implement value_cast<ToQ> and value_cast<ToQP>

CHANGELOG.md

@@ -16,6 +16,7 @@
 - feat: `fma` for quantity points added
 - feat: `quantity_point` support added for `quantity_cast` and `value_cast`
 - feat: `value_cast<Unit, Representation>` added
+- feat: `value_cast<Quantity>(q)`, `value_cast<Quantity>(qp)` and `value_cast<QuantityPoint>(qp)` added by [@burnpanck](https://github.com/burnpanck)
 - feat: `interconvertible(QuantitySpec, QuantitySpec)` added
 - feat: `qp.quantity_from_zero()` added
 - feat: `value_type` type trait added

docs/users_guide/framework_basics/value_conversions.md

@@ -147,3 +147,17 @@ using namespace unit_symbols;
 Price price{12.95 * USD};
 Scaled spx = value_cast<USD_s, std::int64_t>(price);
 ```
+
+As a shortcut, instead of providing a unit and a representation type to `value_cast`, you may also provide a
+`Quantity` type directly, from which unit and representation type are taken. However, `value_cast<Quantity>`,
+still only allows for changes in unit and representation type, but not changing the type of the quantity.
+For that, you will have to use a `quantity_cast` instead.
+
+Overloads are also provided for instances of `quantity_point`. Furthermore, in that case, there is
+an overload `value_cast<ToQP>(qp)`, which is roughly equivalent to
+`value_cast<typename ToQP::quantity_type>(qp).point_for(ToQP::point_origin)`.
+In contrast to a separate `value_cast` followed by `point_for` (or vice-versa), the combined
+`value_cast` tries to choose the order of the individual conversion steps in such a way,
+to avoid both overflow and unnecessary loss of precision. Overflow is a risk because the change of origin point
+may require an addition of a potentially large offset (the difference between the origin points),
+which may well be outside the range of one or both quantity types.

src/core/include/mp-units/bits/sudo_cast.h

@@ -37,6 +37,45 @@ template<typename T, typename Other>
 using maybe_common_type = MP_UNITS_TYPENAME std::conditional_t<requires { typename std::common_type_t<T, Other>; },
                                                                get_common_type<T, Other>, std::type_identity<T>>::type;
 
+/**
+ * @brief Details about the conversion from one quantity to another.
+ *
+ * This struct calculates the conversion factor that needs to be applied to a number,
+ * in order to convert from one quantity to another. In addition to that, it also
+ * helps to determine what representations to use at which step in the conversion process,
+ * in order to avoid overflow and underflow while not causing excessive computations.
+ *
+ * @note This is a low-level facility.
+ *
+ * @tparam To a target quantity type to cast to
+ * @tparam From a source quantity type to cast from
+ */
+template<Quantity To, Quantity From>
+  requires(castable(From::quantity_spec, To::quantity_spec))
+struct magnitude_conversion_traits {
+  // scale the number
+  static constexpr Magnitude auto c_mag = get_canonical_unit(From::unit).mag / get_canonical_unit(To::unit).mag;
+  static constexpr Magnitude auto num = numerator(c_mag);
+  static constexpr Magnitude auto den = denominator(c_mag);
+  static constexpr Magnitude auto irr = c_mag * (den / num);
+  using c_rep_type = maybe_common_type<typename std::remove_reference_t<From>::rep, typename To::rep>;
+  using c_mag_type = common_magnitude_type<c_mag>;
+  using multiplier_type = conditional<
+    treat_as_floating_point<c_rep_type>,
+    // ensure that the multiplier is also floating-point
+    conditional<std::is_arithmetic_v<value_type_t<c_rep_type>>,
+                // reuse user's type if possible
+                std::common_type_t<c_mag_type, value_type_t<c_rep_type>>, std::common_type_t<c_mag_type, double>>,
+    c_mag_type>;
+  using c_type = maybe_common_type<c_rep_type, multiplier_type>;
+  static constexpr auto val(Magnitude auto m) { return get_value<multiplier_type>(m); };
+  static constexpr multiplier_type num_mult = val(num);
+  static constexpr multiplier_type den_mult = val(den);
+  static constexpr multiplier_type irr_mult = val(irr);
+  static constexpr multiplier_type ratio = num_mult / den_mult * irr_mult;
+};
+
+
 /**
  * @brief Explicit cast between different quantity types
  *
@@ -64,34 +103,77 @@ template<Quantity To, typename From>
                              // warnings on conversions
   } else {
     // scale the number
-    constexpr Magnitude auto c_mag = get_canonical_unit(q_unit).mag / get_canonical_unit(To::unit).mag;
-    constexpr Magnitude auto num = numerator(c_mag);
-    constexpr Magnitude auto den = denominator(c_mag);
-    constexpr Magnitude auto irr = c_mag * (den / num);
-    using c_rep_type = maybe_common_type<typename std::remove_reference_t<From>::rep, typename To::rep>;
-    using c_mag_type = common_magnitude_type<c_mag>;
-    using multiplier_type = conditional<
-      treat_as_floating_point<c_rep_type>,
-      // ensure that the multiplier is also floating-point
-      conditional<std::is_arithmetic_v<value_type_t<c_rep_type>>,
-                  // reuse user's type if possible
-                  std::common_type_t<c_mag_type, value_type_t<c_rep_type>>, std::common_type_t<c_mag_type, double>>,
-      c_mag_type>;
-    using c_type = maybe_common_type<c_rep_type, multiplier_type>;
-    constexpr auto val = [](Magnitude auto m) { return get_value<multiplier_type>(m); };
-    if constexpr (std::is_floating_point_v<multiplier_type>) {
+    using traits = magnitude_conversion_traits<To, std::remove_reference_t<From>>;
+    if constexpr (std::is_floating_point_v<typename traits::multiplier_type>) {
       // this results in great assembly
-      constexpr auto ratio = val(num) / val(den) * val(irr);
       auto res = static_cast<MP_UNITS_TYPENAME To::rep>(
-        static_cast<c_type>(q.numerical_value_is_an_implementation_detail_) * ratio);
+        static_cast<traits::c_type>(q.numerical_value_is_an_implementation_detail_) * traits::ratio);
       return {res, To::reference};
     } else {
       // this is slower but allows conversions like 2000 m -> 2 km without loosing data
       auto res = static_cast<MP_UNITS_TYPENAME To::rep>(
-        static_cast<c_type>(q.numerical_value_is_an_implementation_detail_) * val(num) / val(den) * val(irr));
+        static_cast<traits::c_type>(q.numerical_value_is_an_implementation_detail_) * traits::num_mult /
+        traits::den_mult * traits::irr_mult);
       return {res, To::reference};
     }
   }
 }
 
+
+/**
+ * @brief Explicit cast between different quantity_point types
+ *
+ * @note This is a low-level facility and is too powerful to be used by the users directly. They should either use
+ * `value_cast` or `quantity_cast`.
+ *
+ * @tparam ToQP a target quantity point type to which to cast to
+ */
+template<QuantityPoint ToQP, typename FromQP>
+  requires QuantityPoint<std::remove_cvref_t<FromQP>> &&
+           (castable(std::remove_reference_t<FromQP>::quantity_spec, ToQP::quantity_spec)) &&
+           (detail::same_absolute_point_origins(ToQP::point_origin, std::remove_reference_t<FromQP>::point_origin)) &&
+           ((std::remove_reference_t<FromQP>::unit == ToQP::unit &&
+             std::constructible_from<typename ToQP::rep, typename std::remove_reference_t<FromQP>::rep>) ||
+            (std::remove_reference_t<FromQP>::unit != ToQP::unit))
+[[nodiscard]] constexpr QuantityPoint auto sudo_cast(FromQP&& qp)
+{
+  using qp_type = std::remove_reference_t<FromQP>;
+  if constexpr (is_same_v<std::remove_const_t<decltype(ToQP::point_origin)>,
+                          std::remove_const_t<decltype(qp_type::point_origin)>>) {
+    return quantity_point{
+      sudo_cast<typename ToQP::quantity_type>(std::forward<FromQP>(qp).quantity_from(qp_type::point_origin)),
+      qp_type::point_origin};
+  } else {
+    // it's unclear how hard we should try to avoid truncation here. For now, the only corner case we cater for,
+    // is when the range of the quantity type of at most one of QP or ToQP doesn't cover the offset between the
+    // point origins. In that case, we need to be careful to ensure we use the quantity type with the larger range
+    // of the two to perform the point_origin conversion.
+    // Numerically, we'll potentially need to do three things:
+    //  (a) cast the representation type
+    //  (b) scale the numerical value
+    //  (c) add/subtract the origin difference
+    // In the following, we carefully select the order of these three operations: each of (a) and (b) is scheduled
+    // either before or after (c), such that (c) acts on the largest range possible among all combination of source
+    // and target unit and represenation.
+    using traits = magnitude_conversion_traits<typename ToQP::quantity_type, typename qp_type::quantity_type>;
+    using c_rep_type = typename traits::c_rep_type;
+    if constexpr (traits::num_mult * traits::irr_mult > traits::den_mult) {
+      // original unit had a larger unit magnitude; if we first convert to the common representation but retain the
+      // unit, we obtain the largest possible range while not causing truncation of fractional values. This is optimal
+      // for the offset computation.
+      return sudo_cast<ToQP>(
+        sudo_cast<quantity_point<qp_type::reference, qp_type::point_origin, c_rep_type>>(std::forward<FromQP>(qp))
+          .point_for(ToQP::point_origin));
+    } else {
+      // new unit may have a larger unit magnitude; we first need to convert to the new unit (potentially causing
+      // truncation, but no more than if we did the conversion later), but make sure we keep the larger of the two
+      // representation types. Then, we can perform the offset computation.
+      return sudo_cast<ToQP>(sudo_cast<quantity_point<make_reference(qp_type::quantity_spec, ToQP::unit),
+                                                      qp_type::point_origin, c_rep_type>>(std::forward<FromQP>(qp))
+                               .point_for(ToQP::point_origin));
+    }
+  }
+}
+
+
 }  // namespace mp_units::detail

src/core/include/mp-units/framework/magnitude.h

@@ -758,7 +758,7 @@ template<auto H1, auto... T1, auto H2, auto... T2>
 template<auto... Ms>
 [[nodiscard]] consteval auto common_magnitude_type_impl(magnitude<Ms...>)
 {
-  return (... * decltype(get_base_value(Ms)){}) * std::intmax_t{};
+  return (decltype(get_base_value(Ms)){} * ... * std::intmax_t{});
 }
 
 // Returns the most precise type to express the magnitude factor

src/core/include/mp-units/framework/value_cast.h

@@ -80,7 +80,8 @@ template<Representation ToRep, typename Q>
  *
  * auto q = value_cast<us, int>(1.23 * ms);
  *
- * @tparam ToRep a representation type to use for a target quantity
+ * @tparam ToU a unit to use for the target quantity
+ * @tparam ToRep a representation type to use for the target quantity
  */
 template<Unit auto ToU, Representation ToRep, typename Q>
   requires Quantity<std::remove_cvref_t<Q>> && (convertible(std::remove_reference_t<Q>::reference, ToU)) &&
@@ -92,6 +93,30 @@ template<Unit auto ToU, Representation ToRep, typename Q>
   return detail::sudo_cast<quantity<detail::make_reference(q_type::quantity_spec, ToU), ToRep>>(std::forward<Q>(q));
 }
 
+
+/**
+ * @brief Explicit cast of a quantity's representation
+ *
+ * Implicit conversions between quantities of different types are allowed only for "safe"
+ * (e.g. non-truncating) conversion. In truncating cases an explicit cast have to be used.
+ *
+ * using ToQ = quantity<us, int>;
+ * auto q = value_cast<ToQ>(1.23 * ms);
+ *
+ * Note that value_cast only changes the "representation aspects" (unit and representation
+ * type), but not the "meaning" (quantity type).
+ *
+ * @tparam ToQ a target quantity type to which to cast the representation
+ */
+template<Quantity ToQ, typename Q>
+  requires Quantity<std::remove_cvref_t<Q>> && (convertible(std::remove_reference_t<Q>::reference, ToQ::unit)) &&
+           (ToQ::quantity_spec == std::remove_reference_t<Q>::quantity_spec) &&
+           std::constructible_from<typename ToQ::rep, typename std::remove_reference_t<Q>::rep>
+[[nodiscard]] constexpr Quantity auto value_cast(Q&& q)
+{
+  return detail::sudo_cast<ToQ>(std::forward<Q>(q));
+}
+
 /**
  * @brief Explicit cast of a quantity point's unit
  *
@@ -133,14 +158,15 @@ value_cast(QP&& qp)
 }
 
 /**
- * @brief Explicit cast of a quantity's unit and representation type
+ * @brief Explicit cast of a quantity point's unit and representation type
  *
  * Implicit conversions between quantities of different types are allowed only for "safe"
  * (e.g. non-truncating) conversion. In truncating cases an explicit cast have to be used.
  *
- * auto q = value_cast<us, int>(1.23 * ms);
+ * auto qp = value_cast<us, int>(quantity_point{1.23 * ms});
  *
- * @tparam ToRep a representation type to use for a target quantity
+ * @tparam ToU a unit to use for the target quantity
+ * @tparam ToRep a representation type to use for the target quantity
  */
 template<Unit auto ToU, Representation ToRep, typename QP>
   requires QuantityPoint<std::remove_cvref_t<QP>> && (convertible(std::remove_reference_t<QP>::reference, ToU)) &&
@@ -152,4 +178,70 @@ template<Unit auto ToU, Representation ToRep, typename QP>
                         std::remove_reference_t<QP>::point_origin};
 }
 
+/**
+ * @brief Explicit cast of a quantity point's representation
+ *
+ * Implicit conversions between quantities of different types are allowed only for "safe"
+ * (e.g. non-truncating) conversion. In truncating cases an explicit cast have to be used.
+ *
+ * inline constexpr struct A : absolute_point_origin<A, isq::distance> A;
+ *
+ * using ToQ = quantity<mm, int>;
+ * auto qp = value_cast<ToQ>(quantity_point{1.23 * m});
+ *
+ * Note that value_cast only changes the "representation aspects" (unit and representation
+ * type), but not the "meaning" (quantity type or the actual point that is being described).
+ *
+ * @tparam ToQ a target quantity type to which to cast the representation of the point
+ */
+template<Quantity ToQ, typename QP>
+  requires QuantityPoint<std::remove_cvref_t<QP>> && (convertible(std::remove_reference_t<QP>::reference, ToQ::unit)) &&
+           (ToQ::quantity_spec == std::remove_reference_t<QP>::quantity_spec) &&
+           std::constructible_from<typename ToQ::rep, typename std::remove_reference_t<QP>::rep>
+[[nodiscard]] constexpr QuantityPoint auto value_cast(QP&& qp)
+{
+  return quantity_point{value_cast<ToQ>(std::forward<QP>(qp).quantity_from_origin_is_an_implementation_detail_),
+                        std::remove_reference_t<QP>::point_origin};
+}
+
+/**
+ * @brief Explicit cast of a quantity point's representation, including potentially the point origin
+ *
+ * Implicit conversions between quantities of different types are allowed only for "safe"
+ * (e.g. non-truncating) conversion. In truncating cases an explicit cast have to be used.
+ *
+ * inline constexpr struct A : absolute_point_origin<A, isq::distance> A;
+ * inline constexpr struct B : relative_point_origin<A + 1*m> B;
+ *
+ * using ToQP = quantity_point<mm, B, int>;
+ * auto qp = value_cast<ToQP>(quantity_point{1.23 * m});
+ *
+ * Note that value_cast only changes the "representation aspects" (unit, representation
+ * type and point origin), but not the "meaning" (quantity type or the actual point that is
+ * being described).
+ *
+ * Note also that changing the point origin bears risks regarding truncation and overflow
+ * similar to other casts that change representation (which is why we require a `value_cast`
+ * and disallow implicit conversions). This cast is guaranteed not to cause overflow of
+ * any intermediate representation type provided that the input quantity point is within
+ * the range of `ToQP`. Calling `value_cast<ToQP>(qp)` on a `qp` outside of the range of `ToQP`
+ * is potentially undefined behaviour.
+ * The implementation further attempts not to cause more than
+ * rounding error than approximately the sum of the resolution of `qp` as represented in `FromQP`,
+ * plust the resolution of `qp` as represented in `ToQP`.
+ *
+ * @tparam ToQP a target quantity point type to which to cast the representation of the point
+ */
+template<QuantityPoint ToQP, typename QP>
+  requires QuantityPoint<std::remove_cvref_t<QP>> &&
+           (convertible(std::remove_reference_t<QP>::reference, ToQP::unit)) &&
+           (ToQP::quantity_spec == std::remove_reference_t<QP>::quantity_spec) &&
+           (detail::same_absolute_point_origins(ToQP::point_origin, std::remove_reference_t<QP>::point_origin)) &&
+           std::constructible_from<typename ToQP::rep, typename std::remove_reference_t<QP>::rep>
+[[nodiscard]] constexpr QuantityPoint auto value_cast(QP&& qp)
+{
+  return detail::sudo_cast<ToQP>(std::forward<QP>(qp));
+}
+
+
 }  // namespace mp_units

test/static/quantity_point_test.cpp

@@ -1704,4 +1704,41 @@ static_assert(value_cast<float>(lvalue_qp).quantity_from_zero().numerical_value_
 static_assert(value_cast<m, float>(lvalue_qp).quantity_from_zero().numerical_value_in(m) == 2000.f);
 }  // namespace lvalue_tests
 
+static_assert(value_cast<quantity<km, int>>(quantity_point{2000 * m}).quantity_from_zero().numerical_value_in(km) == 2);
+static_assert(value_cast<quantity_point<km>>(quantity_point{2000 * m}).quantity_from_zero().numerical_value_in(km) ==
+              2);
+
+template<typename ToQ, typename FromQ>
+constexpr bool value_cast_is_forbidden()
+{
+  // it appears we cannot have the requires clause right inside static_assert
+  return !requires(FromQ q) { value_cast<ToQ>(q); };
+}
+static_assert(value_cast_is_forbidden<quantity_point<m>, quantity_point<isq::width[m]>>(),
+              "value_cast shall not cast between different quantity types");
+static_assert(value_cast_is_forbidden<quantity_point<isq::width[m]>, quantity_point<m>>(),
+              "value_cast shall not cast between different quantity types");
+// value_cast which does not touch the point_origin
+static_assert(value_cast<quantity_point<isq::height[m]>>(quantity_point{2 * isq::height[km]})
+                .quantity_from_origin_is_an_implementation_detail_.numerical_value_in(m) == 2000);
+static_assert(value_cast<quantity_point<isq::height[km]>>(quantity_point{2000 * isq::height[m]})
+                .quantity_from_origin_is_an_implementation_detail_.numerical_value_in(km) == 2);
+// a value_cast which includes a change to the point origin
+static_assert(value_cast<quantity_point<isq::height[m], mean_sea_level>>(quantity_point{2000 * isq::height[m],
+                                                                                        ground_level})
+                .quantity_from_origin_is_an_implementation_detail_.numerical_value_in(m) == 2042);
+// a value_cast which includes a change to the point origin as-well as a change in units
+static_assert(value_cast<quantity_point<isq::height[m], mean_sea_level>>(quantity_point{2 * isq::height[km],
+                                                                                        ground_level})
+                .quantity_from_origin_is_an_implementation_detail_.numerical_value_in(m) == 2042);
+// a value_cast which changes all three of unit, rep, point_origin simultaneously, and the range of either FromQP or
+// ToQP does not include the other's point_origin
+static_assert(value_cast<quantity_point<isq::height[cm], mean_sea_level, int>>(
+                quantity_point{std::int8_t{100} * isq::height[mm], ground_level})
+                .quantity_from_origin_is_an_implementation_detail_.numerical_value_in(cm) == 4210);
+static_assert(value_cast<quantity_point<isq::height[mm], ground_level, std::int8_t>>(
+                quantity_point{4210 * isq::height[cm], mean_sea_level})
+                .quantity_from_origin_is_an_implementation_detail_.numerical_value_in(mm) == 100);
+
+
 }  // namespace