fix: LA support fixed

conanfile.py

@@ -78,7 +78,11 @@ class MPUnitsConan(ConanFile):
 
     @property
     def _build_all(self):
-        return bool(self.conf.get("user.build:all", default=True))
+        return bool(self.conf.get("user.build:all", default=False))
+
+    @property
+    def _skip_la(self):
+        return bool(self.conf.get("user.build:skip_la", default=False))
 
     @property
     def _skip_docs(self):
@@ -114,9 +118,10 @@ class MPUnitsConan(ConanFile):
     def build_requirements(self):
         if self._build_all:
             self.test_requires("catch2/3.1.0")
-            self.test_requires("wg21-linear_algebra/0.7.3")
+            if not self._skip_la:
-        if not self._skip_docs:
+                self.test_requires("wg21-linear_algebra/0.7.3")
-            self.tool_requires("doxygen/1.9.4")
+            if not self._skip_docs:
+                self.tool_requires("doxygen/1.9.4")
 
     def validate(self):
         check_min_cppstd(self, self._min_cppstd)
@@ -140,6 +145,7 @@ class MPUnitsConan(ConanFile):
     def generate(self):
         tc = CMakeToolchain(self)
         tc.variables["UNITS_DOWNCAST_MODE"] = str(self.options.downcast_mode).upper()
+        tc.variables["UNITS_BUILD_LA"] = self._build_all and not self._skip_la
         tc.variables["UNITS_BUILD_DOCS"] = self._build_all and not self._skip_docs
         tc.variables["UNITS_USE_LIBFMT"] = self._use_libfmt
         tc.generate()

docs/usage.rst

@@ -146,8 +146,8 @@ Specifies how :ref:`design/downcasting:The Downcasting Facility` works:
 Conan Configuration Properties
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-build_all
+user.build:all
-+++++++++
+++++++++++++++
 
 **Values**: ``True``/``False``
 
@@ -158,14 +158,24 @@ To support this it requires some additional Conan build dependencies described i
 `Repository Structure and Dependencies`_.
 It also runs unit tests during Conan build (unless ``tools.build:skip_test`` configuration property is set to ``True``)
 
-skip_docs
+user.build:skip_la
-+++++++++
+++++++++++++++++++
 
 **Values**: ``True``/``False``
 
 **Defaulted to**: ``False``
 
-If `build_all`_ is enabled, among others, Conan installs the documentation generation dependencies (i.e. doxygen) and
+If `user.build:all`_ is enabled, among others, Conan installs the external `wg21-linear_algebra<https://conan.io/center/wg21-linear_algebra>`_
+dependency and enables compilation of linear algebra based usage examples. Such behavior can be disabled with this option.
+
+user.build:skip_docs
+++++++++++++++++++++
+
+**Values**: ``True``/``False``
+
+**Defaulted to**: ``False``
+
+If `user.build:all`_ is enabled, among others, Conan installs the documentation generation dependencies (i.e. doxygen) and
 turns on the project documentation generation. Such behavior can be disabled with this option.
 
 CMake Options
@@ -181,6 +191,16 @@ UNITS_AS_SYSTEM_HEADERS
 Exports library as system headers.
 
 
+UNITS_BUILD_LA
+++++++++++++++
+
+**Values**: ``ON``/``OFF``
+
+**Defaulted to**: ``ON``
+
+Enables building code depending on the linear algebra library.
+
+
 UNITS_BUILD_DOCS
 ++++++++++++++++
 
@@ -414,8 +434,8 @@ In case you would like to build all the source code (with unit tests and example
 you should:
 
 1. Use the *CMakeLists.txt* from the top-level directory.
-2. Run Conan with `build_all`_ = ``True``
+2. Run Conan with `user.build:all`_ = ``True``
-   (use ``-o build_docs=False`` if you want to skip the documentation generation).
+   (use ``-c user.build:skip_docs=True`` if you want to skip the documentation generation).
 
 .. code-block:: shell
 
@@ -443,7 +463,7 @@ In case you would like to build the project's documentation, you should:
 
 1. Use the *CMakeLists.txt* from the top-level directory.
 2. Obtain Python dependencies.
-3. Run Conan with `build_all`_ = ``True``.
+3. Run Conan with `user.build:all`_ = ``True``.
 
 .. code-block:: shell
 

docs/use_cases/linear_algebra.rst

@@ -14,7 +14,7 @@ enough to be used with other Linear Algebra libraries existing on the market.
     or `Conan <https://conan.io/center/wg21-linear_algebra>`_.
     Also, to simplify the examples all of them assume::
 
-        using namespace std::math;
+        using namespace STD_LA;
 
 
 Linear Algebra of Quantities
@@ -27,16 +27,16 @@ The official :term:`quantity` definition states:
 
 So the most common use case would be to create a vector or matrix of quantities::
 
-    fs_vector<si::length<si::metre>, 3> v = { 1 * m, 2 * m, 3 * m };
+    fixed_size_column_vector<si::length<si::metre>, 3> v = { 1 * m, 2 * m, 3 * m };
-    fs_vector<si::length<si::metre>, 3> u = { 3 * m, 2 * m, 1 * m };
+    fixed_size_column_vector<si::length<si::metre>, 3> u = { 3 * m, 2 * m, 1 * m };
-    fs_vector<si::length<si::kilometre>, 3> t = { 3 * km, 2 * km, 1 * km };
+    fixed_size_column_vector<si::length<si::kilometre>, 3> t = { 3 * km, 2 * km, 1 * km };
 
 Having such definitions we can perform full dimensional analysis operations for the operations
 allowed by the Linear Algebra rules. For example::
 
     std::cout << "v + u     = " << v + u << "\n";
     std::cout << "v + t     = " << v + t << "\n";
-    std::cout << "t[m]      = " << fs_vector<si::length<si::metre>, 3>(t) << "\n";
+    std::cout << "t[m]      = " << fixed_size_column_vector<si::length<si::metre>, 3>(t) << "\n";
     std::cout << "v * u     = " << v * u << "\n";
     std::cout << "2 * m * v = " << 2 * m * v << "\n";
 
@@ -66,9 +66,9 @@ types provided to a `quantity` class template.
 
 With this the above vector definitions can be rewritten as follows::
 
-    si::length<si::metre, fs_vector<int, 3>> v(fs_vector<int, 3>{ 1, 2, 3 });
+    si::length<si::metre, fixed_size_column_vector<int, 3>> v(fixed_size_column_vector<int, 3>{ 1, 2, 3 });
-    si::length<si::metre, fs_vector<int, 3>> u(fs_vector<int, 3>{ 3, 2, 1 });
+    si::length<si::metre, fixed_size_column_vector<int, 3>> u(fixed_size_column_vector<int, 3>{ 3, 2, 1 });
-    si::length<si::kilometre, fs_vector<int, 3>> t(fs_vector<int, 3>{ 3, 2, 1 });
+    si::length<si::kilometre, fixed_size_column_vector<int, 3>> t(fixed_size_column_vector<int, 3>{ 3, 2, 1 });
 
 Now the same code doing basic Linear Algebra operations will provide the following
 output:

example/aliases/CMakeLists.txt

@@ -57,8 +57,9 @@ if(NOT ${projectPrefix}LIBCXX)
         glide_computer_example-aliases PRIVATE ${projectPrefix}NO_LITERALS ${projectPrefix}NO_REFERENCES
     )
 
-    # TODO uncomment the below when recipes in ConanCenter are fixed
+    if(${projectPrefix}BUILD_LA)
-    # find_package(wg21_linear_algebra CONFIG REQUIRED)
+        find_package(wg21_linear_algebra CONFIG REQUIRED)
-    # add_example(linear_algebra mp-units::core-fmt mp-units::core-io mp-units::si)
+        add_example(linear_algebra mp-units::core-fmt mp-units::core-io mp-units::si)
-    # target_link_libraries(linear_algebra-aliases PRIVATE wg21_linear_algebra::wg21_linear_algebra)
+        target_link_libraries(linear_algebra-aliases PRIVATE wg21_linear_algebra::wg21_linear_algebra)
+    endif()
 endif()

example/aliases/linear_algebra.cpp

@@ -27,12 +27,18 @@
 #include <units/isq/si/speed.h>  // IWYU pragma: keep
 #include <units/quantity_io.h>
 #include <iostream>
-#include <linear_algebra.hpp>
+#include <matrix>
+
+template<typename Rep = double>
+using vector = STD_LA::fixed_size_column_vector<Rep, 3>;
+
+template<typename Rep = double>
+using matrix = STD_LA::fixed_size_matrix<Rep, 3, 3>;
 
 namespace STD_LA {
 
-template<class ET, class OT>
+template<typename Rep>
-std::ostream& operator<<(std::ostream& os, const vector<ET, OT>& v)
+std::ostream& operator<<(std::ostream& os, const ::vector<Rep>& v)
 {
   os << "|";
   for (auto i = 0U; i < v.size(); ++i) {
@@ -42,8 +48,8 @@ std::ostream& operator<<(std::ostream& os, const vector<ET, OT>& v)
   return os;
 }
 
-template<class ET, class OT>
+template<typename Rep>
-std::ostream& operator<<(std::ostream& os, const matrix<ET, OT>& v)
+std::ostream& operator<<(std::ostream& os, const ::matrix<Rep>& v)
 {
   for (auto i = 0U; i < v.rows(); ++i) {
     os << "|";
@@ -61,18 +67,11 @@ namespace {
 
 using namespace units::aliases::isq::si;
 
-template<typename Rep = double>
-using vector = std::math::fs_vector<Rep, 3>;
-
-template<typename Rep = double>
-using matrix = std::math::fs_matrix<Rep, 3, 3>;
-
-
 void vector_of_quantity_add()
 {
   std::cout << "\nvector_of_quantity_add:\n";
 
-  vector<length::m<>> v = {m<>(1), m<>(2), m<>(3)};
+  vector<length::m<>> v = {m<>(4), m<>(8), m<>(12)};
   vector<length::m<>> u = {m<>(3), m<>(2), m<>(1)};
   vector<length::km<>> t = {km<>(3), km<>(2), km<>(1)};
 
@@ -85,35 +84,6 @@ void vector_of_quantity_add()
   std::cout << "t[m]  = " << vector<length::m<>>(t) << "\n";
 }
 
-void vector_of_quantity_multiply_same()
-{
-  std::cout << "\nvector_of_quantity_multiply_same:\n";
-
-  vector<length::m<>> v = {m<>(1), m<>(2), m<>(3)};
-  vector<length::m<>> u = {m<>(3), m<>(2), m<>(1)};
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "m<>(2) * v = " << m<>(2.) * v << "\n";
-}
-
-void vector_of_quantity_multiply_different()
-{
-  std::cout << "\nvector_of_quantity_multiply_different:\n";
-
-  vector<force::N<>> v = {N<>(1), N<>(2), N<>(3)};
-  vector<length::m<>> u = {m<>(3), m<>(2), m<>(1)};
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "N<>(2) * u = " << N<>(2.) * u << "\n";
-  std::cout << "2 * u    = " << 2 * u << "\n";
-}
-
 void vector_of_quantity_divide_by_scalar()
 {
   std::cout << "\nvector_of_quantity_divide_by_scalar:\n";
@@ -122,16 +92,13 @@ void vector_of_quantity_divide_by_scalar()
 
   std::cout << "v = " << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / s<>(2) = " << v / s<>(2) << "\n";
-  // std::cout << "v / s<>(2) = " << v / s<>(2) << "\n";
+  std::cout << "v / 2 = " << v / 2 << "\n";
-  // std::cout << "v / 2 = " << v / 2 << "\n";
 }
 
 void vector_of_quantity_tests()
 {
   vector_of_quantity_add();
-  vector_of_quantity_multiply_same();
-  vector_of_quantity_multiply_different();
   vector_of_quantity_divide_by_scalar();
 }
 
@@ -150,37 +117,7 @@ void matrix_of_quantity_add()
   std::cout << "v + u =\n" << v + u << "\n";
   std::cout << "v + t =\n" << v + t << "\n";
 
-  // TODO Uncomment when fixed in the LA lib
+  std::cout << "v[mm] =\n" << matrix<length::mm<>>(v) << "\n";
-  // std::cout << "v[mm] =\n" << matrix<length::mm<>>(v) << "\n";
-}
-
-void matrix_of_quantity_multiply_same()
-{
-  std::cout << "\nmatrix_of_quantity_multiply_same:\n";
-
-  matrix<length::m<>> v = {{m<>(1), m<>(2), m<>(3)}, {m<>(4), m<>(5), m<>(6)}, {m<>(7), m<>(8), m<>(9)}};
-  vector<length::m<>> u = {m<>(3), m<>(2), m<>(1)};
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "m<>(2) * u =\n" << m<>(2.) * u << "\n";
-}
-
-void matrix_of_quantity_multiply_different()
-{
-  std::cout << "\nmatrix_of_quantity_multiply_different:\n";
-
-  vector<force::N<>> v = {N<>(1), N<>(2), N<>(3)};
-  matrix<length::m<>> u = {{m<>(1), m<>(2), m<>(3)}, {m<>(4), m<>(5), m<>(6)}, {m<>(7), m<>(8), m<>(9)}};
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "N<>(2) * u =\n" << N<>(2.) * u << "\n";
-  std::cout << "2 * u =\n" << 2 * u << "\n";
 }
 
 void matrix_of_quantity_divide_by_scalar()
@@ -191,16 +128,13 @@ void matrix_of_quantity_divide_by_scalar()
 
   std::cout << "v =\n" << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / s<>(2) =\n" << v / s<>(2) << "\n";
-  // std::cout << "v / s<>(2) =\n" << v / s<>(2) << "\n";
+  std::cout << "v / 2 =\n" << v / 2 << "\n";
-  // std::cout << "v / 2 =\n" << v / 2 << "\n";
 }
 
 void matrix_of_quantity_tests()
 {
   matrix_of_quantity_add();
-  matrix_of_quantity_multiply_same();
-  matrix_of_quantity_multiply_different();
   matrix_of_quantity_divide_by_scalar();
 }
 
@@ -216,7 +150,7 @@ void quantity_of_vector_add()
 {
   std::cout << "\nquantity_of_vector_add:\n";
 
-  length_v<> v(vector<>{1, 2, 3});
+  length_v<> v(vector<>{4, 8, 12});
   length_v<> u(vector<>{3, 2, 1});
   length_v<si::kilometre> t(vector<>{3, 2, 1});
 
@@ -229,35 +163,6 @@ void quantity_of_vector_add()
   std::cout << "t[m]  = " << quantity_cast<si::metre>(t) << "\n";
 }
 
-void quantity_of_vector_multiply_same()
-{
-  std::cout << "\nquantity_of_vector_multiply_same:\n";
-
-  length_v<> v(vector<>{1, 2, 3});
-  length_v<> u(vector<>{3, 2, 1});
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "m<>(2) * v = " << m<>(2.) * v << "\n";
-}
-
-void quantity_of_vector_multiply_different()
-{
-  std::cout << "\nquantity_of_vector_multiply_different:\n";
-
-  force_v<> v(vector<>{1, 2, 3});
-  length_v<> u(vector<>{3, 2, 1});
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "N<>(2) * u = " << N<>(2.) * u << "\n";
-  std::cout << "2 * u    = " << 2 * u << "\n";
-}
-
 void quantity_of_vector_divide_by_scalar()
 {
   std::cout << "\nquantity_of_vector_divide_by_scalar:\n";
@@ -266,16 +171,13 @@ void quantity_of_vector_divide_by_scalar()
 
   std::cout << "v = " << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / s<>(2) = " << v / s<>(2) << "\n";
-  // std::cout << "v / s<>(2) = " << v / s<>(2) << "\n";
+  std::cout << "v / 2 = " << v / 2 << "\n";
-  // std::cout << "v / 2 = " << v / 2 << "\n";
 }
 
 void quantity_of_vector_tests()
 {
   quantity_of_vector_add();
-  quantity_of_vector_multiply_same();
-  quantity_of_vector_multiply_different();
   quantity_of_vector_divide_by_scalar();
 }
 
@@ -297,39 +199,10 @@ void quantity_of_matrix_add()
   std::cout << "v + u =\n" << v + u << "\n";
   std::cout << "v + t =\n" << v + t << "\n";
 
-  // TODO Uncomment when fixed in the LA lib
+  // TODO Fix it
   // std::cout << "v[mm] =\n" << matrix<length::mm<>>(v) << "\n";
 }
 
-void quantity_of_matrix_multiply_same()
-{
-  std::cout << "\nquantity_of_matrix_multiply_same:\n";
-
-  length_m<> v(matrix<>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});
-  length_v<> u(vector<>{3, 2, 1});
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "m<>(2) * u =\n" << m<>(2.) * u << "\n";
-}
-
-void quantity_of_matrix_multiply_different()
-{
-  std::cout << "\nquantity_of_matrix_multiply_different:\n";
-
-  force_v<> v(vector<>{1, 2, 3});
-  length_m<> u(matrix<>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "N<>(2) * u =\n" << N<>(2.) * u << "\n";
-  std::cout << "2 * u =\n" << 2 * u << "\n";
-}
-
 void quantity_of_matrix_divide_by_scalar()
 {
   std::cout << "\nquantity_of_matrix_divide_by_scalar:\n";
@@ -338,16 +211,13 @@ void quantity_of_matrix_divide_by_scalar()
 
   std::cout << "v =\n" << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / s<>(2) =\n" << v / s<>(2) << "\n";
-  // std::cout << "v / s<>(2) =\n" << v / s<>(2) << "\n";
+  std::cout << "v / 2 =\n" << v / 2 << "\n";
-  // std::cout << "v / 2 =\n" << v / 2 << "\n";
 }
 
 void quantity_of_matrix_tests()
 {
   quantity_of_matrix_add();
-  quantity_of_matrix_multiply_same();
-  quantity_of_matrix_multiply_different();
   quantity_of_matrix_divide_by_scalar();
 }
 

example/literals/CMakeLists.txt

@@ -56,8 +56,9 @@ if(NOT ${projectPrefix}LIBCXX)
         glide_computer_example-literals PRIVATE ${projectPrefix}NO_REFERENCES ${projectPrefix}NO_ALIASES
     )
 
-    # TODO uncomment the below when recipes in ConanCenter are fixed
+    if(${projectPrefix}BUILD_LA)
-    # find_package(wg21_linear_algebra CONFIG REQUIRED)
+        find_package(wg21_linear_algebra CONFIG REQUIRED)
-    # add_example(linear_algebra mp-units::core-fmt mp-units::core-io mp-units::si)
+        add_example(linear_algebra mp-units::core-fmt mp-units::core-io mp-units::si)
-    # target_link_libraries(linear_algebra-literals PRIVATE wg21_linear_algebra::wg21_linear_algebra)
+        target_link_libraries(linear_algebra-literals PRIVATE wg21_linear_algebra::wg21_linear_algebra)
+    endif()
 endif()

example/literals/linear_algebra.cpp

@@ -27,12 +27,18 @@
 #include <units/isq/si/speed.h>  // IWYU pragma: keep
 #include <units/quantity_io.h>
 #include <iostream>
-#include <linear_algebra.hpp>
+#include <matrix>
+
+template<typename Rep = double>
+using vector = STD_LA::fixed_size_column_vector<Rep, 3>;
+
+template<typename Rep = double>
+using matrix = STD_LA::fixed_size_matrix<Rep, 3, 3>;
 
 namespace STD_LA {
 
-template<class ET, class OT>
+template<typename Rep>
-std::ostream& operator<<(std::ostream& os, const vector<ET, OT>& v)
+std::ostream& operator<<(std::ostream& os, const ::vector<Rep>& v)
 {
   os << "|";
   for (auto i = 0U; i < v.size(); ++i) {
@@ -42,8 +48,8 @@ std::ostream& operator<<(std::ostream& os, const vector<ET, OT>& v)
   return os;
 }
 
-template<class ET, class OT>
+template<typename Rep>
-std::ostream& operator<<(std::ostream& os, const matrix<ET, OT>& v)
+std::ostream& operator<<(std::ostream& os, const ::matrix<Rep>& v)
 {
   for (auto i = 0U; i < v.rows(); ++i) {
     os << "|";
@@ -62,18 +68,11 @@ namespace {
 using namespace units::isq;
 using namespace units::isq::si::literals;
 
-template<typename Rep = double>
-using vector = std::math::fs_vector<Rep, 3>;
-
-template<typename Rep = double>
-using matrix = std::math::fs_matrix<Rep, 3, 3>;
-
-
 void vector_of_quantity_add()
 {
   std::cout << "\nvector_of_quantity_add:\n";
 
-  vector<si::length<si::metre>> v = {1_q_m, 2_q_m, 3_q_m};
+  vector<si::length<si::metre>> v = {4_q_m, 8_q_m, 12_q_m};
   vector<si::length<si::metre>> u = {3_q_m, 2_q_m, 1_q_m};
   vector<si::length<si::kilometre>> t = {3_q_km, 2_q_km, 1_q_km};
 
@@ -86,35 +85,6 @@ void vector_of_quantity_add()
   std::cout << "t[m]  = " << vector<si::length<si::metre>>(t) << "\n";
 }
 
-void vector_of_quantity_multiply_same()
-{
-  std::cout << "\nvector_of_quantity_multiply_same:\n";
-
-  vector<si::length<si::metre>> v = {1_q_m, 2_q_m, 3_q_m};
-  vector<si::length<si::metre>> u = {3_q_m, 2_q_m, 1_q_m};
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "2_q_m * v = " << 2._q_m * v << "\n";
-}
-
-void vector_of_quantity_multiply_different()
-{
-  std::cout << "\nvector_of_quantity_multiply_different:\n";
-
-  vector<si::force<si::newton>> v = {1_q_N, 2_q_N, 3_q_N};
-  vector<si::length<si::metre>> u = {3_q_m, 2_q_m, 1_q_m};
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "2_q_N * u = " << 2._q_N * u << "\n";
-  std::cout << "2 * u    = " << 2 * u << "\n";
-}
-
 void vector_of_quantity_divide_by_scalar()
 {
   std::cout << "\nvector_of_quantity_divide_by_scalar:\n";
@@ -123,16 +93,13 @@ void vector_of_quantity_divide_by_scalar()
 
   std::cout << "v = " << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / 2_q_s = " << v / quantity_cast<double>(2_q_s) << "\n";
-  // std::cout << "v / 2_q_s = " << v / 2_q_s << "\n";
+  std::cout << "v / 2 = " << v / 2 << "\n";
-  // std::cout << "v / 2 = " << v / 2 << "\n";
 }
 
 void vector_of_quantity_tests()
 {
   vector_of_quantity_add();
-  vector_of_quantity_multiply_same();
-  vector_of_quantity_multiply_different();
   vector_of_quantity_divide_by_scalar();
 }
 
@@ -151,37 +118,7 @@ void matrix_of_quantity_add()
   std::cout << "v + u =\n" << v + u << "\n";
   std::cout << "v + t =\n" << v + t << "\n";
 
-  // TODO Uncomment when fixed in the LA lib
+  std::cout << "v[mm] =\n" << matrix<si::length<si::millimetre>>(v) << "\n";
-  // std::cout << "v[mm] =\n" << matrix<si::length<si::millimetre>>(v) << "\n";
-}
-
-void matrix_of_quantity_multiply_same()
-{
-  std::cout << "\nmatrix_of_quantity_multiply_same:\n";
-
-  matrix<si::length<si::metre>> v = {{1_q_m, 2_q_m, 3_q_m}, {4_q_m, 5_q_m, 6_q_m}, {7_q_m, 8_q_m, 9_q_m}};
-  vector<si::length<si::metre>> u = {3_q_m, 2_q_m, 1_q_m};
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "2_q_m * u =\n" << 2._q_m * u << "\n";
-}
-
-void matrix_of_quantity_multiply_different()
-{
-  std::cout << "\nmatrix_of_quantity_multiply_different:\n";
-
-  vector<si::force<si::newton>> v = {1_q_N, 2_q_N, 3_q_N};
-  matrix<si::length<si::metre>> u = {{1_q_m, 2_q_m, 3_q_m}, {4_q_m, 5_q_m, 6_q_m}, {7_q_m, 8_q_m, 9_q_m}};
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "2_q_N * u =\n" << 2._q_N * u << "\n";
-  std::cout << "2 * u =\n" << 2 * u << "\n";
 }
 
 void matrix_of_quantity_divide_by_scalar()
@@ -192,16 +129,13 @@ void matrix_of_quantity_divide_by_scalar()
 
   std::cout << "v =\n" << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / 2_q_s =\n" << v / quantity_cast<double>(2_q_s) << "\n";
-  // std::cout << "v / 2_q_s =\n" << v / 2_q_s << "\n";
+  std::cout << "v / 2 =\n" << v / 2 << "\n";
-  // std::cout << "v / 2 =\n" << v / 2 << "\n";
 }
 
 void matrix_of_quantity_tests()
 {
   matrix_of_quantity_add();
-  matrix_of_quantity_multiply_same();
-  matrix_of_quantity_multiply_different();
   matrix_of_quantity_divide_by_scalar();
 }
 
@@ -215,7 +149,7 @@ void quantity_of_vector_add()
 {
   std::cout << "\nquantity_of_vector_add:\n";
 
-  length_v<> v(vector<>{1, 2, 3});
+  length_v<> v(vector<>{4, 8, 12});
   length_v<> u(vector<>{3, 2, 1});
   length_v<si::kilometre> t(vector<>{3, 2, 1});
 
@@ -228,35 +162,6 @@ void quantity_of_vector_add()
   std::cout << "t[m]  = " << quantity_cast<si::metre>(t) << "\n";
 }
 
-void quantity_of_vector_multiply_same()
-{
-  std::cout << "\nquantity_of_vector_multiply_same:\n";
-
-  length_v<> v(vector<>{1, 2, 3});
-  length_v<> u(vector<>{3, 2, 1});
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "2_q_m * v = " << 2._q_m * v << "\n";
-}
-
-void quantity_of_vector_multiply_different()
-{
-  std::cout << "\nquantity_of_vector_multiply_different:\n";
-
-  force_v<> v(vector<>{1, 2, 3});
-  length_v<> u(vector<>{3, 2, 1});
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "2_q_N * u = " << 2._q_N * u << "\n";
-  std::cout << "2 * u    = " << 2 * u << "\n";
-}
-
 void quantity_of_vector_divide_by_scalar()
 {
   std::cout << "\nquantity_of_vector_divide_by_scalar:\n";
@@ -265,16 +170,13 @@ void quantity_of_vector_divide_by_scalar()
 
   std::cout << "v = " << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / 2_q_s = " << v / 2_q_s << "\n";
-  // std::cout << "v / 2_q_s = " << v / 2_q_s << "\n";
+  std::cout << "v / 2 = " << v / 2 << "\n";
-  // std::cout << "v / 2 = " << v / 2 << "\n";
 }
 
 void quantity_of_vector_tests()
 {
   quantity_of_vector_add();
-  quantity_of_vector_multiply_same();
-  quantity_of_vector_multiply_different();
   quantity_of_vector_divide_by_scalar();
 }
 
@@ -296,39 +198,10 @@ void quantity_of_matrix_add()
   std::cout << "v + u =\n" << v + u << "\n";
   std::cout << "v + t =\n" << v + t << "\n";
 
-  // TODO Uncomment when fixed in the LA lib
+  // TODO Fix it
   // std::cout << "v[mm] =\n" << matrix<si::length<si::millimetre>>(v) << "\n";
 }
 
-void quantity_of_matrix_multiply_same()
-{
-  std::cout << "\nquantity_of_matrix_multiply_same:\n";
-
-  length_m<> v(matrix<>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});
-  length_v<> u(vector<>{3, 2, 1});
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "2_q_m * u =\n" << 2._q_m * u << "\n";
-}
-
-void quantity_of_matrix_multiply_different()
-{
-  std::cout << "\nquantity_of_matrix_multiply_different:\n";
-
-  force_v<> v(vector<>{1, 2, 3});
-  length_m<> u(matrix<>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "2_q_N * u =\n" << 2._q_N * u << "\n";
-  std::cout << "2 * u =\n" << 2 * u << "\n";
-}
-
 void quantity_of_matrix_divide_by_scalar()
 {
   std::cout << "\nquantity_of_matrix_divide_by_scalar:\n";
@@ -337,16 +210,13 @@ void quantity_of_matrix_divide_by_scalar()
 
   std::cout << "v =\n" << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / 2_q_s =\n" << v / 2_q_s << "\n";
-  // std::cout << "v / 2_q_s =\n" << v / 2_q_s << "\n";
+  std::cout << "v / 2 =\n" << v / 2 << "\n";
-  // std::cout << "v / 2 =\n" << v / 2 << "\n";
 }
 
 void quantity_of_matrix_tests()
 {
   quantity_of_matrix_add();
-  quantity_of_matrix_multiply_same();
-  quantity_of_matrix_multiply_different();
   quantity_of_matrix_divide_by_scalar();
 }
 

example/references/CMakeLists.txt

@@ -56,8 +56,9 @@ if(NOT ${projectPrefix}LIBCXX)
         glide_computer_example-references PRIVATE ${projectPrefix}NO_LITERALS ${projectPrefix}NO_ALIASES
     )
 
-    # TODO uncomment the below when recipes in ConanCenter are fixed
+    if(${projectPrefix}BUILD_LA)
-    # find_package(wg21_linear_algebra CONFIG REQUIRED)
+        find_package(wg21_linear_algebra CONFIG REQUIRED)
-    # add_example(linear_algebra mp-units::core-fmt mp-units::core-io mp-units::si)
+        add_example(linear_algebra mp-units::core-fmt mp-units::core-io mp-units::si)
-    # target_link_libraries(linear_algebra-references PRIVATE wg21_linear_algebra::wg21_linear_algebra)
+        target_link_libraries(linear_algebra-references PRIVATE wg21_linear_algebra::wg21_linear_algebra)
+    endif()
 endif()

example/references/linear_algebra.cpp

@@ -27,12 +27,18 @@
 #include <units/isq/si/speed.h>  // IWYU pragma: keep
 #include <units/quantity_io.h>
 #include <iostream>
-#include <linear_algebra.hpp>
+#include <matrix>
+
+template<typename Rep = double>
+using vector = STD_LA::fixed_size_column_vector<Rep, 3>;
+
+template<typename Rep = double>
+using matrix = STD_LA::fixed_size_matrix<Rep, 3, 3>;
 
 namespace STD_LA {
 
-template<class ET, class OT>
+template<typename Rep>
-std::ostream& operator<<(std::ostream& os, const vector<ET, OT>& v)
+std::ostream& operator<<(std::ostream& os, const ::vector<Rep>& v)
 {
   os << "|";
   for (auto i = 0U; i < v.size(); ++i) {
@@ -42,8 +48,8 @@ std::ostream& operator<<(std::ostream& os, const vector<ET, OT>& v)
   return os;
 }
 
-template<class ET, class OT>
+template<typename Rep>
-std::ostream& operator<<(std::ostream& os, const matrix<ET, OT>& v)
+std::ostream& operator<<(std::ostream& os, const ::matrix<Rep>& v)
 {
   for (auto i = 0U; i < v.rows(); ++i) {
     os << "|";
@@ -61,19 +67,13 @@ namespace {
 
 using namespace units::isq;
 using namespace units::isq::si::length_references;
-using namespace units::isq::si::force_references;
+using namespace units::isq::si::time_references;
-
-template<typename Rep = double>
-using vector = std::math::fs_vector<Rep, 3>;
-
-template<typename Rep = double>
-using matrix = std::math::fs_matrix<Rep, 3, 3>;
 
 void vector_of_quantity_add()
 {
   std::cout << "\nvector_of_quantity_add:\n";
 
-  vector<si::length<si::metre>> v = {1 * m, 2 * m, 3 * m};
+  vector<si::length<si::metre>> v = {4 * m, 8 * m, 12 * m};
   vector<si::length<si::metre>> u = {3 * m, 2 * m, 1 * m};
   vector<si::length<si::kilometre>> t = {3 * km, 2 * km, 1 * km};
 
@@ -86,35 +86,6 @@ void vector_of_quantity_add()
   std::cout << "t[m]  = " << vector<si::length<si::metre>>(t) << "\n";
 }
 
-void vector_of_quantity_multiply_same()
-{
-  std::cout << "\nvector_of_quantity_multiply_same:\n";
-
-  vector<si::length<si::metre>> v = {1 * m, 2 * m, 3 * m};
-  vector<si::length<si::metre>> u = {3 * m, 2 * m, 1 * m};
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "2 * m * v = " << 2. * m * v << "\n";
-}
-
-void vector_of_quantity_multiply_different()
-{
-  std::cout << "\nvector_of_quantity_multiply_different:\n";
-
-  vector<si::force<si::newton>> v = {1 * N, 2 * N, 3 * N};
-  vector<si::length<si::metre>> u = {3 * m, 2 * m, 1 * m};
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "2 * N * u = " << 2. * N * u << "\n";
-  std::cout << "2 * u    = " << 2 * u << "\n";
-}
-
 void vector_of_quantity_divide_by_scalar()
 {
   std::cout << "\nvector_of_quantity_divide_by_scalar:\n";
@@ -123,16 +94,13 @@ void vector_of_quantity_divide_by_scalar()
 
   std::cout << "v = " << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / (2 * s) = " << v / (2 * s) << "\n";
-  // std::cout << "v / (2 * s) = " << v / (2 * s) << "\n";
+  std::cout << "v / 2 = " << v / 2 << "\n";
-  // std::cout << "v / 2 = " << v / 2 << "\n";
 }
 
 void vector_of_quantity_tests()
 {
   vector_of_quantity_add();
-  vector_of_quantity_multiply_same();
-  vector_of_quantity_multiply_different();
   vector_of_quantity_divide_by_scalar();
 }
 
@@ -151,37 +119,7 @@ void matrix_of_quantity_add()
   std::cout << "v + u =\n" << v + u << "\n";
   std::cout << "v + t =\n" << v + t << "\n";
 
-  // TODO Uncomment when fixed in the LA lib
+  std::cout << "v[mm] =\n" << matrix<si::length<si::millimetre>>(v) << "\n";
-  // std::cout << "v[mm] =\n" << matrix<si::length<si::millimetre>>(v) << "\n";
-}
-
-void matrix_of_quantity_multiply_same()
-{
-  std::cout << "\nmatrix_of_quantity_multiply_same:\n";
-
-  matrix<si::length<si::metre>> v = {{1 * m, 2 * m, 3 * m}, {4 * m, 5 * m, 6 * m}, {7 * m, 8 * m, 9 * m}};
-  vector<si::length<si::metre>> u = {3 * m, 2 * m, 1 * m};
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "2 * m * u =\n" << 2. * m * u << "\n";
-}
-
-void matrix_of_quantity_multiply_different()
-{
-  std::cout << "\nmatrix_of_quantity_multiply_different:\n";
-
-  vector<si::force<si::newton>> v = {1 * N, 2 * N, 3 * N};
-  matrix<si::length<si::metre>> u = {{1 * m, 2 * m, 3 * m}, {4 * m, 5 * m, 6 * m}, {7 * m, 8 * m, 9 * m}};
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "2 * N * u =\n" << 2. * N * u << "\n";
-  std::cout << "2 * u =\n" << 2 * u << "\n";
 }
 
 void matrix_of_quantity_divide_by_scalar()
@@ -192,16 +130,13 @@ void matrix_of_quantity_divide_by_scalar()
 
   std::cout << "v =\n" << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / (2 * s) =\n" << v / (2 * s) << "\n";
-  // std::cout << "v / (2 * s) =\n" << v / (2 * s) << "\n";
+  std::cout << "v / 2 =\n" << v / 2 << "\n";
-  // std::cout << "v / 2 =\n" << v / 2 << "\n";
 }
 
 void matrix_of_quantity_tests()
 {
   matrix_of_quantity_add();
-  matrix_of_quantity_multiply_same();
-  matrix_of_quantity_multiply_different();
   matrix_of_quantity_divide_by_scalar();
 }
 
@@ -215,7 +150,7 @@ void quantity_of_vector_add()
 {
   std::cout << "\nquantity_of_vector_add:\n";
 
-  length_v<> v(vector<>{1, 2, 3});
+  length_v<> v(vector<>{4, 8, 12});
   length_v<> u(vector<>{3, 2, 1});
   length_v<si::kilometre> t(vector<>{3, 2, 1});
 
@@ -228,35 +163,6 @@ void quantity_of_vector_add()
   std::cout << "t[m]  = " << quantity_cast<si::metre>(t) << "\n";
 }
 
-void quantity_of_vector_multiply_same()
-{
-  std::cout << "\nquantity_of_vector_multiply_same:\n";
-
-  length_v<> v(vector<>{1, 2, 3});
-  length_v<> u(vector<>{3, 2, 1});
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "2 * m * v = " << 2. * m * v << "\n";
-}
-
-void quantity_of_vector_multiply_different()
-{
-  std::cout << "\nquantity_of_vector_multiply_different:\n";
-
-  force_v<> v(vector<>{1, 2, 3});
-  length_v<> u(vector<>{3, 2, 1});
-
-  std::cout << "v = " << v << "\n";
-  std::cout << "u = " << u << "\n";
-
-  std::cout << "v * u    = " << v * u << "\n";
-  std::cout << "2 * N * u = " << 2. * N * u << "\n";
-  std::cout << "2 * u    = " << 2 * u << "\n";
-}
-
 void quantity_of_vector_divide_by_scalar()
 {
   std::cout << "\nquantity_of_vector_divide_by_scalar:\n";
@@ -265,16 +171,13 @@ void quantity_of_vector_divide_by_scalar()
 
   std::cout << "v = " << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / (2 * s) = " << v / (2 * s) << "\n";
-  // std::cout << "v / 2 * s = " << v / 2 * s << "\n";
+  std::cout << "v / 2 = " << v / 2 << "\n";
-  // std::cout << "v / 2 = " << v / 2 << "\n";
 }
 
 void quantity_of_vector_tests()
 {
   quantity_of_vector_add();
-  quantity_of_vector_multiply_same();
-  quantity_of_vector_multiply_different();
   quantity_of_vector_divide_by_scalar();
 }
 
@@ -296,39 +199,10 @@ void quantity_of_matrix_add()
   std::cout << "v + u =\n" << v + u << "\n";
   std::cout << "v + t =\n" << v + t << "\n";
 
-  // TODO Uncomment when fixed in the LA lib
+  // TODO Fix it
   // std::cout << "v[mm] =\n" << matrix<si::length<si::millimetre>>(v) << "\n";
 }
 
-void quantity_of_matrix_multiply_same()
-{
-  std::cout << "\nquantity_of_matrix_multiply_same:\n";
-
-  length_m<> v(matrix<>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});
-  length_v<> u(vector<>{3, 2, 1});
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "2 * m * u =\n" << 2. * m * u << "\n";
-}
-
-void quantity_of_matrix_multiply_different()
-{
-  std::cout << "\nquantity_of_matrix_multiply_different:\n";
-
-  force_v<> v(vector<>{1, 2, 3});
-  length_m<> u(matrix<>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});
-
-  std::cout << "v =\n" << v << "\n";
-  std::cout << "u =\n" << u << "\n";
-
-  std::cout << "v * u =\n" << v * u << "\n";
-  std::cout << "2 * N * u =\n" << 2. * N * u << "\n";
-  std::cout << "2 * u =\n" << 2 * u << "\n";
-}
-
 void quantity_of_matrix_divide_by_scalar()
 {
   std::cout << "\nquantity_of_matrix_divide_by_scalar:\n";
@@ -337,16 +211,13 @@ void quantity_of_matrix_divide_by_scalar()
 
   std::cout << "v =\n" << v << "\n";
 
-  // TODO Uncomment when bug in the LA is fixed
+  std::cout << "v / (2 * s) =\n" << v / (2 * s) << "\n";
-  // std::cout << "v / (2 * s) =\n" << v / (2 * s) << "\n";
+  std::cout << "v / 2 =\n" << v / 2 << "\n";
-  // std::cout << "v / 2 =\n" << v / 2 << "\n";
 }
 
 void quantity_of_matrix_tests()
 {
   quantity_of_matrix_add();
-  quantity_of_matrix_multiply_same();
-  quantity_of_matrix_multiply_different();
   quantity_of_matrix_divide_by_scalar();
 }
 

src/CMakeLists.txt

@@ -28,6 +28,9 @@ set(projectPrefix UNITS_)
 option(${projectPrefix}AS_SYSTEM_HEADERS "Exports library as system headers" OFF)
 message(STATUS "${projectPrefix}AS_SYSTEM_HEADERS: ${${projectPrefix}AS_SYSTEM_HEADERS}")
 
+option(${projectPrefix}BUILD_LA "Build code depending on the linear algebra library" ON)
+message(STATUS "${projectPrefix}BUILD_LA: ${${projectPrefix}BUILD_LA}")
+
 list(APPEND CMAKE_MODULE_PATH "${PROJECT_SOURCE_DIR}/cmake")
 
 include(AddUnitsModule)

src/core/include/units/bits/basic_concepts.h

@@ -401,8 +401,11 @@ concept castable_number_ =  // exposition only
 
 template<typename T>
 concept scalable_ =  // exposition only
-  castable_number_<T> || (requires { typename T::value_type; } && castable_number_<typename T::value_type> &&
+  castable_number_<T> ||
-                          scalable_number_<T, std::common_type_t<typename T::value_type, std::intmax_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>>) ||
+  (requires { typename T::element_type; } && castable_number_<typename T::element_type> &&
+   scalable_number_<T, std::common_type_t<typename T::element_type, std::intmax_t>>);
 
 template<typename T, typename U>
 concept scalable_with_ =  // exposition only
@@ -420,6 +423,12 @@ inline constexpr bool is_wrapped_quantity<T> =
   Quantity<typename T::value_type> || QuantityLike<typename T::value_type> ||
   is_wrapped_quantity<typename T::value_type>;
 
+template<typename T>
+  requires requires { typename T::element_type; }
+inline constexpr bool is_wrapped_quantity<T> =
+  Quantity<typename T::element_type> || QuantityLike<typename T::element_type> ||
+  is_wrapped_quantity<typename T::element_type>;
+
 template<typename T>
   requires requires { typename T::quantity_type; }
 inline constexpr bool is_wrapped_quantity<T> = Quantity<typename T::quantity_type>;
@@ -429,8 +438,9 @@ inline constexpr bool is_wrapped_quantity<T> = Quantity<typename T::quantity_typ
 /**
  * @brief A concept matching types that wrap quantity objects.
  *
- * Satisfied by all wrapper types that satisfy `Quantity<typename T::value_type>`
+ * Satisfied by all wrapper types that satisfy `Quantity<typename T::value_type>` or
- * recursively (i.e. `std::optional<si::length<si::metre>>`).
+ * `Quantity<typename T::element_type>` recursively
+ * (i.e. `std::optional<si::length<si::metre>>`).
  */
 template<typename T>
 concept wrapped_quantity_ =  // exposition only

src/core/include/units/customization_points.h

@@ -44,6 +44,10 @@ template<typename T>
   requires requires { typename T::value_type; }
 inline constexpr bool treat_as_floating_point<T> = treat_as_floating_point<typename T::value_type>;
 
+template<typename T>
+  requires requires { typename T::element_type; }
+inline constexpr bool treat_as_floating_point<T> = treat_as_floating_point<typename T::element_type>;
+
 /**
  * @brief A type trait that defines zero, one, min, and max for a representation type
  *

src/core/include/units/quantity_cast.h

@@ -83,6 +83,16 @@ struct cast_traits<From, To> {
   using rep_type = std::common_type_t<From, To>;
 };
 
+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>::element_type; } &&
+           common_type_with_<typename std::common_type_t<From, To>::element_type, std::intmax_t>)
+struct cast_traits<From, To> {
+  using ratio_type = std::common_type_t<typename std::common_type_t<From, To>::element_type, std::intmax_t>;
+  using rep_type = std::common_type_t<From, To>;
+};
+
 }  // namespace detail
 
 /**