename Rep2>
+  template<typename Value>
-    requires std::regular_invocable<std::minus<>, Rep, Rep2> && equivalent<D, D2>
+    requires (!Quantity<Value>) &&
-  [[nodiscard]] friend constexpr Quantity auto operator-(const quantity& lhs, const quantity<D2, U2, Rep2>& rhs)
+          invoke_result_convertible_to_<rep, std::multiplies<>, rep, Value>
-  {
-    using common_rep = decltype(lhs.count() - rhs.count());
-    using ret = common_quantity<quantity, quantity<D2, U2, Rep2>, common_rep>;
-    return ret(ret(lhs).count() - ret(rhs).count());
-  }
-
-  template<ScalableNumber Value>
-    requires std::regular_invocable<std::multiplies<>, Rep, Value>
   [[nodiscard]] friend constexpr Quantity auto operator*(const quantity& q, const Value& v)
   {
-    using common_rep = decltype(q.count() * v);
+    using ret = quantity<D, U, std::invoke_result_t<std::multiplies<>, rep, Value>>;
-    using ret = quantity<D, U, common_rep>;
     return ret(q.count() * v);
   }
 
-  template<ScalableNumber Value>
+  template<typename Value>
-    requires std::regular_invocable<std::multiplies<>, Value, Rep>
+    requires (!Quantity<Value>) &&
+          invoke_result_convertible_to_<rep, std::multiplies<>, rep, Value>
   [[nodiscard]] friend constexpr Quantity auto operator*(const Value& v, const quantity& q)
   {
     return q * v;
   }
 
-  template<typename D2, typename U2, typename Rep2>
+  template<typename Value>
-    requires std::regular_invocable<std::multiplies<>, Rep, Rep2>
+    requires (!Quantity<Value>) &&
-  [[nodiscard]] friend constexpr Quantity auto operator*(const quantity& lhs, const quantity<D2, U2, Rep2>& rhs)
+          invoke_result_convertible_to_<rep, std::divides<>, rep, Value>
-  {
-    using dim = dimension_multiply<D, D2>;
-    using ret_unit = downcast_unit<dim, (U::ratio / dimension_unit<D>::ratio) * (U2::ratio / dimension_unit<D2>::ratio) * dimension_unit<dim>::ratio>;
-    using common_rep = decltype(lhs.count() * rhs.count());
-    using ret = quantity<dim, ret_unit, common_rep>;
-    return ret(lhs.count() * rhs.count());
-  }
-
-  template<ScalableNumber Value>
-    requires std::regular_invocable<std::divides<>, Value, Rep>
-  [[nodiscard]] friend constexpr Quantity auto operator/(const Value& v, const quantity& q)
-  {
-    // Expects(q.count() != zero().count());
-
-    using dim = dim_invert<D>;
-    using ret_unit = downcast_unit<dim, ratio(U::ratio.den, U::ratio.num, -U::ratio.exp)>;
-    using common_rep = decltype(v / q.count());
-    using ret = quantity<dim, ret_unit, common_rep>;
-    return ret(v / q.count());
-  }
-
-  template<ScalableNumber Value>
-    requires std::regular_invocable<std::divides<>, Rep, Value>
   [[nodiscard]] friend constexpr Quantity auto operator/(const quantity& q, const Value& v)
   {
     // Expects(v != zero().count());
-
+    using ret = quantity<D, U, std::invoke_result_t<std::divides<>, rep, Value>>;
-    using common_rep = decltype(q.count() / v);
-    using ret = quantity<D, U, common_rep>;
     return ret(q.count() / v);
   }
 
-  template<typename D2, typename U2, typename Rep2>
+  template<typename Value>
-    requires std::regular_invocable<std::divides<>, Rep, Rep2>
+    requires (!Quantity<Value>) &&
-  [[nodiscard]] friend constexpr Quantity auto operator/(const quantity& lhs, const quantity<D2, U2, Rep2>& rhs)
+          invoke_result_convertible_to_<rep, std::divides<>, Value, rep>
+  [[nodiscard]] friend constexpr Quantity auto operator/(const Value& v, const quantity& q)
   {
-    // Expects(rhs.count() != zero().count());
+    // Expects(q.count() != zero().count());
-
+    using dim = dim_invert<D>;
-    using common_rep = decltype(lhs.count() / rhs.count());
+    using ret_unit = downcast_unit<dim, inverse(U::ratio)>;
-    using dim = dimension_divide<D, D2>;
+    using ret = quantity<dim, ret_unit, std::invoke_result_t<std::divides<>, Value, rep>>;
-    using ret_unit = downcast_unit<dim, (U::ratio / dimension_unit<D>::ratio) / (U2::ratio / dimension_unit<D2>::ratio) * dimension_unit<dim>::ratio>;
+    return ret(v / q.count());
-    using ret = quantity<dim, ret_unit, common_rep>;
-    return ret(lhs.count() / rhs.count());
   }
 
-  template<ScalableNumber Value>
+  template<typename Value>
-    requires (!treat_as_floating_point<Rep>) &&
+    requires (!Quantity<Value>) && (!floating_point_<rep>) && (!floating_point_<Value>) &&
-            (!treat_as_floating_point<Value>) &&
+            invoke_result_convertible_to_<rep, std::modulus<>, rep, Value>
-            std::regular_invocable<std::modulus<>, Rep, Value>
   [[nodiscard]] friend constexpr Quantity auto operator%(const quantity& q, const Value& v)
   {
-    using common_rep = decltype(q.count() % v);
+    using ret = quantity<D, U, std::invoke_result_t<std::modulus<>, rep, Value>>;
-    using ret = quantity<D, U, common_rep>;
     return ret(q.count() % v);
   }
 
-  template<typename U2, typename Rep2>
+  [[nodiscard]] friend constexpr quantity operator%(const quantity& lhs, const quantity& rhs)
-    requires (!treat_as_floating_point<Rep>) &&
+    requires (!floating_point_<rep>) &&
-            (!treat_as_floating_point<Rep2>) &&
+            invoke_result_convertible_to_<rep, std::modulus<>, rep, rep>
-            std::regular_invocable<std::modulus<>, Rep, Rep2>
-  [[nodiscard]] friend constexpr Quantity auto operator%(const quantity& lhs, const quantity<D, U2, Rep2>& rhs)
   {
-    using common_rep = decltype(lhs.count() % rhs.count());
+    return quantity(lhs.count() % rhs.count());
-    using ret = common_quantity<quantity, quantity<D, U2, Rep2>, common_rep>;
-    return ret(ret(lhs).count() % ret(rhs).count());
   }
 
-  template<typename D2, typename U2, typename Rep2>
+  [[nodiscard]] friend constexpr auto operator<=>(const quantity& lhs, const quantity& rhs)
-    requires equivalent<D, D2> &&
+    requires std::three_way_comparable<rep>
-             std::three_way_comparable_with<Rep, Rep2>
+#if COMP_GCC == 10 && COMP_GCC_MINOR >= 2
-  [[nodiscard]] friend constexpr auto operator<=>(const quantity& lhs, const quantity<D2, U2, Rep2>& rhs)
+  = default;
+#else
   {
-    using cq = common_quantity<quantity, quantity<D2, U2, Rep2>>;
+    return lhs.count() <=> rhs.count();
-    return cq(lhs).count() <=> cq(rhs).count();
   }
+#endif
 
-  template<typename D2, typename U2, typename Rep2>
+  [[nodiscard]] friend constexpr bool operator==(const quantity& lhs, const quantity& rhs) = default;
-    requires equivalent<D, D2> &&
-             std::equality_comparable_with<Rep, Rep2>
-  [[nodiscard]] friend constexpr bool operator==(const quantity& lhs, const quantity<D2, U2, Rep2>& rhs)
-  {
-    using cq = common_quantity<quantity, quantity<D2, U2, Rep2>>;
-    return cq(lhs).count() == cq(rhs).count();
-  }
 
   template<class CharT, class Traits>
   friend std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const quantity& q)
+    requires requires { os << q.count(); }
   {
     if(os.width()) {
       // std::setw() applies to the whole quantity output so it has to be first put into std::string
@@ -345,9 +323,82 @@ public:
   }
 };
 
-template<ScalableNumber V>
+// CTAD
+template<QuantityValue V>
 /* implicit */ quantity(V) -> quantity<dim_one, one, V>;
 
+template<Quantity Q1, QuantityEquivalentTo<Q1> Q2>
+  requires quantity_value_for_<std::plus<>, typename Q1::rep, typename Q2::rep>
+[[nodiscard]] constexpr Quantity auto operator+(const Q1& lhs, const Q2& rhs)
+{
+  using ret = common_quantity_for<std::plus<>, Q1, Q2>;
+  return ret(ret(lhs).count() + ret(rhs).count());
+}
+
+template<Quantity Q1, QuantityEquivalentTo<Q1> Q2>
+  requires quantity_value_for_<std::minus<>, typename Q1::rep, typename Q2::rep>
+[[nodiscard]] constexpr Quantity auto operator-(const Q1& lhs, const Q2& rhs)
+{
+  using ret = common_quantity_for<std::minus<>, Q1, Q2>;
+  return ret(ret(lhs).count() - ret(rhs).count());
+}
+
+template<typename D1, typename U1, typename Rep1, typename D2, typename U2, typename Rep2>
+  requires quantity_value_for_<std::multiplies<>, Rep1, Rep2>
+[[nodiscard]] constexpr Quantity auto operator*(const quantity<D1, U1, Rep1>& lhs, const quantity<D2, U2, Rep2>& rhs)
+{
+  using dim = dimension_multiply<D1, D2>;
+  using unit = downcast_unit<dim, (U1::ratio / dimension_unit<D1>::ratio) * (U2::ratio / dimension_unit<D2>::ratio) * dimension_unit<dim>::ratio>;
+  using ret = quantity<dim, unit, std::invoke_result_t<std::multiplies<>, Rep1, Rep2>>;
+  return ret(lhs.count() * rhs.count());
+}
+
+template<typename D1, typename U1, typename Rep1, typename D2, typename U2, typename Rep2>
+  requires quantity_value_for_<std::divides<>, Rep1, Rep2>
+[[nodiscard]] constexpr Quantity auto operator/(const quantity<D1, U1, Rep1>& lhs, const quantity<D2, U2, Rep2>& rhs)
+{
+  // Expects(rhs.count() != zero().count());
+  using dim = dimension_divide<D1, D2>;
+  using unit = downcast_unit<dim, (U1::ratio / dimension_unit<D1>::ratio) / (U2::ratio / dimension_unit<D2>::ratio) * dimension_unit<dim>::ratio>;
+  using ret = quantity<dim, unit, std::invoke_result_t<std::divides<>, Rep1, Rep2>>;
+  return ret(lhs.count() / rhs.count());
+}
+
+template<typename D1, typename U1, typename Rep1, typename U2, typename Rep2>
+  requires (!floating_point_<Rep1>) && (!floating_point_<Rep2>) &&
+          quantity_value_for_<std::modulus<>, Rep1, Rep2>
+[[nodiscard]] constexpr Quantity auto operator%(const quantity<D1, U1, Rep1>& lhs, const quantity<dim_one, U2, Rep2>& rhs)
+{
+  using unit = downcast_unit<D1, U1::ratio * U2::ratio>;
+  using ret = quantity<D1, unit, std::invoke_result_t<std::modulus<>, Rep1, Rep2>>;
+  return ret(lhs.count() % rhs.count());
+}
+
+template<Quantity Q1, QuantityEquivalentTo<Q1> Q2>
+  requires (!floating_point_<typename Q1::rep>) && (!floating_point_<typename Q2::rep>) &&
+          quantity_value_for_<std::modulus<>, typename Q1::rep, typename Q2::rep>
+[[nodiscard]] constexpr Quantity auto operator%(const Q1& lhs, const Q2& rhs)
+{
+  using ret = common_quantity_for<std::modulus<>, Q1, Q2>;
+  return ret(ret(lhs).count() % ret(rhs).count());
+}
+
+template<Quantity Q1, QuantityEquivalentTo<Q1> Q2>
+  requires std::three_way_comparable_with<typename Q1::rep, typename Q2::rep>
+[[nodiscard]] constexpr auto operator<=>(const Q1& lhs, const Q2& rhs)
+{
+  using cq = common_quantity<Q1, Q2>;
+  return cq(lhs).count() <=> cq(rhs).count();
+}
+
+template<Quantity Q1, QuantityEquivalentTo<Q1> Q2>
+  requires std::equality_comparable_with<typename Q1::rep, typename Q2::rep>
+[[nodiscard]] constexpr bool operator==(const Q1& lhs, const Q2& rhs)
+{
+  using cq = common_quantity<Q1, Q2>;
+  return cq(lhs).count() == cq(rhs).count();
+}
+
 namespace detail {
 
 template<typename D, typename U, typename Rep>

src/include/units/quantity_cast.h

@@ -36,10 +36,10 @@
 
 namespace units {
 
-template<Dimension D, UnitOf<D> U, ScalableNumber Rep>
+template<Dimension D, UnitOf<D> U, QuantityValue Rep>
 class quantity;
 
-template<Dimension D, UnitOf<D> U, ScalableNumber Rep>
+template<Dimension D, UnitOf<D> U, QuantityValue Rep>
 class quantity_point;
 
 namespace detail {
@@ -55,232 +55,6 @@ constexpr auto quantity_ratio(const quantity<D, U, Rep>&)
   }
 }
 
-} // namespace detail
-
-// quantity_cast
-namespace detail {
-
-template<typename To, ratio CRatio, typename CRep, bool NumIsOne, bool DenIsOne, bool ExpIsZero>
-struct quantity_cast_impl;
-
-template<typename To, ratio CRatio, typename CRep>
-struct quantity_cast_impl<To, CRatio, CRep, true, true, true> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    return To(static_cast<TYPENAME To::rep>(q.count()));
-  }
-};
-
-template<typename To, ratio CRatio, constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, true, true, false> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    if constexpr (treat_as_floating_point<CRep>) {
-      return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) * static_cast<CRep>(detail::fpow10<CRep>(CRatio.exp))));
-    } else {
-      if constexpr (CRatio.exp > 0) {
-        return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) * static_cast<CRep>(detail::ipow10(CRatio.exp))));
-      }
-      else {
-        return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) / static_cast<CRep>(detail::ipow10(-CRatio.exp))));
-      }
-    }
-  }
-};
-
-template<typename To, ratio CRatio, constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, false, false, true> {
-  template<typename Q>
-  static constexpr To cast(const Q& q)
-  {
-    return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) *
-                                     (static_cast<CRep>(CRatio.num) /
-                                      static_cast<CRep>(CRatio.den))));
-  }
-};
-
-template<typename To, ratio CRatio, constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, false, false, false> {
-  template<typename Q>
-  static constexpr To cast(const Q& q)
-  {
-    if constexpr (treat_as_floating_point<CRep>) {
-      return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) *
-                                     (static_cast<CRep>(detail::fpow10<CRep>(CRatio.exp)) *
-                                     (static_cast<CRep>(CRatio.num) /
-                                      static_cast<CRep>(CRatio.den)))));
-    } else {
-      if constexpr (CRatio.exp > 0) {
-        return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) *
-                                      (static_cast<CRep>(CRatio.num) *
-                                      static_cast<CRep>(detail::ipow10(CRatio.exp)) /
-                                      static_cast<CRep>(CRatio.den))));
-      }
-      else {
-        return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) *
-                                      (static_cast<CRep>(CRatio.num) /
-                                      (static_cast<CRep>(CRatio.den) *
-                                       static_cast<CRep>(detail::ipow10(-CRatio.exp))))));
-      }
-    }
-  }
-};
-
-template<typename To, ratio CRatio, constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, true, false, true> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) / static_cast<CRep>(CRatio.den)));
-  }
-};
-
-template<typename To, ratio CRatio, constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, true, false, false> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    if constexpr (treat_as_floating_point<CRep>) {
-      return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) * (static_cast<CRep>(detail::fpow10<CRep>(CRatio.exp)) * (CRep{1} / static_cast<CRep>(CRatio.den)))));
-    } else {
-      if constexpr (CRatio.exp > 0) {
-        return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) * (static_cast<CRep>(detail::ipow10(CRatio.exp)) / static_cast<CRep>(CRatio.den))));
-      }
-      else {
-        return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) / (static_cast<CRep>(detail::ipow10(-CRatio.exp)) * static_cast<CRep>(CRatio.den))));
-      }
-    }
-  }
-};
-
-template<typename To, ratio CRatio, constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, false, true, true> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) * static_cast<CRep>(CRatio.num)));
-  }
-};
-
-template<typename To, ratio CRatio, constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, false, true, false> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    if constexpr (treat_as_floating_point<CRep>) {
-      return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) * (static_cast<CRep>(CRatio.num) * static_cast<CRep>(detail::fpow10<CRep>(CRatio.exp)))));
-    } else {
-      if constexpr (CRatio.exp > 0) {
-        return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) * (static_cast<CRep>(CRatio.num) * static_cast<CRep>(detail::ipow10(CRatio.exp)))));
-      }
-      else {
-        return To(static_cast<TYPENAME To::rep>(static_cast<CRep>(q.count()) * (static_cast<CRep>(CRatio.num) / static_cast<CRep>(detail::ipow10(-CRatio.exp)))));
-      }
-    }
-  }
-};
-
-template<typename To, ratio CRatio, not_constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, true, true, false> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    if constexpr (treat_as_floating_point<CRep>) {
-      return To(static_cast<TYPENAME To::rep>(q.count() * detail::fpow10<CRep>(CRatio.exp)));
-    } else {
-      if constexpr (CRatio.exp > 0) {
-        return To(static_cast<TYPENAME To::rep>(q.count() * detail::ipow10(CRatio.exp)));
-      }
-      else {
-        return To(static_cast<TYPENAME To::rep>(q.count() / detail::ipow10(-CRatio.exp)));
-      }
-    }
-  }
-};
-
-template<typename To, ratio CRatio, not_constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, false, false, true> {
-  template<typename Q>
-  static constexpr To cast(const Q& q)
-  {
-    return To(static_cast<TYPENAME To::rep>(q.count() * (CRatio.num / CRatio.den)));
-  }
-};
-
-template<typename To, ratio CRatio, not_constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, false, false, false> {
-  template<typename Q>
-  static constexpr To cast(const Q& q)
-  {
-    if constexpr (treat_as_floating_point<CRep>) {
-      return To(static_cast<TYPENAME To::rep>(q.count() * (detail::fpow10<CRep>(CRatio.exp) * (CRatio.num / CRatio.den))));
-    } else {
-      if constexpr (CRatio.exp > 0) {
-        return To(static_cast<TYPENAME To::rep>(q.count() * (CRatio.num * detail::ipow10(CRatio.exp) / CRatio.den)));
-      }
-      else {
-        return To(static_cast<TYPENAME To::rep>(q.count()) * (CRatio.num / (CRatio.den * detail::ipow10(-CRatio.exp))));
-      }
-    }
-  }
-};
-
-template<typename To, ratio CRatio, not_constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, true, false, true> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    return To(static_cast<TYPENAME To::rep>(q.count() / CRatio.den));
-  }
-};
-
-template<typename To, ratio CRatio, not_constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, true, false, false> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    if constexpr (treat_as_floating_point<CRep>) {
-      return To(static_cast<TYPENAME To::rep>(q.count() * (detail::fpow10<CRep>(CRatio.exp) / CRatio.den)));
-    } else {
-      if constexpr (CRatio.exp > 0) {
-        return To(static_cast<TYPENAME To::rep>(q.count() * (detail::ipow10(CRatio.exp) / CRatio.den)));
-      }
-      else {
-        return To(static_cast<TYPENAME To::rep>(q.count() / (detail::ipow10(-CRatio.exp) * CRatio.den)));
-      }
-    }
-  }
-};
-
-template<typename To, ratio CRatio, not_constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, false, true, true> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    return To(static_cast<TYPENAME To::rep>(q.count() * CRatio.num));
-  }
-};
-
-template<typename To, ratio CRatio, not_constructible_from_integral CRep>
-struct quantity_cast_impl<To, CRatio, CRep, false, true, false> {
-  template<Quantity Q>
-  static constexpr To cast(const Q& q)
-  {
-    if constexpr (treat_as_floating_point<CRep>) {
-      return To(static_cast<TYPENAME To::rep>(q.count() * (CRatio.num * detail::fpow10<CRep>(CRatio.exp))));
-    } else {
-      if constexpr (CRatio.exp > 0) {
-        return To(static_cast<TYPENAME To::rep>(q.count() * (CRatio.num * detail::ipow10(CRatio.exp))));
-      }
-      else {
-        return To(static_cast<TYPENAME To::rep>(q.count() * (CRatio.num / detail::ipow10(-CRatio.exp))));
-      }
-    }
-  }
-};
-
 template<typename Q1, typename Q2>
 constexpr ratio cast_ratio(const Q1& from, const Q2& to)
 {
@@ -294,6 +68,26 @@ constexpr ratio cast_ratio(const Q1& from, const Q2& to)
   }
 }
 
+template<typename From, typename To>
+struct cast_traits;
+
+template<typename From, typename To>
+  requires common_type_with_<std::common_type_t<From, To>, std::intmax_t>
+struct cast_traits<From, To> {
+  using ratio_type = std::common_type_t<std::common_type_t<From, To>, std::intmax_t>;
+  using rep_type = ratio_type;
+};
+
+template<typename From, typename To>
+  requires (!common_type_with_<std::common_type_t<From, To>, std::intmax_t>) &&
+          scalable_number_<std::common_type_t<From, To>, std::intmax_t> && 
+          requires { typename std::common_type_t<From, To>::value_type; } &&
+          common_type_with_<typename std::common_type_t<From, To>::value_type, std::intmax_t>
+struct cast_traits<From, To> {
+  using ratio_type = std::common_type_t<typename std::common_type_t<From, To>::value_type, std::intmax_t>;
+  using rep_type = std::common_type_t<From, To>;
+};
+
 }  // namespace detail
 
 /**
@@ -308,16 +102,33 @@ constexpr ratio cast_ratio(const Q1& from, const Q2& to)
  *
  * @tparam To a target quantity type to cast to
  */
-template<Quantity To, typename D, typename U, typename Rep>
+template<Quantity To, typename D, typename U, scalable_with_<typename To::rep> Rep>
   requires QuantityOf<To, D>
 [[nodiscard]] constexpr auto quantity_cast(const quantity<D, U, Rep>& q)
 {
-  using c_ratio = std::integral_constant<ratio, detail::cast_ratio(quantity<D, U, Rep>(), To())>;
-  using c_rep = std::common_type_t<typename To::rep, Rep>;
   using ret_unit = downcast_unit<typename To::dimension, To::unit::ratio>;
   using ret = quantity<typename To::dimension, ret_unit, typename To::rep>;
-  using cast = detail::quantity_cast_impl<ret, c_ratio::value, c_rep, c_ratio::value.num == 1, c_ratio::value.den == 1, c_ratio::value.exp == 0>;
+  using traits = detail::cast_traits<Rep, typename To::rep>;
-  return cast::cast(q);
+  using ratio_type = TYPENAME traits::ratio_type;
+  using rep_type = TYPENAME traits::rep_type;
+  constexpr auto c_ratio = detail::cast_ratio(quantity<D, U, Rep>(), To());
+
+  if constexpr (treat_as_floating_point<rep_type>) {
+    return ret(static_cast<TYPENAME To::rep>(static_cast<rep_type>(q.count()) *
+                              (static_cast<ratio_type>(c_ratio.num) * detail::fpow10<ratio_type>(c_ratio.exp) / static_cast<ratio_type>(c_ratio.den))));
+  }
+  else {
+    if constexpr (c_ratio.exp > 0) {
+      return ret(static_cast<TYPENAME To::rep>(static_cast<rep_type>(q.count()) *
+                              (static_cast<ratio_type>(c_ratio.num) * static_cast<ratio_type>(detail::ipow10(c_ratio.exp))) /
+                              static_cast<ratio_type>(c_ratio.den)));
+    }
+    else {
+      return ret(static_cast<TYPENAME To::rep>(static_cast<rep_type>(q.count()) *
+                              static_cast<ratio_type>(c_ratio.num) /
+                              (static_cast<ratio_type>(c_ratio.den) * static_cast<ratio_type>(detail::ipow10(-c_ratio.exp)))));
+    }
+  }
 }
 
 /**
@@ -393,7 +204,7 @@ template<Dimension ToD, Unit ToU, typename D, typename U, typename Rep>
  *
  * @tparam ToRep a representation type to use for a target quantity
  */
-template<ScalableNumber ToRep, typename D, typename U, typename Rep>
+template<QuantityValue ToRep, typename D, typename U, scalable_with_<ToRep> Rep>
 [[nodiscard]] constexpr auto quantity_cast(const quantity<D, U, Rep>& q)
 {
   return quantity_cast<quantity<D, U, ToRep>>(q);

src/include/units/quantity_point.h

@@ -37,7 +37,7 @@ namespace units {
  * @tparam U a measurement unit of the quantity point
  * @tparam Rep a type to be used to represent values of a quantity point
  */
-template<Dimension D, UnitOf<D> U, ScalableNumber Rep = double>
+template<Dimension D, UnitOf<D> U, QuantityValue Rep = double>
 class quantity_point {
 public:
   using quantity_type = quantity<D, U, Rep>;

test/unit_test/static/CMakeLists.txt

@@ -24,7 +24,9 @@ cmake_minimum_required(VERSION 3.12)
 
 add_library(unit_tests_static
     cgs_test.cpp
-    custom_rep_min_req_test.cpp
+    concepts_test.cpp
+    custom_rep_test_min_expl.cpp
+    custom_rep_test_min_impl.cpp
     custom_unit_test.cpp
     data_test.cpp
     dimension_op_test.cpp

test/unit_test/static/concepts_test.cpp

@@ -0,0 +1,130 @@
+// The MIT License (MIT)
+//
+// Copyright (c) 2018 Mateusz Pusz
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "units/physical/si/cgs/derived/speed.h"
+#include "units/physical/si/derived/speed.h"
+#include "units/physical/si/fps/derived/speed.h"
+#include "units/quantity_point.h"
+#include <chrono>
+#include <complex>
+#include <mutex>
+#include <optional>
+#include <string>
+
+namespace {
+
+using namespace units;
+using namespace units::physical;
+
+// Prefix family
+
+static_assert(PrefixFamily<si::prefix>);
+static_assert(!PrefixFamily<si::kilo>);
+
+// Prefix
+
+static_assert(Prefix<si::kilo>);
+static_assert(!Prefix<si::prefix>);
+static_assert(!Prefix<std::kilo>);
+
+// UnitRatio
+
+static_assert(UnitRatio<ratio(1000)>);
+static_assert(!UnitRatio<ratio(0)>);
+// static_assert(UnitRatio<ratio(1000, 0)>);  // static_assert in ratio
+static_assert(UnitRatio<ratio(-1000, -1)>);
+static_assert(!UnitRatio<ratio(-1000, 1)>);
+static_assert(!UnitRatio<ratio(1, -1000)>);
+
+// BaseDimension
+
+static_assert(BaseDimension<si::dim_length>);
+static_assert(!BaseDimension<si::dim_speed>);
+static_assert(!BaseDimension<int>);
+
+// DerivedDimension
+
+static_assert(DerivedDimension<si::dim_speed>);
+static_assert(!DerivedDimension<si::dim_length>);
+static_assert(!DerivedDimension<int>);
+
+// Dimension
+
+static_assert(Dimension<si::dim_length>);
+static_assert(Dimension<si::dim_speed>);
+static_assert(!Dimension<si::metre>);
+static_assert(!Dimension<int>);
+static_assert(!Dimension<std::chrono::seconds>);
+
+// Unit
+
+static_assert(Unit<si::metre>);
+static_assert(Unit<si::kilometre>);
+static_assert(Unit<si::fps::mile>);
+static_assert(Unit<si::metre_per_second>);
+static_assert(!Unit<si::dim_length>);
+static_assert(!Unit<int>);
+static_assert(!Unit<std::chrono::seconds>);
+
+// UnitOf
+
+static_assert(UnitOf<si::metre, si::dim_length>);
+static_assert(UnitOf<si::kilometre, si::dim_length>);
+static_assert(UnitOf<si::fps::mile, si::dim_length>);
+static_assert(!UnitOf<si::second, si::dim_length>);
+
+// QuantityValue
+
+static_assert(QuantityValue<int>);
+static_assert(QuantityValue<std::complex<double>>);
+static_assert(!QuantityValue<si::length<si::metre>>);
+static_assert(!QuantityValue<std::optional<si::length<si::metre>>>);
+static_assert(!QuantityValue<std::mutex>);
+static_assert(!QuantityValue<std::string>);
+
+// Quantity
+
+static_assert(Quantity<si::length<si::metre>>);
+static_assert(!Quantity<std::chrono::seconds>);
+static_assert(!Quantity<quantity_point<si::dim_length, si::metre>>);
+
+// QuantityPoint
+
+static_assert(QuantityPoint<quantity_point<si::dim_length, si::metre>>);
+static_assert(!QuantityPoint<si::length<si::metre>>);
+static_assert(!QuantityPoint<std::chrono::seconds>);
+
+// WrappedQuantity
+
+static_assert(wrapped_quantity_<std::optional<si::length<si::metre>>>);
+static_assert(!wrapped_quantity_<std::pair<si::length<si::metre>, si::length<si::metre>>>);
+
+// QuantityOf
+
+static_assert(QuantityOf<si::length<si::metre>, si::dim_length>);
+// TODO it seems `QuantityOf` is a bad name if `si::cgs::length<si::cgs::centimetre>` matches `si::fps::dim_length`
+static_assert(QuantityOf<si::cgs::length<si::cgs::centimetre>, si::dim_length>);
+static_assert(QuantityOf<si::cgs::length<si::metre>, si::dim_length>);
+static_assert(QuantityOf<si::cgs::length<si::cgs::centimetre>, si::fps::dim_length>);
+static_assert(!QuantityOf<si::cgs::length<si::cgs::centimetre>, si::dim_time>);
+
+}  // namespace

test/unit_test/static/custom_rep_min_req_test.cpp

@@ -1,251 +0,0 @@
-// The MIT License (MIT)
-//
-// Copyright (c) 2018 Mateusz Pusz
-//
-// Permission is hereby granted, free of charge, to any person obtaining a copy
-// of this software and associated documentation files (the "Software"), to deal
-// in the Software without restriction, including without limitation the rights
-// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-// copies of the Software, and to permit persons to whom the Software is
-// furnished to do so, subject to the following conditions:
-//
-// The above copyright notice and this permission notice shall be included in all
-// copies or substantial portions of the Software.
-//
-// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-// SOFTWARE.
-
-#include "units/math.h"
-#include "units/physical/si/si.h"
-#include <chrono>
-#include <type_traits>
-#include <utility>
-
-using namespace units;
-
-namespace {
-
-template<typename T>
-struct equality_ops {
-  [[nodiscard]] friend constexpr bool operator==(T lhs, T rhs) { return lhs.value_ == rhs.value_; }
-  [[nodiscard]] friend constexpr bool operator!=(T lhs, T rhs) { return !(lhs == rhs); }
-};
-
-template<typename T>
-struct scaling_ops {
-  [[nodiscard]] friend constexpr T operator*(T lhs, T rhs) {
-    return T(lhs.value_ * rhs.value_);
-  }
-  [[nodiscard]] friend constexpr T operator/(T lhs, T rhs) {
-    return T(lhs.value_ / rhs.value_);
-  }
-};
-
-template<typename T>
-struct scalar_ops : equality_ops<T>, scaling_ops<T> {};
-
-template<typename T>
-struct impl_constructible : scalar_ops<impl_constructible<T>> {
-  T value_{};
-  impl_constructible() = default;
-  constexpr impl_constructible(T v) : value_(std::move(v)) {}
-  // no conversion to fundamental arithmetic types
-};
-
-template<typename T>
-using impl = impl_constructible<T>;
-
-template<typename T>
-struct expl_constructible : scalar_ops<expl_constructible<T>> {
-  T value_{};
-  expl_constructible() = default;
-  constexpr explicit expl_constructible(T v) : value_(std::move(v)) {}
-  // no conversion to fundamental arithmetic types
-};
-
-template<typename T>
-using expl = expl_constructible<T>;
-
-template<typename T>
-struct impl_constructible_impl_convertible : scalar_ops<impl_constructible_impl_convertible<T>> /*, int_scaling_ops<impl_constructible_impl_convertible<T>> */ {
-  T value_{};
-  impl_constructible_impl_convertible() = default;
-  constexpr impl_constructible_impl_convertible(T v) : value_(std::move(v)) {}
-  constexpr operator const T&() const& { return value_; }
-};
-
-template<typename T>
-using impl_impl = impl_constructible_impl_convertible<T>;
-
-static_assert(std::convertible_to<float, impl_impl<float>>);
-static_assert(std::convertible_to<impl_impl<float>, float>);
-static_assert(units::ScalableNumber<impl_impl<float>>);
-
-template<typename T>
-struct expl_constructible_impl_convertible : scalar_ops<expl_constructible_impl_convertible<T>> {
-  T value_{};
-  expl_constructible_impl_convertible() = default;
-  constexpr explicit expl_constructible_impl_convertible(T v) : value_(std::move(v)) {}
-  constexpr operator const T&() const& { return value_; }
-};
-
-template<typename T>
-using expl_impl = expl_constructible_impl_convertible<T>;
-
-static_assert(!std::convertible_to<float, expl_impl<float>>);
-static_assert(std::convertible_to<expl_impl<float>, float>);
-static_assert(units::ScalableNumber<expl_impl<float>>);
-
-template<typename T>
-struct impl_constructible_expl_convertible : scalar_ops<impl_constructible_expl_convertible<T>> {
-  T value_{};
-  impl_constructible_expl_convertible() = default;
-  constexpr impl_constructible_expl_convertible(T v) : value_(std::move(v)) {}
-  constexpr explicit operator const T&() const& { return value_; }
-};
-
-template<typename T>
-using impl_expl = impl_constructible_expl_convertible<T>;
-
-static_assert(std::convertible_to<float, impl_expl<float>>);
-static_assert(!std::convertible_to<impl_expl<float>, float>);
-static_assert(units::ScalableNumber<impl_expl<float>>);
-
-template<typename T>
-struct expl_constructible_expl_convertible : scalar_ops<expl_constructible_expl_convertible<T>> {
-  T value_{};
-  expl_constructible_expl_convertible() = default;
-  constexpr explicit expl_constructible_expl_convertible(T v) : value_(std::move(v)) {}
-  constexpr explicit operator const T&() const& { return value_; }
-};
-
-template<typename T>
-using expl_expl = expl_constructible_expl_convertible<T>;
-
-static_assert(!std::convertible_to<float, expl_expl<float>>);
-static_assert(!std::convertible_to<expl_expl<float>, float>);
-static_assert(units::ScalableNumber<expl_expl<float>>);
-
-}  // namespace
-
-namespace units {
-
-template<typename T>
-inline constexpr bool treat_as_floating_point<impl<T>> = std::is_floating_point_v<T>;
-
-template<typename T>
-inline constexpr bool treat_as_floating_point<expl_constructible<T>> = std::is_floating_point_v<T>;
-
-template<typename T>
-inline constexpr bool treat_as_floating_point<impl_impl<T>> = std::is_floating_point_v<T>;
-
-template<typename T>
-inline constexpr bool treat_as_floating_point<expl_impl<T>> = std::is_floating_point_v<T>;
-
-template<typename T>
-inline constexpr bool treat_as_floating_point<impl_expl<T>> = std::is_floating_point_v<T>;
-
-template<typename T>
-inline constexpr bool treat_as_floating_point<expl_expl<T>> = std::is_floating_point_v<T>;
-
-template<typename T>
-struct quantity_values<impl<T>> {
-  static constexpr impl<T> zero() { return 0; }
-  static constexpr impl<T> max() { return std::numeric_limits<T>::max(); }
-  static constexpr impl<T> min() { return std::numeric_limits<T>::lowest(); }
-};
-
-}  // namespace units
-
-namespace {
-
-using namespace units::physical::si;
-
-// constructors
-
-// Quantity from ScalableNumber
-// int <- int
-static_assert(length<metre, int>(expl_impl<int>(1)).count() == 1);
-static_assert(!std::is_constructible_v<length<metre, int>, impl_expl<int>>);
-static_assert(length<metre, int>(int(impl_expl<int>(1))).count() == 1);
-static_assert(!std::is_constructible_v<length<metre, expl_impl<int>>, int>);
-static_assert(length<metre, expl_impl<int>>(expl_impl<int>(1)).count() == expl_impl<int>{1});
-static_assert(length<metre, impl_expl<int>>(1).count() == impl_expl<int>{1});
-
-// double <- double
-static_assert(length<metre, double>(expl_impl<double>(1.0)).count() == 1.0);
-static_assert(!std::is_constructible_v<length<metre, double>, impl_expl<double>>);
-static_assert(length<metre, double>(double(impl_expl<double>(1.0))).count() == 1.0);
-static_assert(!std::is_constructible_v<length<metre, expl_impl<double>>, double>);
-static_assert(length<metre, expl_impl<double>>(expl_impl<double>(1.0)).count() == expl_impl<double>{1.0});
-static_assert(length<metre, impl_expl<double>>(1.0).count() == impl_expl<double>{1.0});
-
-// double <- int
-static_assert(length<metre, double>(expl_impl<int>(1)).count() == 1.0);
-static_assert(!std::is_constructible_v<length<metre, double>, impl_expl<int>>);
-static_assert(length<metre, double>(int(impl_expl<int>(1))).count() == 1.0);
-static_assert(!std::is_constructible_v<length<metre, expl_impl<double>>, int>);
-static_assert(length<metre, expl_impl<double>>(expl_impl<double>(1)).count() == expl_impl<double>{1});
-static_assert(length<metre, impl_expl<double>>(1).count() == impl_expl<double>{1.0});
-
-// int <- double
-static_assert(!std::is_constructible_v<length<metre, int>, expl_impl<double>>);
-static_assert(!std::is_constructible_v<length<metre, impl_expl<int>>, double>);
-
-// Quantity from other Quantity with different Rep
-// int <- int
-static_assert(length<metre, int>(length<metre, expl_impl<int>>(expl_impl<int>(1))).count() == 1);
-static_assert(!std::is_constructible_v<length<metre, int>, length<metre, impl_expl<int>>>);
-static_assert(length<metre, int>(quantity_cast<int>(length<metre, impl_expl<int>>(1))).count() == 1);
-static_assert(!std::is_constructible_v<length<metre, expl_impl<int>>, length<metre, int>>);
-static_assert(length<metre, expl_impl<int>>(quantity_cast<expl_impl<int>>(length<metre, int>(1))).count() == expl_impl<int>{1});
-static_assert(length<metre, impl_expl<int>>(length<metre, int>(1)).count() == impl_expl<int>{1});
-
-// double <- double
-static_assert(length<metre, double>(length<metre, expl_impl<double>>(expl_impl<double>(1.0))).count() == 1.0);
-static_assert(!std::is_constructible_v<length<metre, double>, length<metre, impl_expl<double>>>);
-static_assert(length<metre, double>(quantity_cast<double>(length<metre, impl_expl<double>>(1.0))).count() == 1.0);
-static_assert(!std::is_constructible_v<length<metre, expl_impl<double>>, length<metre, double>>);
-static_assert(length<metre, expl_impl<double>>(quantity_cast<expl_impl<double>>(length<metre>(1.0))).count() == expl_impl<double>{1.0});
-static_assert(length<metre, impl_expl<double>>(length<metre>(1.0)).count() == impl_expl<double>{1.0});
-
-// double <- int
-static_assert(length<metre, double>(length<metre, expl_impl<int>>(expl_impl<int>(1))).count() == 1.0);
-static_assert(!std::is_constructible_v<length<metre, double>, length<metre, impl_expl<int>>>);
-static_assert(length<metre, double>(quantity_cast<int>(length<metre, impl_expl<int>>(1))).count() == 1.0);
-static_assert(!std::is_constructible_v<length<metre, expl_impl<double>>, length<metre, int>>);
-static_assert(length<metre, expl_impl<double>>(quantity_cast<expl_impl<double>>(length<metre, int>(1))).count() == expl_impl<double>{1});
-static_assert(length<metre, impl_expl<double>>(length<metre, int>(1)).count() == impl_expl<double>{1.0});
-
-// int <- double
-static_assert(!std::is_constructible_v<length<metre, int>, length<metre, expl_impl<double>>>);
-static_assert(!std::is_constructible_v<length<metre, impl_expl<int>>, length<metre, double>>);
-
-// unit conversions
-
-static_assert(length<metre, impl<int>>(length<kilometre, impl<int>>(1)).count() == impl<int>(1000));
-static_assert(length<metre, expl<int>>(length<kilometre, expl<int>>(expl<int>(1))).count() == expl<int>(1000));
-static_assert(length<metre, impl_impl<int>>(length<kilometre, impl_impl<int>>(1)).count() == impl_impl<int>(1000));
-static_assert(length<metre, impl_expl<int>>(length<kilometre, impl_expl<int>>(1)).count() == impl_expl<int>(1000));
-static_assert(length<metre, expl_impl<int>>(length<kilometre, expl_impl<int>>(expl_impl<int>(1))).count() == expl_impl<int>(1000));
-static_assert(length<metre, expl_expl<int>>(length<kilometre, expl_expl<int>>(expl_expl<int>(1))).count() == expl_expl<int>(1000));
-
-static_assert(!std::is_constructible_v<length<kilometre, impl<int>>, length<metre, impl<int>>>);
-static_assert(length<kilometre, impl<int>>(quantity_cast<kilometre>(length<metre, impl<int>>(2000))).count() == impl<int>(2));
-static_assert(!std::is_constructible_v<length<kilometre, expl<int>>, length<metre, expl<int>>>);
-static_assert(length<kilometre, expl<int>>(quantity_cast<kilometre>(length<metre, expl<int>>(expl<int>(2000)))).count() == expl<int>(2));
-static_assert(!std::is_constructible_v<length<kilometre, impl_impl<int>>, length<metre, impl_impl<int>>>);
-static_assert(length<kilometre, impl_impl<int>>(quantity_cast<kilometre>(length<metre, impl_impl<int>>(2000))).count() == impl_impl<int>(2));
-static_assert(!std::is_constructible_v<length<kilometre, impl_expl<int>>, length<metre, impl_expl<int>>>);
-static_assert(length<kilometre, impl_expl<int>>(quantity_cast<kilometre>(length<metre, impl_expl<int>>(2000))).count() == impl_expl<int>(2));
-static_assert(!std::is_constructible_v<length<kilometre, expl_impl<int>>, length<metre, expl_impl<int>>>);
-static_assert(length<kilometre, expl_impl<int>>(quantity_cast<kilometre>(length<metre, expl_impl<int>>(expl_impl<int>(2000)))).count() == expl_impl<int>(2));
-static_assert(!std::is_constructible_v<length<kilometre, expl_expl<int>>, length<metre, expl_expl<int>>>);
-static_assert(length<kilometre, expl_expl<int>>(quantity_cast<kilometre>(length<metre, expl_expl<int>>(expl_expl<int>(2000)))).count() == expl_expl<int>(2));
-
-}  // namespace

test/unit_test/static/custom_rep_test_min_expl.cpp

@@ -0,0 +1,199 @@
+// The MIT License (MIT)
+//
+// Copyright (c) 2018 Mateusz Pusz
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "units/physical/si/base/length.h"
+
+namespace {
+
+/**
+ * @brief Representation type meeting minimum requirements
+ * 
+ * This type with a default Mode = 0 provides the minimum set of requirements to
+ * satisfy @c QuantityValue concept which is used for quantity's representation type.
+ * 
+ * In case of Mode != 0 only one of mandatory operation is removed which should
+ * result in @c QuantityValue concept not being satisfied.
+ * 
+ * @tparam Mode a flag to disable specific type's operations
+ */
+template<int Mode = 0>
+class min_expl {
+  std::intmax_t value_;
+public:
+  // default construction
+  min_expl() requires (Mode != 1) = default;
+
+  // construction from std::int64_t
+  explicit constexpr min_expl(std::intmax_t v) noexcept requires (Mode != 2) : value_(v) {}
+
+  // copy construction
+  min_expl(const min_expl&) requires (Mode != 3) = default;
+
+  // move construction
+  min_expl(min_expl&&) requires (Mode != 4) = default;
+  min_expl(min_expl&&) requires (Mode == 4) = delete;
+
+  // copy assignment
+  min_expl& operator=(const min_expl&) requires (Mode != 5) = default;
+
+  // move assignment
+  min_expl& operator=(min_expl&&) requires (Mode != 6) = default;
+  min_expl& operator=(min_expl&&) requires (Mode == 6) = delete;
+
+  // equality
+  bool operator==(const min_expl&) const requires (Mode != 7) = default;
+
+  // scalability - multiplication
+  friend constexpr min_expl operator*(const min_expl& lhs, const min_expl& rhs) requires (Mode != 8)
+  { return min_expl(lhs.value_ * rhs.value_); }
+
+  // scalability - division
+  friend constexpr min_expl operator/(const min_expl& lhs, const min_expl& rhs) requires (Mode != 9)
+  { return min_expl(lhs.value_ / rhs.value_); }
+};
+
+}
+
+template<int Mode>
+struct std::common_type<std::intmax_t, min_expl<Mode>> : std::type_identity<min_expl<Mode>> {};
+template<int Mode>
+struct std::common_type<min_expl<Mode>, std::intmax_t> : std::type_identity<min_expl<Mode>> {};
+
+namespace {
+
+using namespace units;
+using namespace units::physical::si;
+
+// quantity explicitly constructible (not convertible) from the representation type
+static_assert(std::constructible_from<length<metre, min_expl<>>, min_expl<>>);
+static_assert(!std::convertible_to<min_expl<>, length<metre, min_expl<>>>);
+
+// not constructible from an underlying type
+static_assert(!std::constructible_from<length<metre, min_expl<>>, int>);
+static_assert(!std::convertible_to<int, length<metre, min_expl<>>>);
+
+// dimensionless quantity implicitly convertible from the representation type
+static_assert(std::constructible_from<dimensionless<one, min_expl<>>, min_expl<>>);
+static_assert(std::convertible_to<min_expl<>, dimensionless<one, min_expl<>>>);
+
+// but not from an underlying type
+static_assert(!std::constructible_from<dimensionless<one, min_expl<>>, int>);
+static_assert(!std::convertible_to<int, dimensionless<one, min_expl<>>>);
+
+// or for ratio != 1
+static_assert(std::constructible_from<dimensionless<percent, min_expl<>>, min_expl<>>);
+static_assert(!std::convertible_to<min_expl<>, dimensionless<percent, min_expl<>>>);
+
+// quantity convertible from itself
+static_assert(std::constructible_from<length<metre, min_expl<>>, length<metre, min_expl<>>>);
+static_assert(std::convertible_to<length<metre, min_expl<>>, length<metre, min_expl<>>>);
+
+// not convertible from an underlying type
+static_assert(!std::constructible_from<length<metre, min_expl<>>, length<metre, int>>);
+static_assert(!std::convertible_to<length<metre, int>, length<metre, min_expl<>>>);
+
+// quantity convertible from another non truncating unit
+static_assert(std::constructible_from<length<metre, min_expl<>>, length<kilometre, min_expl<>>>);
+static_assert(std::convertible_to<length<kilometre, min_expl<>>, length<metre, min_expl<>>>);
+
+// quantity not convertible from another truncating unit
+static_assert(!std::constructible_from<length<kilometre, min_expl<>>, length<metre, min_expl<>>>);
+static_assert(!std::convertible_to<length<metre, min_expl<>>, length<kilometre, min_expl<>>>);
+
+// rep type with explicit constructor - implicit construction of rep not allowed
+static_assert(!std::constructible_from<length<metre, min_expl<>>, int>);
+static_assert(!std::convertible_to<int, length<metre, min_expl<>>>);
+
+static_assert(!std::constructible_from<length<metre, min_expl<>>, length<metre, int>>);
+static_assert(!std::convertible_to<length<metre, int>, length<metre, min_expl<>>>);
+
+static_assert(!std::constructible_from<length<metre, int>, min_expl<>>);
+static_assert(!std::convertible_to<min_expl<>, length<metre, int>>);
+
+static_assert(!std::constructible_from<length<metre, int>, length<metre, min_expl<>>>);
+static_assert(!std::convertible_to<length<metre, min_expl<>>, length<metre, int>>);
+
+// all operations needed to satisfy concept
+static_assert(QuantityValue<min_expl<>>);
+static_assert(!QuantityValue<min_expl<1>>);
+static_assert(!QuantityValue<min_expl<2>>);
+static_assert(!QuantityValue<min_expl<3>>);
+static_assert(!QuantityValue<min_expl<4>>);
+static_assert(!QuantityValue<min_expl<5>>);
+static_assert(!QuantityValue<min_expl<6>>);
+static_assert(!QuantityValue<min_expl<7>>);
+static_assert(!QuantityValue<min_expl<8>>);
+static_assert(!QuantityValue<min_expl<9>>);
+
+// quantity's operators should mirror the representation type capabilities
+template<typename Rep>
+concept invalid_member_operations = requires(length<metre, Rep> lhs) {
+  requires !requires { +lhs; };
+  requires !requires { -lhs; };
+  requires !requires { ++lhs; };
+  requires !requires { lhs++; };
+  requires !requires { --lhs; };
+  requires !requires { lhs--; };
+
+  requires !requires(length<metre, Rep> rhs) { lhs += rhs; };
+  requires !requires(length<metre, Rep> rhs) { lhs -= rhs; };
+  requires !requires(Rep rhs) { lhs *= rhs; };
+  requires !requires(Rep rhs) { lhs /= rhs; };
+  requires !requires(Rep rhs) { lhs %= rhs; };
+  requires !requires(length<metre, Rep> rhs) { lhs %= rhs; };
+
+  requires !requires(length<metre, Rep> rhs) { lhs + rhs; };
+  requires !requires(length<metre, Rep> rhs) { lhs - rhs; };
+  requires !requires(Rep rhs) { lhs % rhs; };
+  requires !requires(length<metre, Rep> rhs) { lhs % rhs; };
+  requires !requires(length<metre, Rep> rhs) { lhs < rhs; };
+  requires !requires(length<metre, Rep> rhs) { lhs > rhs; };
+  requires !requires(length<metre, Rep> rhs) { lhs <= rhs; };
+  requires !requires(length<metre, Rep> rhs) { lhs >= rhs; };
+
+  requires !requires(length<metre, int> rhs) { lhs + rhs; };
+  requires !requires(length<metre, int> rhs) { lhs - rhs; };
+  requires !requires(int rhs) { lhs % rhs; };
+  requires !requires(length<metre, int> rhs) { lhs % rhs; };
+  requires !requires(length<metre, int> rhs) { lhs == rhs; };
+  requires !requires(length<metre, int> rhs) { lhs != rhs; };
+  requires !requires(length<metre, int> rhs) { lhs < rhs; };
+  requires !requires(length<metre, int> rhs) { lhs > rhs; };
+  requires !requires(length<metre, int> rhs) { lhs <= rhs; };
+  requires !requires(length<metre, int> rhs) { lhs >= rhs; };
+
+  requires !requires(std::ostream os) { os << lhs; };
+};
+static_assert(invalid_member_operations<min_expl<>>);
+
+// equality
+static_assert(length<kilometre, min_expl<>>(min_expl<>(2)) == length<metre, min_expl<>>(min_expl<>(2000)));
+static_assert(length<metre, min_expl<>>(min_expl<>(123)) * min_expl<>(2) == length<metre, min_expl<>>(min_expl<>(246)));
+static_assert(length<metre, min_expl<>>(min_expl<>(123)) * quantity{min_expl<>(2)} == length<metre, min_expl<>>(min_expl<>(246)));
+static_assert(min_expl<>(2) * length<metre, min_expl<>>(min_expl<>(123)) == length<metre, min_expl<>>(min_expl<>(246)));
+static_assert(quantity{min_expl<>(2)} * length<metre, min_expl<>>(min_expl<>(123)) == length<metre, min_expl<>>(min_expl<>(246)));
+static_assert(length<metre, min_expl<>>(min_expl<>(246)) / min_expl<>(2) == length<metre, min_expl<>>(min_expl<>(123)));
+static_assert(length<metre, min_expl<>>(min_expl<>(246)) / quantity{min_expl<>(2)} == length<metre, min_expl<>>(min_expl<>(123)));
+static_assert(length<metre, min_expl<>>(min_expl<>(246)) / length<metre, min_expl<>>(min_expl<>(2)) == quantity{min_expl<>(123)});
+static_assert(length<metre, min_expl<>>(min_expl<>(246)) / length<metre, min_expl<>>(min_expl<>(2)) == min_expl<>(123));
+
+}  // namespace

test/unit_test/static/custom_rep_test_min_impl.cpp

@@ -0,0 +1,317 @@
+// The MIT License (MIT)
+//
+// Copyright (c) 2018 Mateusz Pusz
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "units/math.h"
+#include "units/physical/si/base/length.h"
+#include <chrono>
+#include <type_traits>
+#include <utility>
+
+namespace {
+
+/**
+ * @brief Implicitly constructible and convertible representation type
+ * 
+ * A wrapper type that is implicitly convertible from and to the contained type.
+ * 
+ * @tparam T element type
+ */
+template<typename T>
+class min_impl {
+  T value_;
+public:
+  using value_type = T;
+
+  min_impl() = default;
+  constexpr min_impl(T v) noexcept : value_(v) {}
+  template<typename U>
+  constexpr min_impl(min_impl<U> i) noexcept : value_(static_cast<T>(i.value_)) {}
+  constexpr operator T() const noexcept { return value_; }
+};
+
+}
+
+template<typename T, typename U>
+struct std::common_type<min_impl<T>, min_impl<U>> : std::common_type<T, U> {};
+template<typename T, typename U>
+struct std::common_type<min_impl<T>, U> : std::common_type<T, U> {};
+template<typename U, typename T>
+struct std::common_type<U, min_impl<T>> : std::common_type<T, U> {};
+
+namespace {
+
+using namespace units;
+using namespace units::physical::si;
+
+static_assert(QuantityValue<min_impl<int>>);
+static_assert(QuantityValue<min_impl<double>>);
+
+// construction from a value
+static_assert(std::constructible_from<length<metre, min_impl<int>>, min_impl<int>>);
+static_assert(!std::convertible_to<min_impl<int>, length<metre, min_impl<int>>>);
+
+static_assert(std::constructible_from<length<metre, min_impl<double>>, min_impl<double>>);
+static_assert(!std::convertible_to<min_impl<double>, length<metre, min_impl<double>>>);
+
+static_assert(std::constructible_from<length<metre, min_impl<double>>, min_impl<int>>);
+static_assert(!std::convertible_to<min_impl<int>, length<metre, min_impl<double>>>);
+
+static_assert(!std::constructible_from<length<metre, min_impl<int>>, min_impl<double>>);  // narrowing conversion
+static_assert(!std::convertible_to<min_impl<double>, length<metre, min_impl<int>>>);
+
+// construction from an underlying type
+static_assert(std::constructible_from<length<metre, min_impl<int>>, int>);
+static_assert(!std::convertible_to<int, length<metre, min_impl<int>>>);
+
+static_assert(std::constructible_from<length<metre, min_impl<double>>, double>);
+static_assert(!std::convertible_to<double, length<metre, min_impl<double>>>);
+
+static_assert(std::constructible_from<length<metre, min_impl<double>>, int>);
+static_assert(!std::convertible_to<int, length<metre, min_impl<double>>>);
+
+static_assert(!std::constructible_from<length<metre, min_impl<int>>, double>);  // narrowing conversion
+static_assert(!std::convertible_to<double, length<metre, min_impl<int>>>);
+
+// dimensionless quantity is convertible from a value
+static_assert(std::constructible_from<dimensionless<one, min_impl<int>>, min_impl<int>>);
+static_assert(std::convertible_to<min_impl<int>, dimensionless<one, min_impl<int>>>);
+
+static_assert(std::constructible_from<dimensionless<one, min_impl<double>>, min_impl<double>>);
+static_assert(std::convertible_to<min_impl<double>, dimensionless<one, min_impl<double>>>);
+
+static_assert(std::constructible_from<dimensionless<one, min_impl<double>>, min_impl<int>>);
+static_assert(std::convertible_to<min_impl<int>, dimensionless<one, min_impl<double>>>);
+
+static_assert(!std::constructible_from<dimensionless<one, min_impl<int>>, min_impl<double>>);  // narrowing conversion
+static_assert(!std::convertible_to<min_impl<double>, dimensionless<one, min_impl<int>>>);
+
+// and underlying type
+static_assert(std::constructible_from<dimensionless<one, min_impl<int>>, int>);
+static_assert(std::convertible_to<int, dimensionless<one, min_impl<int>>>);
+
+static_assert(std::constructible_from<dimensionless<one, min_impl<double>>, double>);
+static_assert(std::convertible_to<double, dimensionless<one, min_impl<double>>>);
+
+static_assert(std::constructible_from<dimensionless<one, min_impl<double>>, int>);
+static_assert(std::convertible_to<int, dimensionless<one, min_impl<double>>>);
+
+static_assert(!std::constructible_from<dimensionless<one, min_impl<int>>, double>);  // narrowing conversion
+static_assert(!std::convertible_to<double, dimensionless<one, min_impl<int>>>);
+
+// but only for ratio(1), otherwise not convertible
+static_assert(std::constructible_from<dimensionless<percent, min_impl<int>>, min_impl<int>>);
+static_assert(!std::convertible_to<min_impl<int>, dimensionless<percent, min_impl<int>>>);
+
+static_assert(std::constructible_from<dimensionless<percent, min_impl<double>>, min_impl<double>>);
+static_assert(!std::convertible_to<min_impl<double>, dimensionless<percent, min_impl<double>>>);
+
+static_assert(std::constructible_from<dimensionless<percent, min_impl<double>>, min_impl<int>>);
+static_assert(!std::convertible_to<min_impl<int>, dimensionless<percent, min_impl<double>>>);
+
+static_assert(!std::constructible_from<dimensionless<percent, min_impl<int>>, min_impl<double>>);  // narrowing conversion
+static_assert(!std::convertible_to<min_impl<double>, dimensionless<percent, min_impl<int>>>);
+
+// implicit conversion tests
+static_assert(std::constructible_from<length<metre, int>, min_impl<int>>);
+static_assert(!std::convertible_to<min_impl<int>, length<metre, int>>);
+
+static_assert(std::constructible_from<length<metre, double>, min_impl<double>>);
+static_assert(!std::convertible_to<min_impl<double>, length<metre, double>>);
+
+static_assert(std::constructible_from<length<metre, double>, min_impl<int>>);
+static_assert(!std::convertible_to<min_impl<int>, length<metre, double>>);
+
+static_assert(!std::constructible_from<length<metre, int>, min_impl<double>>);  // narrowing conversion
+static_assert(!std::convertible_to<min_impl<double>, length<metre, int>>);
+
+// construction from an underlying type
+static_assert(std::constructible_from<length<metre, int>, min_impl<int>>);
+static_assert(!std::convertible_to<min_impl<int>, length<metre, int>>);
+
+static_assert(std::constructible_from<length<metre, double>, min_impl<double>>);
+static_assert(!std::convertible_to<min_impl<double>, length<metre, double>>);
+
+static_assert(std::constructible_from<length<metre, double>, min_impl<int>>);
+static_assert(!std::convertible_to<min_impl<int>, length<metre, double>>);
+
+static_assert(!std::constructible_from<length<metre, int>, min_impl<double>>);  // narrowing conversion
+static_assert(!std::convertible_to<min_impl<double>, length<metre, int>>);
+
+// dimensionless quantity is convertible from a value
+static_assert(std::constructible_from<dimensionless<one, int>, min_impl<int>>);
+static_assert(std::convertible_to<min_impl<int>, dimensionless<one, int>>);
+
+static_assert(std::constructible_from<dimensionless<one, double>, min_impl<double>>);
+static_assert(std::convertible_to<min_impl<double>, dimensionless<one, double>>);
+
+static_assert(std::constructible_from<dimensionless<one, double>, min_impl<int>>);
+static_assert(std::convertible_to<min_impl<int>, dimensionless<one, double>>);
+
+static_assert(!std::constructible_from<dimensionless<one, int>, min_impl<double>>);  // narrowing conversion
+static_assert(!std::convertible_to<min_impl<double>, dimensionless<one, int>>);
+
+// but only for ratio(1), otherwise not convertible
+static_assert(std::constructible_from<dimensionless<percent, int>, min_impl<int>>);
+static_assert(!std::convertible_to<min_impl<int>, dimensionless<percent, int>>);
+
+static_assert(std::constructible_from<dimensionless<percent, double>, min_impl<double>>);
+static_assert(!std::convertible_to<min_impl<double>, dimensionless<percent, double>>);
+
+static_assert(std::constructible_from<dimensionless<percent, double>, min_impl<int>>);
+static_assert(!std::convertible_to<min_impl<int>, dimensionless<percent, double>>);
+
+static_assert(!std::constructible_from<dimensionless<percent, int>, min_impl<double>>);  // narrowing conversion
+static_assert(!std::convertible_to<min_impl<double>, dimensionless<percent, int>>);
+
+// construction from a quantity
+// min_impl<T> -> min_impl<T>
+static_assert(std::constructible_from<length<metre, min_impl<int>>, length<metre, min_impl<int>>>);
+static_assert(std::convertible_to<length<metre, min_impl<int>>, length<metre, min_impl<int>>>);
+
+static_assert(std::constructible_from<length<metre, min_impl<double>>, length<metre, min_impl<double>>>);
+static_assert(std::convertible_to<length<metre, min_impl<double>>, length<metre, min_impl<double>>>);
+
+static_assert(std::constructible_from<length<metre, min_impl<double>>, length<metre, min_impl<int>>>);
+static_assert(std::convertible_to<length<metre, min_impl<int>>, length<metre, min_impl<double>>>);
+
+static_assert(!std::constructible_from<length<metre, min_impl<int>>, length<metre, min_impl<double>>>); // narrowing conversion
+static_assert(!std::convertible_to<length<metre, min_impl<double>>, length<metre, min_impl<int>>>);
+
+// T -> min_impl<T>
+static_assert(std::constructible_from<length<metre, min_impl<int>>, length<metre, int>>);
+static_assert(std::convertible_to<length<metre, int>, length<metre, min_impl<int>>>);
+
+static_assert(std::constructible_from<length<metre, min_impl<double>>, length<metre, double>>);
+static_assert(std::convertible_to<length<metre, double>, length<metre, min_impl<double>>>);
+
+static_assert(std::constructible_from<length<metre, min_impl<double>>, length<metre, int>>);
+static_assert(std::convertible_to<length<metre, int>, length<metre, min_impl<double>>>);
+
+static_assert(!std::constructible_from<length<metre, min_impl<int>>, length<metre, double>>); // narrowing conversion
+static_assert(!std::convertible_to<length<metre, double>, length<metre, min_impl<int>>>);
+
+// min_impl<T> -> T
+static_assert(std::constructible_from<length<metre, int>, length<metre, min_impl<int>>>);
+static_assert(std::convertible_to<length<metre, min_impl<int>>, length<metre, int>>);
+
+static_assert(std::constructible_from<length<metre, double>, length<metre, min_impl<double>>>);
+static_assert(std::convertible_to<length<metre, min_impl<double>>, length<metre, double>>);
+
+static_assert(std::constructible_from<length<metre, double>, length<metre, min_impl<int>>>);
+static_assert(std::convertible_to<length<metre, min_impl<int>>, length<metre, double>>);
+
+static_assert(!std::constructible_from<length<metre, int>, length<metre, min_impl<double>>>); // narrowing conversion
+static_assert(!std::convertible_to<length<metre, min_impl<double>>, length<metre, int>>);
+
+
+// arithmetic operators
+static_assert(length<metre, min_impl<int>>(1) + length<metre, min_impl<int>>(1) == length<metre, min_impl<int>>(2));
+static_assert(length<metre, min_impl<int>>(1) + length<metre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(2.5));
+static_assert(length<metre, int>(1) + length<metre, min_impl<int>>(1) == length<metre, min_impl<int>>(2));
+static_assert(length<metre, int>(1) + length<metre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(2.5));
+static_assert(length<metre, min_impl<int>>(1) + length<metre, int>(1) == length<metre, min_impl<int>>(2));
+static_assert(length<metre, min_impl<int>>(1) + length<metre, double>(1.5) == length<metre, min_impl<double>>(2.5));
+static_assert(length<metre, min_impl<int>>(1) + length<metre, min_impl<int>>(1) == length<metre, int>(2));
+static_assert(length<metre, min_impl<int>>(1) + length<metre, min_impl<double>>(1.5) == length<metre, double>(2.5));
+
+static_assert(length<kilometre, min_impl<int>>(1) + length<metre, min_impl<int>>(1) == length<metre, min_impl<int>>(1001));
+static_assert(length<kilometre, min_impl<int>>(1) + length<metre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(1001.5));
+static_assert(length<kilometre, int>(1) + length<metre, min_impl<int>>(1) == length<metre, min_impl<int>>(1001));
+static_assert(length<kilometre, int>(1) + length<metre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(1001.5));
+static_assert(length<kilometre, min_impl<int>>(1) + length<metre, int>(1) == length<metre, min_impl<int>>(1001));
+static_assert(length<kilometre, min_impl<int>>(1) + length<metre, double>(1.5) == length<metre, min_impl<double>>(1001.5));
+static_assert(length<kilometre, min_impl<int>>(1) + length<metre, min_impl<int>>(1) == length<metre, int>(1001));
+static_assert(length<kilometre, min_impl<int>>(1) + length<metre, min_impl<double>>(1.5) == length<metre, double>(1001.5));
+
+static_assert(length<metre, min_impl<int>>(1) + length<kilometre, min_impl<int>>(1) == length<metre, min_impl<int>>(1001));
+static_assert(length<metre, min_impl<int>>(1) + length<kilometre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(1501));
+static_assert(length<metre, int>(1) + length<kilometre, min_impl<int>>(1) == length<metre, min_impl<int>>(1001));
+static_assert(length<metre, int>(1) + length<kilometre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(1501));
+static_assert(length<metre, min_impl<int>>(1) + length<kilometre, int>(1) == length<metre, min_impl<int>>(1001));
+static_assert(length<metre, min_impl<int>>(1) + length<kilometre, double>(1.5) == length<metre, min_impl<double>>(1501));
+static_assert(length<metre, min_impl<int>>(1) + length<kilometre, min_impl<int>>(1) == length<metre, int>(1001));
+static_assert(length<metre, min_impl<int>>(1) + length<kilometre, min_impl<double>>(1.5) == length<metre, double>(1501));
+
+static_assert(length<metre, min_impl<int>>(2) - length<metre, min_impl<int>>(1) == length<metre, min_impl<int>>(1));
+static_assert(length<metre, min_impl<int>>(2) - length<metre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(0.5));
+static_assert(length<metre, int>(2) - length<metre, min_impl<int>>(1) == length<metre, min_impl<int>>(1));
+static_assert(length<metre, int>(2) - length<metre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(0.5));
+static_assert(length<metre, min_impl<int>>(2) - length<metre, int>(1) == length<metre, min_impl<int>>(1));
+static_assert(length<metre, min_impl<int>>(2) - length<metre, double>(1.5) == length<metre, min_impl<double>>(0.5));
+static_assert(length<metre, min_impl<int>>(2) - length<metre, min_impl<int>>(1) == length<metre, int>(1));
+static_assert(length<metre, min_impl<int>>(2) - length<metre, min_impl<double>>(1.5) == length<metre, double>(0.5));
+
+static_assert(length<kilometre, min_impl<int>>(2) - length<metre, min_impl<int>>(1) == length<metre, min_impl<int>>(1999));
+static_assert(length<kilometre, min_impl<int>>(2) - length<metre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(1998.5));
+static_assert(length<kilometre, int>(2) - length<metre, min_impl<int>>(1) == length<metre, min_impl<int>>(1999));
+static_assert(length<kilometre, int>(2) - length<metre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(1998.5));
+static_assert(length<kilometre, min_impl<int>>(2) - length<metre, int>(1) == length<metre, min_impl<int>>(1999));
+static_assert(length<kilometre, min_impl<int>>(2) - length<metre, double>(1.5) == length<metre, min_impl<double>>(1998.5));
+static_assert(length<kilometre, min_impl<int>>(2) - length<metre, min_impl<int>>(1) == length<metre, int>(1999));
+static_assert(length<kilometre, min_impl<int>>(2) - length<metre, min_impl<double>>(1.5) == length<metre, double>(1998.5));
+
+static_assert(length<metre, min_impl<int>>(2000) - length<kilometre, min_impl<int>>(1) == length<metre, min_impl<int>>(1000));
+static_assert(length<metre, min_impl<int>>(2000) - length<kilometre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(500));
+static_assert(length<metre, int>(2000) - length<kilometre, min_impl<int>>(1) == length<metre, min_impl<int>>(1000));
+static_assert(length<metre, int>(2000) - length<kilometre, min_impl<double>>(1.5) == length<metre, min_impl<double>>(500));
+static_assert(length<metre, min_impl<int>>(2000) - length<kilometre, int>(1) == length<metre, min_impl<int>>(1000));
+static_assert(length<metre, min_impl<int>>(2000) - length<kilometre, double>(1.5) == length<metre, min_impl<double>>(500));
+static_assert(length<metre, min_impl<int>>(2000) - length<kilometre, min_impl<int>>(1) == length<metre, int>(1000));
+static_assert(length<metre, min_impl<int>>(2000) - length<kilometre, min_impl<double>>(1.5) == length<metre, double>(500));
+
+static_assert(length<metre, min_impl<int>>(123) * min_impl<double>(1.5) == length<metre, min_impl<double>>(184.5));
+static_assert(length<metre, min_impl<int>>(123) * 1.5 == length<metre, min_impl<double>>(184.5));
+static_assert(length<metre, int>(123) * min_impl<double>(1.5) == length<metre, min_impl<double>>(184.5));
+
+static_assert(length<metre, min_impl<int>>(123) * quantity{min_impl<double>(1.5)} == length<metre, min_impl<double>>(184.5));
+static_assert(length<metre, min_impl<int>>(123) * quantity{1.5} == length<metre, min_impl<double>>(184.5));
+static_assert(length<metre, int>(123) * quantity{min_impl<double>(1.5)} == length<metre, min_impl<double>>(184.5));
+
+static_assert(min_impl<double>(1.5) * length<metre, min_impl<int>>(123) == length<metre, min_impl<double>>(184.5));
+static_assert(min_impl<double>(1.5) * length<metre, int>(123) == length<metre, min_impl<double>>(184.5));
+static_assert(1.5 * length<metre, min_impl<int>>(123) == length<metre, min_impl<double>>(184.5));
+
+static_assert(quantity{min_impl<double>(1.5)} * length<metre, min_impl<int>>(123) == length<metre, min_impl<double>>(184.5));
+static_assert(quantity{min_impl<double>(1.5)} * length<metre, int>(123) == length<metre, min_impl<double>>(184.5));
+static_assert(quantity{1.5} * length<metre, min_impl<int>>(123) == length<metre, min_impl<double>>(184.5));
+
+static_assert(length<metre, min_impl<int>>(123) / min_impl<double>(2.) == length<metre, min_impl<double>>(61.5));
+static_assert(length<metre, min_impl<int>>(123) / 2. == length<metre, min_impl<double>>(61.5));
+static_assert(length<metre, int>(123) / min_impl<double>(2.) == length<metre, min_impl<double>>(61.5));
+
+static_assert(length<metre, min_impl<int>>(123) / quantity{min_impl<double>(2.)} == length<metre, min_impl<double>>(61.5));
+static_assert(length<metre, min_impl<int>>(123) / quantity{2.} == length<metre, min_impl<double>>(61.5));
+static_assert(length<metre, int>(123) / quantity{min_impl<double>(2.)} == length<metre, min_impl<double>>(61.5));
+
+static_assert(length<metre, min_impl<int>>(123) / length<metre, min_impl<double>>(2.) == 61.5);
+static_assert(length<metre, min_impl<int>>(123) / length<metre, double>(2.) == 61.5);
+static_assert(length<metre, int>(123) / length<metre, min_impl<double>>(2.) == 61.5);
+
+static_assert(length<metre, min_impl<int>>(123) % min_impl<int>(100) == length<metre, int>(23));
+static_assert(length<metre, min_impl<int>>(123) % 100 == length<metre, int>(23));
+static_assert(length<metre, int>(123) % min_impl<int>(100) == length<metre, int>(23));
+
+static_assert(length<metre, min_impl<int>>(123) % quantity{min_impl<int>(100)} == length<metre, int>(23));
+static_assert(length<metre, min_impl<int>>(123) % quantity{100} == length<metre, int>(23));
+static_assert(length<metre, int>(123) % quantity{min_impl<int>(100)} == length<metre, int>(23));
+
+}  // namespace

test/unit_test/static/custom_unit_test.cpp

@@ -36,14 +36,14 @@ using namespace units::physical::si;
 struct sq_volt_per_hertz : unit<sq_volt_per_hertz> {};
 struct dim_power_spectral_density : derived_dimension<dim_power_spectral_density, sq_volt_per_hertz, units::exponent<dim_voltage, 2>, units::exponent<dim_frequency, -1>> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_power_spectral_density> U, QuantityValue Rep = double>
 using power_spectral_density = quantity<dim_power_spectral_density, U, Rep>;
 
 // amplitude spectral density
 struct volt_per_sqrt_hertz : unit<volt_per_sqrt_hertz> {};
 struct dim_amplitude_spectral_density : derived_dimension<dim_amplitude_spectral_density, volt_per_sqrt_hertz, units::exponent<dim_voltage, 1>, units::exponent<dim_frequency, -1, 2>> {};
 
-template<Unit U, ScalableNumber Rep = double>
+template<UnitOf<dim_amplitude_spectral_density> U, QuantityValue Rep = double>
 using amplitude_spectral_density = quantity<dim_amplitude_spectral_density, U, Rep>;
 
 }

test/unit_test/static/quantity_test.cpp

@@ -22,9 +22,16 @@
 
 #include "test_tools.h"
 #include "units/math.h"
-#include "units/physical/si/si.h"
+#include "units/physical/si/cgs/derived/speed.h"
-#include "units/physical/si/us/us.h"
+#include "units/physical/si/derived/area.h"
+#include "units/physical/si/derived/frequency.h"
+#include "units/physical/si/derived/speed.h"
+#include "units/physical/si/derived/volume.h"
+#include "units/physical/si/fps/derived/speed.h"
 #include <chrono>
+#include <complex>
+#include <mutex>
+#include <string>
 #include <utility>
 
 namespace {
@@ -32,54 +39,67 @@ namespace {
 using namespace units;
 using namespace units::physical::si;
 
-// class invariants
 
-template<typename DimLength>
+//////////////////////////////
-concept invalid_types = requires
+// quantity class invariants
-{
+//////////////////////////////
-  requires !requires { typename quantity<DimLength, second, int>; };  // unit of a different dimension
+
-  requires !requires { typename quantity<DimLength, metre, quantity<DimLength, metre, int>>; };  // quantity used as Rep
+static_assert(sizeof(length<metre>) == sizeof(double));
-  requires !requires { typename quantity<metre, DimLength, double>; };  // reordered arguments
+static_assert(sizeof(length<metre, short>) == sizeof(short));
+
+#if COMP_GCC != 10 || COMP_GCC_MINOR != 2  // TODO remove when gcc 10.3 releases
+template<template<typename, typename, typename> typename Q>
+concept invalid_types = requires {
+  requires !requires { typename Q<dim_length, second, int>; };  // unit of a different dimension
+  requires !requires { typename Q<dim_length, metre, length<metre>>; };  // quantity used as Rep
+  requires !requires { typename Q<metre, dim_length, double>; };  // reordered arguments
+  requires !requires { typename Q<metre, double, dim_length>; };  // reordered arguments
 };
+static_assert(invalid_types<quantity>);
+#endif
 
-static_assert(invalid_types<dim_length>);
+static_assert(std::is_trivially_default_constructible_v<length<metre>>);
+static_assert(std::is_trivially_copy_constructible_v<length<metre>>);
+static_assert(std::is_trivially_move_constructible_v<length<metre>>);
+static_assert(std::is_trivially_copy_assignable_v<length<metre>>);
+static_assert(std::is_trivially_move_assignable_v<length<metre>>);
+static_assert(std::is_trivially_destructible_v<length<metre>>);
 
+static_assert(std::is_nothrow_default_constructible_v<length<metre>>);
+static_assert(std::is_nothrow_copy_constructible_v<length<metre>>);
+static_assert(std::is_nothrow_move_constructible_v<length<metre>>);
+static_assert(std::is_nothrow_copy_assignable_v<length<metre>>);
+static_assert(std::is_nothrow_move_assignable_v<length<metre>>);
+static_assert(std::is_nothrow_destructible_v<length<metre>>);
+
+static_assert(std::is_trivially_copyable_v<length<metre>>);
+static_assert(std::is_standard_layout_v<length<metre>>);
+
+static_assert(std::default_initializable<length<metre>>);
+static_assert(std::move_constructible<length<metre>>);
+static_assert(std::copy_constructible<length<metre>>);
+static_assert(std::equality_comparable<length<metre>>);
+static_assert(std::totally_ordered<length<metre>>);
+static_assert(std::regular<length<metre>>);
+
+static_assert(std::three_way_comparable<length<metre>>);
+
+
+//////////////////
 // member types
+//////////////////
 
-static_assert(is_same_v<length<metre, int>::rep, int>);
+static_assert(is_same_v<length<metre, int>::dimension, dim_length>);
-static_assert(is_same_v<length<metre, double>::rep, double>);
+static_assert(is_same_v<fps::length<fps::mile>::dimension, fps::dim_length>);
 static_assert(is_same_v<length<metre, int>::unit, metre>);
-static_assert(is_same_v<length<kilometre, int>::unit, kilometre>);
+static_assert(is_same_v<fps::length<fps::mile>::unit, fps::mile>);
+static_assert(is_same_v<length<metre, int>::rep, int>);
+static_assert(is_same_v<fps::length<fps::mile>::rep, double>);
 
-// constructors
-
-static_assert(length<metre, int>().count() == 0);
-constexpr length<metre, int> km{1000};
-static_assert(km.count() == 1000);
-static_assert(length<metre, int>(km).count() == km.count());
-
-static_assert(length<metre, int>(1).count() == 1);
-static_assert(!std::is_constructible_v<length<metre, int>, double>); // truncating conversion
-static_assert(length<metre, double>(1.0).count() == 1.0);
-static_assert(length<metre, double>(1).count() == 1.0);
-static_assert(length<metre, double>(3.14).count() == 3.14);
-
-static_assert(length<metre, int>(km).count() == 1000);
-static_assert(!std::is_constructible_v<length<metre, int>,
-                                       length<metre, double>>);  // truncating conversion
-static_assert(length<metre, double>(1000.0_q_m).count() == 1000.0);
-static_assert(length<metre, double>(km).count() == 1000.0);
-static_assert(length<metre, int>(1_q_km).count() == 1000);
-static_assert(!std::is_constructible_v<length<metre, int>,
-                                       physical::si::time<second, int>>);  // different dimensions
-static_assert(!std::is_constructible_v<length<kilometre, int>,
-                                       length<metre, int>>);  // truncating conversion
-
-// assignment operator
-
-static_assert([]() { length<metre, int> l1(1), l2(2); return l2 = l1; }().count() == 1);
 
+////////////////////////////
 // static member functions
+////////////////////////////
 
 static_assert(length<metre, int>::zero().count() == 0);
 static_assert(length<metre, int>::min().count() == std::numeric_limits<int>::lowest());
@@ -88,32 +108,165 @@ static_assert(length<metre, double>::zero().count() == 0.0);
 static_assert(length<metre, double>::min().count() == std::numeric_limits<double>::lowest());
 static_assert(length<metre, double>::max().count() == std::numeric_limits<double>::max());
 
-// unary member operators
 
-static_assert((+km).count() == 1000);
+//////////////////////////////
-static_assert((-km).count() == -1000);
+// construction from a value
-static_assert((+(-km)).count() == -1000);
+//////////////////////////////
-static_assert((-(-km)).count() == 1000);
 
-static_assert([](auto v) {
+// only explicit construction from a value
-  auto vv = v++;
+static_assert(std::constructible_from<length<metre>, double>);
-  return std::pair(v, vv);
+static_assert(!std::convertible_to<double, length<metre>>);
-}(km) == std::pair(length<metre, int>(1001), length<metre, int>(1000)));
-static_assert([](auto v) {
-  auto vv = ++v;
-  return std::pair(v, vv);
-}(km) == std::pair(length<metre, int>(1001), length<metre, int>(1001)));
-static_assert([](auto v) {
-  auto vv = v--;
-  return std::pair(v, vv);
-}(km) == std::pair(length<metre, int>(999), length<metre, int>(1000)));
-static_assert([](auto v) {
-  auto vv = --v;
-  return std::pair(v, vv);
-}(km) == std::pair(length<metre, int>(999), length<metre, int>(999)));
 
+static_assert(std::constructible_from<length<metre>, float>);
+static_assert(!std::convertible_to<float, length<metre>>);
+
+static_assert(std::constructible_from<length<metre, float>, double>);  // truncating implicit conversions double -> float allowed
+static_assert(!std::convertible_to<double, length<metre, float>>);
+
+static_assert(std::constructible_from<length<metre>, int>);
+static_assert(!std::convertible_to<int, length<metre>>);
+
+static_assert(std::constructible_from<length<metre>, short>);
+static_assert(!std::convertible_to<short, length<metre>>);
+
+static_assert(std::constructible_from<length<metre, short>, int>);  // truncating implicit conversions int -> short allowed
+static_assert(!std::convertible_to<int, length<metre, short>>);
+
+// exception, implicit construction from a value allowed for a dimensionless quantity
+static_assert(std::constructible_from<dimensionless<one>, double>);
+static_assert(std::convertible_to<double, dimensionless<one>>);
+
+static_assert(std::constructible_from<dimensionless<one>, float>);
+static_assert(std::convertible_to<float, dimensionless<one>>);
+
+static_assert(std::constructible_from<dimensionless<one, float>, double>);
+static_assert(std::convertible_to<double, dimensionless<one, float>>);
+
+static_assert(std::constructible_from<dimensionless<one>, int>);
+static_assert(std::convertible_to<int, dimensionless<one>>);
+
+static_assert(std::constructible_from<dimensionless<one>, short>);
+static_assert(std::convertible_to<short, dimensionless<one>>);
+
+static_assert(std::constructible_from<dimensionless<one, short>, int>);
+static_assert(std::convertible_to<int, dimensionless<one, short>>);
+
+// but only if a dimensionless quantity has a ratio(1)
+static_assert(std::constructible_from<dimensionless<percent>, double>);
+static_assert(!std::convertible_to<double, dimensionless<percent>>);
+
+static_assert(std::constructible_from<dimensionless<percent>, float>);
+static_assert(!std::convertible_to<float, dimensionless<percent>>);
+
+static_assert(std::constructible_from<dimensionless<percent, float>, double>);  // truncating implicit conversions double -> float allowed
+static_assert(!std::convertible_to<double, dimensionless<percent, float>>);
+
+static_assert(std::constructible_from<dimensionless<percent>, int>);
+static_assert(!std::convertible_to<int, dimensionless<percent>>);
+
+static_assert(std::constructible_from<dimensionless<percent>, short>);
+static_assert(!std::convertible_to<short, dimensionless<percent>>);
+
+static_assert(std::constructible_from<dimensionless<percent, short>, int>);  // truncating implicit conversions int -> short allowed
+static_assert(!std::convertible_to<int, dimensionless<percent, short>>);
+
+// floating-point to integral truncating conversion not allowed
+static_assert(!std::constructible_from<length<metre, int>, double>);
+static_assert(!std::convertible_to<double, length<metre, int>>);
+
+static_assert(!std::constructible_from<dimensionless<one, int>, double>);
+static_assert(!std::convertible_to<double, dimensionless<one, int>>);
+
+static_assert(length<metre, int>().count() == 0); // value initialization
+static_assert(length<metre, int>(1).count() == 1);
+static_assert(length<metre, double>(1.0).count() == 1.0);
+static_assert(length<metre, double>(1).count() == 1.0);
+static_assert(length<metre, double>(3.14).count() == 3.14);
+
+
+///////////////////////////////////////
+// construction from another quantity
+///////////////////////////////////////
+
+// conversion only between equivalent dimensions
+static_assert(std::constructible_from<length<metre>, length<metre>>);
+static_assert(std::convertible_to<length<metre>, length<metre>>);
+static_assert(std::constructible_from<length<centimetre>, cgs::length<cgs::centimetre>>);
+static_assert(std::convertible_to<cgs::length<cgs::centimetre>, length<centimetre>>);
+static_assert(std::constructible_from<fps::length<fps::foot>, cgs::length<cgs::centimetre>>);
+static_assert(std::convertible_to<cgs::length<cgs::centimetre>, fps::length<fps::foot>>);
+
+// conversion between different dimensions not allowed
+static_assert(!std::constructible_from<length<metre>, physical::si::time<second>>);
+static_assert(!std::convertible_to<physical::si::time<second>, length<metre>>);
+static_assert(!std::constructible_from<length<metre>, speed<metre_per_second>>);
+static_assert(!std::convertible_to<speed<metre_per_second>, length<metre>>);
+
+// implicit conversion from another quantity only if non-truncating
+static_assert(std::constructible_from<length<metre>, length<metre, int>>);  // int -> double OK
+static_assert(std::convertible_to<length<metre, int>, length<metre>>);  // int -> double OK
+
+static_assert(!std::constructible_from<length<metre, int>, length<metre>>);  // truncating double -> int not allowed
+static_assert(!std::convertible_to<length<metre>, length<metre, int>>);  // truncating double -> int not allowed
+
+static_assert(std::constructible_from<length<metre, int>, length<kilometre, int>>);  // kilometre<int> -> metre<int> OK
+static_assert(std::convertible_to<length<kilometre, int>, length<metre, int>>);  // kilometre<int> -> metre<int> OK
+
+static_assert(!std::constructible_from<length<kilometre, int>, length<metre, int>>);  // truncating metre<int> -> kilometre<int> not allowed
+static_assert(!std::convertible_to<length<metre, int>, length<kilometre, int>>);  // truncating metre<int> -> kilometre<int> not allowed
+
+// converting to double always OK
+static_assert(std::constructible_from<length<metre>, length<kilometre, int>>);  
+static_assert(std::convertible_to<length<kilometre, int>, length<metre>>);
+static_assert(std::constructible_from<length<kilometre>, length<metre, int>>);
+static_assert(std::convertible_to<length<metre, int>, length<kilometre>>);
+
+static_assert(length<metre, int>(123_q_m).count() == 123);
+static_assert(length<kilometre, int>(2_q_km).count() == 2);
+static_assert(length<metre, int>(2_q_km).count() == 2000);
+static_assert(length<kilometre>(1500_q_m).count() == 1.5);
+
+
+/////////
+// CTAD
+/////////
+
+static_assert(std::is_same_v<decltype(quantity{length<metre, int>(123)}), length<metre, int>>);
+static_assert(std::is_same_v<decltype(quantity{speed<metre_per_second>(123)}), speed<metre_per_second>>);
+// static_assert(std::is_same_v<decltype(length{length<metre, int>(123)}), length<metre, int>>);   // TODO gcc ICE
+static_assert(std::is_same_v<decltype(quantity{123_q_m}), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(quantity{1}), dimensionless<one, int>>);
+static_assert(std::is_same_v<decltype(quantity{1.23}), dimensionless<one, double>>);
+
+
+////////////////////////
+// assignment operator
+////////////////////////
+
+static_assert([]() { length<metre, int> l1(1), l2(2); return l2 = l1; }().count() == 1);
+static_assert([]() { length<metre, int> l1(1), l2(2); return l2 = std::move(l1); }().count() == 1);
+
+
+////////////////////
+// unary operators
+////////////////////
+
+static_assert((+123_q_m).count() == 123);
+static_assert((-123_q_m).count() == -123);
+static_assert((+(-123_q_m)).count() == -123);
+static_assert((-(-123_q_m)).count() == 123);
+
+static_assert([](auto v) { auto vv = v++; return std::pair(v, vv); }(123_q_m) == std::pair(124_q_m, 123_q_m));
+static_assert([](auto v) { auto vv = ++v; return std::pair(v, vv); }(123_q_m) == std::pair(124_q_m, 124_q_m));
+static_assert([](auto v) { auto vv = v--; return std::pair(v, vv); }(123_q_m) == std::pair(122_q_m, 123_q_m));
+static_assert([](auto v) { auto vv = --v; return std::pair(v, vv); }(123_q_m) == std::pair(122_q_m, 122_q_m));
+
+
+////////////////////////
 // compound assignment
+////////////////////////
 
+// same type
 static_assert((1_q_m += 1_q_m).count() == 2);
 static_assert((2_q_m -= 1_q_m).count() == 1);
 static_assert((1_q_m *= 2).count() == 2);
@@ -121,190 +274,372 @@ static_assert((2_q_m /= 2).count() == 1);
 static_assert((7_q_m %= 2).count() == 1);
 static_assert((7_q_m %= 2_q_m).count() == 1);
 
+// different types
 static_assert((2.5_q_m += 3_q_m).count() == 5.5);
-static_assert((2.5_q_m += 3.5_q_m).count() == 6);
+static_assert((123_q_m += 1_q_km).count() == 1123);
-
+static_assert((5.5_q_m -= 3_q_m).count() == 2.5);
+static_assert((1123_q_m -= 1_q_km).count() == 123);
 static_assert((2.5_q_m *= 3).count() == 7.5);
-static_assert((2.5_q_m *= 3.5).count() == 8.75);
+static_assert((7.5_q_m /= 3).count() == 2.5);
+static_assert((3500_q_m %= 1_q_km).count() == 500);
 
-// operations not allowed for the respective quantities
 template<typename Metre>
-concept invalid_compound_assignments = requires()
+concept invalid_compound_assignments = requires() {
-{
+  // truncating not allowed
+  requires !requires(length<Metre, int> l) { l += 2.5_q_m; };
+  requires !requires(length<Metre, int> l) { l -= 2.5_q_m; };
+  requires !requires(length<kilometre, int> l) { l += length<Metre, int>(2); };
+  requires !requires(length<kilometre, int> l) { l -= length<Metre, int>(2); };
+  requires !requires(length<kilometre, int> l) { l %= length<Metre, int>(2); };
+
+  // only quantities can be added or subtracted
+  requires !requires(length<Metre, int> l) { l += 2; };
+  requires !requires(length<Metre, int> l) { l -= 2; };
+
+  // compound multiply/divide by another quantity not allowed
+  requires !requires(length<Metre, int> l) { l *= 2_q_m; };
+  requires !requires(length<Metre, int> l) { l /= 2_q_m; };
+
+  // modulo operations on a floating point representation not allowed
   requires !requires(length<Metre, double> l) { l %= 2.; };
   requires !requires(length<Metre, double> l) { l %= 2; };
-  requires !requires(length<Metre, int> l) { l %= 2.; };
   requires !requires(length<Metre, double> l) { l %= 2._q_m; };
   requires !requires(length<Metre, double> l) { l %= 2_q_m; };
   requires !requires(length<Metre, int> l) { l %= 2._q_m; };
-  requires !requires(length<Metre, int> l) { l += 3.5_q_m; };
-  requires !requires(length<Metre, int> l) { l *= 3.5_q_m; };
 };
-
 static_assert(invalid_compound_assignments<metre>);
 
-// non-member arithmetic operators
 
-static_assert(compare<decltype(length<metre, int>() + length<metre, double>()), length<metre, double>>);
+////////////////////
-static_assert(compare<decltype(length<metre, int>() + length<metre, double>()), length<metre, double>>);
+// binary operators
-static_assert(compare<decltype(length<kilometre, int>() + length<metre, double>()), length<metre, double>>);
+////////////////////
-static_assert(compare<decltype(length<metre, double>() - length<metre, int>()), length<metre, double>>);
-static_assert(compare<decltype(length<kilometre, double>() - length<metre, int>()), length<metre, double>>);
-static_assert(compare<decltype(length<metre, int>() * 1.0), length<metre, double>>);
-static_assert(compare<decltype(1.0 * length<metre, int>()), length<metre, double>>);
-static_assert(
-    compare<decltype(speed<metre_per_second, int>() * physical::si::time<second, int>()), length<metre, int>>);
-static_assert(
-    compare<decltype(speed<metre_per_second, int>() * physical::si::time<hour, int>()), length<scaled_unit<ratio(36, 1, 2), metre>, int>>);
-static_assert(compare<decltype(length<metre>() * physical::si::time<minute>()),
-              quantity<unknown_dimension<units::exponent<dim_length, 1>, units::exponent<dim_time, 1>>, scaled_unit<ratio(6, 1, 1), unknown_coherent_unit>>>);
-static_assert(compare<decltype(1 / physical::si::time<second, int>()), frequency<hertz, int>>);
-static_assert(compare<decltype(1 / physical::si::time<minute, int>()), frequency<scaled_unit<ratio(1, 6, -1), hertz>, int>>);
-static_assert(compare<decltype(1 / frequency<hertz, int>()), physical::si::time<second, int>>);
-static_assert(compare<decltype(1 / length<kilometre>()),
-              quantity<unknown_dimension<units::exponent<dim_length, -1>>, scaled_unit<ratio(1, 1, -3), unknown_coherent_unit>>>);
-static_assert(compare<decltype(length<metre, int>() / 1.0), length<metre, double>>);
-static_assert(compare<decltype(length<metre, int>() / length<metre, double>()), dimensionless<one, double>>);
-static_assert(compare<decltype(length<kilometre, int>() / length<metre, double>()), dimensionless<scaled_unit<ratio(1, 1, 3), one>, double>>);
-static_assert(
-    compare<decltype(length<metre, int>() / physical::si::time<second, int>()), speed<metre_per_second, int>>);
-static_assert(
-    compare<decltype(length<metre>() / physical::si::time<minute>()), speed<scaled_unit<ratio(1, 6, -1), metre_per_second>>>);
-static_assert(compare<decltype(physical::si::time<minute>() / length<metre>()),
-              quantity<unknown_dimension<units::exponent<dim_length, -1>, units::exponent<dim_time, 1>>, scaled_unit<ratio(6 ,1 , 1), unknown_coherent_unit>>>);
-static_assert(compare<decltype(length<metre, int>() % short(1)), length<metre, int>>);
-static_assert(compare<decltype(length<metre, int>() % length<metre, short>(1)), length<metre, int>>);
 
-static_assert((1_q_m + km).count() == 1001);
+template<typename Metre>
+concept invalid_binary_operations = requires {
+  // no crossdimensional addition and subtraction
+  requires !requires { 1_q_s + length<Metre, int>(1); };
+  requires !requires { 1_q_s - length<Metre, int>(1); };
+
+  // no floating-point modulo
+  requires !requires(length<Metre, double> a) { a % 2_q_m; };
+  requires !requires(length<Metre, double> a) { 2_q_m % a; };
+  requires !requires(length<Metre, double> a) { a % 2; };
+  requires !requires(length<Metre, double> a, length<Metre, double> b) { a % b; };
+  requires !requires(length<Metre, double> a, length<Metre, int> b) { a % b; };
+  requires !requires(length<Metre, double> a, length<Metre, int> b) { b % a; };
+};
+static_assert(invalid_binary_operations<metre>);
+
+// same representation type
+static_assert(std::is_same_v<decltype(1_q_m + 1_q_m), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1_q_m - 1_q_m), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1_q_m * 1), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1_q_m * quantity{1}), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1 * 1_q_m), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(quantity{1} * 1_q_m), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1_q_m / 1), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1_q_m / quantity{1}), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1_q_m % 1), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1_q_m % quantity{1}), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1_q_m % 1_q_m), length<metre, std::int64_t>>);
+static_assert(compare<decltype(1_q_m * dimensionless<percent, std::int64_t>(1)), length<centimetre, std::int64_t>>);
+static_assert(compare<decltype(dimensionless<percent, std::int64_t>(1) * 1_q_m), length<centimetre, std::int64_t>>);
+static_assert(compare<decltype(1_q_m / dimensionless<percent, std::int64_t>(1)), length<hectometre, std::int64_t>>);
+static_assert(compare<decltype(1_q_m % dimensionless<percent, std::int64_t>(1)), length<centimetre, std::int64_t>>);
+static_assert(compare<decltype(1_q_m * 1_q_m), area<square_metre, std::int64_t>>);
+static_assert(compare<decltype(1_q_m / 1_q_m), dimensionless<one, std::int64_t>>);
+static_assert(compare<decltype(1 / 1_q_s), frequency<hertz, std::int64_t>>);
+static_assert(compare<decltype(quantity{1} / 1_q_s), frequency<hertz, std::int64_t>>);
+static_assert(compare<decltype(dimensionless<percent, std::int64_t>(1) / 1_q_s), frequency<scaled_unit<ratio(1, 100), hertz>, std::int64_t>>);
+
+// different representation types
+static_assert(std::is_same_v<decltype(1_q_m + 1._q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1_q_m - 1._q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1_q_m * 1.L), length<metre, long double>>);  // TODO should we address fundamental types implicit truncating conversions with concepts?
+static_assert(std::is_same_v<decltype(1 * 1._q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1_q_m * quantity{1.L}), length<metre, long double>>);  // TODO should we address fundamental types implicit truncating conversions with concepts?
+static_assert(std::is_same_v<decltype(quantity{1} * 1._q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1_q_m / 1.L), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1_q_m / quantity{1.L}), length<metre, long double>>);
+static_assert(compare<decltype(1_q_m * dimensionless<percent, long double>(1)), length<centimetre, long double>>);
+static_assert(compare<decltype(dimensionless<percent, std::int64_t>(1) * 1._q_m), length<centimetre, long double>>);
+static_assert(compare<decltype(1_q_m * 1._q_m), area<square_metre, long double>>);
+static_assert(compare<decltype(1_q_m / dimensionless<percent, long double>(1)), length<hectometre, long double>>);
+static_assert(compare<decltype(1_q_m / 1._q_m), dimensionless<one, long double>>);
+static_assert(compare<decltype(1 / 1._q_s), frequency<hertz, long double>>);
+static_assert(compare<decltype(quantity{1} / 1._q_s), frequency<hertz, long double>>);
+static_assert(compare<decltype(dimensionless<percent, std::int64_t>(1) / 1._q_s), frequency<scaled_unit<ratio(1, 100), hertz>, long double>>);
+static_assert(compare<decltype(1_q_m % short(1)), length<metre, std::int64_t>>);
+static_assert(compare<decltype(1_q_m % quantity{short(1)}), length<metre, std::int64_t>>);
+static_assert(compare<decltype(1_q_m % dimensionless<percent, short>(1)), length<centimetre, std::int64_t>>);
+static_assert(compare<decltype(1_q_m % length<metre, short>(1)), length<metre, std::int64_t>>);
+
+static_assert(std::is_same_v<decltype(1._q_m + 1_q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1._q_m - 1_q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1._q_m * 1), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1.L * 1_q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1._q_m * quantity{1}), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(quantity{1.L} * 1_q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1._q_m / 1), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1._q_m / quantity{1}), length<metre, long double>>);
+static_assert(compare<decltype(1._q_m * dimensionless<percent, std::int64_t>(1)), length<centimetre, long double>>);
+static_assert(compare<decltype(dimensionless<percent, long double>(1) * 1_q_m), length<centimetre, long double>>);
+static_assert(compare<decltype(1._q_m / dimensionless<percent, std::int64_t>(1)), length<hectometre, long double>>);
+static_assert(compare<decltype(1._q_m * 1_q_m), area<square_metre, long double>>);
+static_assert(compare<decltype(1._q_m / 1_q_m), dimensionless<one, long double>>);
+static_assert(compare<decltype(1.L / 1_q_s), frequency<hertz, long double>>);
+static_assert(compare<decltype(quantity{1.L} / 1_q_s), frequency<hertz, long double>>);
+static_assert(compare<decltype(dimensionless<percent, long double>(1) / 1_q_s), frequency<scaled_unit<ratio(1, 100), hertz>, long double>>);
+
+// different units
+static_assert(std::is_same_v<decltype(1_q_m + 1_q_km), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1._q_m + 1_q_km), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1_q_m + 1._q_km), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1._q_m + 1._q_km), length<metre, long double>>);
+
+static_assert(std::is_same_v<decltype(1_q_km + 1_q_m), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1._q_km + 1_q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1_q_km + 1._q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1._q_km + 1._q_m), length<metre, long double>>);
+
+static_assert(std::is_same_v<decltype(1_q_m - 1_q_km), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1._q_m - 1_q_km), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1_q_m - 1._q_km), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1._q_m - 1._q_km), length<metre, long double>>);
+
+static_assert(std::is_same_v<decltype(1_q_km - 1_q_m), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1._q_km - 1_q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1_q_km - 1._q_m), length<metre, long double>>);
+static_assert(std::is_same_v<decltype(1._q_km - 1._q_m), length<metre, long double>>);
+
+static_assert(std::is_same_v<decltype(1_q_m % 1_q_km), length<metre, std::int64_t>>);
+static_assert(std::is_same_v<decltype(1_q_km % 1_q_m), length<metre, std::int64_t>>);
+
+// different dimensions
+static_assert(compare<decltype(1_q_m_per_s * 1_q_s), length<metre, std::int64_t>>);
+static_assert(compare<decltype(1_q_m_per_s * 1_q_h), length<scaled_unit<ratio(36, 1, 2), metre>, std::int64_t>>);
+static_assert(compare<decltype(1_q_m * 1_q_min), quantity<unknown_dimension<exponent<dim_length, 1>, exponent<dim_time, 1>>, scaled_unit<ratio(60), unknown_coherent_unit>, std::int64_t>>);
+static_assert(compare<decltype(1_q_s * 1_q_Hz), dimensionless<one, std::int64_t>>);
+static_assert(compare<decltype(1 / 1_q_min), frequency<scaled_unit<ratio(1, 60), hertz>, std::int64_t>>);
+static_assert(compare<decltype(1 / 1_q_Hz), physical::si::time<second, std::int64_t>>);
+static_assert(compare<decltype(1 / 1_q_km), quantity<unknown_dimension<exponent<dim_length, -1>>, scaled_unit<ratio(1, 1, -3), unknown_coherent_unit>, std::int64_t>>);
+static_assert(compare<decltype(1_q_km / 1_q_m), dimensionless<scaled_unit<ratio(1000), one>, std::int64_t>>);
+static_assert(compare<decltype(1_q_m / 1_q_s), speed<metre_per_second, std::int64_t>>);
+static_assert(compare<decltype(1_q_m / 1_q_min), speed<scaled_unit<ratio(1, 60), metre_per_second>, std::int64_t>>);
+static_assert(compare<decltype(1_q_min / 1_q_m), quantity<unknown_dimension<exponent<dim_length, -1>, exponent<dim_time, 1>>, scaled_unit<ratio(60), unknown_coherent_unit>, std::int64_t>>);
+
+static_assert((1_q_m + 1_q_m).count() == 2);
 static_assert((1_q_m + 1_q_km).count() == 1001);
-static_assert((km - 1_q_m).count() == 999);
+static_assert((1_q_km + 1_q_m).count() == 1001);
+static_assert((2_q_m - 1_q_m).count() == 1);
 static_assert((1_q_km - 1_q_m).count() == 999);
 static_assert((2_q_m * 2).count() == 4);
+static_assert((2_q_m * quantity{2}).count() == 4);
+static_assert((2_q_m * dimensionless<percent, int>(2)).count() == 4);
 static_assert((3 * 3_q_m).count() == 9);
+static_assert((quantity{3} * 3_q_m).count() == 9);
+static_assert((dimensionless<percent, int>(3) * 3_q_m).count() == 9);
 static_assert((4_q_m / 2).count() == 2);
+static_assert((4_q_m / quantity{2}).count() == 2);
+static_assert((4_q_m / dimensionless<percent, int>(2)).count() == 2);
 static_assert((4_q_km / 2_q_m).count() == 2);
 static_assert((4000_q_m / 2_q_m).count() == 2000);
+
+static_assert((1.5_q_m + 1_q_m).count() == 2.5);
+static_assert((1.5_q_m + 1_q_km).count() == 1001.5);
+static_assert((1.5_q_km + 1_q_m).count() == 1501);
+static_assert((2.5_q_m - 1_q_m).count() == 1.5);
+static_assert((1.5_q_km - 1_q_m).count() == 1499);
+static_assert((2.5_q_m * 2).count() == 5);
+static_assert((2.5_q_m * quantity{2}).count() == 5);
+static_assert((2.5_q_m * dimensionless<percent, int>(2)).count() == 5);
+static_assert((2.5L * 2_q_m).count() == 5);
+static_assert((quantity{2.5L} * 2_q_m).count() == 5);
+static_assert((dimensionless<percent, long double>(2.5L) * 2_q_m).count() == 5);
+static_assert((5._q_m / 2).count() == 2.5);
+static_assert((5._q_m / quantity{2}).count() == 2.5);
+static_assert((5._q_m / dimensionless<percent, int>(2)).count() == 2.5);
+static_assert((5._q_km / 2_q_m).count() == 2.5);
+static_assert((5000._q_m / 2_q_m).count() == 2500);
+
+static_assert((1_q_m + 1.5_q_m).count() == 2.5);
+static_assert((1_q_m + 1.5_q_km).count() == 1501);
+static_assert((1_q_km + 1.5_q_m).count() == 1001.5);
+static_assert((2_q_m - 1.5_q_m).count() == 0.5);
+static_assert((1_q_km - 1.5_q_m).count() == 998.5);
+static_assert((2_q_m * 2.5L).count() == 5);
+static_assert((2_q_m * quantity{2.5L}).count() == 5);
+static_assert((2_q_m * dimensionless<percent, long double>(2.5L)).count() == 5);
+static_assert((2 * 2.5_q_m).count() == 5);
+static_assert((quantity{2} * 2.5_q_m).count() == 5);
+static_assert((dimensionless<percent, int>(2) * 2.5_q_m).count() == 5);
+static_assert((5_q_m / 2.5L).count() == 2);
+static_assert((5_q_m / quantity{2.5L}).count() == 2);
+static_assert((5_q_m / dimensionless<percent, long double>(2.5L)).count() == 2);
+static_assert((5_q_km / 2.5_q_m).count() == 2);
+static_assert((5000_q_m / 2.5_q_m).count() == 2000);
+
 static_assert((7_q_m % 2).count() == 1);
+static_assert((7_q_m % quantity{2}).count() == 1);
+static_assert((7_q_m % dimensionless<percent, int>(2)).count() == 1);
 static_assert((7_q_m % 2_q_m).count() == 1);
 static_assert((7_q_km % 2000_q_m).count() == 1000);
 
 static_assert((10_q_km2 * 10_q_km2) / 50_q_km2 == 2_q_km2);
 
-constexpr auto q1 = 10_q_km / 5_q_m;
+static_assert((10_q_km / 5_q_m).count() == 2);
-static_assert(compare<decltype(q1), const dimensionless<scaled_unit<ratio(1, 1, 3), one>, std::int64_t>>);
+static_assert(dimensionless<one>(10_q_km / 5_q_m).count() == 2000);
-static_assert(q1.count() == 2);
-
-constexpr dimensionless<one> q2 = q1;
-static_assert(q2.count() == 2000);
 
 #if UNITS_DOWNCAST_MODE == 0
-static_assert(quantity_cast<dim_one, one>(q1).count() == 2000);
+static_assert(quantity_cast<dim_one, one>(10_q_km / 5_q_m).count() == 2000);
 #else
-static_assert(quantity_cast<one>(q1).count() == 2000);
+static_assert(quantity_cast<one>(10_q_km / 5_q_m).count() == 2000);
 #endif
 
-constexpr auto q3 = 10_q_s * 2_q_kHz;
+static_assert((10_q_s * 2_q_kHz).count() == 20);
-static_assert(compare<decltype(q3), const dimensionless<scaled_unit<ratio(1, 1, 3), one>, std::int64_t>>);
-static_assert(q3.count() == 20);
 
-// comparators
 
-static_assert(2_q_m + 1_q_m == 3_q_m);
+// dimensionless
-static_assert(!(2_q_m + 2_q_m == 3_q_m));
-static_assert(2_q_m + 2_q_m != 3_q_m);
-static_assert(!(2_q_m + 2_q_m != 4_q_m));
-static_assert(2_q_m > 1_q_m);
-static_assert(!(1_q_m > 1_q_m));
-static_assert(1_q_m < 2_q_m);
-static_assert(!(2_q_m < 2_q_m));
-static_assert(2_q_m >= 1_q_m);
-static_assert(2_q_m >= 2_q_m);
-static_assert(!(2_q_m >= 3_q_m));
-static_assert(1_q_m <= 2_q_m);
-static_assert(2_q_m <= 2_q_m);
-static_assert(!(3_q_m <= 2_q_m));
 
-static_assert(3_q_m == 3.0_q_m);
+static_assert(quantity{1} + quantity{1} == 2);
-static_assert(3_q_m != 3.14_q_m);
+static_assert(1 + quantity{1} == 2);
-static_assert(2_q_m > 1.0_q_m);
+static_assert(quantity{1} + 1 == 2);
-static_assert(1.0_q_m < 2_q_m);
+static_assert(quantity{2} - quantity{1} == 1);
-static_assert(2.0_q_m >= 1_q_m);
+static_assert(2 - quantity{1} == 1);
-static_assert(1_q_m <= 2.0_q_m);
+static_assert(quantity{2} - 1 == 1);
+static_assert(quantity{2} * quantity{2} == 4);
+static_assert(2 * quantity{2} == 4);
+static_assert(quantity{2} * 2 == 4);
+static_assert(quantity{4} / quantity{2} == 2);
+static_assert(4 / quantity{2} == 2);
+static_assert(quantity{4} / 2 == 2);
+static_assert(quantity{4} % quantity{2} == 0);
+static_assert(4 % quantity{2} == 0);
+static_assert(quantity{4} % 2 == 0);
 
-static_assert(1000_q_m == 1_q_km);
-static_assert(1001_q_m != 1_q_km);
-static_assert(1001_q_m > 1_q_km);
-static_assert(999_q_m < 1_q_km);
-static_assert(1000_q_m >= 1_q_km);
-static_assert(1000_q_m <= 1_q_km);
 
-// alias units
+///////////////////////
+// equality operators
+///////////////////////
 
-static_assert(2_q_l + 2_q_ml == 2002_q_ml);
+template<typename Metre>
-static_assert(2_q_l + 2_q_ml == 2002_q_cm3);
+concept no_crossdimensional_equality = requires {
-static_assert(2_q_l + 2_q_cm3 == 2002_q_ml);
+  requires !requires { 1_q_s == length<Metre, int>(1); };
-static_assert(2_q_dm3 + 2_q_cm3 == 2002_q_ml);
+  requires !requires { 1_q_s != length<Metre, int>(1); };
+};
+static_assert(no_crossdimensional_equality<metre>);
 
-// is_quantity
+// same type
+static_assert(length<metre, int>(123) == length<metre, int>(123));
+static_assert(length<metre, int>(321) != length<metre, int>(123));
+static_assert(!(length<metre, int>(123) == length<metre, int>(321)));
+static_assert(!(length<metre, int>(123) != length<metre, int>(123)));
 
-static_assert(Quantity<length<millimetre, int>>);
+// different types
+static_assert(length<metre, double>(123) == length<metre, int>(123));
+static_assert(length<metre, double>(321) != length<metre, int>(123));
+static_assert(!(length<metre, double>(123) == length<metre, int>(321)));
+static_assert(!(length<metre, double>(123) != length<metre, int>(123)));
 
-// common_quantity
+static_assert(length<kilometre, int>(123) == length<metre, int>(123000));
+static_assert(length<kilometre, int>(321) != length<metre, int>(123000));
+static_assert(!(length<kilometre, int>(123) == length<metre, int>(321000)));
+static_assert(!(length<kilometre, int>(123) != length<metre, int>(123000)));
 
-static_assert(compare<common_quantity<length<metre, int>, length<kilometre, int>>, length<metre, int>>);
+// dimensionless
-static_assert(compare<common_quantity<length<kilometre, long long>, length<metre, int>>, length<metre, long long>>);
-static_assert(
-    compare<common_quantity<length<kilometre, long long>, length<millimetre, double>>, length<millimetre, double>>);
 
-// common_type
+static_assert(quantity{123} == 123);
+static_assert(quantity{321} != 123);
+static_assert(123 == quantity{123});
+static_assert(123 != quantity{321});
 
-using namespace units::physical::si::us::literals;
 
-static_assert(std::equality_comparable<decltype(1_q_m)>);
+///////////////////////
-static_assert(std::equality_comparable_with<decltype(1_q_m), decltype(1_q_cm)>);
+// ordering operators
-static_assert(0_q_m == 0_q_ft_us);
+///////////////////////
-static_assert(std::equality_comparable_with<decltype(1_q_m), decltype(1_q_ft_us)>);
+
+template<typename Metre>
+concept no_crossdimensional_ordering = requires {
+  requires !requires { 1_q_s < length<Metre, int>(1); };
+  requires !requires { 1_q_s > length<Metre, int>(1); };
+  requires !requires { 1_q_s <= length<Metre, int>(1); };
+  requires !requires { 1_q_s >= length<Metre, int>(1); };
+};
+static_assert(no_crossdimensional_ordering<metre>);
+
+// same type
+static_assert(length<metre, int>(123) < length<metre, int>(321));
+static_assert(length<metre, int>(123) <= length<metre, int>(123));
+static_assert(length<metre, int>(123) <= length<metre, int>(321));
+static_assert(length<metre, int>(321) > length<metre, int>(123));
+static_assert(length<metre, int>(123) >= length<metre, int>(123));
+static_assert(length<metre, int>(321) >= length<metre, int>(123));
+static_assert(!(length<metre, int>(321) < length<metre, int>(123)));
+static_assert(!(length<metre, int>(123) < length<metre, int>(123)));
+static_assert(!(length<metre, int>(321) <= length<metre, int>(123)));
+static_assert(!(length<metre, int>(123) > length<metre, int>(321)));
+static_assert(!(length<metre, int>(123) > length<metre, int>(123)));
+static_assert(!(length<metre, int>(123) >= length<metre, int>(321)));
+
+// different types
+static_assert(length<metre, double>(123) < length<metre, int>(321));
+static_assert(length<metre, double>(123) <= length<metre, int>(123));
+static_assert(length<metre, double>(123) <= length<metre, int>(321));
+static_assert(length<metre, double>(321) > length<metre, int>(123));
+static_assert(length<metre, double>(123) >= length<metre, int>(123));
+static_assert(length<metre, double>(321) >= length<metre, int>(123));
+static_assert(!(length<metre, double>(321) < length<metre, int>(123)));
+static_assert(!(length<metre, double>(123) < length<metre, int>(123)));
+static_assert(!(length<metre, double>(321) <= length<metre, int>(123)));
+static_assert(!(length<metre, double>(123) > length<metre, int>(321)));
+static_assert(!(length<metre, double>(123) > length<metre, int>(123)));
+static_assert(!(length<metre, double>(123) >= length<metre, int>(321)));
+
+static_assert(length<kilometre, int>(123) < length<metre, int>(321000));
+static_assert(length<kilometre, int>(123) <= length<metre, int>(123000));
+static_assert(length<kilometre, int>(123) <= length<metre, int>(321000));
+static_assert(length<kilometre, int>(321) > length<metre, int>(123000));
+static_assert(length<kilometre, int>(123) >= length<metre, int>(123000));
+static_assert(length<kilometre, int>(321) >= length<metre, int>(123000));
+static_assert(!(length<kilometre, int>(321) < length<metre, int>(123000)));
+static_assert(!(length<kilometre, int>(123) < length<metre, int>(123000)));
+static_assert(!(length<kilometre, int>(321) <= length<metre, int>(123000)));
+static_assert(!(length<kilometre, int>(123) > length<metre, int>(321000)));
+static_assert(!(length<kilometre, int>(123) > length<metre, int>(123000)));
+static_assert(!(length<kilometre, int>(123) >= length<metre, int>(321000)));
+
+// dimensionless
+
+static_assert(quantity{123} < 321);
+static_assert(quantity{123} <= 123);
+static_assert(quantity{123} <= 321);
+static_assert(quantity{321} > 123);
+static_assert(quantity{123} >= 123);
+static_assert(quantity{321} >= 123);
+
+static_assert(123 < quantity{321});
+static_assert(123 <= quantity{123});
+static_assert(123 <= quantity{321});
+static_assert(321 > quantity{123});
+static_assert(123 >= quantity{123});
+static_assert(321 >= quantity{123});
+
+
+//////////////////
+// dimensionless
+//////////////////
+
 static_assert(std::equality_comparable_with<dimensionless<one>, int>);
 static_assert(std::equality_comparable_with<dimensionless<one>, double>);
 static_assert(std::equality_comparable_with<dimensionless<one, int>, int>);
 static_assert(!std::equality_comparable_with<dimensionless<one, int>, double>);
 
-// quantity_cast
-
-static_assert(compare<decltype(quantity_cast<scaled_unit<ratio(1), metre>>(2_q_km))::unit, metre>);
-
-static_assert(quantity_cast<length<metre, int>>(2_q_km).count() == 2000);
-static_assert(quantity_cast<length<kilometre, int>>(2000_q_m).count() == 2);
-static_assert(quantity_cast<length<metre, int>>(1.23_q_m).count() == 1);
-static_assert(quantity_cast<metre>(2_q_km).count() == 2000);
-static_assert(quantity_cast<kilometre>(2000_q_m).count() == 2);
-static_assert(quantity_cast<int>(1.23_q_m).count() == 1);
-static_assert(quantity_cast<dim_speed, kilometre_per_hour>(2000.0_q_m / 3600.0_q_s).count() == 2);
-
-// dimensionless
-
-static_assert(std::is_convertible_v<double, dimensionless<one>>);
-static_assert(std::is_convertible_v<float, dimensionless<one>>);
-static_assert(!std::is_convertible_v<double, dimensionless<one, int>>);
-static_assert(std::is_convertible_v<int, dimensionless<one>>);
-
-static_assert(!std::is_convertible_v<double, dimensionless<scaled_unit<ratio(1, 1, 1), one>>>);
-static_assert(std::is_constructible_v<dimensionless<scaled_unit<ratio(1, 1, 1), one>>, double>);
-
-static_assert(dimensionless<one>(1.23) + dimensionless<one>(1.23) == dimensionless<one>(2.46));
-static_assert(dimensionless<one>(1.23) + dimensionless<one>(1.23) == 2.46);
-static_assert(dimensionless<one>(1.23) + 1.23 == 2.46);
-static_assert(1.23 + dimensionless<one>(1.23) == 2.46);
-static_assert(dimensionless<one>(1) + 1 == 2);
-static_assert(dimensionless<one, int>(1) + 1 == 2);
-
 template<typename Int>
-concept invalid_dimensionless_operations = requires
+concept invalid_dimensionless_operations = requires {
-{
   requires !requires(dimensionless<one, Int> d) { d + 1.23; };
   requires !requires(dimensionless<one, Int> d) { 1.23 + d; };
-  requires !requires(dimensionless<scaled_unit<ratio(1, 1, 1), one>, Int> d) { 1 + d; };
+  requires !requires(dimensionless<percent, Int> d) { 1 + d; };
-  requires !requires(dimensionless<scaled_unit<ratio(1, 1, 1), one>, Int> d) { d + 1; };
+  requires !requires(dimensionless<percent, Int> d) { d + 1; };
 };
 static_assert(invalid_dimensionless_operations<int>);
 
@@ -319,36 +654,36 @@ static_assert(50._q_m / 100._q_m == dimensionless<percent>(50));
 
 static_assert(dimensionless<one>(dimensionless<percent>(50)).count() == 0.5);
 
-static_assert(std::is_same_v<decltype(quantity{1}), dimensionless<one, int>>);
-static_assert(std::is_same_v<decltype(quantity{1.23}), dimensionless<one, double>>);
 
-// time
+////////////////
+// alias units
+////////////////
 
-static_assert(1_q_h == 3600_q_s);
+static_assert(compare<decltype(2_q_l + 2_q_ml), volume<cubic_centimetre, std::int64_t>>);
+static_assert(2_q_l + 2_q_ml == 2002_q_cm3);
+static_assert(2_q_l + 2_q_ml == 2002_q_ml);
+static_assert(2_q_l + 2_q_cm3 == 2002_q_ml);
+static_assert(2_q_dm3 + 2_q_cm3 == 2002_q_ml);
 
-template<typename Metre>
-concept no_crossdimensional_equality = !requires { 1_q_s == length<Metre, int>(1); };
 
-static_assert(no_crossdimensional_equality<metre>);
+//////////////////
+// quantity_cast
+//////////////////
 
-// length
+static_assert(compare<decltype(quantity_cast<scaled_unit<ratio(1), metre>>(2_q_km))::unit, metre>);
 
-static_assert(1_q_km == 1000_q_m);
+static_assert(quantity_cast<length<metre, int>>(2_q_km).count() == 2000);
-static_assert(1_q_km + 1_q_m == 1001_q_m);
+static_assert(quantity_cast<length<kilometre, int>>(2000_q_m).count() == 2);
-static_assert(10_q_km / 5_q_km == 2);
+static_assert(quantity_cast<length<metre, int>>(1.23_q_m).count() == 1);
-static_assert(10_q_km / 2 == 5_q_km);
+static_assert(quantity_cast<metre>(2_q_km).count() == 2000);
+static_assert(quantity_cast<kilometre>(2000_q_m).count() == 2);
+static_assert(quantity_cast<int>(1.23_q_m).count() == 1);
+static_assert(quantity_cast<dim_speed, kilometre_per_hour>(2000.0_q_m / 3600.0_q_s).count() == 2);
 
-// speed
-
-static_assert(10_q_m / 5_q_s == 2_q_m_per_s);
-static_assert(10 / 5_q_s * 1_q_m == 2_q_m_per_s);
-static_assert(1_q_km / 1_q_s == 1000_q_m_per_s);
-static_assert(2_q_km_per_h * 2_q_h == 4_q_km);
-static_assert(2_q_km / 2_q_km_per_h == 1_q_h);
-
-static_assert(compare<decltype(pow<2>(2_q_m)), decltype(4_q_m2)>);
 
+////////////////
 // downcasting
+////////////////
 
 #if UNITS_DOWNCAST_MODE == 0
 

test/unit_test/static/si_test.cpp

@@ -20,8 +20,9 @@
 // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 // SOFTWARE.
 
+#include "test_tools.h"
+#include <units/math.h>
 #include <units/physical/si/si.h>
-#include <utility>
 
 namespace {