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fix: units design refactored and fixed

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This commit is contained in:
Mateusz Pusz
2022-10-20 14:03:15 +02:00
parent c3c0879257
commit 0b9b159695
3 changed files with 292 additions and 199 deletions
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3
src/core/include/units/dimension.h
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@@ -246,6 +246,9 @@ using dim_type = dim_type_impl<T>::type;
} // namespace detail
// Operators
template<Dimension D1, Dimension D2>
[[nodiscard]] consteval Dimension auto operator*(D1, D2)
{

273
src/core/include/units/unit.h
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@@ -43,40 +43,94 @@ namespace detail {
template<typename T>
inline constexpr bool is_unit = false;
}
} // namespace detail
/**
* @brief A concept matching all unit types in the library
*
* Satisfied by all unit types derived from an specialization of :class:`scaled_unit`.
* Satisfied by all unit types provided by the library.
*/
template<typename T>
concept Unit = detail::is_unit<T>;
// User should not instantiate this type!!!
// It should not be exported from the module
/**
* @brief Unit being a scaled version of another unit
*
* @tparam M magnitude describing the scale factor
* @tparam U reference unit being scaled
*
* @note User should not instantiate this type! It is not exported from the C++ module. The library will
* instantiate this type automatically based on the unit arithmetic equation provided by the user.
*/
template<Magnitude auto M, Unit U>
struct scaled_unit {};
struct scaled_unit {
static constexpr UNITS_MSVC_WORKAROUND(Magnitude) auto mag = M;
static constexpr U reference_unit{};
};
namespace detail {
template<typename T>
inline constexpr bool is_specialization_of_scaled_unit = false;
template<auto M, Unit U>
inline constexpr bool is_specialization_of_scaled_unit<scaled_unit<M, U>> = true;
} // namespace detail
/**
* @brief A named unit
*
* Defines a named (in most cases coherent) unit that is then passed to a dimension definition.
* A named unit may be composed with a prefix to create a prefixed_unit.
* Defines a unit with a special name.
* Most of the named units may be composed with a prefix to create a `prefixed_unit`.
*
* For example:
*
* @code{.cpp}
* inline constexpr struct second : named_unit<"s"> {} second;
* inline constexpr struct metre : named_unit<"m"> {} metre;
* inline constexpr struct hertz : named_unit<"Hz", 1 / second> {} hertz;
* inline constexpr struct newton : named_unit<"N", kilogram * metre / square<second>> {} newton;
* inline constexpr struct degree_Celsius : named_unit<basic_symbol_text{"\u00B0C", "`C"}, kelvin> {} degree_Celsius;
* inline constexpr struct minute : named_unit<"min", mag<60> * second> {} minute;
* @endcode
*
* @note A common convention in this library is to assign the same name for a type and an object of this type.
* Besides defining them user never works with the unit types in the source code. All operations
* are done on the objects. Contrarily, the unit types are the only one visible in the compilation
* errors. Having them of the same names improves user experience and somehow blurs those separate domains.
*
* @tparam Symbol a short text representation of the unit
*/
template<basic_symbol_text Symbol, auto...>
struct named_unit;
/**
* @brief Specialization for base unit
*
* Defines a base unit in the system of units (i.e. `metre`).
* or a name assigned to another scaled or derived unit (i.e. `hour`, `joule`).
* Most of the named units may be composed with a prefix to create a `prefixed_unit`.
*
* @tparam Symbol a short text representation of the unit
*/
template<basic_symbol_text Symbol>
struct named_unit<Symbol> {
static constexpr auto symbol = Symbol;
static constexpr auto symbol = Symbol; ///< Unique base unit identifier
};
/**
* @brief Specialization for a unit with special name
*
* Allows assigning a special name to another scaled or derived unit (i.e. `hour`, `joule`).
*
* @tparam Symbol a short text representation of the unit
* @tparam Unit a unit for which we provide a special name
*/
template<basic_symbol_text Symbol, Unit auto U>
struct named_unit<Symbol, U> : std::remove_const_t<decltype(U)> {
static constexpr auto symbol = Symbol;
static constexpr auto symbol = Symbol; ///< Unique unit identifier
};
namespace detail {
@@ -84,27 +138,62 @@ namespace detail {
template<basic_symbol_text Symbol, auto... Args>
void to_base_specialization_of_named_unit(const volatile named_unit<Symbol, Args...>*);
template<typename T>
inline constexpr bool is_specialization_of_named_unit = false;
template<basic_symbol_text Symbol, auto... Args>
inline constexpr bool is_specialization_of_named_unit<named_unit<Symbol, Args...>> = true;
} // namespace detail
/**
* @brief A concept matching all units with special names
*
* Satisfied by all unit types derived from the specialization of `named_unit`.
*/
template<typename T>
concept NamedUnit = Unit<T> && requires(T* t) { detail::to_base_specialization_of_named_unit(t); };
concept NamedUnit = Unit<T> && requires(T* t) { detail::to_base_specialization_of_named_unit(t); } &&
(!detail::is_specialization_of_named_unit<T>);
template<Unit auto V>
inline constexpr bool unit_can_be_prefixed = NamedUnit<std::remove_const_t<decltype(V)>>;
/**
* @brief Prevents assignment of a prefix to specific units
*
* By default all named units allow assigning a prefix for them. There are some notable exceptions like
* `hour` or `degree_Celsius`. For those a partial specialization with the value `false` should be
* provided.
*/
template<NamedUnit auto V>
inline constexpr bool unit_can_be_prefixed = true;
/**
* @brief A concept to be used to define prefixes for a unit
*/
template<typename T>
concept PrefixableUnit = NamedUnit<T> && unit_can_be_prefixed<T{}>;
/**
* @brief A prefixed unit
*
* Defines a new unit that is a scaled version of another unit by the provided prefix. It is
* only possible to create such a unit if the given prefix type matches the one defined in a
* coherent_unit unit.
* Defines a new unit that is a scaled version of another unit with the scaling
* factor specified by a predefined prefix.
*
* @tparam Child inherited class type used by the downcasting facility (CRTP Idiom)
* @tparam P prefix to be appied to the coherent_unit unit
* @tparam U coherent_unit unit
* For example:
*
* @code{.cpp}
* template<PrefixableUnit auto U>
* struct kilo_ : prefixed_unit<"k", mag_power<10, 3>, U> {};
*
* template<PrefixableUnit auto U>
* inline constexpr kilo_<U> kilo;
*
* inline constexpr struct kilogram : decltype(si::kilo<gram>) {} kilogram;
* @endcode
*
* @tparam Symbol a prefix text to prepend to a unit symbol
* @tparam M scaling factor of the prefix
* @tparam U a named unit to be prefixed
*/
template<basic_symbol_text Symbol, Magnitude auto M, PrefixableUnit auto U>
struct prefixed_unit : std::remove_const_t<decltype(M * U)> {
@@ -129,11 +218,54 @@ inline constexpr bool is_per_of_units<per<Ts...>> = (... && UnitLike<Ts>);
} // namespace detail
template<typename T>
concept UnitSpec = detail::UnitLike<T> || detail::is_per_of_units<T>;
concept DerivedUnitSpec = detail::UnitLike<T> || detail::is_per_of_units<T>;
// User should not instantiate this type!!!
// It should not be exported from the module
template<UnitSpec... Us>
/**
* @brief Measurement unit for a derived quantity
*
* Derived units are defined as products of powers of the base units.
*
* Instead of using a raw list of exponents this library decided to use expression template syntax to make types
* more digestable for the user. The positive exponents are ordered first and all negative exponents are put as a list
* into the `per<...>` class template. If a power of exponent is different than `1` the unit type is enclosed in
* `power<Dim, Num, Den>` class template. Otherwise, it is just put directly in the list without any wrapper. There
* is also one special case. In case all of the exponents are negative then the `one` being a coherent unit of
* a dimensionless quantity is put in the front to increase the readability.
*
* For example:
*
* @code{.cpp}
* static_assert(is_of_type<1 / second, derived_unit<one, per<second>>>);
* static_assert(is_of_type<1 / (1 / second), second>);
* static_assert(is_of_type<one * second, second>);
* static_assert(is_of_type<metre * metre, derived_unit<power<metre, 2>>>);
* static_assert(is_of_type<metre * second, derived_unit<metre, second>>);
* static_assert(is_of_type<metre / second, derived_unit<metre, per<second>>>);
* static_assert(is_of_type<metre / square<second>, derived_unit<metre, per<power<second, 2>>>>);
* static_assert(is_of_type<watt / joule, derived_unit<watt, per<joule>>>);
* @endcode
*
* Every unit in the library has its internal canonical representation being the list of exponents of named base units
* (with the exception of `kilogram` which is represented as `gram` here) and a scaling ratio represented with a
* magnitude.
*
* Two units are deemed convertible if their canonical version has units of the same type.
* Two units are equivalent when they are convertible and their canonical versions have the same scaling ratios.
*
* The above means that:
* - `1/s` and `Hz` are both convertible and equal
* - `m` and `km` are convertible but not equal
* - `m` and `m²` ane not convertible and not equal
*
* @note This also means that units like `hertz` and `becquerel` are also considered convertible and equal.
*
* @tparam Us a parameter pack consisting tokens allowed in the unit specification
* (units, `power<U, Num, Den>`, `per<...>`)
*
* @note User should not instantiate this type! It is not exported from the C++ module. The library will
* instantiate this type automatically based on the unit arithmetic equation provided by the user.
*/
template<DerivedUnitSpec... Us>
struct derived_unit : detail::expr_fractions<derived_unit<>, Us...> {};
/**
@@ -161,27 +293,26 @@ template<typename T>
inline constexpr bool is_unit<T> = true;
/**
* @brief A common point for a hierarchy of units
* @brief A canonical representation of a unit
*
* A unit is an entity defined and adopted by convention, with which any other quantity of
* the same kind can be compared to express the ratio of the second quantity to the first
* one as a number.
* A canonical representation of a unit consists of a `reference_unit` and its scaling
* factor represented by the magnitude `mag`.
*
* All units of the same dimension can be convereted between each other. To allow this all of
* them are expressed as different ratios of the same one proprietary chosen coherent_unit unit
* (i.e. all length units are expressed in terms of meter, all mass units are expressed in
* terms of gram, ...)
* `reference_unit` is a unit (possibly derived one) that consists only named base units.
* All of the intermediate derived units are extracted, prefixes and magnitudes of scaled
* units are stripped from them and accounted in the `mag`.
*
* @tparam M a Magnitude representing the (relative) size of this unit
* @tparam U a unit to use as a coherent_unit for this dimension
* All units having the same canonical unit are deemed equal.
* All units having the same `reference_unit` are convertible (their `mag` may differ
* and is the subject of conversion).
*
* @note U cannot be constrained with Unit as for some specializations (i.e. named_unit)
* it gets the incomplete child's type with the CRTP idiom.
* @tparam U a unit to use as a `reference_unit`
* @tparam M a Magnitude representing an absolute scaling factor of this unit
*/
template<UnitLike U, Magnitude M>
template<Magnitude M, UnitLike U>
struct canonical_unit {
U reference_unit;
M mag;
U reference_unit;
};
[[nodiscard]] constexpr auto get_canonical_unit(UnitLike auto u);
@@ -190,13 +321,13 @@ template<UnitLike T, auto M, typename U>
[[nodiscard]] constexpr auto get_canonical_unit_impl(T, const volatile scaled_unit<M, U>&)
{
auto base = get_canonical_unit(U{});
return canonical_unit{base.reference_unit, M * base.mag};
return canonical_unit{M * base.mag, base.reference_unit};
}
template<UnitLike T, basic_symbol_text Symbol>
[[nodiscard]] constexpr auto get_canonical_unit_impl(T t, const volatile named_unit<Symbol>&)
{
return canonical_unit{t, mag<1>};
return canonical_unit{mag<1>, t};
}
template<UnitLike T, basic_symbol_text Symbol, Unit auto U>
@@ -210,27 +341,29 @@ template<UnitLike T, typename F, int Num, int... Den>
{
auto base = get_canonical_unit(F{});
return canonical_unit{
derived_unit<power_or_T<std::remove_const_t<decltype(base.reference_unit)>, power<F, Num, Den...>::exponent>>{},
pow<power<F, Num, Den...>::exponent>(base.mag)};
pow<power<F, Num, Den...>::exponent>(base.mag),
derived_unit<power_or_T<std::remove_const_t<decltype(base.reference_unit)>, power<F, Num, Den...>::exponent>>{}};
}
template<UnitLike T, UnitSpec... Us>
template<UnitLike T, DerivedUnitSpec... Us>
[[nodiscard]] constexpr auto get_canonical_unit_impl(T, const volatile derived_unit<Us...>&)
{
if constexpr (type_list_size<typename derived_unit<Us...>::_den_> != 0) {
auto num = get_canonical_unit(type_list_map<typename derived_unit<Us...>::_num_, derived_unit>{});
auto den = get_canonical_unit(type_list_map<typename derived_unit<Us...>::_den_, derived_unit>{});
return canonical_unit{num.reference_unit / den.reference_unit, num.mag / den.mag};
return canonical_unit{num.mag / den.mag, num.reference_unit / den.reference_unit};
} else {
auto num = (one * ... * get_canonical_unit(Us{}).reference_unit);
auto mag = (units::mag<1> * ... * get_canonical_unit(Us{}).mag);
return canonical_unit{num, mag};
return canonical_unit{mag, num};
}
}
[[nodiscard]] constexpr auto get_canonical_unit(UnitLike auto u) { return get_canonical_unit_impl(u, u); }
// TODO What if the same unit will have different types (i.e. user will inherit its own type from `metre`)?
// Is there a better way to sort units here? Some of them may not have symbol at all (like all units of
// dimensionless quantities).
template<Unit U1, Unit U2>
struct unit_less : std::bool_constant<type_name<U1>() < type_name<U2>()> {};
@@ -242,26 +375,54 @@ using type_list_of_unit_less = expr_less<T1, T2, unit_less>;
// Operators
/**
* Multiplication by `1` returns the same unit, otherwise `scaled_unit` is being returned.
*/
template<Magnitude M, Unit U>
[[nodiscard]] consteval Unit auto operator*(M mag, U)
[[nodiscard]] consteval Unit auto operator*(M mag, U u)
{
// TODO Try passing magnitude parameters rather than magnitude type itself in case of a trivial magnitude
// (single integer, ratio...)
if constexpr (mag == units::mag<1>)
return u;
else
return scaled_unit<mag, std::remove_const_t<U>>{};
}
template<Magnitude M, Unit U>
[[nodiscard]] consteval Unit auto operator*(U, M) = delete;
/**
* `scaled_unit` specializations have priority in this operation. This means that the library framework
* prevents passing it as an element to the `derived_unit`. In such case only the reference unit is passed
* to the derived unit and the magnitude remains outside forming another scaled unit as a result of the operation.
*/
template<Unit U1, Unit U2>
[[nodiscard]] consteval Unit auto operator*(U1, U2)
[[nodiscard]] consteval Unit auto operator*(U1 u1, U2 u2)
{
if constexpr (detail::is_specialization_of_scaled_unit<U1> && detail::is_specialization_of_scaled_unit<U2>)
return (U1::mag * U2::mag) * (U1::reference_unit * U2::reference_unit);
else if constexpr (detail::is_specialization_of_scaled_unit<U1>)
return U1::mag * (U1::reference_unit * u2);
else if constexpr (detail::is_specialization_of_scaled_unit<U2>)
return U2::mag * (u1 * U2::reference_unit);
else
return detail::expr_multiply<U1, U2, struct one, detail::type_list_of_unit_less, derived_unit>();
}
/**
* `scaled_unit` specializations have priority in this operation. This means that the library framework
* prevents passing it as an element to the `derived_unit`. In such case only the reference unit is passed
* to the derived unit and the magnitude remains outside forming another scaled unit as a result of the operation.
*/
template<Unit U1, Unit U2>
[[nodiscard]] consteval Unit auto operator/(U1, U2)
[[nodiscard]] consteval Unit auto operator/(U1 u1, U2 u2)
{
if constexpr (detail::is_specialization_of_scaled_unit<U1> && detail::is_specialization_of_scaled_unit<U2>)
return (U1::mag / U2::mag) * (U1::reference_unit / U2::reference_unit);
else if constexpr (detail::is_specialization_of_scaled_unit<U1>)
return U1::mag * (U1::reference_unit / u2);
else if constexpr (detail::is_specialization_of_scaled_unit<U2>)
return U2::mag * (u1 / U2::reference_unit);
else
return detail::expr_divide<U1, U2, struct one, detail::type_list_of_unit_less, derived_unit>();
}
@@ -294,20 +455,12 @@ template<Unit U1, Unit U2>
return is_same_v<decltype(canonical_lhs.reference_unit), decltype(canonical_rhs.reference_unit)>;
}
// Helper types and variable factories
template<Unit U>
struct square_ : decltype(U{} * U{}) {};
template<Unit U>
struct cubic_ : decltype(U{} * U{} * U{}) {};
// it is not allowed to use the same name for a variable and class template
// (even though it works for objects of regular class types)
// Helper variable templates to create common powers
template<Unit auto U>
inline constexpr square_<std::remove_const_t<decltype(U)>> square;
inline constexpr decltype(U * U) square;
template<Unit auto U>
inline constexpr cubic_<std::remove_const_t<decltype(U)>> cubic;
inline constexpr decltype(U * U * U) cubic;
} // namespace units

209
test/unit_test/static/unit_test.cpp
View File

@@ -45,7 +45,7 @@ inline constexpr struct kelvin_ : named_unit<"K"> {} kelvin;
inline constexpr struct radian_ : named_unit<"rad", metre / metre> {} radian;
inline constexpr struct steradian_ : named_unit<"sr", square<metre> / square<metre>> {} steradian;
inline constexpr struct hertz_ : named_unit<"Hz", 1 / second> {} hertz;
inline constexpr struct becquerel : named_unit<"Bq", 1 / second> {} becquerel;
inline constexpr struct becquerel_ : named_unit<"Bq", 1 / second> {} becquerel;
inline constexpr struct newton_ : named_unit<"N", kilogram * metre / square<second>> {} newton;
inline constexpr struct pascal_ : named_unit<"Pa", newton / square<metre>> {} pascal;
inline constexpr struct joule_ : named_unit<"J", newton * metre> {} joule;
@@ -94,9 +94,6 @@ static_assert(!NamedUnit<decltype(cubic<metre>)>);
static_assert(!NamedUnit<decltype(mag<60> * second)>);
static_assert(!NamedUnit<kilometre_>);
template<typename T>
constexpr bool print();
// named unit
static_assert(is_of_type<metre, metre_>);
static_assert(is_of_type<get_canonical_unit(metre).reference_unit, metre_>);
@@ -201,21 +198,26 @@ static_assert(si::yotta<metre>.symbol == "Ym");
// scaled_unit
constexpr auto u1 = mag<1> * metre;
static_assert(is_of_type<u1, scaled_unit<mag<1>, metre_>>);
static_assert(is_of_type<get_canonical_unit(u1).reference_unit, metre_>);
static_assert(get_canonical_unit(u1).mag == mag<1>);
constexpr auto m_1 = mag<1> * metre;
static_assert(is_of_type<m_1, metre_>);
static_assert(is_of_type<get_canonical_unit(m_1).reference_unit, metre_>);
static_assert(get_canonical_unit(m_1).mag == mag<1>);
constexpr auto u2 = mag<2> * kilometre;
static_assert(is_of_type<u2, scaled_unit<mag<2>, kilometre_>>);
static_assert(is_of_type<get_canonical_unit(u2).reference_unit, metre_>);
static_assert(get_canonical_unit(u2).mag == mag<2000>);
constexpr auto m_2 = mag<2> * metre;
static_assert(is_of_type<m_2, scaled_unit<mag<2>, metre_>>);
static_assert(is_of_type<get_canonical_unit(m_2).reference_unit, metre_>);
static_assert(get_canonical_unit(m_2).mag == mag<2>);
constexpr auto u3 = mag<42> * si::kilo<joule>;
static_assert(is_of_type<u3, scaled_unit<mag<42>, si::kilo_<joule>>>);
constexpr auto km_2 = mag<2> * kilometre;
static_assert(is_of_type<km_2, scaled_unit<mag<2>, kilometre_>>);
static_assert(is_of_type<get_canonical_unit(km_2).reference_unit, metre_>);
static_assert(get_canonical_unit(km_2).mag == mag<2000>);
constexpr auto kJ_42 = mag<42> * si::kilo<joule>;
static_assert(is_of_type<kJ_42, scaled_unit<mag<42>, si::kilo_<joule>>>);
static_assert(
is_of_type<get_canonical_unit(u3).reference_unit, derived_unit<gram_, power<metre_, 2>, per<power<second_, 2>>>>);
static_assert(get_canonical_unit(u3).mag == mag<42'000'000>);
is_of_type<get_canonical_unit(kJ_42).reference_unit, derived_unit<gram_, power<metre_, 2>, per<power<second_, 2>>>>);
static_assert(get_canonical_unit(kJ_42).mag == mag<42'000'000>);
// derived unit expression template syntax verification
@@ -229,6 +231,14 @@ static_assert(is_of_type<1 / second * one, derived_unit<one_, per<second_>>>);
static_assert(is_of_type<metre * second, derived_unit<metre_, second_>>);
static_assert(is_of_type<metre * metre, derived_unit<power<metre_, 2>>>);
static_assert(is_of_type<square<metre>, derived_unit<power<metre_, 2>>>);
static_assert(is_of_type<cubic<metre>, derived_unit<power<metre_, 3>>>);
static_assert(is_of_type<square<metre> * metre, derived_unit<power<metre_, 3>>>);
static_assert(is_of_type<metre * square<metre>, derived_unit<power<metre_, 3>>>);
static_assert(is_of_type<metre / second, derived_unit<metre_, per<second_>>>);
static_assert(is_of_type<metre / square<second>, derived_unit<metre_, per<power<second_, 2>>>>);
static_assert(is_of_type<metre / square<second> / second, derived_unit<metre_, per<power<second_, 3>>>>);
static_assert(is_of_type<metre * metre * second, derived_unit<power<metre_, 2>, second_>>);
static_assert(is_of_type<metre * second * metre, derived_unit<power<metre_, 2>, second_>>);
@@ -254,40 +264,52 @@ static_assert(is_of_type<metre / second*(second / metre), one_>);
static_assert(is_of_type<watt / joule, derived_unit<watt_, per<joule_>>>);
static_assert(is_of_type<joule / watt, derived_unit<joule_, per<watt_>>>);
static_assert(std::is_same_v<decltype(1 / second * metre), decltype(metre / second)>);
static_assert(std::is_same_v<decltype(metre * (1 / second)), decltype(metre / second)>);
static_assert(std::is_same_v<decltype((metre / second) * (1 / second)), decltype(metre / second / second)>);
static_assert(std::is_same_v<decltype((metre / second) * (1 / second)), decltype(metre / (second * second))>);
static_assert(std::is_same_v<decltype((metre / second) * (1 / second)), decltype(metre / square<second>)>);
// derived unit normalization
constexpr auto u4 = metre / second;
static_assert(is_of_type<get_canonical_unit(u4).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(u4).mag == mag<1>);
constexpr auto m_per_s = metre / second;
static_assert(is_of_type<get_canonical_unit(m_per_s).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(m_per_s).mag == mag<1>);
constexpr auto u5 = kilometre / second;
static_assert(is_of_type<u5, derived_unit<kilometre_, per<second_>>>);
static_assert(is_of_type<get_canonical_unit(u5).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(u5).mag == mag<1000>);
constexpr auto km_per_s = kilometre / second;
static_assert(is_of_type<km_per_s, derived_unit<kilometre_, per<second_>>>);
static_assert(is_of_type<get_canonical_unit(km_per_s).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(km_per_s).mag == mag<1000>);
constexpr auto u6 = kilometre / hour;
static_assert(is_of_type<u6, derived_unit<kilometre_, per<hour_>>>);
static_assert(is_of_type<get_canonical_unit(u6).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(u6).mag == mag<ratio{1000, 3600}>);
constexpr auto km_per_h = kilometre / hour;
static_assert(is_of_type<km_per_h, derived_unit<kilometre_, per<hour_>>>);
static_assert(is_of_type<get_canonical_unit(km_per_h).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(km_per_h).mag == mag<ratio{1000, 3600}>);
constexpr auto u7 = mag<1000> * kilometre / hour;
static_assert(is_of_type<u7, derived_unit<scaled_unit<mag<1000>, kilometre_>, per<hour_>>>);
static_assert(is_of_type<get_canonical_unit(u7).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(u7).mag == mag<ratio{1'000'000, 3'600}>);
// operations commutativity
constexpr auto u1 = mag<1000> * kilometre / hour;
static_assert(is_of_type<u1, scaled_unit<mag<1000>, derived_unit<kilometre_, per<hour_>>>>);
static_assert(is_of_type<get_canonical_unit(u1).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(u1).mag == mag<ratio{1'000'000, 3'600}>);
constexpr auto u8 = mag<1000> * (kilometre / hour);
static_assert(is_of_type<u8, scaled_unit<mag<1000>, derived_unit<kilometre_, per<hour_>>>>);
static_assert(is_of_type<get_canonical_unit(u8).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(u8).mag == mag<ratio{1'000'000, 3'600}>);
constexpr auto u2 = mag<1000> * (kilometre / hour);
static_assert(is_of_type<u2, scaled_unit<mag<1000>, derived_unit<kilometre_, per<hour_>>>>);
static_assert(is_of_type<get_canonical_unit(u2).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(u2).mag == mag<ratio{1'000'000, 3'600}>);
constexpr auto u9 = 1 / hour * (mag<1000> * kilometre);
static_assert(is_of_type<u9, derived_unit<scaled_unit<mag<1000>, kilometre_>, per<hour_>>>);
static_assert(is_of_type<get_canonical_unit(u9).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(u9).mag == mag<ratio{1'000'000, 3'600}>);
constexpr auto u3 = 1 / hour * (mag<1000> * kilometre);
static_assert(is_of_type<u3, scaled_unit<mag<1000>, derived_unit<kilometre_, per<hour_>>>>);
static_assert(is_of_type<get_canonical_unit(u3).reference_unit, derived_unit<metre_, per<second_>>>);
static_assert(get_canonical_unit(u3).mag == mag<ratio{1'000'000, 3'600}>);
// comparisons of the same units
static_assert(second == second);
static_assert(metre / second == metre / second);
static_assert(si::milli<metre> / si::milli<second> == si::micro<metre> / si::micro<second>);
static_assert(si::milli<metre> / si::micro<second> == si::micro<metre> / si::nano<second>);
static_assert(si::micro<metre> / si::milli<second> == si::nano<metre> / si::micro<second>);
static_assert(si::milli<metre> * si::kilo<metre> == si::deci<metre> * si::deca<metre>);
static_assert(si::kilo<metre> * si::milli<metre> == si::deca<metre> * si::deci<metre>);
// comparisons of equivalent units (named vs unnamed/derived)
static_assert(1 / second == hertz);
@@ -312,109 +334,24 @@ static_assert(convertible(mag<100> * metre, kilometre));
static_assert(si::milli<metre> != kilometre);
static_assert(convertible(si::milli<metre>, kilometre));
// comparisons of non-convertible units
static_assert(metre != metre * metre);
static_assert(!convertible(metre, metre* metre));
// one
static_assert(is_of_type<metre / metre, one_>);
static_assert(metre / metre == one);
// static_assert(metre * metre == square_metre);
// static_assert(second * second == second_squared);
// static_assert(second * second * second == second_cubed);
// static_assert(second * (second * second) == second_cubed);
// static_assert(second_squared * second == second_cubed);
// static_assert(second * second_squared == second_cubed);
static_assert(hertz * second == one);
// static_assert(1 / second * metre == metre / second);
// static_assert(metre * (1 / second) == metre / second);
// static_assert((metre / second) * (1 / second) == metre / second / second);
// static_assert((metre / second) * (1 / second) == metre / (second * second));
// static_assert((metre / second) * (1 / second) == metre / second_squared);
// static_assert(hertz == 1 / second);
// static_assert(newton == kilogram * metre / second_squared);
// static_assert(joule == kilogram * square_metre / second_squared);
// static_assert(joule == newton * metre);
// static_assert(watt == joule / second);
// static_assert(watt == kilogram * square_metre / second_cubed);
// static_assert(1 / frequency_dim == second);
// static_assert(frequency_dim * second == one);
// static_assert(metre * metre == area_dim);
// static_assert(metre * metre != volume_dim);
// static_assert(area_dim / metre == metre);
// static_assert(metre * metre * metre == volume_dim);
// static_assert(area_dim * metre == volume_dim);
// static_assert(volume_dim / metre == area_dim);
// static_assert(volume_dim / metre / metre == metre);
// static_assert(area_dim * area_dim / metre == volume_dim);
// static_assert(area_dim * (area_dim / metre) == volume_dim);
// static_assert(volume_dim / (metre * metre) == metre);
// static_assert(metre / second == speed_dim);
// static_assert(metre * second != speed_dim);
// static_assert(metre / second / second != speed_dim);
// static_assert(metre / speed_dim == second);
// static_assert(speed_dim * second == metre);
// static_assert(metre / second / second == acceleration_dim);
// static_assert(metre / (second * second) == acceleration_dim);
// static_assert(speed_dim / second == acceleration_dim);
// static_assert(speed_dim / acceleration_dim == second);
// static_assert(acceleration_dim * second == speed_dim);
// static_assert(acceleration_dim * (second * second) == metre);
// static_assert(acceleration_dim / speed_dim == frequency_dim);
// milli<metre> / milli<second> == micro<metre> / micro<second>;
// milli<metre> * kilo<metre> == deci<metre> * deca<metre>;
// Bq + Hz should not compile
// Bq + Hz + 1/s should compile?
// using namespace units;
// using namespace units::isq;
// struct metre : named_unit<metre, "m"> {};
// struct centimetre : prefixed_unit<centimetre, si::centi, metre> {};
// struct kilometre : prefixed_unit<kilometre, si::kilo, metre> {};
// struct yard : named_scaled_unit<yard, "yd", mag<ratio{9'144, 10'000}>(), metre> {};
// struct foot : named_scaled_unit<foot, "ft", mag<ratio(1, 3)>(), yard> {};
// struct dim_length : base_dimension<"length", metre> {};
// struct second : named_unit<second, "s"> {};
// struct hour : named_scaled_unit<hour, "h", mag<3600>(), second> {};
// struct dim_time : base_dimension<"time", second> {};
// struct kelvin : named_unit<kelvin, "K"> {};
// #if !UNITS_COMP_MSVC
// static_assert([]<Prefix P>(P) {
// return !requires { typename prefixed_unit<struct kilokilometre, P, kilometre>; };
// }(si::kilo{})); // no prefix allowed
// #endif
// struct metre_per_second : derived_unit<metre_per_second> {};
// struct dim_speed :
// derived_dimension<dim_speed, metre_per_second, units::exponent<dim_length, 1>, units::exponent<dim_time, -1>> {};
// struct kilometre_per_hour : derived_scaled_unit<kilometre_per_hour, dim_speed, kilometre, hour> {};
// static_assert(equivalent<metre::named_unit, metre>);
// static_assert(equivalent<metre::scaled_unit, metre>);
// static_assert(compare<downcast<scaled_unit<mag<1>(), metre>>, metre>);
// static_assert(compare<downcast<scaled_unit<mag<ratio(1, 100)>(), metre>>, centimetre>);
// static_assert(compare<downcast<scaled_unit<yard::mag, metre>>, yard>);
// static_assert(compare<downcast<scaled_unit<yard::mag / mag<3>(), metre>>, foot>);
// static_assert(compare<downcast<scaled_unit<kilometre::mag / hour::mag, metre_per_second>>, kilometre_per_hour>);
static_assert(hertz == 1 / second);
static_assert(newton == kilogram * metre / square<second>);
static_assert(joule == kilogram * square<metre> / square<second>);
static_assert(joule == newton * metre);
static_assert(watt == joule / second);
static_assert(watt == kilogram * square<metre> / cubic<second>);
// static_assert(centimetre::symbol == "cm");
// static_assert(kilometre::symbol == "km");
// static_assert(kilometre_per_hour::symbol == "km/h");
// static_assert(si::metre != si::kilometre);
// static_assert(!equivalent(si::metre, si::kilometre));
// static_assert(convertible(si::metre, si::kilometre));
} // namespace