concept quantity

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Description

A measurable quantity ¹ with a unit and a numeric_value ².

Relation of numeric_value and conversion factor

• See example

Notation

type	model of	notes
Q, Qj, Qk, Qr	quantity
U	unit
V, Vr	dimensionless_quantity
Sm	measurement_system
D	dimension
Ds	simple_dimension
C	conversion_factor<...>

value	type	notes
q	Q
qJ	Qj
qK	Qk
qR	Qr	local result
vR	Vr	local result
v	V	The numeric value of q
b	bool

Provides

concept	notes
scalar< Q >	A model of quantity is implicitly a model of scalar

operation	result	requires	notes
qJ + qK	qR	DA and provide_operator< Qj, plus, Qk> == true	To disable, set impl::provide_operator_plus_impl<Qj,Qk> false
qJ - qK	qR	DA and provide_operator< Qj ,minus, Qk> == true	To disable, set impl::provide_operator_minus_impl<Qj,Qk> false
qJ * qK	qR	DA and provide_operator< Qj, times, Qk> == true	To disable, set impl::provide_operator_times_impl<Qj,Qk> false
qJ * qK	vR	DA and provide_operator< Qj, times, Qk> == true	To disable, set impl::provide_operator_times_impl<Qj,Qk> false
qJ / qK	qR	DA and provide_operator< Qj, divides, Qk> == true	To disable, set impl::provide_operator_divides_impl<Qj,Qk> false
qJ / qK	vR	DA and provide_operator< Qj, divides, Qk> == true	To disable, set impl::provide_operator_divides_impl<Qj,Qk> false
pow<N>(q)	qR	DA and provide_operator< Qj, pow, std::ratio<N,1> > == true	To disable, set impl::provide_operator_pow_impl<Qj,N,1> false
pow<N,D>(q)	qR	DA and provide_operator< Qj, pow, std::ratio<N,D> > ==true	To disable, set impl::provide_operator_pow_impl<Qj,N,D> false
qJ < qK	b	DA and provide_operator_cmp< Qj, Qk > == true	To disable, set impl::provide_operator_cmp_impl<Qj,Qk> false
qJ <= qK	b	DA and provide_operator_cmp< Qj, Qk > == true	To disable, set impl::provide_operator_cmp_impl<Qj,Qk> false
qJ != qK	b	DA and provide_operator_cmp< Qj, Qk > == true	To disable, set impl::provide_operator_cmp_impl<Qj,Qk> false
qJ == qK	b	DA and provide_operator_cmp< Qj, Qk > == true	To disable, set impl::provide_operator_cmp_impl<Qj,Qk> false
qJ >= qK	b	DA and provide_operator_cmp< Qj, Qk > == true	To disable, set impl::provide_operator_cmp_impl<Qj,Qk> false
qJ > qK	b	DA and provide_operator_cmp< Qj, Qk > == true	To disable, set impl::provide_operator_cmp_impl<Qj,Qk> false

alias_template	result	notes
get_measurement_system< Q >	Sm	The measurement_system of U
get_dimension< Q >	D	the dimension of U
get_conversion_factor< Q >	C	the conversion factor for U
get_simple_dimension< Q >	Ds	the simple_dimension of U
get_unit< Q >	U
get_numeric_type< Q >	V

inline_bool_constant	value	notes
dimensionally_equivalent< Qj, Qk >	true if Qj and Qk are dimensionally equivalent else false	applies std::remove_cvref_t to Qj,Qk before testing
same_measurement_system< Qj, Qk >	true if units of Qj and Qk are in same measurement system else false	applies std::remove_cvref_t to Qj,Qk before testing

Requires:

inline_bool_constant	value	notes
impl::is_quantity_impl< Q >	true	states that Q fulfills the requirements below

typestruct	result	notes
impl::get_unit_impl< Q >	U
impl::get_numeric_type_impl< Q >	V

function	result	notes
get_numeric_value( q )	v

Relation of numeric value of quantities of same dimension:

For a model of quantity q, the conversion_factor is the factor by which to multiply the numeric_value of q, to convert q to a dimensionally_equivalent quantity in the same measurement system, with a conversion_factor that evaluates to 1.
Let Qb be a model of quantity where evaluate<get_conversion_factor< Qb > >() == 1.
Let Q be a dimensionally_equivalent model of quantity in same measurement_system as Qb , where evaluate<get_conversion_factor<Q> >() != 1.

   using namespace pqs;

   using Qb = si::length::m<>;
   using Q  = si::length::ft<>;

   static_assert( same_measurement_system< Q,Qb > );
   static_assert( evaluate<get_conversion_factor< Qb > >() == 1 );
   static_assert( evaluate<get_conversion_factor< Q > >() != 1 );

   constexpr dimensionless_quantity n = -12345.678;
   
   constexpr Q  q{n};
   constexpr Qb qB = q;

   static_assert( 
      get_numeric_value(qB) == 
         get_numeric_value(q) * evaluate<get_conversion_factor<Q> >() 
   );

Notes

• [1] https://en.wikipedia.org/wiki/Physical_quantity
• [2] https://en.wikipedia.org/wiki/Number.