refactor: quantity_cast refactored

src/core/include/units/concepts.h

@@ -81,10 +81,6 @@ 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 T, typename U>
-concept scalable_with_ =  // exposition only
-  common_type_with_<T, U> && scalable_<std::common_type_t<T, U>>;
-
 template<typename T>
 concept Representation = (!Quantity<T>) &&
                          // (!QuantityLike<T>) && (!wrapped_quantity_<T>) &&

src/core/include/units/quantity.h

@@ -56,10 +56,10 @@ 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_to_ =  // exposition only
-  (!Quantity<From>) && (!Quantity<To>) && std::convertible_to<From, To> &&
-  (floating_point_<To> || (!floating_point_<From>));
+template<typename T, typename Arg>
+concept rep_safe_constructible_from_ =  // exposition only
+  (!Quantity<std::remove_cvref_t<Arg>>) && std::constructible_from<T, Arg> &&
+  (floating_point_<T> || (!floating_point_<Arg>));
 
 // QFrom ratio is an exact multiple of QTo
 template<typename QFrom, typename QTo>
@@ -69,16 +69,15 @@ concept harmonic_ =  // exposition only
 
 template<typename QFrom, typename QTo>
 concept quantity_convertible_to_ =  // exposition only
-  Quantity<QFrom> && Quantity<QTo> &&
-  interconvertible(QFrom::reference, QTo::reference) && scalable_with_<typename QFrom::rep, typename QTo::rep> &&
+  Quantity<QFrom> && Quantity<QTo> && requires(QFrom q) { quantity_cast<QTo>(q); } &&
   (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> && Representation<std::invoke_result_t<Func, T, U>>;
 
 template<typename T, typename Func, typename U, typename V>
-concept invoke_result_convertible_to_ =
-  Representation<T> && quantity_value_for_<Func, U, V> && safe_convertible_to_<T, std::invoke_result_t<Func, U, V>>;
+concept invoke_result_convertible_to_ = Representation<T> && quantity_value_for_<Func, U, V> &&
+                                        rep_safe_constructible_from_<std::invoke_result_t<Func, U, V>, T>;
 
 template<typename Func, typename Q, typename V>
 concept have_quantity_for_ = Quantity<Q> && (!Quantity<V>) && quantity_value_for_<Func, typename Q::rep, V>;
@@ -151,7 +150,7 @@ public:
   quantity(quantity&&) = default;
 
   template<typename Value>
-    requires safe_convertible_to_<std::remove_cvref_t<Value>, rep>
+    requires rep_safe_constructible_from_<rep, Value>
   constexpr explicit(!detail::quantity_one<quantity>) quantity(Value&& v) : number_(std::forward<Value>(v))
   {
   }

src/core/include/units/quantity_cast.h

@@ -48,30 +48,6 @@ class quantity;
 // template<PointKind PK, UnitOf<typename PK::dimension> U, Representation Rep>
 // class quantity_point_kind;
 
-namespace detail {
-
-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 multiplier_type = std::common_type_t<std::common_type_t<From, To>, std::intmax_t>;
-  using rep_type = multiplier_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 multiplier_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
-
 /**
  * @brief Explicit cast of a quantity
  *
@@ -84,16 +60,41 @@ struct cast_traits<From, To> {
  *
  * @tparam To a target quantity type to cast to
  */
-template<Quantity To, auto R, scalable_with_<typename To::rep> Rep>
-  requires(interconvertible(To::reference, R))
+template<Quantity To, auto R, typename Rep>
+  requires(interconvertible(To::reference, R)) &&
+          ((R.unit == To::unit && std::constructible_from<typename To::rep, Rep>) ||
+           (R.unit != To::unit))  // && scalable_with_<typename To::rep>))
+// TODO how to constrain the second part here?
 [[nodiscard]] constexpr auto quantity_cast(const quantity<R, Rep>& q)
 {
   if constexpr (R.unit == To::unit) {
-    return To(static_cast<TYPENAME To::rep>(q.number()));
+    // no scaling of the number needed
+    return To(static_cast<TYPENAME To::rep>(q.number()));  // this is the only (and recommended) way to do
+                                                           // a truncating conversion on a number, so we are
+                                                           // using static_cast to suppress all the compiler
+                                                           // warnings on conversions
   } else {
-    using traits = detail::cast_traits<Rep, typename To::rep>;
-    using multiplier_type = TYPENAME traits::multiplier_type;
-    using rep_type = TYPENAME traits::rep_type;
+    // scale the number
+    using rep_type = decltype([] {
+      // determines the best representation type
+      if constexpr (requires { typename std::common_type_t<Rep, typename To::rep>; })
+        // returns a common type of two representation types if available
+        // i.e. `double` and `int` will end up with `double` precision
+        return std::common_type_t<Rep, typename To::rep>{};
+      else
+        return Rep{};
+    }());
+    using multiplier_type = decltype([] {
+      // widen the type to prevent overflows
+      using wider_type = decltype(rep_type{} * std::intmax_t{});
+      // check if `wider_type` supports scaling operations
+      if constexpr (requires(wider_type v) { v* v / v; })
+        // if the `wider_type` can handle scaling operations then use it to improve accuracy
+        return wider_type{};
+      else
+        // needed for example for linear algebra where `op/` on matrix types is not available
+        return std::intmax_t{};
+    }());
 
     constexpr Magnitude auto c_mag = detail::get_canonical_unit(R.unit).mag / detail::get_canonical_unit(To::unit).mag;
     constexpr Magnitude auto num = numerator(c_mag);
@@ -181,8 +182,8 @@ template<Unit auto ToU, auto R, typename Rep>
  *
  * @tparam ToRep a representation type to use for a target quantity
  */
-template<Representation ToRep, auto R, scalable_with_<ToRep> Rep>
-// requires(std::constructible_from<ToRep, std::common_type_t<ToRep, Rep>>)
+template<Representation ToRep, auto R, typename Rep>
+  requires std::constructible_from<ToRep, Rep>
 [[nodiscard]] constexpr auto quantity_cast(const quantity<R, Rep>& q)
 {
   return quantity_cast<quantity<R, ToRep>>(q);
@@ -308,7 +309,8 @@ template<Representation ToRep, auto R, scalable_with_<ToRep> Rep>
 //  * Implicit conversions between quantity point kinds of different types are allowed only for "safe"
 //  * (i.e. non-truncating) conversion. In other cases an explicit cast has to be used.
 //  *
-//  * This cast gets the target (quantity) point kind type to cast to or anything that works for quantity_kind_cast. For
+//  * This cast gets the target (quantity) point kind type to cast to or anything that works for quantity_kind_cast.
+//  For
 //  * example:
 //  *
 //  * auto q1 = units::quantity_point_kind_cast<decltype(ns::x_coordinate{1 * m))>(ns::x_coordinate{1 * mm});