refactor: 💥 ratio hidden as an implementation detail behind `mag_ra…

…tio`

docs/users_guide/framework_basics/dimensionless_quantities.md

@@ -114,7 +114,7 @@ units of _length_:
 
 ```cpp
 inline constexpr struct hubble_constant :
-    named_unit<{u8"H₀", "H_0"}, mag<ratio{701, 10}> * si::kilo<si::metre> / si::second / si::mega<parsec>> {} hubble_constant;
+    named_unit<{u8"H₀", "H_0"}, mag_ratio<701, 10> * si::kilo<si::metre> / si::second / si::mega<parsec>> {} hubble_constant;
 ```
 
 
@@ -158,9 +158,9 @@ Besides the unit `one`, there are a few other scaled units predefined in the lib
 with dimensionless quantities:
 
 ```cpp
-inline constexpr struct percent : named_unit<"%", mag<ratio{1, 100}> * one> {} percent;
-inline constexpr struct per_mille : named_unit<{u8"‰", "%o"}, mag<ratio(1, 1000)> * one> {} per_mille;
-inline constexpr struct parts_per_million : named_unit<"ppm", mag<ratio(1, 1'000'000)> * one> {} parts_per_million;
+inline constexpr struct percent : named_unit<"%", mag_ratio<1, 100> * one> {} percent;
+inline constexpr struct per_mille : named_unit<{u8"‰", "%o"}, mag_ratio<1, 1000> * one> {} per_mille;
+inline constexpr struct parts_per_million : named_unit<"ppm", mag_ratio<1, 1'000'000> * one> {} parts_per_million;
 inline constexpr auto ppm = parts_per_million;
 ```
 

docs/users_guide/framework_basics/systems_of_units.md

@@ -170,14 +170,14 @@ electronvolt:
 ```cpp
 inline constexpr struct minute : named_unit<"min", mag<60> * si::second> {} minute;
 inline constexpr struct hour : named_unit<"h", mag<60> * minute> {} hour;
-inline constexpr struct electronvolt : named_unit<"eV", mag<ratio{1'602'176'634, 1'000'000'000}> * mag_power<10, -19> * si::joule> {} electronvolt;
+inline constexpr struct electronvolt : named_unit<"eV", mag_ratio<1'602'176'634, 1'000'000'000> * mag_power<10, -19> * si::joule> {} electronvolt;
 ```
 
 Also, units of other [systems of units](../../appendix/glossary.md#system-of-units) are often defined
 in terms of scaled versions of the SI units. For example, the international yard is defined as:
 
 ```cpp
-inline constexpr struct yard : named_unit<"yd", mag<ratio{9'144, 10'000}> * si::metre> {} yard;
+inline constexpr struct yard : named_unit<"yd", mag_ratio<9'144, 10'000> * si::metre> {} yard;
 ```
 
 For some units, a magnitude might also be irrational. The best example here is a `degree` which

docs/users_guide/framework_basics/text_output.md

@@ -77,10 +77,10 @@ and units of derived quantities.
     ```cpp
     inline constexpr struct hyperfine_structure_transition_frequency_of_cs : named_unit<{u8"Δν_Cs", "dv_Cs"}, mag<9'192'631'770> * hertz> {} hyperfine_structure_transition_frequency_of_cs;
     inline constexpr struct speed_of_light_in_vacuum : named_unit<"c", mag<299'792'458> * metre / second> {} speed_of_light_in_vacuum;
-    inline constexpr struct planck_constant : named_unit<"h", mag<ratio{662'607'015, 100'000'000}> * mag_power<10, -34> * joule * second> {} planck_constant;
-    inline constexpr struct elementary_charge : named_unit<"e", mag<ratio{1'602'176'634, 1'000'000'000}> * mag_power<10, -19> * coulomb> {} elementary_charge;
-    inline constexpr struct boltzmann_constant : named_unit<"k", mag<ratio{1'380'649, 1'000'000}> * mag_power<10, -23> * joule / kelvin> {} boltzmann_constant;
-    inline constexpr struct avogadro_constant : named_unit<"N_A", mag<ratio{602'214'076, 100'000'000}> * mag_power<10, 23> / mole> {} avogadro_constant;
+    inline constexpr struct planck_constant : named_unit<"h", mag_ratio<662'607'015, 100'000'000> * mag_power<10, -34> * joule * second> {} planck_constant;
+    inline constexpr struct elementary_charge : named_unit<"e", mag_ratio<1'602'176'634, 1'000'000'000> * mag_power<10, -19> * coulomb> {} elementary_charge;
+    inline constexpr struct boltzmann_constant : named_unit<"k", mag_ratio<1'380'649, 1'000'000> * mag_power<10, -23> * joule / kelvin> {} boltzmann_constant;
+    inline constexpr struct avogadro_constant : named_unit<"N_A", mag_ratio<602'214'076, 100'000'000> * mag_power<10, 23> / mole> {} avogadro_constant;
     inline constexpr struct luminous_efficacy : named_unit<"K_cd", mag<683> * lumen / watt> {} luminous_efficacy;
     ```
 

docs/users_guide/framework_basics/the_affine_space.md

@@ -403,7 +403,7 @@ inline constexpr struct zeroth_degree_Celsius : decltype(ice_point) {} zeroth_de
 namespace usc {
 
 inline constexpr struct zeroth_degree_Fahrenheit :
-  relative_point_origin<si::zeroth_degree_Celsius - 32 * (mag<ratio{5, 9}> * si::degree_Celsius)> {} zeroth_degree_Fahrenheit;
+  relative_point_origin<si::zeroth_degree_Celsius - 32 * (mag_ratio<5, 9> * si::degree_Celsius)> {} zeroth_degree_Fahrenheit;
 
 }
 ```
@@ -436,7 +436,7 @@ inline constexpr struct degree_Celsius :
 namespace usc {
 
 inline constexpr struct degree_Fahrenheit :
-    named_unit<{u8"°F", "`F"}, mag<ratio{5, 9}> * si::degree_Celsius,
+    named_unit<{u8"°F", "`F"}, mag_ratio<5, 9> * si::degree_Celsius,
                zeroth_degree_Fahrenheit> {} degree_Fahrenheit;
 
 }

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

@@ -99,7 +99,7 @@ template<typename F, int Num, int... Den>
   requires(detail::valid_ratio<Num, Den...> && detail::positive_ratio<Num, Den...> && !detail::ratio_one<Num, Den...>)
 struct power {
   using factor = F;
-  static constexpr ratio exponent{Num, Den...};
+  static constexpr detail::ratio exponent{Num, Den...};
 };
 
 namespace detail {

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

@@ -166,7 +166,7 @@ template<PowerVBase auto V, int Num, int... Den>
   requires(detail::valid_ratio<Num, Den...> && !detail::ratio_one<Num, Den...>)
 struct power_v {
   static constexpr auto base = V;
-  static constexpr ratio exponent{Num, Den...};
+  static constexpr detail::ratio exponent{Num, Den...};
 };
 
 namespace detail {
@@ -565,7 +565,8 @@ template<std::intmax_t Num, std::intmax_t Den = 1, auto... Ms>
   if constexpr (Num == 0) {
     return magnitude<>{};
   } else {
-    return magnitude<detail::power_v_or_T<detail::get_base(Ms), detail::get_exponent(Ms) * ratio{Num, Den}>()...>{};
+    return magnitude<
+      detail::power_v_or_T<detail::get_base(Ms), detail::get_exponent(Ms) * detail::ratio{Num, Den}>()...>{};
   }
 }
 
@@ -675,8 +676,6 @@ template<auto M>
   }
 }
 
-}  // namespace detail
-
 template<auto... Ms>
 [[nodiscard]] consteval auto numerator(magnitude<Ms...>)
 {
@@ -685,8 +684,8 @@ template<auto... Ms>
 
 [[nodiscard]] consteval auto denominator(Magnitude auto m) { return numerator(pow<-1>(m)); }
 
-// Implementation of conversion to ratio goes here, because it needs `numerator()` and `denominator()`.
-constexpr ratio as_ratio(Magnitude auto m)
+// TODO This probably should not be exported but is used in chrono.h
+MP_UNITS_EXPORT constexpr ratio as_ratio(Magnitude auto m)
   requires(is_rational(decltype(m){}))
 {
   return ratio{
@@ -695,7 +694,6 @@ constexpr ratio as_ratio(Magnitude auto m)
   };
 }
 
-
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 // Common Magnitude.
 //
@@ -714,8 +712,6 @@ constexpr ratio as_ratio(Magnitude auto m)
 // Thus, we make the _simplest_ choice which reproduces the correct convention in the rational case: namely, taking the
 // minimum power for each base (where absent bases implicitly have a power of 0).
 
-namespace detail {
-
 template<auto M>
 [[nodiscard]] consteval auto remove_positive_power(magnitude<M> m)
 {
@@ -830,16 +826,20 @@ inline constexpr auto prime_factorization_v = prime_factorization<N>::value;
  * This will be the main way end users create Magnitudes.  They should rarely (if ever) create a magnitude<...> by
  * manually adding base powers.
  */
-MP_UNITS_EXPORT template<ratio R>
-  requires detail::gt_zero<R.num>
-inline constexpr Magnitude auto mag = detail::prime_factorization_v<R.num> / detail::prime_factorization_v<R.den>;
+MP_UNITS_EXPORT template<std::intmax_t V>
+  requires detail::gt_zero<V>
+inline constexpr Magnitude auto mag = detail::prime_factorization_v<V>;
+
+MP_UNITS_EXPORT template<std::intmax_t N, std::intmax_t D>
+  requires detail::gt_zero<N>
+inline constexpr Magnitude auto mag_ratio = detail::prime_factorization_v<N> / detail::prime_factorization_v<D>;
 
 /**
  * @brief  Create a Magnitude which is some rational number raised to a rational power.
  */
-MP_UNITS_EXPORT template<ratio Base, ratio Pow>
-  requires detail::gt_zero<Base.num>
-inline constexpr Magnitude auto mag_power = pow<Pow.num, Pow.den>(mag<Base>);
+MP_UNITS_EXPORT template<std::intmax_t Base, std::intmax_t Pow>
+  requires detail::gt_zero<Base>
+inline constexpr Magnitude auto mag_power = pow<Pow>(mag<Base>);
 
 namespace detail {
 

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

@@ -32,9 +32,7 @@
 #include <numeric>
 #endif
 
-namespace mp_units {
-
-namespace detail {
+namespace mp_units::detail {
 
 template<typename T>
 [[nodiscard]] MP_UNITS_CONSTEVAL T abs(T v) noexcept
@@ -59,14 +57,13 @@ template<typename T>
   return lhs * rhs;
 }
 
-}  // namespace detail
-
 /**
  * @brief Provides compile-time rational arithmetic support.
  *
  * This class is really similar to @c std::ratio.  An important difference is the fact that the objects of that class
  * are used as class NTTPs rather then a type template parameter kind.
  */
+// TODO This probably should not be exported but is used in chrono.h
 MP_UNITS_EXPORT struct ratio {
   std::intmax_t num;
   std::intmax_t den;
@@ -123,4 +120,4 @@ MP_UNITS_EXPORT struct ratio {
   return ratio{num / gcd, den / gcd};
 }
 
-}  // namespace mp_units
+}  // namespace mp_units::detail

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

@@ -56,7 +56,7 @@ template<std::intmax_t Num, std::intmax_t Den = 1, auto R, typename Rep>
 {
   if constexpr (Num == 0) {
     return quantity<pow<Num, Den>(R), Rep>::one();
-  } else if constexpr (ratio{Num, Den} == 1) {
+  } else if constexpr (Num == Den) {
     return q;
   } else {
     using std::pow;

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

@@ -555,7 +555,7 @@ template<std::intmax_t Num, std::intmax_t Den = 1, QuantitySpec Q>
   // all are dimensionless quantities :-(
   if constexpr (Num == 0 || Q{} == dimensionless)
     return dimensionless;
-  else if constexpr (ratio{Num, Den} == 1)
+  else if constexpr (detail::ratio{Num, Den} == 1)
     return q;
   else if constexpr (detail::IntermediateDerivedQuantitySpec<Q>)
     return detail::clone_kind_of<Q{}>(

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

@@ -566,7 +566,7 @@ template<std::intmax_t Num, std::intmax_t Den = 1, Unit U>
 {
   if constexpr (Num == 0 || is_same_v<U, struct one>)
     return one;
-  else if constexpr (ratio{Num, Den} == 1)
+  else if constexpr (detail::ratio{Num, Den} == 1)
     return u;
   else if constexpr (detail::is_specialization_of_scaled_unit<U>)
     return scaled_unit<pow<Num, Den>(U::mag), std::remove_const_t<decltype(pow<Num, Den>(U::reference_unit))>>{};
@@ -617,9 +617,9 @@ template<std::intmax_t Num, std::intmax_t Den = 1, Unit U>
 
 // common dimensionless units
 // clang-format off
-inline constexpr struct percent : named_unit<"%", mag<ratio{1, 100}> * one> {} percent;
-inline constexpr struct per_mille : named_unit<symbol_text{u8"‰", "%o"}, mag<ratio(1, 1000)> * one> {} per_mille;
-inline constexpr struct parts_per_million : named_unit<"ppm", mag<ratio(1, 1'000'000)> * one> {} parts_per_million;
+inline constexpr struct percent : named_unit<"%", mag_ratio<1, 100> * one> {} percent;
+inline constexpr struct per_mille : named_unit<symbol_text{u8"‰", "%o"}, mag_ratio<1, 1000> * one> {} per_mille;
+inline constexpr struct parts_per_million : named_unit<"ppm", mag_ratio<1, 1'000'000> * one> {} parts_per_million;
 inline constexpr auto ppm = parts_per_million;
 // clang-format on
 

src/systems/include/mp-units/systems/angular/units.h

@@ -40,8 +40,8 @@ QUANTITY_SPEC(solid_angle, pow<2>(angle));
 
 inline constexpr struct radian : named_unit<"rad", kind_of<angle>> {} radian;
 inline constexpr struct revolution : named_unit<"rev", mag<2> * mag_pi * radian> {} revolution;
-inline constexpr struct degree : named_unit<symbol_text{u8"°", "deg"}, mag<ratio{1, 360}> * revolution> {} degree;
-inline constexpr struct gradian : named_unit<symbol_text{u8"ᵍ", "grad"}, mag<ratio{1, 400}> * revolution> {} gradian;
+inline constexpr struct degree : named_unit<symbol_text{u8"°", "deg"}, mag_ratio<1, 360> * revolution> {} degree;
+inline constexpr struct gradian : named_unit<symbol_text{u8"ᵍ", "grad"}, mag_ratio<1, 400> * revolution> {} gradian;
 inline constexpr struct steradian : named_unit<"sr", square(radian)> {} steradian;
 // clang-format on
 

src/systems/include/mp-units/systems/hep/hep.h

@@ -49,9 +49,9 @@ using si::electronvolt;
 inline constexpr struct barn : named_unit<"b", mag_power<10, -28> * square(si::metre)> {} barn;
 
 // mass
-inline constexpr struct electron_mass : named_unit<"m_e", mag<ratio{9'109'383'701'528, 1'000'000'000'000}> * mag_power<10, -31> * si::kilogram> {} electron_mass;
-inline constexpr struct proton_mass : named_unit<"m_p", mag<ratio{1'672'621'923'695, 1'000'000'000'000}> * mag_power<10, -27> * si::kilogram> {} proton_mass;
-inline constexpr struct neutron_mass : named_unit<"m_n", mag<ratio{1'674'927'498'049, 1'000'000'000'000}> * mag_power<10, -27> * si::kilogram> {} neutron_mass;
+inline constexpr struct electron_mass : named_unit<"m_e", mag_ratio<9'109'383'701'528, 1'000'000'000'000> * mag_power<10, -31> * si::kilogram> {} electron_mass;
+inline constexpr struct proton_mass : named_unit<"m_p", mag_ratio<1'672'621'923'695, 1'000'000'000'000> * mag_power<10, -27> * si::kilogram> {} proton_mass;
+inline constexpr struct neutron_mass : named_unit<"m_n", mag_ratio<1'674'927'498'049, 1'000'000'000'000> * mag_power<10, -27> * si::kilogram> {} neutron_mass;
 
 // speed
 inline constexpr struct speed_of_light : decltype(si::si2019::speed_of_light_in_vacuum) {} speed_of_light;

src/systems/include/mp-units/systems/iau/iau.h

@@ -38,14 +38,14 @@ namespace mp_units::iau {
 // clang-format off
 // time
 inline constexpr struct day : named_unit<"D", si::day> {} day;
-inline constexpr struct Julian_year : named_unit<"a", mag<ratio{365'25, 100}> * day> {} Julian_year;
+inline constexpr struct Julian_year : named_unit<"a", mag_ratio<365'25, 100> * day> {} Julian_year;
 
 // mass
 // https://en.wikipedia.org/wiki/Solar_mass
 // TODO What is the official mass of sun (every source in the Internet provides a different value)
-inline constexpr struct solar_mass : named_unit<symbol_text{u8"M_☉", "M_SUN"}, mag<ratio{198'847, 100'000}> * mag_power<10, 30> * si::kilogram> {} solar_mass;
-inline constexpr struct Jupiter_mass : named_unit<"M_JUP", mag<ratio{1'898, 1'000}> * mag_power<10, 27> * si::kilogram> {} Jupiter_mass;
-inline constexpr struct Earth_mass : named_unit<"M_EARTH", mag<ratio{59'742, 10'000}> * mag_power<10, 24> * si::kilogram> {} Earth_mass;
+inline constexpr struct solar_mass : named_unit<symbol_text{u8"M_☉", "M_SUN"}, mag_ratio<198'847, 100'000> * mag_power<10, 30> * si::kilogram> {} solar_mass;
+inline constexpr struct Jupiter_mass : named_unit<"M_JUP", mag_ratio<1'898, 1'000> * mag_power<10, 27> * si::kilogram> {} Jupiter_mass;
+inline constexpr struct Earth_mass : named_unit<"M_EARTH", mag_ratio<59'742, 10'000> * mag_power<10, 24> * si::kilogram> {} Earth_mass;
 
 // length
 inline constexpr struct astronomical_unit : decltype(si::astronomical_unit) {} astronomical_unit;
@@ -57,24 +57,24 @@ inline constexpr struct lunar_distance : named_unit<"LD", mag<384'399> * si::kil
 inline constexpr struct light_year : named_unit<"ly", mag<9'460'730'472'580'800> * si::metre> {} light_year;
 
 // https://en.wikipedia.org/wiki/Parsec
-inline constexpr struct parsec : named_unit<"pc", astronomical_unit / (mag<ratio{1, 60 * 60}> * si::degree)> {} parsec;
+inline constexpr struct parsec : named_unit<"pc", astronomical_unit / (mag_ratio<1, 60 * 60> * si::degree)> {} parsec;
 
 // https://en.wikipedia.org/wiki/Angstrom
 inline constexpr struct angstrom : named_unit<symbol_text{u8"Å", "A"}, mag_power<10, -10> * si::metre> {} angstrom;
 
 // selected constants
 // https://en.wikipedia.org/wiki/Astronomical_constant
 inline constexpr struct gaussian_gravitational_constant :
-    named_unit<"k", mag<ratio{1'720'209'895, 100'000'000'000}> * pow<3, 2>(astronomical_unit) / pow<1,2>(solar_mass) / day> {} gaussian_gravitational_constant;
+    named_unit<"k", mag_ratio<1'720'209'895, 100'000'000'000> * pow<3, 2>(astronomical_unit) / pow<1,2>(solar_mass) / day> {} gaussian_gravitational_constant;
 
 inline constexpr struct speed_of_light :
     named_unit<symbol_text{u8"c₀", "c_0"}, si::si2019::speed_of_light_in_vacuum> {} speed_of_light;
 
 inline constexpr struct constant_of_gravitation :
-    named_unit<"G", mag<ratio{667'430, 100'000}> * mag_power<10, -11> * cubic(si::metre) / si::kilogram / square(si::second)> {} constant_of_gravitation;
+    named_unit<"G", mag_ratio<667'430, 100'000> * mag_power<10, -11> * cubic(si::metre) / si::kilogram / square(si::second)> {} constant_of_gravitation;
 
 inline constexpr struct hubble_constant :
-    named_unit<symbol_text{u8"H₀", "H_0"}, mag<ratio{701, 10}> * si::kilo<si::metre> / si::second / si::mega<parsec>> {} hubble_constant;
+    named_unit<symbol_text{u8"H₀", "H_0"}, mag_ratio<701, 10> * si::kilo<si::metre> / si::second / si::mega<parsec>> {} hubble_constant;
 // clang-format on
 
 namespace unit_symbols {

src/systems/include/mp-units/systems/imperial/imperial.h

@@ -36,18 +36,18 @@ using namespace international;
 
 // clang-format off
 // https://en.wikipedia.org/wiki/Imperial_units#Length
-inline constexpr struct hand : named_unit<"hh", mag<ratio{1, 3}> * foot> {} hand;
-inline constexpr struct barleycorn : named_unit<"Bc", mag<ratio(1, 3)> * inch> {} barleycorn;
-inline constexpr struct thou : named_unit<"th", mag<ratio{1, 12'000}> * foot> {} thou;
+inline constexpr struct hand : named_unit<"hh", mag_ratio<1, 3> * foot> {} hand;
+inline constexpr struct barleycorn : named_unit<"Bc", mag_ratio<1, 3> * inch> {} barleycorn;
+inline constexpr struct thou : named_unit<"th", mag_ratio<1, 12'000> * foot> {} thou;
 inline constexpr struct chain : named_unit<"ch", mag<22> * yard> {} chain;
 inline constexpr struct furlong : named_unit<"fur", mag<10> * chain> {} furlong;
 
 // maritime units
-inline constexpr struct cable : named_unit<"cb", mag<ratio{1, 10}> * nautical_mile> {} cable;
-inline constexpr struct fathom : named_unit<"ftm", mag<ratio{1, 1000}> * nautical_mile> {} fathom;
+inline constexpr struct cable : named_unit<"cb", mag_ratio<1, 10> * nautical_mile> {} cable;
+inline constexpr struct fathom : named_unit<"ftm", mag_ratio<1, 1000> * nautical_mile> {} fathom;
 
 // survey
-inline constexpr struct link : named_unit<"li", mag<ratio{1, 100}> * chain> {} link;
+inline constexpr struct link : named_unit<"li", mag_ratio<1, 100> * chain> {} link;
 inline constexpr struct rod : named_unit<"rd", mag<25> * link> {} rod;
 
 // https://en.wikipedia.org/wiki/Imperial_units#Area
@@ -56,11 +56,11 @@ inline constexpr struct rood : decltype(mag<40> * perch) {} rood;
 inline constexpr struct acre : decltype(mag<4> * rood) {} acre;
 
 // https://en.wikipedia.org/wiki/Imperial_units#Volume
-inline constexpr struct gallon : named_unit<"gal", mag<ratio{454'609, 100'000}> * si::litre> {} gallon;
-inline constexpr struct quart : named_unit<"qt", mag<ratio{1, 4}> * gallon> {} quart;
-inline constexpr struct pint : named_unit<"pt", mag<ratio{1, 2}> * quart> {} pint;
-inline constexpr struct gill : named_unit<"gi", mag<ratio{1, 4}> * pint> {} gill;
-inline constexpr struct fluid_ounce : named_unit<"fl oz", mag<ratio{1, 5}> * gill> {} fluid_ounce;
+inline constexpr struct gallon : named_unit<"gal", mag_ratio<454'609, 100'000> * si::litre> {} gallon;
+inline constexpr struct quart : named_unit<"qt", mag_ratio<1, 4> * gallon> {} quart;
+inline constexpr struct pint : named_unit<"pt", mag_ratio<1, 2> * quart> {} pint;
+inline constexpr struct gill : named_unit<"gi", mag_ratio<1, 4> * pint> {} gill;
+inline constexpr struct fluid_ounce : named_unit<"fl oz", mag_ratio<1, 5> * gill> {} fluid_ounce;
 
 // https://en.wikipedia.org/wiki/Avoirdupois_system#Post-Elizabethan_units
 inline constexpr auto drachm = dram;