Chris@47: // Copyright (c) 2013-2014 Sandstorm Development Group, Inc. and contributors
Chris@47: // Licensed under the MIT License:
Chris@47: //
Chris@47: // Permission is hereby granted, free of charge, to any person obtaining a copy
Chris@47: // of this software and associated documentation files (the "Software"), to deal
Chris@47: // in the Software without restriction, including without limitation the rights
Chris@47: // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
Chris@47: // copies of the Software, and to permit persons to whom the Software is
Chris@47: // furnished to do so, subject to the following conditions:
Chris@47: //
Chris@47: // The above copyright notice and this permission notice shall be included in
Chris@47: // all copies or substantial portions of the Software.
Chris@47: //
Chris@47: // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
Chris@47: // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
Chris@47: // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
Chris@47: // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
Chris@47: // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
Chris@47: // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
Chris@47: // THE SOFTWARE.
Chris@47: 
Chris@47: // This file contains types which are intended to help detect incorrect usage at compile
Chris@47: // time, but should then be optimized down to basic primitives (usually, integers) by the
Chris@47: // compiler.
Chris@47: 
Chris@47: #ifndef KJ_UNITS_H_
Chris@47: #define KJ_UNITS_H_
Chris@47: 
Chris@47: #if defined(__GNUC__) && !KJ_HEADER_WARNINGS
Chris@47: #pragma GCC system_header
Chris@47: #endif
Chris@47: 
Chris@47: #include "common.h"
Chris@47: 
Chris@47: namespace kj {
Chris@47: 
Chris@47: // =======================================================================================
Chris@47: // IDs
Chris@47: 
Chris@47: template <typename UnderlyingType, typename Label>
Chris@47: struct Id {
Chris@47:   // A type-safe numeric ID.  `UnderlyingType` is the underlying integer representation.  `Label`
Chris@47:   // distinguishes this Id from other Id types.  Sample usage:
Chris@47:   //
Chris@47:   //   class Foo;
Chris@47:   //   typedef Id<uint, Foo> FooId;
Chris@47:   //
Chris@47:   //   class Bar;
Chris@47:   //   typedef Id<uint, Bar> BarId;
Chris@47:   //
Chris@47:   // You can now use the FooId and BarId types without any possibility of accidentally using a
Chris@47:   // FooId when you really wanted a BarId or vice-versa.
Chris@47: 
Chris@47:   UnderlyingType value;
Chris@47: 
Chris@47:   inline constexpr Id(): value(0) {}
Chris@47:   inline constexpr explicit Id(int value): value(value) {}
Chris@47: 
Chris@47:   inline constexpr bool operator==(const Id& other) const { return value == other.value; }
Chris@47:   inline constexpr bool operator!=(const Id& other) const { return value != other.value; }
Chris@47:   inline constexpr bool operator<=(const Id& other) const { return value <= other.value; }
Chris@47:   inline constexpr bool operator>=(const Id& other) const { return value >= other.value; }
Chris@47:   inline constexpr bool operator< (const Id& other) const { return value <  other.value; }
Chris@47:   inline constexpr bool operator> (const Id& other) const { return value >  other.value; }
Chris@47: };
Chris@47: 
Chris@47: // =======================================================================================
Chris@47: // Quantity and UnitRatio -- implement unit analysis via the type system
Chris@47: 
Chris@47: template <typename T> constexpr bool isIntegral() { return false; }
Chris@47: template <> constexpr bool isIntegral<char>() { return true; }
Chris@47: template <> constexpr bool isIntegral<signed char>() { return true; }
Chris@47: template <> constexpr bool isIntegral<short>() { return true; }
Chris@47: template <> constexpr bool isIntegral<int>() { return true; }
Chris@47: template <> constexpr bool isIntegral<long>() { return true; }
Chris@47: template <> constexpr bool isIntegral<long long>() { return true; }
Chris@47: template <> constexpr bool isIntegral<unsigned char>() { return true; }
Chris@47: template <> constexpr bool isIntegral<unsigned short>() { return true; }
Chris@47: template <> constexpr bool isIntegral<unsigned int>() { return true; }
Chris@47: template <> constexpr bool isIntegral<unsigned long>() { return true; }
Chris@47: template <> constexpr bool isIntegral<unsigned long long>() { return true; }
Chris@47: 
Chris@47: template <typename Number, typename Unit1, typename Unit2>
Chris@47: class UnitRatio {
Chris@47:   // A multiplier used to convert Quantities of one unit to Quantities of another unit.  See
Chris@47:   // Quantity, below.
Chris@47:   //
Chris@47:   // Construct this type by dividing one Quantity by another of a different unit.  Use this type
Chris@47:   // by multiplying it by a Quantity, or dividing a Quantity by it.
Chris@47: 
Chris@47:   static_assert(isIntegral<Number>(), "Underlying type for UnitRatio must be integer.");
Chris@47: 
Chris@47: public:
Chris@47:   inline UnitRatio() {}
Chris@47: 
Chris@47:   constexpr explicit UnitRatio(Number unit1PerUnit2): unit1PerUnit2(unit1PerUnit2) {}
Chris@47:   // This constructor was intended to be private, but GCC complains about it being private in a
Chris@47:   // bunch of places that don't appear to even call it, so I made it public.  Oh well.
Chris@47: 
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr UnitRatio(const UnitRatio<OtherNumber, Unit1, Unit2>& other)
Chris@47:       : unit1PerUnit2(other.unit1PerUnit2) {}
Chris@47: 
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr UnitRatio<decltype(Number(1)+OtherNumber(1)), Unit1, Unit2>
Chris@47:       operator+(UnitRatio<OtherNumber, Unit1, Unit2> other) const {
Chris@47:     return UnitRatio<decltype(Number(1)+OtherNumber(1)), Unit1, Unit2>(
Chris@47:         unit1PerUnit2 + other.unit1PerUnit2);
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr UnitRatio<decltype(Number(1)-OtherNumber(1)), Unit1, Unit2>
Chris@47:       operator-(UnitRatio<OtherNumber, Unit1, Unit2> other) const {
Chris@47:     return UnitRatio<decltype(Number(1)-OtherNumber(1)), Unit1, Unit2>(
Chris@47:         unit1PerUnit2 - other.unit1PerUnit2);
Chris@47:   }
Chris@47: 
Chris@47:   template <typename OtherNumber, typename Unit3>
Chris@47:   inline constexpr UnitRatio<decltype(Number(1)*OtherNumber(1)), Unit3, Unit2>
Chris@47:       operator*(UnitRatio<OtherNumber, Unit3, Unit1> other) const {
Chris@47:     // U1 / U2 * U3 / U1 = U3 / U2
Chris@47:     return UnitRatio<decltype(Number(1)*OtherNumber(1)), Unit3, Unit2>(
Chris@47:         unit1PerUnit2 * other.unit1PerUnit2);
Chris@47:   }
Chris@47:   template <typename OtherNumber, typename Unit3>
Chris@47:   inline constexpr UnitRatio<decltype(Number(1)*OtherNumber(1)), Unit1, Unit3>
Chris@47:       operator*(UnitRatio<OtherNumber, Unit2, Unit3> other) const {
Chris@47:     // U1 / U2 * U2 / U3 = U1 / U3
Chris@47:     return UnitRatio<decltype(Number(1)*OtherNumber(1)), Unit1, Unit3>(
Chris@47:         unit1PerUnit2 * other.unit1PerUnit2);
Chris@47:   }
Chris@47: 
Chris@47:   template <typename OtherNumber, typename Unit3>
Chris@47:   inline constexpr UnitRatio<decltype(Number(1)*OtherNumber(1)), Unit3, Unit2>
Chris@47:       operator/(UnitRatio<OtherNumber, Unit1, Unit3> other) const {
Chris@47:     // (U1 / U2) / (U1 / U3) = U3 / U2
Chris@47:     return UnitRatio<decltype(Number(1)*OtherNumber(1)), Unit3, Unit2>(
Chris@47:         unit1PerUnit2 / other.unit1PerUnit2);
Chris@47:   }
Chris@47:   template <typename OtherNumber, typename Unit3>
Chris@47:   inline constexpr UnitRatio<decltype(Number(1)*OtherNumber(1)), Unit1, Unit3>
Chris@47:       operator/(UnitRatio<OtherNumber, Unit3, Unit2> other) const {
Chris@47:     // (U1 / U2) / (U3 / U2) = U1 / U3
Chris@47:     return UnitRatio<decltype(Number(1)*OtherNumber(1)), Unit1, Unit3>(
Chris@47:         unit1PerUnit2 / other.unit1PerUnit2);
Chris@47:   }
Chris@47: 
Chris@47:   template <typename OtherNumber>
Chris@47:   inline decltype(Number(1) / OtherNumber(1))
Chris@47:       operator/(UnitRatio<OtherNumber, Unit1, Unit2> other) const {
Chris@47:     return unit1PerUnit2 / other.unit1PerUnit2;
Chris@47:   }
Chris@47: 
Chris@47:   inline bool operator==(UnitRatio other) const { return unit1PerUnit2 == other.unit1PerUnit2; }
Chris@47:   inline bool operator!=(UnitRatio other) const { return unit1PerUnit2 != other.unit1PerUnit2; }
Chris@47: 
Chris@47: private:
Chris@47:   Number unit1PerUnit2;
Chris@47: 
Chris@47:   template <typename OtherNumber, typename OtherUnit>
Chris@47:   friend class Quantity;
Chris@47:   template <typename OtherNumber, typename OtherUnit1, typename OtherUnit2>
Chris@47:   friend class UnitRatio;
Chris@47: 
Chris@47:   template <typename N1, typename N2, typename U1, typename U2>
Chris@47:   friend inline constexpr UnitRatio<decltype(N1(1) * N2(1)), U1, U2>
Chris@47:       operator*(N1, UnitRatio<N2, U1, U2>);
Chris@47: };
Chris@47: 
Chris@47: template <typename N1, typename N2, typename U1, typename U2>
Chris@47: inline constexpr UnitRatio<decltype(N1(1) * N2(1)), U1, U2>
Chris@47:     operator*(N1 n, UnitRatio<N2, U1, U2> r) {
Chris@47:   return UnitRatio<decltype(N1(1) * N2(1)), U1, U2>(n * r.unit1PerUnit2);
Chris@47: }
Chris@47: 
Chris@47: template <typename Number, typename Unit>
Chris@47: class Quantity {
Chris@47:   // A type-safe numeric quantity, specified in terms of some unit.  Two Quantities cannot be used
Chris@47:   // in arithmetic unless they use the same unit.  The `Unit` type parameter is only used to prevent
Chris@47:   // accidental mixing of units; this type is never instantiated and can very well be incomplete.
Chris@47:   // `Number` is the underlying primitive numeric type.
Chris@47:   //
Chris@47:   // Quantities support most basic arithmetic operators, intelligently handling units, and
Chris@47:   // automatically casting the underlying type in the same way that the compiler would.
Chris@47:   //
Chris@47:   // To convert a primitive number to a Quantity, multiply it by unit<Quantity<N, U>>().
Chris@47:   // To convert a Quantity to a primitive number, divide it by unit<Quantity<N, U>>().
Chris@47:   // To convert a Quantity of one unit to another unit, multiply or divide by a UnitRatio.
Chris@47:   //
Chris@47:   // The Quantity class is not well-suited to hardcore physics as it does not allow multiplying
Chris@47:   // one quantity by another.  For example, multiplying meters by meters won't get you square
Chris@47:   // meters; it will get you a compiler error.  It would be interesting to see if template
Chris@47:   // metaprogramming could properly deal with such things but this isn't needed for the present
Chris@47:   // use case.
Chris@47:   //
Chris@47:   // Sample usage:
Chris@47:   //
Chris@47:   //   class SecondsLabel;
Chris@47:   //   typedef Quantity<double, SecondsLabel> Seconds;
Chris@47:   //   constexpr Seconds SECONDS = unit<Seconds>();
Chris@47:   //
Chris@47:   //   class MinutesLabel;
Chris@47:   //   typedef Quantity<double, MinutesLabel> Minutes;
Chris@47:   //   constexpr Minutes MINUTES = unit<Minutes>();
Chris@47:   //
Chris@47:   //   constexpr UnitRatio<double, SecondsLabel, MinutesLabel> SECONDS_PER_MINUTE =
Chris@47:   //       60 * SECONDS / MINUTES;
Chris@47:   //
Chris@47:   //   void waitFor(Seconds seconds) {
Chris@47:   //     sleep(seconds / SECONDS);
Chris@47:   //   }
Chris@47:   //   void waitFor(Minutes minutes) {
Chris@47:   //     waitFor(minutes * SECONDS_PER_MINUTE);
Chris@47:   //   }
Chris@47:   //
Chris@47:   //   void waitThreeMinutes() {
Chris@47:   //     waitFor(3 * MINUTES);
Chris@47:   //   }
Chris@47: 
Chris@47:   static_assert(isIntegral<Number>(), "Underlying type for Quantity must be integer.");
Chris@47: 
Chris@47: public:
Chris@47:   inline constexpr Quantity() {}
Chris@47: 
Chris@47:   inline constexpr Quantity(MaxValue_): value(maxValue) {}
Chris@47:   inline constexpr Quantity(MinValue_): value(minValue) {}
Chris@47:   // Allow initialization from maxValue and minValue.
Chris@47:   // TODO(msvc): decltype(maxValue) and decltype(minValue) deduce unknown-type for these function
Chris@47:   // parameters, causing the compiler to complain of a duplicate constructor definition, so we
Chris@47:   // specify MaxValue_ and MinValue_ types explicitly.
Chris@47: 
Chris@47:   inline explicit constexpr Quantity(Number value): value(value) {}
Chris@47:   // This constructor was intended to be private, but GCC complains about it being private in a
Chris@47:   // bunch of places that don't appear to even call it, so I made it public.  Oh well.
Chris@47: 
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr Quantity(const Quantity<OtherNumber, Unit>& other)
Chris@47:       : value(other.value) {}
Chris@47: 
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr Quantity<decltype(Number(1) + OtherNumber(1)), Unit>
Chris@47:       operator+(const Quantity<OtherNumber, Unit>& other) const {
Chris@47:     return Quantity<decltype(Number(1) + OtherNumber(1)), Unit>(value + other.value);
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr Quantity<decltype(Number(1) - OtherNumber(1)), Unit>
Chris@47:       operator-(const Quantity<OtherNumber, Unit>& other) const {
Chris@47:     return Quantity<decltype(Number(1) - OtherNumber(1)), Unit>(value - other.value);
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr Quantity<decltype(Number(1) * OtherNumber(1)), Unit>
Chris@47:       operator*(OtherNumber other) const {
Chris@47:     static_assert(isIntegral<OtherNumber>(), "Multiplied Quantity by non-integer.");
Chris@47:     return Quantity<decltype(Number(1) * other), Unit>(value * other);
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr Quantity<decltype(Number(1) / OtherNumber(1)), Unit>
Chris@47:       operator/(OtherNumber other) const {
Chris@47:     static_assert(isIntegral<OtherNumber>(), "Divided Quantity by non-integer.");
Chris@47:     return Quantity<decltype(Number(1) / other), Unit>(value / other);
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr decltype(Number(1) / OtherNumber(1))
Chris@47:       operator/(const Quantity<OtherNumber, Unit>& other) const {
Chris@47:     return value / other.value;
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr decltype(Number(1) % OtherNumber(1))
Chris@47:       operator%(const Quantity<OtherNumber, Unit>& other) const {
Chris@47:     return value % other.value;
Chris@47:   }
Chris@47: 
Chris@47:   template <typename OtherNumber, typename OtherUnit>
Chris@47:   inline constexpr Quantity<decltype(Number(1) * OtherNumber(1)), OtherUnit>
Chris@47:       operator*(const UnitRatio<OtherNumber, OtherUnit, Unit>& ratio) const {
Chris@47:     return Quantity<decltype(Number(1) * OtherNumber(1)), OtherUnit>(
Chris@47:         value * ratio.unit1PerUnit2);
Chris@47:   }
Chris@47:   template <typename OtherNumber, typename OtherUnit>
Chris@47:   inline constexpr Quantity<decltype(Number(1) / OtherNumber(1)), OtherUnit>
Chris@47:       operator/(const UnitRatio<OtherNumber, Unit, OtherUnit>& ratio) const {
Chris@47:     return Quantity<decltype(Number(1) / OtherNumber(1)), OtherUnit>(
Chris@47:         value / ratio.unit1PerUnit2);
Chris@47:   }
Chris@47:   template <typename OtherNumber, typename OtherUnit>
Chris@47:   inline constexpr Quantity<decltype(Number(1) % OtherNumber(1)), Unit>
Chris@47:       operator%(const UnitRatio<OtherNumber, Unit, OtherUnit>& ratio) const {
Chris@47:     return Quantity<decltype(Number(1) % OtherNumber(1)), Unit>(
Chris@47:         value % ratio.unit1PerUnit2);
Chris@47:   }
Chris@47:   template <typename OtherNumber, typename OtherUnit>
Chris@47:   inline constexpr UnitRatio<decltype(Number(1) / OtherNumber(1)), Unit, OtherUnit>
Chris@47:       operator/(const Quantity<OtherNumber, OtherUnit>& other) const {
Chris@47:     return UnitRatio<decltype(Number(1) / OtherNumber(1)), Unit, OtherUnit>(value / other.value);
Chris@47:   }
Chris@47: 
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr bool operator==(const Quantity<OtherNumber, Unit>& other) const {
Chris@47:     return value == other.value;
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr bool operator!=(const Quantity<OtherNumber, Unit>& other) const {
Chris@47:     return value != other.value;
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr bool operator<=(const Quantity<OtherNumber, Unit>& other) const {
Chris@47:     return value <= other.value;
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr bool operator>=(const Quantity<OtherNumber, Unit>& other) const {
Chris@47:     return value >= other.value;
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr bool operator<(const Quantity<OtherNumber, Unit>& other) const {
Chris@47:     return value < other.value;
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline constexpr bool operator>(const Quantity<OtherNumber, Unit>& other) const {
Chris@47:     return value > other.value;
Chris@47:   }
Chris@47: 
Chris@47:   template <typename OtherNumber>
Chris@47:   inline Quantity& operator+=(const Quantity<OtherNumber, Unit>& other) {
Chris@47:     value += other.value;
Chris@47:     return *this;
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline Quantity& operator-=(const Quantity<OtherNumber, Unit>& other) {
Chris@47:     value -= other.value;
Chris@47:     return *this;
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline Quantity& operator*=(OtherNumber other) {
Chris@47:     value *= other;
Chris@47:     return *this;
Chris@47:   }
Chris@47:   template <typename OtherNumber>
Chris@47:   inline Quantity& operator/=(OtherNumber other) {
Chris@47:     value /= other.value;
Chris@47:     return *this;
Chris@47:   }
Chris@47: 
Chris@47: private:
Chris@47:   Number value;
Chris@47: 
Chris@47:   template <typename OtherNumber, typename OtherUnit>
Chris@47:   friend class Quantity;
Chris@47: 
Chris@47:   template <typename Number1, typename Number2, typename Unit2>
Chris@47:   friend inline constexpr auto operator*(Number1 a, Quantity<Number2, Unit2> b)
Chris@47:       -> Quantity<decltype(Number1(1) * Number2(1)), Unit2>;
Chris@47: 
Chris@47:   template <typename T>
Chris@47:   friend inline constexpr T unit();
Chris@47: };
Chris@47: 
Chris@47: template <typename T>
Chris@47: inline constexpr T unit() { return T(1); }
Chris@47: // unit<Quantity<T, U>>() returns a Quantity of value 1.  It also, intentionally, works on basic
Chris@47: // numeric types.
Chris@47: 
Chris@47: template <typename Number1, typename Number2, typename Unit>
Chris@47: inline constexpr auto operator*(Number1 a, Quantity<Number2, Unit> b)
Chris@47:     -> Quantity<decltype(Number1(1) * Number2(1)), Unit> {
Chris@47:   return Quantity<decltype(Number1(1) * Number2(1)), Unit>(a * b.value);
Chris@47: }
Chris@47: 
Chris@47: template <typename Number1, typename Number2, typename Unit, typename Unit2>
Chris@47: inline constexpr auto operator*(UnitRatio<Number1, Unit2, Unit> ratio,
Chris@47:     Quantity<Number2, Unit> measure)
Chris@47:     -> decltype(measure * ratio) {
Chris@47:   return measure * ratio;
Chris@47: }
Chris@47: 
Chris@47: // =======================================================================================
Chris@47: // Absolute measures
Chris@47: 
Chris@47: template <typename T, typename Label>
Chris@47: class Absolute {
Chris@47:   // Wraps some other value -- typically a Quantity -- but represents a value measured based on
Chris@47:   // some absolute origin.  For example, if `Duration` is a type representing a time duration,
Chris@47:   // Absolute<Duration, UnixEpoch> might be a calendar date.
Chris@47:   //
Chris@47:   // Since Absolute represents measurements relative to some arbitrary origin, the only sensible
Chris@47:   // arithmetic to perform on them is addition and subtraction.
Chris@47: 
Chris@47:   // TODO(someday):  Do the same automatic expansion of integer width that Quantity does?  Doesn't
Chris@47:   //   matter for our time use case, where we always use 64-bit anyway.  Note that fixing this
Chris@47:   //   would implicitly allow things like multiplying an Absolute by a UnitRatio to change its
Chris@47:   //   units, which is actually totally logical and kind of neat.
Chris@47: 
Chris@47: public:
Chris@47:   inline constexpr Absolute operator+(const T& other) const { return Absolute(value + other); }
Chris@47:   inline constexpr Absolute operator-(const T& other) const { return Absolute(value - other); }
Chris@47:   inline constexpr T operator-(const Absolute& other) const { return value - other.value; }
Chris@47: 
Chris@47:   inline Absolute& operator+=(const T& other) { value += other; return *this; }
Chris@47:   inline Absolute& operator-=(const T& other) { value -= other; return *this; }
Chris@47: 
Chris@47:   inline constexpr bool operator==(const Absolute& other) const { return value == other.value; }
Chris@47:   inline constexpr bool operator!=(const Absolute& other) const { return value != other.value; }
Chris@47:   inline constexpr bool operator<=(const Absolute& other) const { return value <= other.value; }
Chris@47:   inline constexpr bool operator>=(const Absolute& other) const { return value >= other.value; }
Chris@47:   inline constexpr bool operator< (const Absolute& other) const { return value <  other.value; }
Chris@47:   inline constexpr bool operator> (const Absolute& other) const { return value >  other.value; }
Chris@47: 
Chris@47: private:
Chris@47:   T value;
Chris@47: 
Chris@47:   explicit constexpr Absolute(T value): value(value) {}
Chris@47: 
Chris@47:   template <typename U>
Chris@47:   friend inline constexpr U origin();
Chris@47: };
Chris@47: 
Chris@47: template <typename T, typename Label>
Chris@47: inline constexpr Absolute<T, Label> operator+(const T& a, const Absolute<T, Label>& b) {
Chris@47:   return b + a;
Chris@47: }
Chris@47: 
Chris@47: template <typename T> struct UnitOf_ { typedef T Type; };
Chris@47: template <typename T, typename Label> struct UnitOf_<Absolute<T, Label>> { typedef T Type; };
Chris@47: template <typename T>
Chris@47: using UnitOf = typename UnitOf_<T>::Type;
Chris@47: // UnitOf<Absolute<T, U>> is T.  UnitOf<AnythingElse> is AnythingElse.
Chris@47: 
Chris@47: template <typename T>
Chris@47: inline constexpr T origin() { return T(0 * unit<UnitOf<T>>()); }
Chris@47: // origin<Absolute<T, U>>() returns an Absolute of value 0.  It also, intentionally, works on basic
Chris@47: // numeric types.
Chris@47: 
Chris@47: }  // namespace kj
Chris@47: 
Chris@47: #endif  // KJ_UNITS_H_