feat: quantities can now be multiplied and divided by units

README.md

@@ -63,10 +63,9 @@ static_assert(1 * h == 3600 * s);
 static_assert(1 * km + 1 * m == 1001 * m);
 
 // derived quantities
-inline constexpr auto kmph = km / h;
-static_assert(1 * km / (1 * s) == 1000 * (m / s));
-static_assert(2 * kmph * (2 * h) == 4 * km);
-static_assert(2 * km / (2 * kmph) == 1 * h);
+static_assert(1 * km / (1 * s) == 1000 * m / s);
+static_assert(2 * km / h * (2 * h) == 4 * km);
+static_assert(2 * km / (2 * km / h) == 1 * h);
 
 static_assert(2 * m * (3 * m) == 6 * m2);
 
@@ -103,7 +102,7 @@ int main()
   using namespace mp_units::si::unit_symbols;
   using namespace mp_units::international::unit_symbols;
 
-  constexpr quantity v1 = 110 * (km / h);
+  constexpr quantity v1 = 110 * km / h;
   constexpr quantity v2 = 70 * mph;
   constexpr quantity v3 = avg_speed(220. * isq::distance[km], 2 * h);
   constexpr quantity v4 = avg_speed(isq::distance(140. * mi), 2 * h);

docs/getting_started/code_example.md

@@ -16,10 +16,9 @@ static_assert(1 * h == 3600 * s);
 static_assert(1 * km + 1 * m == 1001 * m);
 
 // derived quantities
-inline constexpr auto kmph = km / h;
-static_assert(1 * km / (1 * s) == 1000 * (m / s));
-static_assert(2 * kmph * (2 * h) == 4 * km);
-static_assert(2 * km / (2 * kmph) == 1 * h);
+static_assert(1 * km / (1 * s) == 1000 * m / s);
+static_assert(2 * km / h * (2 * h) == 4 * km);
+static_assert(2 * km / (2 * km / h) == 1 * h);
 
 static_assert(2 * m * (3 * m) == 6 * m2);
 
@@ -59,7 +58,7 @@ int main()
   using namespace mp_units::si::unit_symbols;
   using namespace mp_units::international::unit_symbols;
 
-  constexpr quantity v1 = 110 * (km / h);
+  constexpr quantity v1 = 110 * km / h;
   constexpr quantity v2 = 70 * mph;
   constexpr quantity v3 = avg_speed(220. * isq::distance[km], 2 * h);
   constexpr quantity v4 = avg_speed(isq::distance(140. * mi), 2 * h);

docs/getting_started/faq.md

@@ -92,47 +92,6 @@ In the **mp-units** library, both a number and a unit have to always be explicit
 form a quantity.
 
 
-## Why `60 * km / h` does not compile?
-
-The library design does not allow multiplying or dividing a quantity (the result of `60 * km`)
-by another unit. This significantly limits the number of possible errors and surprises in the
-quantity equations.
-
-Consider the following expression:
-
-```cpp
-auto q = 60 * km / 2 * h;
-```
-
-Looks like `30 km/h`, right? But it is not. If the above code was allowed, it would result
-in `30 km⋅h`. In case you want to divide `60 * km` by `2 * h` a parenthesis is needed:
-
-```cpp
-auto q = 60 * km / (2 * h);
-```
-
-Another surprising issue could result from the following code:
-
-```cpp
-template<typename T>
-auto make_length(T v) { return v * si::metre; }
-
-auto v = 42;
-auto q = make_length(v);
-```
-
-The above might look like a good idea, but consider what would happen in the user provided
-an already existing quantity:
-
-```cpp
-auto v = 42 * m;
-auto q = make_length(v);
-```
-
-Fortunately, with the current design, such issues are detected at compile-time as
-multiplying or dividing a quantity by a unit is not be supported.
-
-
 ## Why a dimensionless quantity is not just a fundamental arithmetic type?
 
 In the initial design of this library, the resulting type of division of two quantities was their

docs/getting_started/quick_start.md

@@ -67,14 +67,9 @@ quantity q = make_quantity<si::metre>(42);
 Sometimes it might be awkward to type some derived units:
 
 ```cpp
-quantity speed = 60 * (km / h);
+quantity speed = 60 * km / h;
 ```
 
-!!! note
-
-    Please note that `60 * km / h` will not compile. To read more about the rationale for such
-    a design please check our [FAQ](faq.md#why-dont-we-use-udls-to-create-a-quantity).
-
 In case such a unit is used a lot in the project, a user can easily provide a nicely named
 wrapper for it with:
 

docs/users_guide/framework_basics/character_of_a_quantity.md

@@ -212,9 +212,9 @@ either:
     The following does not work:
 
     ```cpp
-    Quantity auto q1 = la_vector{1, 2, 3} * (m / s);
-    Quantity auto q2 = isq::velocity(la_vector{1, 2, 3} * (m / s));
-    quantity<isq::velocity[m/s]> q3{la_vector{1, 2, 3} * (m / s)};
+    Quantity auto q1 = la_vector{1, 2, 3} * m / s;
+    Quantity auto q2 = isq::velocity(la_vector{1, 2, 3} * m / s);
+    quantity<isq::velocity[m/s]> q3{la_vector{1, 2, 3} * m / s};
     ```
 
     In all the cases above, the SI unit `m / s` has an associated scalar quantity of `isq::length / isq::time`.

docs/users_guide/framework_basics/quantity_arithmetics.md

@@ -136,7 +136,7 @@ However, suppose we multiply or divide quantities of the same or different types
 number by a quantity. In that case, we most probably will end up in a quantity of yet another type:
 
 ```cpp
-static_assert(120 * km / (2 * h) == 60 * (km / h));
+static_assert(120 * km / (2 * h) == 60 * km / h);
 static_assert(isq::width(2 * m) * isq::length(2 * m) == isq::area(4 * m2));
 static_assert(50 / isq::time(1 * s) == isq::frequency(50 * Hz));
 ```
@@ -283,7 +283,7 @@ every time when we want to ensure that we deal with a non-zero or positive value
 We could implement such checks in the following way:
 
 ```cpp
-if (q1 / q2 != 0 * (m / s))
+if (q1 / q2 != 0 * m / s)
   // ...
 ```
 

docs/users_guide/framework_basics/text_output.md

@@ -291,12 +291,12 @@ in the denominator), or never in which case a parenthesis will be added to enclo
 units.
 
 ```cpp
-std::println("{:%Q %q}", 1 * (m / s));         // 1 m/s
-std::println("{:%Q %q}", 1 * (kg / m / s2));   // 1 kg m⁻¹ s⁻²
-std::println("{:%Q %aq}", 1 * (m / s));        // 1 m/s
-std::println("{:%Q %aq}", 1 * (kg / m / s2));  // 1 kg/(m s²)
-std::println("{:%Q %nq}", 1 * (m / s));        // 1 m s⁻¹
-std::println("{:%Q %nq}", 1 * (kg / m / s2));  // 1 kg m⁻¹ s⁻²
+std::println("{:%Q %q}", 1 * m / s);         // 1 m/s
+std::println("{:%Q %q}", 1 * kg / m / s2);   // 1 kg m⁻¹ s⁻²
+std::println("{:%Q %aq}", 1 * m / s);        // 1 m/s
+std::println("{:%Q %aq}", 1 * kg / m / s2);  // 1 kg/(m s²)
+std::println("{:%Q %nq}", 1 * m / s);        // 1 m s⁻¹
+std::println("{:%Q %nq}", 1 * kg / m / s2);  // 1 kg m⁻¹ s⁻²
 ```
 
 Also, there are a few options to separate the units being multiplied:
@@ -319,6 +319,6 @@ to just use the `·` symbol as a separator.
 The `units-unit-symbol-separator` token allows us to obtain the following outputs:
 
 ```cpp
-std::println("{:%Q %q}", 1 * (kg * m2 / s2));   // 1 kg m²/s²
-std::println("{:%Q %dq}", 1 * (kg * m2 / s2));  // 1 kg⋅m²/s²
+std::println("{:%Q %q}", 1 * kg * m2 / s2);   // 1 kg m²/s²
+std::println("{:%Q %dq}", 1 * kg * m2 / s2);  // 1 kg⋅m²/s²
 ```

example/foot_pound_second.cpp

@@ -82,11 +82,11 @@ int main()
   auto bismark = Ship{.length{251. * m},
                       .draft{9.3 * m},
                       .beam{36 * m},
-                      .speed{56 * (km / h)},
+                      .speed{56 * km / h},
                       .mass{50'300 * t},
                       .mainGuns{380 * mm},
                       .shellMass{800 * kg},
-                      .shellSpeed{820. * (m / s)},
+                      .shellSpeed{820. * m / s},
                       .power{110.45 * kW}};
 
   // USS Iowa, using units from the foot-pound-second system
@@ -97,7 +97,7 @@ int main()
                    .mass{57'540 * imperial::long_ton},
                    .mainGuns{16 * in},
                    .shellMass{2700 * lb},
-                   .shellSpeed{2690. * (ft / s)},
+                   .shellSpeed{2690. * ft / s},
                    .power{212'000 * hp}};
 
   // HMS King George V, using units from the foot-pound-second system
@@ -108,7 +108,7 @@ int main()
                   .mass{42'245 * imperial::long_ton},
                   .mainGuns{14 * in},
                   .shellMass{1590 * lb},
-                  .shellSpeed{2483. * (ft / s)},
+                  .shellSpeed{2483. * ft / s},
                   .power{110'000 * hp}};
 
   print_details("KMS Bismark, defined in appropriate units from the SI system", bismark);

example/glide_computer.cpp

@@ -45,20 +45,20 @@ auto get_gliders()
   using namespace mp_units::si::unit_symbols;
   MP_UNITS_DIAGNOSTIC_PUSH
   MP_UNITS_DIAGNOSTIC_IGNORE_MISSING_BRACES
-  static const std::array gliders = {glider{"SZD-30 Pirat", {83 * (km / h), -0.7389 * (m / s)}},
-                                     glider{"SZD-51 Junior", {80 * (km / h), -0.6349 * (m / s)}},
-                                     glider{"SZD-48 Jantar Std 3", {110 * (km / h), -0.77355 * (m / s)}},
-                                     glider{"SZD-56 Diana", {110 * (km / h), -0.63657 * (m / s)}}};
+  static const std::array gliders = {glider{"SZD-30 Pirat", {83 * km / h, -0.7389 * m / s}},
+                                     glider{"SZD-51 Junior", {80 * km / h, -0.6349 * m / s}},
+                                     glider{"SZD-48 Jantar Std 3", {110 * km / h, -0.77355 * m / s}},
+                                     glider{"SZD-56 Diana", {110 * km / h, -0.63657 * m / s}}};
   MP_UNITS_DIAGNOSTIC_POP
   return gliders;
 }
 
 auto get_weather_conditions()
 {
   using namespace mp_units::si::unit_symbols;
-  static const std::array weather_conditions = {std::pair{"Good", weather{1900 * m, 4.3 * (m / s)}},
-                                                std::pair{"Medium", weather{1550 * m, 2.8 * (m / s)}},
-                                                std::pair{"Bad", weather{850 * m, 1.8 * (m / s)}}};
+  static const std::array weather_conditions = {std::pair{"Good", weather{1900 * m, 4.3 * m / s}},
+                                                std::pair{"Medium", weather{1550 * m, 2.8 * m / s}},
+                                                std::pair{"Bad", weather{850 * m, 1.8 * m / s}}};
   return weather_conditions;
 }
 
@@ -164,7 +164,7 @@ void example()
   const auto waypoints = get_waypoints();
   const auto weather_conditions = get_weather_conditions();
   const task t = {waypoints[0], waypoints[1], waypoints[0]};
-  const aircraft_tow tow = {400 * m, 1.6 * (m / s)};
+  const aircraft_tow tow = {400 * m, 1.6 * m / s};
   // TODO use C++20 date library when available
   // set `start_time` to 11:00 am today
   const timestamp start_time(std::chrono::system_clock::now());

example/hello_units.cpp

@@ -44,7 +44,7 @@ int main()
   using namespace mp_units::si::unit_symbols;
   using namespace mp_units::international::unit_symbols;
 
-  constexpr quantity v1 = 110 * (km / h);
+  constexpr quantity v1 = 110 * km / h;
   constexpr quantity v2 = 70 * mph;
   constexpr quantity v3 = avg_speed(220. * km, 2 * h);
   constexpr quantity v4 = avg_speed(isq::distance(140. * mi), 2 * isq::duration[h]);

example/kalman_filter/kalman_filter-example_2.cpp

@@ -53,7 +53,7 @@ int main()
   using state = kalman::state<quantity<isq::position_vector[m]>, quantity<isq::velocity[m / s]>>;
 
   const auto interval = isq::duration(5 * s);
-  const state initial = {30 * km, 40 * (m / s)};
+  const state initial = {30 * km, 40 * m / s};
   const quantity<isq::position_vector[m], int> measurements[] = {30'110 * m, 30'265 * m, 30'740 * m, 30'750 * m,
                                                                  31'135 * m, 31'015 * m, 31'180 * m, 31'610 * m,
                                                                  31'960 * m, 31'865 * m};

example/kalman_filter/kalman_filter-example_3.cpp

@@ -53,7 +53,7 @@ int main()
   using state = kalman::state<quantity<isq::position_vector[m]>, quantity<isq::velocity[m / s]>>;
 
   const auto interval = isq::duration(5 * s);
-  const state initial = {30 * km, 50 * (m / s)};
+  const state initial = {30 * km, 50 * m / s};
   const quantity<isq::position_vector[m], int> measurements[] = {30'160 * m, 30'365 * m, 30'890 * m, 31'050 * m,
                                                                  31'785 * m, 32'215 * m, 33'130 * m, 34'510 * m,
                                                                  36'010 * m, 37'265 * m};

example/kalman_filter/kalman_filter-example_4.cpp

@@ -53,7 +53,7 @@ int main()
   using state = kalman::state<quantity<isq::position_vector[m]>, quantity<isq::velocity[m / s]>,
                               quantity<isq::acceleration[m / s2]>>;
   const auto interval = isq::duration(5. * s);
-  const state initial = {30 * km, 50 * (m / s), 0 * (m / s2)};
+  const state initial = {30 * km, 50 * m / s, 0 * m / s2};
 
   const quantity<isq::position_vector[m], int> measurements[] = {30'160 * m, 30'365 * m, 30'890 * m, 31'050 * m,
                                                                  31'785 * m, 32'215 * m, 33'130 * m, 34'510 * m,

example/measurement.cpp

@@ -134,7 +134,7 @@ void example()
   using namespace mp_units;
   using namespace mp_units::si::unit_symbols;
 
-  const auto a = isq::acceleration(measurement{9.8, 0.1} * (m / s2));
+  const auto a = isq::acceleration(measurement{9.8, 0.1} * m / s2);
   const auto t = measurement{1.2, 0.1} * s;
 
   const QuantityOf<isq::velocity> auto v = a * t;

example/storage_tank.cpp

@@ -53,7 +53,7 @@ QUANTITY_SPEC(horizontal_length, isq::length);
 QUANTITY_SPEC(horizontal_area, isq::area, horizontal_length* isq::width);
 
 inline constexpr auto g = 1 * si::standard_gravity;
-inline constexpr auto air_density = isq::mass_density(1.225 * (kg / m3));
+inline constexpr auto air_density = isq::mass_density(1.225 * kg / m3);
 
 class StorageTank {
   quantity<horizontal_area[m2]> base_;
@@ -114,7 +114,7 @@ int main()
 {
   const quantity height = isq::height(200 * mm);
   auto tank = RectangularStorageTank(horizontal_length(1'000 * mm), isq::width(500 * mm), height);
-  tank.set_contents_density(1'000 * isq::mass_density[kg / m3]);
+  tank.set_contents_density(1'000 * kg / m3);
 
   const auto duration = std::chrono::seconds{200};
   const quantity fill_time = value_cast<int>(quantity{duration});  // time since starting fill

src/core/include/mp-units/reference.h

@@ -164,7 +164,21 @@ template<typename Rep, Reference R>
   return make_quantity<R{}>(std::forward<Rep>(lhs));
 }
 
-void /*Use `q * (1 * r)` rather than `q * r`.*/ operator*(Quantity auto, Reference auto) = delete;
+template<typename Q, Reference R>
+  requires Quantity<std::remove_cvref_t<Q>>
+[[nodiscard]] constexpr quantity<std::remove_cvref_t<Q>::reference * R{}, typename std::remove_cvref_t<Q>::rep>
+operator*(Q&& q, R)
+{
+  return make_quantity<std::remove_cvref_t<Q>::reference * R{}>(std::forward<Q>(q).numerical_value_);
+}
+
+template<typename Q, Reference R>
+  requires Quantity<std::remove_cvref_t<Q>>
+[[nodiscard]] constexpr quantity<std::remove_cvref_t<Q>::reference / R{}, typename std::remove_cvref_t<Q>::rep>
+operator/(Q&& q, R)
+{
+  return make_quantity<std::remove_cvref_t<Q>::reference / R{}>(std::forward<Q>(q).numerical_value_);
+}
 
 [[nodiscard]] consteval AssociatedUnit auto common_reference(AssociatedUnit auto u1, AssociatedUnit auto u2,
                                                              AssociatedUnit auto... rest)