coherent_derived_unit and custom prefixes support added

README.md

@@ -63,6 +63,8 @@ NOTE: This library as of now compiles correctly only with gcc-9.1 and newer.
   - Downcasting facility refactored so the user does not have to write the boilerplate code anymore
   - From now on base dimensions should inherit from `base_dimension` class template
   - Added unit symbols definitions to `base_dimension` and `derived_unit`
+  - Added `coherent_derived_unit` helper
+  - Added support for `operator<<` on `quantity`
 
 - 0.3.1 Sep 18, 2019
   - cmcstl2 dependency changed to range-v3 0.9.1

doc/DESIGN.md

@@ -1,5 +1,6 @@
 # `mp-units` - A Units Library for C++
 
+
 ## Summary
 
 `Units` is a compile-time enabled Modern C++ library that provides compile-time dimensional
@@ -71,6 +72,7 @@ constexpr units::Velocity auto avg_speed(units::Length auto d, units::Time auto
 }
 ```
 
+
 ## Basic Concepts
 
 Below UML diagram shows the most important entities in the library design and how they relate to
@@ -256,35 +258,35 @@ struct unit : downcast_base<unit<D, R>> {
 };
 ```
 
-All units are created with a `derived_unit` helper:
+Coherent derived units (units with `ratio<1>`) are created with a `coherent_derived_unit` helper:
+
+```cpp
+template<typename Child, fixed_string Symbol, Dimension D, typename Prefix = no_prefix>
+struct coherent_derived_unit;
+```
+
+The above type exposes public `symbol` and `prefix` member types used to print unit symbol names.
+
+For example to define the base unit of `length`:
+
+```cpp
+struct metre : coherent_derived_unit<metre, "m", length, si_prefix> {};
+```
+
+Again, similarly to `derived_dimension`, the first class template parameter is a CRTP idiom used
+to provide downcasting facility (described below).
+
+All other units are created with a `derived_unit` helper:
 
 ```cpp
 template<typename Child, fixed_string Symbol, typename...>
 struct derived_unit;
 ```
 
-For example to define the base unit of `length`:
+The above type exposes public `symbol` member type used to print unit symbol names.
 
-```cpp
+`derived_unit` has a few useful partial specializations:
-struct metre : derived_unit<metre, "m", length> {};
+- helper to create non-coherent units for a specified dimension
-```
-
-Again, similarly to `derived_dimension`, the first class template parameter is a CRTP idiom used
-to provide downcasting facility (described below).
-
-`derived_unit` has a few partial useful specializations:
-- helper to create a base unit of a specified dimension
-
-```cpp
-template<typename Child, fixed_string Symbol, Dimension D>
-struct derived_unit<Child, Symbol, D>;
-```
-
-```cpp
-struct metre : derived_unit<metre, "m", length> {};
-```
-
-- helper to create other units for a specified dimension
 
 ```cpp
 template<typename Child, fixed_string Symbol, Dimension D, Ratio R>
@@ -295,7 +297,7 @@ struct derived_unit<Child, Symbol, D, R>;
 struct yard : derived_unit<yard, "yd", length, ratio<9'144, 10'000>> {};
 ```
 
-- helper to create a unit with a SI prefix
+- helper to create a named unit with a SI prefix
 
 ```cpp
 template<typename Child, fixed_string Symbol, Unit U>
@@ -428,6 +430,22 @@ template<Scalar ToRep, typename U, typename Rep>
 [[nodiscard]] constexpr quantity<U, ToRep> quantity_cast(const quantity<U, Rep>& q);
 ```
 
+#### `operator<<`
+
+The library tries its best to print a correct unit of the quantity. This is why it performs a series
+of checks:
+1. If the user predefined a unit with a `coherent_derived_unit` or `derived_unit` class templates,
+  the symbol provided by the user will be used (i.e. `60 W`).
+2. If a quantity has an unknown unit for a dimension predefined by the user with `derived_dimension`,
+  the symbol of a coherent unit of this dimension will be used. Additionally:
+    - if `Prefix` template parameter of a `coherent_derived_unit` is different than `no_prefix` then
+      the prefix symbol (i.e. `8 cJ`) defined by the specialization of `units::prefix_symbol` will be
+      aded wherever possible (`Ratio` matches the prefix ratio),
+    - otherwise, non-standard ratio (i.e. `2 [60]Hz`) will be printed.
+3. If a quantity has an unknown dimension, the symbols of base dimensions will be used to construct
+  a unit symbol (i.e. `2 m/kg^2`). In this case no prefix symbols are added.
+
+
 ## Strong types instead of aliases, and type downcasting facility
 
 Most of the important design decisions in the library are dictated by the requirement of providing
@@ -658,14 +676,24 @@ In order to extend the library with custom dimensions the user has to:
     concept DigitalInformation = units::QuantityOf<T, digital_information>;
     ```
 
-4. Define units and register them to a downcasting facility:
+4. If non-SI prefixes should be applied to the unit symbol, define a new prefix tag and provide
+   `prefix_symbol` specializations to provide their text representation:
 
     ```cpp
-    struct bit : units::derived_unit<bit, "b", digital_information> {};
+    struct data_prefix;
+
+    template<> inline constexpr std::string_view units::prefix_symbol<data_prefix, units::ratio<    1'024>> = "Ki";
+    template<> inline constexpr std::string_view units::prefix_symbol<data_prefix, units::ratio<1'048'576>> = "Mi";
+    ```
+
+5. Define units and register them to a downcasting facility:
+
+    ```cpp
+    struct bit : units::coherent_derived_unit<bit, "b", digital_information, data_prefix> {};
     struct byte : units::derived_unit<byte, "B", digital_information, units::ratio<8>> {};
     ```
 
-5. Provide user-defined literals for the most important units:
+6. Provide user-defined literals for the most important units:
 
     ```cpp
     inline namespace literals {

src/include/units/dimensions/acceleration.h

@@ -31,7 +31,7 @@ namespace units {
   template<typename T>
   concept Acceleration = QuantityOf<T, acceleration>;
 
-  struct metre_per_second_sq : derived_unit<metre_per_second_sq, decltype("m/s^2"_fs), acceleration, metre, second> {};
+  struct metre_per_second_sq : coherent_derived_unit<metre_per_second_sq, decltype("m/s^2"_fs), acceleration> {};
 
   inline namespace literals {
 

src/include/units/dimensions/area.h

@@ -31,14 +31,18 @@ namespace units {
   template<typename T>
   concept Area = QuantityOf<T, area>;
 
+  struct square_metre : coherent_derived_unit<square_metre, decltype("m^2"_fs), area> {};
   struct square_millimetre : derived_unit<square_millimetre, decltype("mm^2"_fs), area, millimetre> {};
   struct square_centimetre : derived_unit<square_centimetre, decltype("cm^2"_fs), area, centimetre> {};
-  struct square_metre : derived_unit<square_metre, decltype("m^2"_fs), area, metre> {};
   struct square_kilometre : derived_unit<square_kilometre, decltype("km^2"_fs), area, kilometre> {};
   struct square_foot : derived_unit<square_foot, decltype("ft^2"_fs), area, foot> {};
 
   inline namespace literals {
 
+    // sq_m
+    constexpr auto operator""sq_m(unsigned long long l) { return quantity<square_metre, std::int64_t>(l); }
+    constexpr auto operator""sq_m(long double l) { return quantity<square_metre, long double>(l); }
+
     // sq_mm
     constexpr auto operator""sq_mm(unsigned long long l) { return quantity<square_millimetre, std::int64_t>(l); }
     constexpr auto operator""sq_mm(long double l) { return quantity<square_millimetre, long double>(l); }
@@ -47,10 +51,6 @@ namespace units {
     constexpr auto operator""sq_cm(unsigned long long l) { return quantity<square_centimetre, std::int64_t>(l); }
     constexpr auto operator""sq_cm(long double l) { return quantity<square_centimetre, long double>(l); }
 
-    // sq_m
-    constexpr auto operator""sq_m(unsigned long long l) { return quantity<square_metre, std::int64_t>(l); }
-    constexpr auto operator""sq_m(long double l) { return quantity<square_metre, long double>(l); }
-
     // sq_km
     constexpr auto operator""sq_km(unsigned long long l) { return quantity<square_kilometre, std::int64_t>(l); }
     constexpr auto operator""sq_km(long double l) { return quantity<square_kilometre, long double>(l); }

src/include/units/dimensions/capacitance.h

@@ -33,7 +33,7 @@ namespace units {
   template<typename T>
   concept Capacitance =  QuantityOf<T, capacitance>;
 
-  struct farad : derived_unit<farad, decltype("F"_fs), capacitance, kilogram, metre, second, ampere> {};
+  struct farad : coherent_derived_unit<farad, decltype("F"_fs), capacitance, si_prefix> {};
 
   inline namespace literals {
 

src/include/units/dimensions/current.h

@@ -32,7 +32,7 @@ namespace units {
   template<typename T>
   concept Current = QuantityOf<T, current>;
 
-  struct ampere : derived_unit<ampere, decltype("A"_fs), current> {};
+  struct ampere : coherent_derived_unit<ampere, decltype("A"_fs), current, si_prefix> {};
 
   inline namespace literals {
 

src/include/units/dimensions/electric_charge.h

@@ -33,7 +33,7 @@ namespace units {
   template<typename T>
   concept ElectricCharge =  QuantityOf<T, electric_charge>;
 
-  struct coulomb : derived_unit<coulomb, decltype("C"_fs), electric_charge, second, ampere> {};
+  struct coulomb : coherent_derived_unit<coulomb, decltype("C"_fs), electric_charge, si_prefix> {};
 
   inline namespace literals {
 

src/include/units/dimensions/energy.h

@@ -33,7 +33,7 @@ namespace units {
   template<typename T>
   concept Energy =  QuantityOf<T, energy>;
 
-  struct joule : derived_unit<joule, decltype("J"_fs), energy, kilogram, metre, second> {};
+  struct joule : coherent_derived_unit<joule, decltype("J"_fs), energy, si_prefix> {};
   struct millijoule : derived_unit<millijoule, decltype("mJ"_fs), milli<joule>> {};
   struct kilojoule : derived_unit<kilojoule, decltype("kJ"_fs), kilo<joule>> {};
   struct megajoule : derived_unit<megajoule, decltype("MJ"_fs), mega<joule>> {};

src/include/units/dimensions/force.h

@@ -33,7 +33,7 @@ namespace units {
   template<typename T>
   concept Force =  QuantityOf<T, force>;
 
-  struct newton : derived_unit<newton, decltype("N"_fs), force, kilogram, metre, second> {};
+  struct newton : coherent_derived_unit<newton, decltype("N"_fs), force, si_prefix> {};
 
   inline namespace literals {
 

src/include/units/dimensions/frequency.h

@@ -32,7 +32,7 @@ namespace units {
   template<typename T>
   concept Frequency =  QuantityOf<T, frequency>;
 
-  struct hertz : derived_unit<hertz, decltype("Hz"_fs), frequency, second> {};
+  struct hertz : coherent_derived_unit<hertz, decltype("Hz"_fs), frequency, si_prefix> {};
   struct millihertz : derived_unit<millihertz, decltype("mHz"_fs), milli<hertz>> {};
   struct kilohertz : derived_unit<kilohertz, decltype("kHz"_fs), kilo<hertz>> {};
   struct megahertz : derived_unit<megahertz, decltype("MHz"_fs), mega<hertz>> {};

src/include/units/dimensions/length.h

@@ -33,7 +33,7 @@ namespace units {
   concept Length = QuantityOf<T, length>;
 
   // SI units
-  struct metre : derived_unit<metre, decltype("m"_fs), length> {};
+  struct metre : coherent_derived_unit<metre, decltype("m"_fs), length, si_prefix> {};
   struct millimetre : derived_unit<millimetre, decltype("mm"_fs), milli<metre>> {};
   struct centimetre : derived_unit<centimetre, decltype("cm"_fs), centi<metre>> {};
   struct kilometre : derived_unit<kilometre, decltype("km"_fs), kilo<metre>> {};

src/include/units/dimensions/luminous_intensity.h

@@ -32,7 +32,7 @@ namespace units {
   template<typename T>
   concept LuminousIntensity = QuantityOf<T, luminous_intensity>;
 
-  struct candela : derived_unit<candela, decltype("cd"_fs), luminous_intensity> {};
+  struct candela : coherent_derived_unit<candela, decltype("cd"_fs), luminous_intensity, si_prefix> {};
 
   inline namespace literals {
 

src/include/units/dimensions/mass.h

@@ -32,8 +32,8 @@ namespace units {
   template<typename T>
   concept Mass = QuantityOf<T, mass>;
 
+  struct kilogram : coherent_derived_unit<kilogram, decltype("kg"_fs), mass> {};
   struct gram : derived_unit<gram, decltype("g"_fs), mass, ratio<1, 1000>> {};
-  struct kilogram : derived_unit<kilogram, decltype("kg"_fs), kilo<gram>> {};
 
   inline namespace literals {
 

src/include/units/dimensions/power.h

@@ -32,7 +32,7 @@ namespace units {
   template<typename T>
   concept Power =  QuantityOf<T, power>;
 
-  struct watt : derived_unit<watt, decltype("W"_fs), power, kilogram, metre, second> {};
+  struct watt : coherent_derived_unit<watt, decltype("W"_fs), power, si_prefix> {};
   struct milliwatt : derived_unit<milliwatt, decltype("mW"_fs), milli<watt>> {};
   struct kilowatt : derived_unit<kilowatt, decltype("kW"_fs), kilo<watt>> {};
   struct megawatt : derived_unit<megawatt, decltype("MW"_fs), mega<watt>> {};

src/include/units/dimensions/pressure.h

@@ -33,7 +33,7 @@ namespace units {
   template<typename T>
   concept Pressure =  QuantityOf<T, pressure>;
 
-  struct pascal : derived_unit<pascal, decltype("Pa"_fs), pressure, kilogram, metre, second> {};
+  struct pascal : coherent_derived_unit<pascal, decltype("Pa"_fs), pressure, si_prefix> {};
 
   inline namespace literals {
 

src/include/units/dimensions/substance.h

@@ -32,7 +32,7 @@ namespace units {
   template<typename T>
   concept Substance = QuantityOf<T, substance>;
 
-  struct mole : derived_unit<mole, decltype("mol"_fs), substance> {};
+  struct mole : coherent_derived_unit<mole, decltype("mol"_fs), substance, si_prefix> {};
 
   inline namespace literals {
 

src/include/units/dimensions/temperature.h

@@ -32,7 +32,7 @@ namespace units {
   template<typename T>
   concept ThermodynamicTemperature = QuantityOf<T, temperature>;
 
-  struct kelvin : derived_unit<kelvin, decltype("K"_fs), temperature> {};
+  struct kelvin : coherent_derived_unit<kelvin, decltype("K"_fs), temperature> {};
 
   inline namespace literals {
 

src/include/units/dimensions/time.h

@@ -32,7 +32,7 @@ namespace units {
   template<typename T>
   concept Time = QuantityOf<T, time>;
 
-  struct second : derived_unit<second, decltype("s"_fs), time> {};
+  struct second : coherent_derived_unit<second, decltype("s"_fs), time, si_prefix> {};
   struct nanosecond : derived_unit<nanosecond, decltype("ns"_fs), nano<second>> {};
   struct microsecond : derived_unit<microsecond, decltype("us"_fs), micro<second>> {};
   struct millisecond : derived_unit<millisecond, decltype("ms"_fs), milli<second>> {};

src/include/units/dimensions/velocity.h

@@ -32,7 +32,7 @@ namespace units {
   template<typename T>
   concept Velocity = QuantityOf<T, velocity>;
 
-  struct metre_per_second : derived_unit<metre_per_second, decltype("m/s"_fs), velocity, metre, second> {};
+  struct metre_per_second : coherent_derived_unit<metre_per_second, decltype("m/s"_fs), velocity> {};
   struct kilometre_per_hour : derived_unit<kilometre_per_hour, decltype("km/h"_fs), velocity, kilometre, hour> {};
   struct mile_per_hour : derived_unit<mile_per_hour, decltype("mi/h"_fs), velocity, mile, hour> {};
 

src/include/units/dimensions/voltage.h

@@ -35,7 +35,7 @@ namespace units {
   template<typename T>
   concept Voltage =  QuantityOf<T, voltage>;
 
-  struct volt : derived_unit<volt, decltype("V"_fs), voltage, kilogram, metre, second, ampere> {};
+  struct volt : coherent_derived_unit<volt, decltype("V"_fs), voltage, si_prefix> {};
 
   inline namespace literals {
 

src/include/units/dimensions/volume.h

@@ -31,9 +31,9 @@ namespace units {
   template<typename T>
   concept Volume = QuantityOf<T, volume>;
 
+  struct cubic_metre : coherent_derived_unit<cubic_metre, decltype("m^3"_fs), volume> {};
   struct cubic_millimetre : derived_unit<cubic_millimetre, decltype("mm^3"_fs), volume, millimetre> {};
   struct cubic_centimetre : derived_unit<cubic_centimetre, decltype("cm^3"_fs), volume, centimetre> {};
-  struct cubic_metre : derived_unit<cubic_metre, decltype("m^3"_fs), volume, metre> {};
   struct cubic_kilometre : derived_unit<cubic_kilometre, decltype("km^3"_fs), volume, kilometre, metre> {};
   struct cubic_foot : derived_unit<cubic_foot, decltype("ft^3"_fs), volume, foot> {};
 

src/include/units/format.h

@@ -26,6 +26,9 @@
 
 namespace units {
 
+  template<typename Prefix, typename Ratio>
+  inline constexpr std::string_view prefix_symbol = "";
+
   namespace detail {
 
     template<typename Ratio, typename CharT, typename Traits>
@@ -41,31 +44,11 @@ namespace units {
       }
     }
 
-    template<typename Ratio>
+    template<typename Ratio, typename Prefix, typename CharT, typename Traits>
-    inline constexpr std::string_view ratio_txt = "";
-
-    template<> inline constexpr std::string_view ratio_txt<ratio<1, std::atto::den>> = "a";
-    template<> inline constexpr std::string_view ratio_txt<ratio<1, std::femto::den>> = "f";
-    template<> inline constexpr std::string_view ratio_txt<ratio<1, std::pico::den>> = "p";
-    template<> inline constexpr std::string_view ratio_txt<ratio<1, std::nano::den>> = "n";
-    template<> inline constexpr std::string_view ratio_txt<ratio<1, std::micro::den>> = "\u00b5\u0073";
-    template<> inline constexpr std::string_view ratio_txt<ratio<1, std::milli::den>> = "m";
-    template<> inline constexpr std::string_view ratio_txt<ratio<1, std::centi::den>> = "c";
-    template<> inline constexpr std::string_view ratio_txt<ratio<1, std::deci::den>> = "d";
-    template<> inline constexpr std::string_view ratio_txt<ratio<std::deca::num>> = "da";
-    template<> inline constexpr std::string_view ratio_txt<ratio<std::hecto::num>> = "h";
-    template<> inline constexpr std::string_view ratio_txt<ratio<std::kilo::num>> = "k";
-    template<> inline constexpr std::string_view ratio_txt<ratio<std::mega::num>> = "M";
-    template<> inline constexpr std::string_view ratio_txt<ratio<std::giga::num>> = "G";
-    template<> inline constexpr std::string_view ratio_txt<ratio<std::tera::num>> = "T";
-    template<> inline constexpr std::string_view ratio_txt<ratio<std::peta::num>> = "P";
-    template<> inline constexpr std::string_view ratio_txt<ratio<std::exa::num>> = "E";
-
-    template<typename Ratio, typename CharT, typename Traits>
     void print_prefix_or_ratio(std::basic_ostream<CharT, Traits>& os)
     {
       if constexpr(Ratio::num != 1 || Ratio::den != 1) {
-        constexpr auto prefix = ratio_txt<Ratio>;
+        constexpr auto prefix = prefix_symbol<Prefix, Ratio>;
 
         if constexpr(prefix != "") {
           // print as a prefixed unit

src/include/units/prefix.h

@@ -0,0 +1,68 @@
+// The MIT License (MIT)
+//
+// Copyright (c) 2018 Mateusz Pusz
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#pragma once
+
+#include <units/unit.h>
+#include <units/format.h>
+
+namespace units {
+
+  // prefix tags
+  struct si_prefix;
+  
+  // SI prefixes
+
+  template<Unit U> using atto = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::atto::den>>>;
+  template<Unit U> using femto = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::femto::den>>>;
+  template<Unit U> using pico = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::pico::den>>>;
+  template<Unit U> using nano = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::nano::den>>>;
+  template<Unit U> using micro = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::micro::den>>>;
+  template<Unit U> using milli = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::milli::den>>>;
+  template<Unit U> using centi = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::centi::den>>>;
+  template<Unit U> using deca = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::deca::num>>>;
+  template<Unit U> using hecto = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::hecto::num>>>;
+  template<Unit U> using kilo = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::kilo::num>>>;
+  template<Unit U> using mega = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::mega::num>>>;
+  template<Unit U> using giga = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::giga::num>>>;
+  template<Unit U> using tera = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::tera::num>>>;
+  template<Unit U> using peta = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::peta::num>>>;
+  template<Unit U> using exa = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::exa::num>>>;
+
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<1, std::atto::den>> = "a";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<1, std::femto::den>> = "f";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<1, std::pico::den>> = "p";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<1, std::nano::den>> = "n";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<1, std::micro::den>> = "\u00b5\u0073";  // µ
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<1, std::milli::den>> = "m";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<1, std::centi::den>> = "c";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<1, std::deci::den>> = "d";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<std::deca::num>> = "da";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<std::hecto::num>> = "h";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<std::kilo::num>> = "k";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<std::mega::num>> = "M";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<std::giga::num>> = "G";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<std::tera::num>> = "T";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<std::peta::num>> = "P";
+  template<> inline constexpr std::string_view prefix_symbol<si_prefix, ratio<std::exa::num>> = "E";
+
+}

src/include/units/quantity.h

@@ -23,8 +23,7 @@
 #pragma once
 
 #include <units/bits/concepts.h>
-#include <units/unit.h>
+#include <units/prefix.h>
-#include <units/format.h>
 #include <limits>
 #include <ostream>
 
@@ -290,13 +289,10 @@ namespace units {
         using ratio = quantity::unit::ratio;
         using dim = quantity::unit::dimension;
         if constexpr(!detail::is_dimension<dim>) {
-          // print as a prefix or ratio of a coherent unit
+          // print as a prefix or ratio of a coherent unit symbol defined by the user
-          detail::print_prefix_or_ratio<ratio>(os);
+          using coherent_unit = downcast_target<units::unit<dim, units::ratio<1>>>;
-
+          detail::print_prefix_or_ratio<ratio, typename coherent_unit::prefix>(os);
-          if constexpr(!detail::is_dimension<dim>) {
+          os << coherent_unit::symbol::c_str();
-            // print coherent unit symbol defined by the user
-            os << downcast_target<units::unit<dim>>::symbol::c_str();
-          }
         }
         else {
           // print as a ratio of a coherent unit

src/include/units/unit.h

@@ -28,7 +28,7 @@
 
 namespace units {
 
-  template<Dimension D, Ratio R = ratio<1>>
+  template<Dimension D, Ratio R>
     requires (R::num * R::den > 0)
   struct unit : downcast_base<unit<D, R>> {
     using dimension = D;
@@ -141,14 +141,17 @@ namespace units {
   //   static constexpr auto symbol = Symbol;
   // };
 
+  struct no_prefix;
+
+  template<typename Child, typename Symbol, Dimension D, typename Prefix = no_prefix>
+  struct coherent_derived_unit : downcast_helper<Child, unit<D, ratio<1>>> {
+    using symbol = Symbol;
+    using prefix = Prefix;
+  };
+
   template<typename Child, typename Symbol, typename...>
   struct derived_unit;
   
-  template<typename Child, typename Symbol, Dimension D>
-  struct derived_unit<Child, Symbol, D> : downcast_helper<Child, unit<D, ratio<1>>> {
-    using symbol = Symbol;
-  };
-
   template<typename Child, typename Symbol, Dimension D, Ratio R>
   struct derived_unit<Child, Symbol, D, R> : downcast_helper<Child, unit<D, R>> {
     using symbol = Symbol;
@@ -164,22 +167,4 @@ namespace units {
     using symbol = Symbol;
   };
 
-  // SI prefixes
-
-  template<Unit U> using atto = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::atto::den>>>;
-  template<Unit U> using femto = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::femto::den>>>;
-  template<Unit U> using pico = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::pico::den>>>;
-  template<Unit U> using nano = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::nano::den>>>;
-  template<Unit U> using micro = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::micro::den>>>;
-  template<Unit U> using milli = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::milli::den>>>;
-  template<Unit U> using centi = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<1, std::centi::den>>>;
-  template<Unit U> using deca = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::deca::num>>>;
-  template<Unit U> using hecto = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::hecto::num>>>;
-  template<Unit U> using kilo = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::kilo::num>>>;
-  template<Unit U> using mega = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::mega::num>>>;
-  template<Unit U> using giga = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::giga::num>>>;
-  template<Unit U> using tera = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::tera::num>>>;
-  template<Unit U> using peta = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::peta::num>>>;
-  template<Unit U> using exa = unit<typename U::dimension, ratio_multiply<typename U::ratio, ratio<std::exa::num>>>;
-
 }  // namespace units

test/unit_test/runtime/CMakeLists.txt

@@ -22,6 +22,7 @@
 
 add_executable(unit_tests_runtime
     catch_main.cpp
+    digital_information_test.cpp
     math_test.cpp
     text_test.cpp
 )

test/unit_test/runtime/digital_information_test.cpp

@@ -0,0 +1,77 @@
+// The MIT License (MIT)
+//
+// Copyright (c) 2018 Mateusz Pusz
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include <units/quantity.h>
+#include <catch2/catch.hpp>
+#include <sstream>
+
+namespace data {
+
+  struct base_dim_digital_information : units::base_dimension<"digital information", "b"> {};
+
+  struct digital_information : units::derived_dimension<digital_information, units::exp<base_dim_digital_information, 1>> {};
+
+  template<typename T>
+  concept DigitalInformation = units::QuantityOf<T, digital_information>;
+
+  using namespace units::hacks;
+
+  struct data_prefix;
+
+  struct bit : units::coherent_derived_unit<bit, decltype("b"_fs), digital_information, data_prefix> {};
+  struct kilobit : units::derived_unit<bit, decltype("Kib"_fs), digital_information, units::ratio<1'024>> {};
+  struct byte : units::derived_unit<byte, decltype("B"_fs), digital_information, units::ratio<8>> {};
+
+  inline namespace literals {
+
+    constexpr auto operator""_b(unsigned long long l) { return units::quantity<bit, std::int64_t>(l); }
+    constexpr auto operator""_Kib(unsigned long long l) { return units::quantity<kilobit, std::int64_t>(l); }
+    constexpr auto operator""_B(unsigned long long l) { return units::quantity<byte, std::int64_t>(l); }
+
+  }
+
+}
+
+template<> inline constexpr std::string_view units::prefix_symbol<data::data_prefix, units::ratio<    1'024>> = "Ki";
+template<> inline constexpr std::string_view units::prefix_symbol<data::data_prefix, units::ratio<1'048'576>> = "Mi";
+
+using namespace data;
+
+TEST_CASE("operator<< on a custom quantity", "[text][ostream]")
+{
+  std::stringstream stream;
+
+  SECTION("quantity with a predefined unit and prefix")
+  {
+    SECTION("named unit")
+    {
+      stream << 64_B;
+      REQUIRE(stream.str() == "64 B");
+    }
+
+    SECTION("other unit matching prefix")
+    {
+      stream << 8_Kib * 8_Kib / 2_b;
+      REQUIRE(stream.str() == "32 Mib");
+    }
+  }
+}

test/unit_test/runtime/text_test.cpp

@@ -39,25 +39,31 @@ TEST_CASE("operator<< on a quantity", "[text][ostream]")
   {
     SECTION("integral representation")
     {
-      stream << 16sq_m;
+      stream << 60W;
-      REQUIRE(stream.str() == "16 m^2");
+      REQUIRE(stream.str() == "60 W");
     }
 
     SECTION("floating-point representation")
     {
-      stream << 72.5kmph;
+      stream << 72.5kJ;
-      REQUIRE(stream.str() == "72.5 km/h");
+      REQUIRE(stream.str() == "72.5 kJ");
     }
   }
 
   SECTION("quantity with a predefined dimension but unknown unit")
   {
-    SECTION("unit::ratio as an SI prefix")
+    SECTION("unit::ratio as an SI prefix for a dimension with a special symbol")
     {
       stream << 4.N * 2cm;
       REQUIRE(stream.str() == "8 cJ");
     }
 
+    SECTION("unit::ratio for a dimension without a special symbol")
+    {
+      stream << 2.cm * 2m * 2m;
+      REQUIRE(stream.str() == "8 [1/100]m^3");
+    }
+
     SECTION("unit::ratio::num != 1 && unit::ratio::den == 1")
     {
       stream << 4 * 2min / (2s * 2s);

test/unit_test/static/custom_unit_test.cpp

@@ -37,7 +37,9 @@ namespace {
 
   using namespace units::hacks;
 
-  struct bit : units::derived_unit<bit, decltype("b"_fs), digital_information> {};
+  struct data_prefix {};
+
+  struct bit : units::coherent_derived_unit<bit, decltype("b"_fs), digital_information, data_prefix> {};
   struct byte : units::derived_unit<byte, decltype("B"_fs), digital_information, units::ratio<8>> {};
 
   inline namespace literals {
@@ -63,13 +65,11 @@ namespace {
 
   // power spectral density
   struct power_spectral_density : derived_dimension<power_spectral_density, units::exp<voltage, 2>, units::exp<frequency, -1>> {};
-  struct sq_volt_per_hertz : derived_unit<sq_volt_per_hertz, decltype("V^2/Hz"_fs), power_spectral_density> {};
+  struct sq_volt_per_hertz : coherent_derived_unit<sq_volt_per_hertz, decltype("V^2/Hz"_fs), power_spectral_density> {};
 
   // amplitude spectral density
   struct amplitude_spectral_density : derived_dimension<amplitude_spectral_density, units::exp<voltage, 1>, units::exp<frequency, -1, 2>> {};
-  // TODO: add support for derived_unit
+  struct volt_per_sqrt_hertz : coherent_derived_unit<volt_per_sqrt_hertz, decltype("V/Hz^(1/2)"_fs), amplitude_spectral_density> {};
-  //struct volt_per_sq_hertz : derived_unit<volt_per_sq_hertz, amplitude_spectral_density, volt, hertz> {};
-  struct volt_per_sqrt_hertz : derived_unit<volt_per_sqrt_hertz, decltype("V/Hz^(1/2)"_fs), amplitude_spectral_density> {};
 }
 
 namespace {