Temperature support is one the most challenging parts of any physical +quantities and units library design. This is why it is probably +reasonable to dedicate a chapter to this subject to describe how they +are intended to work and what are the potential pitfalls or +surprises.
+First, let’s run the following code:
+quantity q1 = isq::thermodynamic_temperature(30. * K);
+quantity q2 = isq::Celsius_temperature(30. * deg_C);
+
+std::println("q1: {}, {}, {}", q1, q1.in(deg_C), q1.in(deg_F));
+std::println("q2: {}, {}, {}", q2.in(K), q2, q2.in(deg_F));This outputs:
+q1: 30 K, 30 °C, 54 °F
+q2: 30 K, 30 °C, 54 °FAlso doing the following:
+quantity q3 = isq::Celsius_temperature(q1);
+quantity q4 = isq::thermodynamic_temperature(q2);outputs:
+q3: 30 K
+q4: 30 °CEven though the [ISO 80000] provides +dedicated quantity types for thermodynamic temperature and Celsius +temperature, it explicitly states in the description of the first +one:
+++Differences of thermodynamic temperatures or changes may be expressed +either in kelvin, symbol K, or in degrees Celsius, symbol °C
+
In the description of the second quantity type, we can read:
+++The unit degree Celsius is a special name for the kelvin for use in +stating values of Celsius temperature. The unit degree Celsius is by +definition equal in magnitude to the kelvin. A difference or interval of +temperature may be expressed in kelvin or in degrees Celsius.
+
As the quantity is a
+differential quantity type, it is okay to use any temperature unit for
+those, and the results should differ only by the conversion factor. No
+offset should be applied here to convert between the origins of
+different unit scales.
It is important to mention here that the existence of Celsius +temperature quantity type in [ISO +80000] is controversial.
+[ISO 80000] (part 1) says:
+++The system of quantities presented in this document is named the +International System of Quantities (ISQ), in all languages. This name +was not used in ISO 31 series, from which the present harmonized series +has evolved. However, the ISQ does appear in ISO/IEC Guide 99 and is the +system of quantities underlying the International System of Units, +denoted “SI”, in all languages according to the SI Brochure.
+
According to the [ISO/IEC Guide 99], +a system of quantities is a “set of quantities together with a set of +non-contradictory equations relating those quantities”. It also defines +the system of units as “set of base units and derived units, together +with their multiples and submultiples, defined in accordance with given +rules, for a given system of quantities”.
+To say it explicitly, the system of quantities should not assume or +use any specific units in its definitions. It is essential as various +systems of units can be defined on top of it, and none of those should +be favored.
+However, the Celsius temperature quantity type is defined in [ISO 80000] (part 5) as:
+++temperature difference from the thermodynamic temperature of the ice +point is called the Celsius temperature \(t\), which is defined by the quantity +equation:
+\(t = T − T_0\)
+where \(T\) is thermodynamic +temperature (item 5-1) and \(T_0 = +273,15\:K\)
+
Celsius temperature is an exceptional quantity in the ISQ as it uses +specific SI units in its definition. This breaks the direction of +dependencies between systems of quantities and units and imposes +significant implementation issues.
+As [mp-units] +implementation clearly distinguishes between systems of quantities and +units and assumes that the latter directly depends on the former, this +quantity definition does not enforce any units or offsets. It is defined +as just a more specialized quantity of the kind of thermodynamic +temperature. We have added the Celsius temperature quantity type for +completeness and to gain more experience with it. Still, maybe a good +decision would be to skip it in the standardization process not to +confuse users.
+After quoting the official definitions and terms and presenting how +quantities work, let’s discuss quantity points. Those describe specific +points and are measured relative to a provided origin:
+quantity_point qp1 = si::absolute_zero + isq::thermodynamic_temperature(300. * K);
+quantity_point qp2 = si::ice_point + isq::Celsius_temperature(30. * deg_C);The above provides two different temperature points. The first one is
+measured as a relative quantity to the absolute zero
+(0 K), and the second one stores
+the value relative to the ice point being the beginning of the degree
+Celsius scale.
It is essential to understand that the origins of quantity points +will not change if we convert their units:
+quantity_point qp3 = qp1.in(deg_C);
+quantity_point qp4 = qp2.in(K);
+
+static_assert(std::is_same_v<decltype(qp3.point_origin), decltype(si::absolute_zero)>);
+static_assert(std::is_same_v<decltype(qp4.point_origin), decltype(si::ice_point)>);If we want to obtain the values of quantities in specific units +relative to the origins of their scales, we have to be explicit:
+std::println("qp1: {}, {}, {}",
+ qp1.quantity_from(si::absolute_zero),
+ qp1.quantity_from(si::ice_point).in(deg_C),
+ qp1.quantity_from(usc::zero_Fahrenheit).in(deg_F));
+std::println("qp2: {}, {}, {}",
+ qp2.quantity_from(si::absolute_zero).in(K),
+ qp2.quantity_from(si::ice_point),
+ qp2.quantity_from(usc::zero_Fahrenheit).in(deg_F));The above outputs:
+qp1: 300 K, 26.85 °C, 80.33 °F
+qp2: 303.15 K, 30 °C, 86 °FOf course, all other combinations are also possible. For example,
+nothing should prevent us from checking how many degrees of Celsius are
+there starting from the
+zero_Fahrenheit for a quantity
+point using kelvins with the
+absolute_zero origin:
quantity q = qp1.quantity_from(usc::zero_Fahrenheit).in(deg_C);Please also note that there is no text output support for quantity +points in the [mp-units] +library.
+The quantity and
quantity_point class templates
are structural types to allow them to be passed as template arguments.
For example, we can write the following:
constexpr struct amsterdam_sea_level : absolute_point_origin<isq::altitude> {
-} amsterdam_sea_level;
-
-constexpr struct mediterranean_sea_level : relative_point_origin<amsterdam_sea_level + isq::altitude(-27 * cm)> {
-} mediterranean_sea_level;
-
-using altitude_DE = quantity_point<isq::altitude[m], amsterdam_sea_level>;
-using altitude_CH = quantity_point<isq::altitude[m], mediterranean_sea_level>;constexpr struct amsterdam_sea_level : absolute_point_origin<isq::altitude> {
+} amsterdam_sea_level;
+
+constexpr struct mediterranean_sea_level : relative_point_origin<amsterdam_sea_level + isq::altitude(-27 * cm)> {
+} mediterranean_sea_level;
+
+using altitude_DE = quantity_point<isq::altitude[m], amsterdam_sea_level>;
+using altitude_CH = quantity_point<isq::altitude[m], mediterranean_sea_level>;Unfortunately, current language rules require that all member data of
a structural type are public. This could be considered a safety issue.
We try really hard to provide unit-safe interfaces, but at the same time
diff --git a/src/2981R1_improving_our_safety_with_a_physical_quantities_and_units_library.md b/src/2981R1_improving_our_safety_with_a_physical_quantities_and_units_library.md
index a28a89a..4cfa861 100644
--- a/src/2981R1_improving_our_safety_with_a_physical_quantities_and_units_library.md
+++ b/src/2981R1_improving_our_safety_with_a_physical_quantities_and_units_library.md
@@ -24,6 +24,7 @@ author:
- Value-preserving type trait mentioned in [Lack of safe numeric types].
- [Non-negative quantities] rewritten.
- [Limitations of systems of quantities] added.
+- [Temperatures] added.
- Some small editorial fixes.
@@ -1402,6 +1403,155 @@ quantity<(isq::length / isq::length)[m / m]> ok7 = q3;
quantity<(isq::height / isq::length)[m / m]> bad2 = q3;
```
+## Temperatures
+
+Temperature support is one the most challenging parts of any physical quantities and units library
+design. This is why it is probably reasonable to dedicate a chapter to this subject to describe how
+they are intended to work and what are the potential pitfalls or surprises.
+
+First, let's run the following code:
+
+```cpp
+quantity q1 = isq::thermodynamic_temperature(30. * K);
+quantity q2 = isq::Celsius_temperature(30. * deg_C);
+
+std::println("q1: {}, {}, {}", q1, q1.in(deg_C), q1.in(deg_F));
+std::println("q2: {}, {}, {}", q2.in(K), q2, q2.in(deg_F));
+```
+
+This outputs:
+
+```text
+q1: 30 K, 30 °C, 54 °F
+q2: 30 K, 30 °C, 54 °F
+```
+
+Also doing the following:
+
+```cpp
+quantity q3 = isq::Celsius_temperature(q1);
+quantity q4 = isq::thermodynamic_temperature(q2);
+```
+
+outputs:
+
+```text
+q3: 30 K
+q4: 30 °C
+```
+
+Even though the [@ISO80000] provides dedicated quantity types for thermodynamic temperature
+and Celsius temperature, it explicitly states in the description of the first one:
+
+> Differences of thermodynamic temperatures or changes may be expressed either in kelvin,
+> symbol K, or in degrees Celsius, symbol °C
+
+In the description of the second quantity type, we can read:
+
+> The unit degree Celsius is a special name for the kelvin for use in stating values of Celsius
+> temperature. The unit degree Celsius is by definition equal in magnitude to the kelvin. A
+> difference or interval of temperature may be expressed in kelvin or in degrees Celsius.
+
+As the `quantity` is a differential quantity type, it is okay to use any temperature unit for
+those, and the results should differ only by the conversion factor. No offset should be applied
+here to convert between the origins of different unit scales.
+
+It is important to mention here that the existence of Celsius temperature quantity type
+in [@ISO80000] is controversial.
+
+[@ISO80000] (part 1) says:
+
+> The system of quantities presented in this document is named the International System of
+> Quantities (ISQ), in all languages. This name was not used in ISO 31 series, from which
+> the present harmonized series has evolved. However, the ISQ does appear in ISO/IEC Guide 99
+> and is the system of quantities underlying the International System of Units, denoted “SI”,
+> in all languages according to the SI Brochure.
+
+According to the [@ISO-GUIDE], a system of quantities is a "set of quantities together with
+a set of non-contradictory equations relating those quantities". It also defines the
+system of units as "set of base units and derived units, together with their multiples
+and submultiples, defined in accordance with given rules, for a given system of quantities".
+
+To say it explicitly, the system of quantities should not assume or use any specific units
+in its definitions. It is essential as various systems of units can be defined on top of it,
+and none of those should be favored.
+
+However, the Celsius temperature quantity type is defined in [@ISO80000] (part 5) as:
+
+> temperature difference from the thermodynamic temperature of the ice point is called the
+> Celsius temperature $t$, which is defined by the quantity equation:
+>
+> $t = T − T_0$
+>
+> where $T$ is thermodynamic temperature (item 5-1) and $T_0 = 273,15\:K$
+
+Celsius temperature is an exceptional quantity in the ISQ as it uses specific SI units in
+its definition. This breaks the direction of dependencies between systems of quantities and
+units and imposes significant implementation issues.
+
+As [@MP-UNITS] implementation clearly distinguishes between systems of quantities
+and units and assumes that the latter directly depends on the former, this quantity
+definition does not enforce any units or offsets. It is defined as just a more specialized
+quantity of the kind of thermodynamic temperature. We have added the Celsius temperature
+quantity type for completeness and to gain more experience with it. Still, maybe a good
+decision would be to skip it in the standardization process not to confuse users.
+
+After quoting the official definitions and terms and presenting how quantities
+work, let's discuss quantity points. Those describe specific points and are measured
+relative to a provided origin:
+
+```cpp
+quantity_point qp1 = si::absolute_zero + isq::thermodynamic_temperature(300. * K);
+quantity_point qp2 = si::ice_point + isq::Celsius_temperature(30. * deg_C);
+```
+
+The above provides two different temperature points. The first one is measured as a relative
+quantity to the absolute zero (`0 K`), and the second one stores the value relative to
+the ice point being the beginning of the degree Celsius scale.
+
+It is essential to understand that the origins of quantity points will not change if
+we convert their units:
+
+```cpp
+quantity_point qp3 = qp1.in(deg_C);
+quantity_point qp4 = qp2.in(K);
+
+static_assert(std::is_same_v