5 Quantities and units library [quantities]

5.4 Reference [qty.ref]

5.4.2 Dimension [qty.dim]

5.4.2.1 General [qty.dim.general]

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Subclause [qty.dim] specifies the components for defining the dimension of a quantity (IEC 60050, 112-01-11).

5.4.2.2 Concepts [qty.dim.concepts]

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template<typename T> concept Dimension = SymbolicConstant<T> && std::derived_from<T, dimension-interface>; template<typename T> concept BaseDimension = // exposition only Dimension<T> && (is-derived-from-specialization-of<T, base_dimension>()); template<typename T, auto D> concept DimensionOf = Dimension<T> && Dimension<decltype(D)> && (T{} == D);

5.4.2.3 Types [qty.dim.types]

namespace mp_units { template<symbol_text Symbol> struct base_dimension : dimension-interface { static constexpr auto symbol = Symbol; // exposition only }; }
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base_dimension is used to define the dimension of a base quantity (IEC 60050, 112-01-08).
Symbol is its symbolic representation.
[Example 1: inline constexpr struct dim_length final : base_dimension<"L"> {} dim_length; — end example]
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namespace mp_units { template<typename... Expr> struct derived-dimension-impl // exposition only : expr-fractions<struct dimension_one, Expr...> {}; template<SymbolicConstant... Expr> struct derived_dimension final : dimension-interface, derived-dimension-impl<Expr...> {}; }
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derived_dimension is used by the library to represent the dimension of a derived quantity (IEC 60050, 112-01-10).
[Example 2: constexpr auto dim_acceleration = isq::speed.dimension / isq::dim_time; int x = dim_acceleration; // error: cannot construct from // derived_dimension<isq​::​dim_length, per<power<isq​::​dim_time, 2>>> — end example]
A program that instantiates a specialization of derived_dimension that is not a possible result of the library specifications is ill-formed, no diagnostic required.
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namespace mp_units { struct dimension_one final : dimension-interface, derived-dimension-impl<> {}; }
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dimension_one represents the dimension of a quantity of dimension one (IEC 60050, 112-01-13).

5.4.2.4 Operations [qty.dim.ops]

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namespace mp_units { struct dimension-interface { // exposition only template<Dimension Lhs, Dimension Rhs> friend consteval Dimension auto operator*(Lhs, Rhs); template<Dimension Lhs, Dimension Rhs> friend consteval Dimension auto operator/(Lhs, Rhs); template<Dimension Lhs, Dimension Rhs> friend consteval bool operator==(Lhs, Rhs); }; }
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template<Dimension Lhs, Dimension Rhs> friend consteval Dimension auto operator*(Lhs, Rhs);
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Returns: expr-multiply<derived_dimension, struct dimension_one>(Lhs{}, Rhs{}).
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template<Dimension Lhs, Dimension Rhs> friend consteval Dimension auto operator/(Lhs, Rhs);
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Returns: expr-divide<derived_dimension, struct dimension_one>(Lhs{}, Rhs{}).
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template<Dimension Lhs, Dimension Rhs> friend consteval bool operator==(Lhs, Rhs);
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Returns: std​::​is_same_v<Lhs, Rhs>.
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consteval Dimension auto inverse(Dimension auto d);
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Returns: dimension_one / d.
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template<std::intmax_t Num, std::intmax_t Den = 1, Dimension D> requires(Den != 0) consteval Dimension auto pow(D d);
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Returns: expr-pow<Num, Den, derived_dimension, struct dimension_one>(d).
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consteval Dimension auto sqrt(Dimension auto d);
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Returns: pow<1, 2>(d).
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consteval Dimension auto cbrt(Dimension auto d);
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Returns: pow<1, 3>(d).

5.4.2.5 Symbol formatting [qty.dim.sym.fmt]

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template<typename CharT = char, std::output_iterator<CharT> Out, Dimension D> constexpr Out dimension_symbol_to(Out out, D d, const dimension_symbol_formatting& fmt = {});
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Effects: TBD.
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Returns: TBD.
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template<dimension_symbol_formatting fmt = {}, typename CharT = char, Dimension D> consteval std::string_view dimension_symbol(D);
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Effects: Equivalent to: TBD.