cannam@62: // Copyright (c) 2013-2014 Sandstorm Development Group, Inc. and contributors
cannam@62: // Licensed under the MIT License:
cannam@62: //
cannam@62: // Permission is hereby granted, free of charge, to any person obtaining a copy
cannam@62: // of this software and associated documentation files (the "Software"), to deal
cannam@62: // in the Software without restriction, including without limitation the rights
cannam@62: // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
cannam@62: // copies of the Software, and to permit persons to whom the Software is
cannam@62: // furnished to do so, subject to the following conditions:
cannam@62: //
cannam@62: // The above copyright notice and this permission notice shall be included in
cannam@62: // all copies or substantial portions of the Software.
cannam@62: //
cannam@62: // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
cannam@62: // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
cannam@62: // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
cannam@62: // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
cannam@62: // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
cannam@62: // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
cannam@62: // THE SOFTWARE.
cannam@62: 
cannam@62: // This file contains types which are intended to help detect incorrect usage at compile
cannam@62: // time, but should then be optimized down to basic primitives (usually, integers) by the
cannam@62: // compiler.
cannam@62: 
cannam@62: #ifndef KJ_UNITS_H_
cannam@62: #define KJ_UNITS_H_
cannam@62: 
cannam@62: #if defined(__GNUC__) && !KJ_HEADER_WARNINGS
cannam@62: #pragma GCC system_header
cannam@62: #endif
cannam@62: 
cannam@62: #include "common.h"
cannam@62: #include <inttypes.h>
cannam@62: 
cannam@62: namespace kj {
cannam@62: 
cannam@62: // =======================================================================================
cannam@62: // IDs
cannam@62: 
cannam@62: template <typename UnderlyingType, typename Label>
cannam@62: struct Id {
cannam@62:   // A type-safe numeric ID.  `UnderlyingType` is the underlying integer representation.  `Label`
cannam@62:   // distinguishes this Id from other Id types.  Sample usage:
cannam@62:   //
cannam@62:   //   class Foo;
cannam@62:   //   typedef Id<uint, Foo> FooId;
cannam@62:   //
cannam@62:   //   class Bar;
cannam@62:   //   typedef Id<uint, Bar> BarId;
cannam@62:   //
cannam@62:   // You can now use the FooId and BarId types without any possibility of accidentally using a
cannam@62:   // FooId when you really wanted a BarId or vice-versa.
cannam@62: 
cannam@62:   UnderlyingType value;
cannam@62: 
cannam@62:   inline constexpr Id(): value(0) {}
cannam@62:   inline constexpr explicit Id(int value): value(value) {}
cannam@62: 
cannam@62:   inline constexpr bool operator==(const Id& other) const { return value == other.value; }
cannam@62:   inline constexpr bool operator!=(const Id& other) const { return value != other.value; }
cannam@62:   inline constexpr bool operator<=(const Id& other) const { return value <= other.value; }
cannam@62:   inline constexpr bool operator>=(const Id& other) const { return value >= other.value; }
cannam@62:   inline constexpr bool operator< (const Id& other) const { return value <  other.value; }
cannam@62:   inline constexpr bool operator> (const Id& other) const { return value >  other.value; }
cannam@62: };
cannam@62: 
cannam@62: // =======================================================================================
cannam@62: // Quantity and UnitRatio -- implement unit analysis via the type system
cannam@62: 
cannam@62: struct Unsafe_ {};
cannam@62: constexpr Unsafe_ unsafe = Unsafe_();
cannam@62: // Use as a parameter to constructors that are unsafe to indicate that you really do mean it.
cannam@62: 
cannam@62: template <uint64_t maxN, typename T>
cannam@62: class Bounded;
cannam@62: template <uint value>
cannam@62: class BoundedConst;
cannam@62: 
cannam@62: template <typename T> constexpr bool isIntegral() { return false; }
cannam@62: template <> constexpr bool isIntegral<char>() { return true; }
cannam@62: template <> constexpr bool isIntegral<signed char>() { return true; }
cannam@62: template <> constexpr bool isIntegral<short>() { return true; }
cannam@62: template <> constexpr bool isIntegral<int>() { return true; }
cannam@62: template <> constexpr bool isIntegral<long>() { return true; }
cannam@62: template <> constexpr bool isIntegral<long long>() { return true; }
cannam@62: template <> constexpr bool isIntegral<unsigned char>() { return true; }
cannam@62: template <> constexpr bool isIntegral<unsigned short>() { return true; }
cannam@62: template <> constexpr bool isIntegral<unsigned int>() { return true; }
cannam@62: template <> constexpr bool isIntegral<unsigned long>() { return true; }
cannam@62: template <> constexpr bool isIntegral<unsigned long long>() { return true; }
cannam@62: 
cannam@62: template <typename T>
cannam@62: struct IsIntegralOrBounded_ { static constexpr bool value = isIntegral<T>(); };
cannam@62: template <uint64_t m, typename T>
cannam@62: struct IsIntegralOrBounded_<Bounded<m, T>> { static constexpr bool value = true; };
cannam@62: template <uint v>
cannam@62: struct IsIntegralOrBounded_<BoundedConst<v>> { static constexpr bool value = true; };
cannam@62: 
cannam@62: template <typename T>
cannam@62: inline constexpr bool isIntegralOrBounded() { return IsIntegralOrBounded_<T>::value; }
cannam@62: 
cannam@62: template <typename Number, typename Unit1, typename Unit2>
cannam@62: class UnitRatio {
cannam@62:   // A multiplier used to convert Quantities of one unit to Quantities of another unit.  See
cannam@62:   // Quantity, below.
cannam@62:   //
cannam@62:   // Construct this type by dividing one Quantity by another of a different unit.  Use this type
cannam@62:   // by multiplying it by a Quantity, or dividing a Quantity by it.
cannam@62: 
cannam@62:   static_assert(isIntegralOrBounded<Number>(),
cannam@62:       "Underlying type for UnitRatio must be integer.");
cannam@62: 
cannam@62: public:
cannam@62:   inline UnitRatio() {}
cannam@62: 
cannam@62:   constexpr UnitRatio(Number unit1PerUnit2, decltype(unsafe)): unit1PerUnit2(unit1PerUnit2) {}
cannam@62:   // This constructor was intended to be private, but GCC complains about it being private in a
cannam@62:   // bunch of places that don't appear to even call it, so I made it public.  Oh well.
cannam@62: 
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr UnitRatio(const UnitRatio<OtherNumber, Unit1, Unit2>& other)
cannam@62:       : unit1PerUnit2(other.unit1PerUnit2) {}
cannam@62: 
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr UnitRatio<decltype(Number()+OtherNumber()), Unit1, Unit2>
cannam@62:       operator+(UnitRatio<OtherNumber, Unit1, Unit2> other) const {
cannam@62:     return UnitRatio<decltype(Number()+OtherNumber()), Unit1, Unit2>(
cannam@62:         unit1PerUnit2 + other.unit1PerUnit2, unsafe);
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr UnitRatio<decltype(Number()-OtherNumber()), Unit1, Unit2>
cannam@62:       operator-(UnitRatio<OtherNumber, Unit1, Unit2> other) const {
cannam@62:     return UnitRatio<decltype(Number()-OtherNumber()), Unit1, Unit2>(
cannam@62:         unit1PerUnit2 - other.unit1PerUnit2, unsafe);
cannam@62:   }
cannam@62: 
cannam@62:   template <typename OtherNumber, typename Unit3>
cannam@62:   inline constexpr UnitRatio<decltype(Number()*OtherNumber()), Unit3, Unit2>
cannam@62:       operator*(UnitRatio<OtherNumber, Unit3, Unit1> other) const {
cannam@62:     // U1 / U2 * U3 / U1 = U3 / U2
cannam@62:     return UnitRatio<decltype(Number()*OtherNumber()), Unit3, Unit2>(
cannam@62:         unit1PerUnit2 * other.unit1PerUnit2, unsafe);
cannam@62:   }
cannam@62:   template <typename OtherNumber, typename Unit3>
cannam@62:   inline constexpr UnitRatio<decltype(Number()*OtherNumber()), Unit1, Unit3>
cannam@62:       operator*(UnitRatio<OtherNumber, Unit2, Unit3> other) const {
cannam@62:     // U1 / U2 * U2 / U3 = U1 / U3
cannam@62:     return UnitRatio<decltype(Number()*OtherNumber()), Unit1, Unit3>(
cannam@62:         unit1PerUnit2 * other.unit1PerUnit2, unsafe);
cannam@62:   }
cannam@62: 
cannam@62:   template <typename OtherNumber, typename Unit3>
cannam@62:   inline constexpr UnitRatio<decltype(Number()*OtherNumber()), Unit3, Unit2>
cannam@62:       operator/(UnitRatio<OtherNumber, Unit1, Unit3> other) const {
cannam@62:     // (U1 / U2) / (U1 / U3) = U3 / U2
cannam@62:     return UnitRatio<decltype(Number()*OtherNumber()), Unit3, Unit2>(
cannam@62:         unit1PerUnit2 / other.unit1PerUnit2, unsafe);
cannam@62:   }
cannam@62:   template <typename OtherNumber, typename Unit3>
cannam@62:   inline constexpr UnitRatio<decltype(Number()*OtherNumber()), Unit1, Unit3>
cannam@62:       operator/(UnitRatio<OtherNumber, Unit3, Unit2> other) const {
cannam@62:     // (U1 / U2) / (U3 / U2) = U1 / U3
cannam@62:     return UnitRatio<decltype(Number()*OtherNumber()), Unit1, Unit3>(
cannam@62:         unit1PerUnit2 / other.unit1PerUnit2, unsafe);
cannam@62:   }
cannam@62: 
cannam@62:   template <typename OtherNumber>
cannam@62:   inline decltype(Number() / OtherNumber())
cannam@62:       operator/(UnitRatio<OtherNumber, Unit1, Unit2> other) const {
cannam@62:     return unit1PerUnit2 / other.unit1PerUnit2;
cannam@62:   }
cannam@62: 
cannam@62:   inline bool operator==(UnitRatio other) const { return unit1PerUnit2 == other.unit1PerUnit2; }
cannam@62:   inline bool operator!=(UnitRatio other) const { return unit1PerUnit2 != other.unit1PerUnit2; }
cannam@62: 
cannam@62: private:
cannam@62:   Number unit1PerUnit2;
cannam@62: 
cannam@62:   template <typename OtherNumber, typename OtherUnit>
cannam@62:   friend class Quantity;
cannam@62:   template <typename OtherNumber, typename OtherUnit1, typename OtherUnit2>
cannam@62:   friend class UnitRatio;
cannam@62: 
cannam@62:   template <typename N1, typename N2, typename U1, typename U2, typename>
cannam@62:   friend inline constexpr UnitRatio<decltype(N1() * N2()), U1, U2>
cannam@62:       operator*(N1, UnitRatio<N2, U1, U2>);
cannam@62: };
cannam@62: 
cannam@62: template <typename N1, typename N2, typename U1, typename U2,
cannam@62:           typename = EnableIf<isIntegralOrBounded<N1>() && isIntegralOrBounded<N2>()>>
cannam@62: inline constexpr UnitRatio<decltype(N1() * N2()), U1, U2>
cannam@62:     operator*(N1 n, UnitRatio<N2, U1, U2> r) {
cannam@62:   return UnitRatio<decltype(N1() * N2()), U1, U2>(n * r.unit1PerUnit2, unsafe);
cannam@62: }
cannam@62: 
cannam@62: template <typename Number, typename Unit>
cannam@62: class Quantity {
cannam@62:   // A type-safe numeric quantity, specified in terms of some unit.  Two Quantities cannot be used
cannam@62:   // in arithmetic unless they use the same unit.  The `Unit` type parameter is only used to prevent
cannam@62:   // accidental mixing of units; this type is never instantiated and can very well be incomplete.
cannam@62:   // `Number` is the underlying primitive numeric type.
cannam@62:   //
cannam@62:   // Quantities support most basic arithmetic operators, intelligently handling units, and
cannam@62:   // automatically casting the underlying type in the same way that the compiler would.
cannam@62:   //
cannam@62:   // To convert a primitive number to a Quantity, multiply it by unit<Quantity<N, U>>().
cannam@62:   // To convert a Quantity to a primitive number, divide it by unit<Quantity<N, U>>().
cannam@62:   // To convert a Quantity of one unit to another unit, multiply or divide by a UnitRatio.
cannam@62:   //
cannam@62:   // The Quantity class is not well-suited to hardcore physics as it does not allow multiplying
cannam@62:   // one quantity by another.  For example, multiplying meters by meters won't get you square
cannam@62:   // meters; it will get you a compiler error.  It would be interesting to see if template
cannam@62:   // metaprogramming could properly deal with such things but this isn't needed for the present
cannam@62:   // use case.
cannam@62:   //
cannam@62:   // Sample usage:
cannam@62:   //
cannam@62:   //   class SecondsLabel;
cannam@62:   //   typedef Quantity<double, SecondsLabel> Seconds;
cannam@62:   //   constexpr Seconds SECONDS = unit<Seconds>();
cannam@62:   //
cannam@62:   //   class MinutesLabel;
cannam@62:   //   typedef Quantity<double, MinutesLabel> Minutes;
cannam@62:   //   constexpr Minutes MINUTES = unit<Minutes>();
cannam@62:   //
cannam@62:   //   constexpr UnitRatio<double, SecondsLabel, MinutesLabel> SECONDS_PER_MINUTE =
cannam@62:   //       60 * SECONDS / MINUTES;
cannam@62:   //
cannam@62:   //   void waitFor(Seconds seconds) {
cannam@62:   //     sleep(seconds / SECONDS);
cannam@62:   //   }
cannam@62:   //   void waitFor(Minutes minutes) {
cannam@62:   //     waitFor(minutes * SECONDS_PER_MINUTE);
cannam@62:   //   }
cannam@62:   //
cannam@62:   //   void waitThreeMinutes() {
cannam@62:   //     waitFor(3 * MINUTES);
cannam@62:   //   }
cannam@62: 
cannam@62:   static_assert(isIntegralOrBounded<Number>(),
cannam@62:       "Underlying type for Quantity must be integer.");
cannam@62: 
cannam@62: public:
cannam@62:   inline constexpr Quantity() = default;
cannam@62: 
cannam@62:   inline constexpr Quantity(MaxValue_): value(maxValue) {}
cannam@62:   inline constexpr Quantity(MinValue_): value(minValue) {}
cannam@62:   // Allow initialization from maxValue and minValue.
cannam@62:   // TODO(msvc): decltype(maxValue) and decltype(minValue) deduce unknown-type for these function
cannam@62:   // parameters, causing the compiler to complain of a duplicate constructor definition, so we
cannam@62:   // specify MaxValue_ and MinValue_ types explicitly.
cannam@62: 
cannam@62:   inline constexpr Quantity(Number value, decltype(unsafe)): value(value) {}
cannam@62:   // This constructor was intended to be private, but GCC complains about it being private in a
cannam@62:   // bunch of places that don't appear to even call it, so I made it public.  Oh well.
cannam@62: 
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr Quantity(const Quantity<OtherNumber, Unit>& other)
cannam@62:       : value(other.value) {}
cannam@62: 
cannam@62:   template <typename OtherNumber>
cannam@62:   inline Quantity& operator=(const Quantity<OtherNumber, Unit>& other) {
cannam@62:     value = other.value;
cannam@62:     return *this;
cannam@62:   }
cannam@62: 
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr Quantity<decltype(Number() + OtherNumber()), Unit>
cannam@62:       operator+(const Quantity<OtherNumber, Unit>& other) const {
cannam@62:     return Quantity<decltype(Number() + OtherNumber()), Unit>(value + other.value, unsafe);
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr Quantity<decltype(Number() - OtherNumber()), Unit>
cannam@62:       operator-(const Quantity<OtherNumber, Unit>& other) const {
cannam@62:     return Quantity<decltype(Number() - OtherNumber()), Unit>(value - other.value, unsafe);
cannam@62:   }
cannam@62:   template <typename OtherNumber, typename = EnableIf<isIntegralOrBounded<OtherNumber>()>>
cannam@62:   inline constexpr Quantity<decltype(Number() * OtherNumber()), Unit>
cannam@62:       operator*(OtherNumber other) const {
cannam@62:     return Quantity<decltype(Number() * other), Unit>(value * other, unsafe);
cannam@62:   }
cannam@62:   template <typename OtherNumber, typename = EnableIf<isIntegralOrBounded<OtherNumber>()>>
cannam@62:   inline constexpr Quantity<decltype(Number() / OtherNumber()), Unit>
cannam@62:       operator/(OtherNumber other) const {
cannam@62:     return Quantity<decltype(Number() / other), Unit>(value / other, unsafe);
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr decltype(Number() / OtherNumber())
cannam@62:       operator/(const Quantity<OtherNumber, Unit>& other) const {
cannam@62:     return value / other.value;
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr Quantity<decltype(Number() % OtherNumber()), Unit>
cannam@62:       operator%(const Quantity<OtherNumber, Unit>& other) const {
cannam@62:     return Quantity<decltype(Number() % OtherNumber()), Unit>(value % other.value, unsafe);
cannam@62:   }
cannam@62: 
cannam@62:   template <typename OtherNumber, typename OtherUnit>
cannam@62:   inline constexpr Quantity<decltype(Number() * OtherNumber()), OtherUnit>
cannam@62:       operator*(UnitRatio<OtherNumber, OtherUnit, Unit> ratio) const {
cannam@62:     return Quantity<decltype(Number() * OtherNumber()), OtherUnit>(
cannam@62:         value * ratio.unit1PerUnit2, unsafe);
cannam@62:   }
cannam@62:   template <typename OtherNumber, typename OtherUnit>
cannam@62:   inline constexpr Quantity<decltype(Number() / OtherNumber()), OtherUnit>
cannam@62:       operator/(UnitRatio<OtherNumber, Unit, OtherUnit> ratio) const {
cannam@62:     return Quantity<decltype(Number() / OtherNumber()), OtherUnit>(
cannam@62:         value / ratio.unit1PerUnit2, unsafe);
cannam@62:   }
cannam@62:   template <typename OtherNumber, typename OtherUnit>
cannam@62:   inline constexpr Quantity<decltype(Number() % OtherNumber()), Unit>
cannam@62:       operator%(UnitRatio<OtherNumber, Unit, OtherUnit> ratio) const {
cannam@62:     return Quantity<decltype(Number() % OtherNumber()), Unit>(
cannam@62:         value % ratio.unit1PerUnit2, unsafe);
cannam@62:   }
cannam@62:   template <typename OtherNumber, typename OtherUnit>
cannam@62:   inline constexpr UnitRatio<decltype(Number() / OtherNumber()), Unit, OtherUnit>
cannam@62:       operator/(Quantity<OtherNumber, OtherUnit> other) const {
cannam@62:     return UnitRatio<decltype(Number() / OtherNumber()), Unit, OtherUnit>(
cannam@62:         value / other.value, unsafe);
cannam@62:   }
cannam@62: 
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr bool operator==(const Quantity<OtherNumber, Unit>& other) const {
cannam@62:     return value == other.value;
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr bool operator!=(const Quantity<OtherNumber, Unit>& other) const {
cannam@62:     return value != other.value;
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr bool operator<=(const Quantity<OtherNumber, Unit>& other) const {
cannam@62:     return value <= other.value;
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr bool operator>=(const Quantity<OtherNumber, Unit>& other) const {
cannam@62:     return value >= other.value;
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr bool operator<(const Quantity<OtherNumber, Unit>& other) const {
cannam@62:     return value < other.value;
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline constexpr bool operator>(const Quantity<OtherNumber, Unit>& other) const {
cannam@62:     return value > other.value;
cannam@62:   }
cannam@62: 
cannam@62:   template <typename OtherNumber>
cannam@62:   inline Quantity& operator+=(const Quantity<OtherNumber, Unit>& other) {
cannam@62:     value += other.value;
cannam@62:     return *this;
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline Quantity& operator-=(const Quantity<OtherNumber, Unit>& other) {
cannam@62:     value -= other.value;
cannam@62:     return *this;
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline Quantity& operator*=(OtherNumber other) {
cannam@62:     value *= other;
cannam@62:     return *this;
cannam@62:   }
cannam@62:   template <typename OtherNumber>
cannam@62:   inline Quantity& operator/=(OtherNumber other) {
cannam@62:     value /= other.value;
cannam@62:     return *this;
cannam@62:   }
cannam@62: 
cannam@62: private:
cannam@62:   Number value;
cannam@62: 
cannam@62:   template <typename OtherNumber, typename OtherUnit>
cannam@62:   friend class Quantity;
cannam@62: 
cannam@62:   template <typename Number1, typename Number2, typename Unit2>
cannam@62:   friend inline constexpr auto operator*(Number1 a, Quantity<Number2, Unit2> b)
cannam@62:       -> Quantity<decltype(Number1() * Number2()), Unit2>;
cannam@62: };
cannam@62: 
cannam@62: template <typename T> struct Unit_ {
cannam@62:   static inline constexpr T get() { return T(1); }
cannam@62: };
cannam@62: template <typename T, typename U>
cannam@62: struct Unit_<Quantity<T, U>> {
cannam@62:   static inline constexpr Quantity<decltype(Unit_<T>::get()), U> get() {
cannam@62:     return Quantity<decltype(Unit_<T>::get()), U>(Unit_<T>::get(), unsafe);
cannam@62:   }
cannam@62: };
cannam@62: 
cannam@62: template <typename T>
cannam@62: inline constexpr auto unit() -> decltype(Unit_<T>::get()) { return Unit_<T>::get(); }
cannam@62: // unit<Quantity<T, U>>() returns a Quantity of value 1.  It also, intentionally, works on basic
cannam@62: // numeric types.
cannam@62: 
cannam@62: template <typename Number1, typename Number2, typename Unit>
cannam@62: inline constexpr auto operator*(Number1 a, Quantity<Number2, Unit> b)
cannam@62:     -> Quantity<decltype(Number1() * Number2()), Unit> {
cannam@62:   return Quantity<decltype(Number1() * Number2()), Unit>(a * b.value, unsafe);
cannam@62: }
cannam@62: 
cannam@62: template <typename Number1, typename Number2, typename Unit, typename Unit2>
cannam@62: inline constexpr auto operator*(UnitRatio<Number1, Unit2, Unit> ratio,
cannam@62:     Quantity<Number2, Unit> measure)
cannam@62:     -> decltype(measure * ratio) {
cannam@62:   return measure * ratio;
cannam@62: }
cannam@62: 
cannam@62: // =======================================================================================
cannam@62: // Absolute measures
cannam@62: 
cannam@62: template <typename T, typename Label>
cannam@62: class Absolute {
cannam@62:   // Wraps some other value -- typically a Quantity -- but represents a value measured based on
cannam@62:   // some absolute origin.  For example, if `Duration` is a type representing a time duration,
cannam@62:   // Absolute<Duration, UnixEpoch> might be a calendar date.
cannam@62:   //
cannam@62:   // Since Absolute represents measurements relative to some arbitrary origin, the only sensible
cannam@62:   // arithmetic to perform on them is addition and subtraction.
cannam@62: 
cannam@62:   // TODO(someday):  Do the same automatic expansion of integer width that Quantity does?  Doesn't
cannam@62:   //   matter for our time use case, where we always use 64-bit anyway.  Note that fixing this
cannam@62:   //   would implicitly allow things like multiplying an Absolute by a UnitRatio to change its
cannam@62:   //   units, which is actually totally logical and kind of neat.
cannam@62: 
cannam@62: public:
cannam@62:   inline constexpr Absolute operator+(const T& other) const { return Absolute(value + other); }
cannam@62:   inline constexpr Absolute operator-(const T& other) const { return Absolute(value - other); }
cannam@62:   inline constexpr T operator-(const Absolute& other) const { return value - other.value; }
cannam@62: 
cannam@62:   inline Absolute& operator+=(const T& other) { value += other; return *this; }
cannam@62:   inline Absolute& operator-=(const T& other) { value -= other; return *this; }
cannam@62: 
cannam@62:   inline constexpr bool operator==(const Absolute& other) const { return value == other.value; }
cannam@62:   inline constexpr bool operator!=(const Absolute& other) const { return value != other.value; }
cannam@62:   inline constexpr bool operator<=(const Absolute& other) const { return value <= other.value; }
cannam@62:   inline constexpr bool operator>=(const Absolute& other) const { return value >= other.value; }
cannam@62:   inline constexpr bool operator< (const Absolute& other) const { return value <  other.value; }
cannam@62:   inline constexpr bool operator> (const Absolute& other) const { return value >  other.value; }
cannam@62: 
cannam@62: private:
cannam@62:   T value;
cannam@62: 
cannam@62:   explicit constexpr Absolute(T value): value(value) {}
cannam@62: 
cannam@62:   template <typename U>
cannam@62:   friend inline constexpr U origin();
cannam@62: };
cannam@62: 
cannam@62: template <typename T, typename Label>
cannam@62: inline constexpr Absolute<T, Label> operator+(const T& a, const Absolute<T, Label>& b) {
cannam@62:   return b + a;
cannam@62: }
cannam@62: 
cannam@62: template <typename T> struct UnitOf_ { typedef T Type; };
cannam@62: template <typename T, typename Label> struct UnitOf_<Absolute<T, Label>> { typedef T Type; };
cannam@62: template <typename T>
cannam@62: using UnitOf = typename UnitOf_<T>::Type;
cannam@62: // UnitOf<Absolute<T, U>> is T.  UnitOf<AnythingElse> is AnythingElse.
cannam@62: 
cannam@62: template <typename T>
cannam@62: inline constexpr T origin() { return T(0 * unit<UnitOf<T>>()); }
cannam@62: // origin<Absolute<T, U>>() returns an Absolute of value 0.  It also, intentionally, works on basic
cannam@62: // numeric types.
cannam@62: 
cannam@62: // =======================================================================================
cannam@62: // Overflow avoidance
cannam@62: 
cannam@62: template <uint64_t n, uint accum = 0>
cannam@62: struct BitCount_ {
cannam@62:   static constexpr uint value = BitCount_<(n >> 1), accum + 1>::value;
cannam@62: };
cannam@62: template <uint accum>
cannam@62: struct BitCount_<0, accum> {
cannam@62:   static constexpr uint value = accum;
cannam@62: };
cannam@62: 
cannam@62: template <uint64_t n>
cannam@62: inline constexpr uint bitCount() { return BitCount_<n>::value; }
cannam@62: // Number of bits required to represent the number `n`.
cannam@62: 
cannam@62: template <uint bitCountBitCount> struct AtLeastUInt_ {
cannam@62:   static_assert(bitCountBitCount < 7, "don't know how to represent integers over 64 bits");
cannam@62: };
cannam@62: template <> struct AtLeastUInt_<0> { typedef uint8_t Type; };
cannam@62: template <> struct AtLeastUInt_<1> { typedef uint8_t Type; };
cannam@62: template <> struct AtLeastUInt_<2> { typedef uint8_t Type; };
cannam@62: template <> struct AtLeastUInt_<3> { typedef uint8_t Type; };
cannam@62: template <> struct AtLeastUInt_<4> { typedef uint16_t Type; };
cannam@62: template <> struct AtLeastUInt_<5> { typedef uint32_t Type; };
cannam@62: template <> struct AtLeastUInt_<6> { typedef uint64_t Type; };
cannam@62: 
cannam@62: template <uint bits>
cannam@62: using AtLeastUInt = typename AtLeastUInt_<bitCount<max(bits, 1) - 1>()>::Type;
cannam@62: // AtLeastUInt<n> is an unsigned integer of at least n bits. E.g. AtLeastUInt<12> is uint16_t.
cannam@62: 
cannam@62: // -------------------------------------------------------------------
cannam@62: 
cannam@62: template <uint value>
cannam@62: class BoundedConst {
cannam@62:   // A constant integer value on which we can do bit size analysis.
cannam@62: 
cannam@62: public:
cannam@62:   BoundedConst() = default;
cannam@62: 
cannam@62:   inline constexpr uint unwrap() const { return value; }
cannam@62: 
cannam@62: #define OP(op, check) \
cannam@62:   template <uint other> \
cannam@62:   inline constexpr BoundedConst<(value op other)> \
cannam@62:       operator op(BoundedConst<other>) const { \
cannam@62:     static_assert(check, "overflow in BoundedConst arithmetic"); \
cannam@62:     return BoundedConst<(value op other)>(); \
cannam@62:   }
cannam@62: #define COMPARE_OP(op) \
cannam@62:   template <uint other> \
cannam@62:   inline constexpr bool operator op(BoundedConst<other>) const { \
cannam@62:     return value op other; \
cannam@62:   }
cannam@62: 
cannam@62:   OP(+, value + other >= value)
cannam@62:   OP(-, value - other <= value)
cannam@62:   OP(*, value * other / other == value)
cannam@62:   OP(/, true)   // div by zero already errors out; no other division ever overflows
cannam@62:   OP(%, true)   // mod by zero already errors out; no other modulus ever overflows
cannam@62:   OP(<<, value << other >= value)
cannam@62:   OP(>>, true)  // right shift can't overflow
cannam@62:   OP(&, true)   // bitwise ops can't overflow
cannam@62:   OP(|, true)   // bitwise ops can't overflow
cannam@62: 
cannam@62:   COMPARE_OP(==)
cannam@62:   COMPARE_OP(!=)
cannam@62:   COMPARE_OP(< )
cannam@62:   COMPARE_OP(> )
cannam@62:   COMPARE_OP(<=)
cannam@62:   COMPARE_OP(>=)
cannam@62: #undef OP
cannam@62: #undef COMPARE_OP
cannam@62: };
cannam@62: 
cannam@62: template <uint64_t m, typename T>
cannam@62: struct Unit_<Bounded<m, T>> {
cannam@62:   static inline constexpr BoundedConst<1> get() { return BoundedConst<1>(); }
cannam@62: };
cannam@62: 
cannam@62: template <uint value>
cannam@62: struct Unit_<BoundedConst<value>> {
cannam@62:   static inline constexpr BoundedConst<1> get() { return BoundedConst<1>(); }
cannam@62: };
cannam@62: 
cannam@62: template <uint value>
cannam@62: inline constexpr BoundedConst<value> bounded() {
cannam@62:   return BoundedConst<value>();
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t a, uint64_t b>
cannam@62: static constexpr uint64_t boundedAdd() {
cannam@62:   static_assert(a + b >= a, "possible overflow detected");
cannam@62:   return a + b;
cannam@62: }
cannam@62: template <uint64_t a, uint64_t b>
cannam@62: static constexpr uint64_t boundedSub() {
cannam@62:   static_assert(a - b <= a, "possible underflow detected");
cannam@62:   return a - b;
cannam@62: }
cannam@62: template <uint64_t a, uint64_t b>
cannam@62: static constexpr uint64_t boundedMul() {
cannam@62:   static_assert(a * b / b == a, "possible overflow detected");
cannam@62:   return a * b;
cannam@62: }
cannam@62: template <uint64_t a, uint64_t b>
cannam@62: static constexpr uint64_t boundedLShift() {
cannam@62:   static_assert(a << b >= a, "possible overflow detected");
cannam@62:   return a << b;
cannam@62: }
cannam@62: 
cannam@62: template <uint a, uint b>
cannam@62: inline constexpr BoundedConst<kj::min(a, b)> min(BoundedConst<a>, BoundedConst<b>) {
cannam@62:   return bounded<kj::min(a, b)>();
cannam@62: }
cannam@62: template <uint a, uint b>
cannam@62: inline constexpr BoundedConst<kj::max(a, b)> max(BoundedConst<a>, BoundedConst<b>) {
cannam@62:   return bounded<kj::max(a, b)>();
cannam@62: }
cannam@62: // We need to override min() and max() between constants because the ternary operator in the
cannam@62: // default implementation would complain.
cannam@62: 
cannam@62: // -------------------------------------------------------------------
cannam@62: 
cannam@62: template <uint64_t maxN, typename T>
cannam@62: class Bounded {
cannam@62: public:
cannam@62:   static_assert(maxN <= T(kj::maxValue), "possible overflow detected");
cannam@62: 
cannam@62:   Bounded() = default;
cannam@62: 
cannam@62:   Bounded(const Bounded& other) = default;
cannam@62:   template <typename OtherInt, typename = EnableIf<isIntegral<OtherInt>()>>
cannam@62:   inline constexpr Bounded(OtherInt value): value(value) {
cannam@62:     static_assert(OtherInt(maxValue) <= maxN, "possible overflow detected");
cannam@62:   }
cannam@62:   template <uint64_t otherMax, typename OtherT>
cannam@62:   inline constexpr Bounded(const Bounded<otherMax, OtherT>& other)
cannam@62:       : value(other.value) {
cannam@62:     static_assert(otherMax <= maxN, "possible overflow detected");
cannam@62:   }
cannam@62:   template <uint otherValue>
cannam@62:   inline constexpr Bounded(BoundedConst<otherValue>)
cannam@62:       : value(otherValue) {
cannam@62:     static_assert(otherValue <= maxN, "overflow detected");
cannam@62:   }
cannam@62: 
cannam@62:   Bounded& operator=(const Bounded& other) = default;
cannam@62:   template <typename OtherInt, typename = EnableIf<isIntegral<OtherInt>()>>
cannam@62:   Bounded& operator=(OtherInt other) {
cannam@62:     static_assert(OtherInt(maxValue) <= maxN, "possible overflow detected");
cannam@62:     value = other;
cannam@62:     return *this;
cannam@62:   }
cannam@62:   template <uint64_t otherMax, typename OtherT>
cannam@62:   inline Bounded& operator=(const Bounded<otherMax, OtherT>& other) {
cannam@62:     static_assert(otherMax <= maxN, "possible overflow detected");
cannam@62:     value = other.value;
cannam@62:     return *this;
cannam@62:   }
cannam@62:   template <uint otherValue>
cannam@62:   inline Bounded& operator=(BoundedConst<otherValue>) {
cannam@62:     static_assert(otherValue <= maxN, "overflow detected");
cannam@62:     value = otherValue;
cannam@62:     return *this;
cannam@62:   }
cannam@62: 
cannam@62:   inline constexpr T unwrap() const { return value; }
cannam@62: 
cannam@62: #define OP(op, newMax) \
cannam@62:   template <uint64_t otherMax, typename otherT> \
cannam@62:   inline constexpr Bounded<newMax, decltype(T() op otherT())> \
cannam@62:       operator op(const Bounded<otherMax, otherT>& other) const { \
cannam@62:     return Bounded<newMax, decltype(T() op otherT())>(value op other.value, unsafe); \
cannam@62:   }
cannam@62: #define COMPARE_OP(op) \
cannam@62:   template <uint64_t otherMax, typename OtherT> \
cannam@62:   inline constexpr bool operator op(const Bounded<otherMax, OtherT>& other) const { \
cannam@62:     return value op other.value; \
cannam@62:   }
cannam@62: 
cannam@62:   OP(+, (boundedAdd<maxN, otherMax>()))
cannam@62:   OP(*, (boundedMul<maxN, otherMax>()))
cannam@62:   OP(/, maxN)
cannam@62:   OP(%, otherMax - 1)
cannam@62: 
cannam@62:   // operator- is intentionally omitted because we mostly use this with unsigned types, and
cannam@62:   // subtraction requires proof that subtrahend is not greater than the minuend.
cannam@62: 
cannam@62:   COMPARE_OP(==)
cannam@62:   COMPARE_OP(!=)
cannam@62:   COMPARE_OP(< )
cannam@62:   COMPARE_OP(> )
cannam@62:   COMPARE_OP(<=)
cannam@62:   COMPARE_OP(>=)
cannam@62: 
cannam@62: #undef OP
cannam@62: #undef COMPARE_OP
cannam@62: 
cannam@62:   template <uint64_t newMax, typename ErrorFunc>
cannam@62:   inline Bounded<newMax, T> assertMax(ErrorFunc&& func) const {
cannam@62:     // Assert that the number is no more than `newMax`. Otherwise, call `func`.
cannam@62:     static_assert(newMax < maxN, "this bounded size assertion is redundant");
cannam@62:     if (KJ_UNLIKELY(value > newMax)) func();
cannam@62:     return Bounded<newMax, T>(value, unsafe);
cannam@62:   }
cannam@62: 
cannam@62:   template <uint64_t otherMax, typename OtherT, typename ErrorFunc>
cannam@62:   inline Bounded<maxN, decltype(T() - OtherT())> subtractChecked(
cannam@62:       const Bounded<otherMax, OtherT>& other, ErrorFunc&& func) const {
cannam@62:     // Subtract a number, calling func() if the result would underflow.
cannam@62:     if (KJ_UNLIKELY(value < other.value)) func();
cannam@62:     return Bounded<maxN, decltype(T() - OtherT())>(value - other.value, unsafe);
cannam@62:   }
cannam@62: 
cannam@62:   template <uint otherValue, typename ErrorFunc>
cannam@62:   inline Bounded<maxN - otherValue, T> subtractChecked(
cannam@62:       BoundedConst<otherValue>, ErrorFunc&& func) const {
cannam@62:     // Subtract a number, calling func() if the result would underflow.
cannam@62:     static_assert(otherValue <= maxN, "underflow detected");
cannam@62:     if (KJ_UNLIKELY(value < otherValue)) func();
cannam@62:     return Bounded<maxN - otherValue, T>(value - otherValue, unsafe);
cannam@62:   }
cannam@62: 
cannam@62:   template <uint64_t otherMax, typename OtherT>
cannam@62:   inline Maybe<Bounded<maxN, decltype(T() - OtherT())>> trySubtract(
cannam@62:       const Bounded<otherMax, OtherT>& other) const {
cannam@62:     // Subtract a number, calling func() if the result would underflow.
cannam@62:     if (value < other.value) {
cannam@62:       return nullptr;
cannam@62:     } else {
cannam@62:       return Bounded<maxN, decltype(T() - OtherT())>(value - other.value, unsafe);
cannam@62:     }
cannam@62:   }
cannam@62: 
cannam@62:   template <uint otherValue>
cannam@62:   inline Maybe<Bounded<maxN - otherValue, T>> trySubtract(BoundedConst<otherValue>) const {
cannam@62:     // Subtract a number, calling func() if the result would underflow.
cannam@62:     if (value < otherValue) {
cannam@62:       return nullptr;
cannam@62:     } else {
cannam@62:       return Bounded<maxN - otherValue, T>(value - otherValue, unsafe);
cannam@62:     }
cannam@62:   }
cannam@62: 
cannam@62:   inline constexpr Bounded(T value, decltype(unsafe)): value(value) {}
cannam@62:   template <uint64_t otherMax, typename OtherT>
cannam@62:   inline constexpr Bounded(Bounded<otherMax, OtherT> value, decltype(unsafe))
cannam@62:       : value(value.value) {}
cannam@62:   // Mainly for internal use.
cannam@62:   //
cannam@62:   // Only use these as a last resort, with ample commentary on why you think it's safe.
cannam@62: 
cannam@62: private:
cannam@62:   T value;
cannam@62: 
cannam@62:   template <uint64_t, typename>
cannam@62:   friend class Bounded;
cannam@62: };
cannam@62: 
cannam@62: template <typename Number>
cannam@62: inline constexpr Bounded<Number(kj::maxValue), Number> bounded(Number value) {
cannam@62:   return Bounded<Number(kj::maxValue), Number>(value, unsafe);
cannam@62: }
cannam@62: 
cannam@62: inline constexpr Bounded<1, uint8_t> bounded(bool value) {
cannam@62:   return Bounded<1, uint8_t>(value, unsafe);
cannam@62: }
cannam@62: 
cannam@62: template <uint bits, typename Number>
cannam@62: inline constexpr Bounded<maxValueForBits<bits>(), Number> assumeBits(Number value) {
cannam@62:   return Bounded<maxValueForBits<bits>(), Number>(value, unsafe);
cannam@62: }
cannam@62: 
cannam@62: template <uint bits, uint64_t maxN, typename T>
cannam@62: inline constexpr Bounded<maxValueForBits<bits>(), T> assumeBits(Bounded<maxN, T> value) {
cannam@62:   return Bounded<maxValueForBits<bits>(), T>(value, unsafe);
cannam@62: }
cannam@62: 
cannam@62: template <uint bits, typename Number, typename Unit>
cannam@62: inline constexpr auto assumeBits(Quantity<Number, Unit> value)
cannam@62:     -> Quantity<decltype(assumeBits<bits>(value / unit<Quantity<Number, Unit>>())), Unit> {
cannam@62:   return Quantity<decltype(assumeBits<bits>(value / unit<Quantity<Number, Unit>>())), Unit>(
cannam@62:       assumeBits<bits>(value / unit<Quantity<Number, Unit>>()), unsafe);
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t maxN, typename Number>
cannam@62: inline constexpr Bounded<maxN, Number> assumeMax(Number value) {
cannam@62:   return Bounded<maxN, Number>(value, unsafe);
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t newMaxN, uint64_t maxN, typename T>
cannam@62: inline constexpr Bounded<newMaxN, T> assumeMax(Bounded<maxN, T> value) {
cannam@62:   return Bounded<newMaxN, T>(value, unsafe);
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t maxN, typename Number, typename Unit>
cannam@62: inline constexpr auto assumeMax(Quantity<Number, Unit> value)
cannam@62:     -> Quantity<decltype(assumeMax<maxN>(value / unit<Quantity<Number, Unit>>())), Unit> {
cannam@62:   return Quantity<decltype(assumeMax<maxN>(value / unit<Quantity<Number, Unit>>())), Unit>(
cannam@62:       assumeMax<maxN>(value / unit<Quantity<Number, Unit>>()), unsafe);
cannam@62: }
cannam@62: 
cannam@62: template <uint maxN, typename Number>
cannam@62: inline constexpr Bounded<maxN, Number> assumeMax(BoundedConst<maxN>, Number value) {
cannam@62:   return assumeMax<maxN>(value);
cannam@62: }
cannam@62: 
cannam@62: template <uint newMaxN, uint64_t maxN, typename T>
cannam@62: inline constexpr Bounded<newMaxN, T> assumeMax(BoundedConst<maxN>, Bounded<maxN, T> value) {
cannam@62:   return assumeMax<maxN>(value);
cannam@62: }
cannam@62: 
cannam@62: template <uint maxN, typename Number, typename Unit>
cannam@62: inline constexpr auto assumeMax(Quantity<BoundedConst<maxN>, Unit>, Quantity<Number, Unit> value)
cannam@62:     -> decltype(assumeMax<maxN>(value)) {
cannam@62:   return assumeMax<maxN>(value);
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t newMax, uint64_t maxN, typename T, typename ErrorFunc>
cannam@62: inline Bounded<newMax, T> assertMax(Bounded<maxN, T> value, ErrorFunc&& errorFunc) {
cannam@62:   // Assert that the bounded value is less than or equal to the given maximum, calling errorFunc()
cannam@62:   // if not.
cannam@62:   static_assert(newMax < maxN, "this bounded size assertion is redundant");
cannam@62:   return value.template assertMax<newMax>(kj::fwd<ErrorFunc>(errorFunc));
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t newMax, uint64_t maxN, typename T, typename Unit, typename ErrorFunc>
cannam@62: inline Quantity<Bounded<newMax, T>, Unit> assertMax(
cannam@62:     Quantity<Bounded<maxN, T>, Unit> value, ErrorFunc&& errorFunc) {
cannam@62:   // Assert that the bounded value is less than or equal to the given maximum, calling errorFunc()
cannam@62:   // if not.
cannam@62:   static_assert(newMax < maxN, "this bounded size assertion is redundant");
cannam@62:   return (value / unit<decltype(value)>()).template assertMax<newMax>(
cannam@62:       kj::fwd<ErrorFunc>(errorFunc)) * unit<decltype(value)>();
cannam@62: }
cannam@62: 
cannam@62: template <uint newMax, uint64_t maxN, typename T, typename ErrorFunc>
cannam@62: inline Bounded<newMax, T> assertMax(
cannam@62:     BoundedConst<newMax>, Bounded<maxN, T> value, ErrorFunc&& errorFunc) {
cannam@62:   return assertMax<newMax>(value, kj::mv(errorFunc));
cannam@62: }
cannam@62: 
cannam@62: template <uint newMax, uint64_t maxN, typename T, typename Unit, typename ErrorFunc>
cannam@62: inline Quantity<Bounded<newMax, T>, Unit> assertMax(
cannam@62:     Quantity<BoundedConst<newMax>, Unit>,
cannam@62:     Quantity<Bounded<maxN, T>, Unit> value, ErrorFunc&& errorFunc) {
cannam@62:   return assertMax<newMax>(value, kj::mv(errorFunc));
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t newBits, uint64_t maxN, typename T, typename ErrorFunc = ThrowOverflow>
cannam@62: inline Bounded<maxValueForBits<newBits>(), T> assertMaxBits(
cannam@62:     Bounded<maxN, T> value, ErrorFunc&& errorFunc = ErrorFunc()) {
cannam@62:   // Assert that the bounded value requires no more than the given number of bits, calling
cannam@62:   // errorFunc() if not.
cannam@62:   return assertMax<maxValueForBits<newBits>()>(value, kj::fwd<ErrorFunc>(errorFunc));
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t newBits, uint64_t maxN, typename T, typename Unit,
cannam@62:           typename ErrorFunc = ThrowOverflow>
cannam@62: inline Quantity<Bounded<maxValueForBits<newBits>(), T>, Unit> assertMaxBits(
cannam@62:     Quantity<Bounded<maxN, T>, Unit> value, ErrorFunc&& errorFunc = ErrorFunc()) {
cannam@62:   // Assert that the bounded value requires no more than the given number of bits, calling
cannam@62:   // errorFunc() if not.
cannam@62:   return assertMax<maxValueForBits<newBits>()>(value, kj::fwd<ErrorFunc>(errorFunc));
cannam@62: }
cannam@62: 
cannam@62: template <typename newT, uint64_t maxN, typename T>
cannam@62: inline constexpr Bounded<maxN, newT> upgradeBound(Bounded<maxN, T> value) {
cannam@62:   return value;
cannam@62: }
cannam@62: 
cannam@62: template <typename newT, uint64_t maxN, typename T, typename Unit>
cannam@62: inline constexpr Quantity<Bounded<maxN, newT>, Unit> upgradeBound(
cannam@62:     Quantity<Bounded<maxN, T>, Unit> value) {
cannam@62:   return value;
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t maxN, typename T, typename Other, typename ErrorFunc>
cannam@62: inline auto subtractChecked(Bounded<maxN, T> value, Other other, ErrorFunc&& errorFunc)
cannam@62:     -> decltype(value.subtractChecked(other, kj::fwd<ErrorFunc>(errorFunc))) {
cannam@62:   return value.subtractChecked(other, kj::fwd<ErrorFunc>(errorFunc));
cannam@62: }
cannam@62: 
cannam@62: template <typename T, typename U, typename Unit, typename ErrorFunc>
cannam@62: inline auto subtractChecked(Quantity<T, Unit> value, Quantity<U, Unit> other, ErrorFunc&& errorFunc)
cannam@62:     -> Quantity<decltype(subtractChecked(T(), U(), kj::fwd<ErrorFunc>(errorFunc))), Unit> {
cannam@62:   return subtractChecked(value / unit<Quantity<T, Unit>>(),
cannam@62:                          other / unit<Quantity<U, Unit>>(),
cannam@62:                          kj::fwd<ErrorFunc>(errorFunc))
cannam@62:       * unit<Quantity<T, Unit>>();
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t maxN, typename T, typename Other>
cannam@62: inline auto trySubtract(Bounded<maxN, T> value, Other other)
cannam@62:     -> decltype(value.trySubtract(other)) {
cannam@62:   return value.trySubtract(other);
cannam@62: }
cannam@62: 
cannam@62: template <typename T, typename U, typename Unit>
cannam@62: inline auto trySubtract(Quantity<T, Unit> value, Quantity<U, Unit> other)
cannam@62:     -> Maybe<Quantity<decltype(subtractChecked(T(), U(), int())), Unit>> {
cannam@62:   return trySubtract(value / unit<Quantity<T, Unit>>(),
cannam@62:                      other / unit<Quantity<U, Unit>>())
cannam@62:       .map([](decltype(subtractChecked(T(), U(), int())) x) {
cannam@62:     return x * unit<Quantity<T, Unit>>();
cannam@62:   });
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t aN, uint64_t bN, typename A, typename B>
cannam@62: inline constexpr Bounded<kj::min(aN, bN), WiderType<A, B>>
cannam@62: min(Bounded<aN, A> a, Bounded<bN, B> b) {
cannam@62:   return Bounded<kj::min(aN, bN), WiderType<A, B>>(kj::min(a.unwrap(), b.unwrap()), unsafe);
cannam@62: }
cannam@62: template <uint64_t aN, uint64_t bN, typename A, typename B>
cannam@62: inline constexpr Bounded<kj::max(aN, bN), WiderType<A, B>>
cannam@62: max(Bounded<aN, A> a, Bounded<bN, B> b) {
cannam@62:   return Bounded<kj::max(aN, bN), WiderType<A, B>>(kj::max(a.unwrap(), b.unwrap()), unsafe);
cannam@62: }
cannam@62: // We need to override min() and max() because:
cannam@62: // 1) WiderType<> might not choose the correct bounds.
cannam@62: // 2) One of the two sides of the ternary operator in the default implementation would fail to
cannam@62: //    typecheck even though it is OK in practice.
cannam@62: 
cannam@62: // -------------------------------------------------------------------
cannam@62: // Operators between Bounded and BoundedConst
cannam@62: 
cannam@62: #define OP(op, newMax) \
cannam@62: template <uint64_t maxN, uint cvalue, typename T> \
cannam@62: inline constexpr Bounded<(newMax), decltype(T() op uint())> operator op( \
cannam@62:     Bounded<maxN, T> value, BoundedConst<cvalue>) { \
cannam@62:   return Bounded<(newMax), decltype(T() op uint())>(value.unwrap() op cvalue, unsafe); \
cannam@62: }
cannam@62: 
cannam@62: #define REVERSE_OP(op, newMax) \
cannam@62: template <uint64_t maxN, uint cvalue, typename T> \
cannam@62: inline constexpr Bounded<(newMax), decltype(uint() op T())> operator op( \
cannam@62:     BoundedConst<cvalue>, Bounded<maxN, T> value) { \
cannam@62:   return Bounded<(newMax), decltype(uint() op T())>(cvalue op value.unwrap(), unsafe); \
cannam@62: }
cannam@62: 
cannam@62: #define COMPARE_OP(op) \
cannam@62: template <uint64_t maxN, uint cvalue, typename T> \
cannam@62: inline constexpr bool operator op(Bounded<maxN, T> value, BoundedConst<cvalue>) { \
cannam@62:   return value.unwrap() op cvalue; \
cannam@62: } \
cannam@62: template <uint64_t maxN, uint cvalue, typename T> \
cannam@62: inline constexpr bool operator op(BoundedConst<cvalue>, Bounded<maxN, T> value) { \
cannam@62:   return cvalue op value.unwrap(); \
cannam@62: }
cannam@62: 
cannam@62: OP(+, (boundedAdd<maxN, cvalue>()))
cannam@62: REVERSE_OP(+, (boundedAdd<maxN, cvalue>()))
cannam@62: 
cannam@62: OP(*, (boundedMul<maxN, cvalue>()))
cannam@62: REVERSE_OP(*, (boundedAdd<maxN, cvalue>()))
cannam@62: 
cannam@62: OP(/, maxN / cvalue)
cannam@62: REVERSE_OP(/, cvalue)  // denominator could be 1
cannam@62: 
cannam@62: OP(%, cvalue - 1)
cannam@62: REVERSE_OP(%, maxN - 1)
cannam@62: 
cannam@62: OP(<<, (boundedLShift<maxN, cvalue>()))
cannam@62: REVERSE_OP(<<, (boundedLShift<cvalue, maxN>()))
cannam@62: 
cannam@62: OP(>>, maxN >> cvalue)
cannam@62: REVERSE_OP(>>, cvalue >> maxN)
cannam@62: 
cannam@62: OP(&, maxValueForBits<bitCount<maxN>()>() & cvalue)
cannam@62: REVERSE_OP(&, maxValueForBits<bitCount<maxN>()>() & cvalue)
cannam@62: 
cannam@62: OP(|, maxN | cvalue)
cannam@62: REVERSE_OP(|, maxN | cvalue)
cannam@62: 
cannam@62: COMPARE_OP(==)
cannam@62: COMPARE_OP(!=)
cannam@62: COMPARE_OP(< )
cannam@62: COMPARE_OP(> )
cannam@62: COMPARE_OP(<=)
cannam@62: COMPARE_OP(>=)
cannam@62: 
cannam@62: #undef OP
cannam@62: #undef REVERSE_OP
cannam@62: #undef COMPARE_OP
cannam@62: 
cannam@62: template <uint64_t maxN, uint cvalue, typename T>
cannam@62: inline constexpr Bounded<cvalue, decltype(uint() - T())>
cannam@62:     operator-(BoundedConst<cvalue>, Bounded<maxN, T> value) {
cannam@62:   // We allow subtraction of a variable from a constant only if the constant is greater than or
cannam@62:   // equal to the maximum possible value of the variable. Since the variable could be zero, the
cannam@62:   // result can be as large as the constant.
cannam@62:   //
cannam@62:   // We do not allow subtraction of a constant from a variable because there's never a guarantee it
cannam@62:   // won't underflow (unless the constant is zero, which is silly).
cannam@62:   static_assert(cvalue >= maxN, "possible underflow detected");
cannam@62:   return Bounded<cvalue, decltype(uint() - T())>(cvalue - value.unwrap(), unsafe);
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t aN, uint b, typename A>
cannam@62: inline constexpr Bounded<kj::min(aN, b), A> min(Bounded<aN, A> a, BoundedConst<b>) {
cannam@62:   return Bounded<kj::min(aN, b), A>(kj::min(b, a.unwrap()), unsafe);
cannam@62: }
cannam@62: template <uint64_t aN, uint b, typename A>
cannam@62: inline constexpr Bounded<kj::min(aN, b), A> min(BoundedConst<b>, Bounded<aN, A> a) {
cannam@62:   return Bounded<kj::min(aN, b), A>(kj::min(a.unwrap(), b), unsafe);
cannam@62: }
cannam@62: template <uint64_t aN, uint b, typename A>
cannam@62: inline constexpr Bounded<kj::max(aN, b), A> max(Bounded<aN, A> a, BoundedConst<b>) {
cannam@62:   return Bounded<kj::max(aN, b), A>(kj::max(b, a.unwrap()), unsafe);
cannam@62: }
cannam@62: template <uint64_t aN, uint b, typename A>
cannam@62: inline constexpr Bounded<kj::max(aN, b), A> max(BoundedConst<b>, Bounded<aN, A> a) {
cannam@62:   return Bounded<kj::max(aN, b), A>(kj::max(a.unwrap(), b), unsafe);
cannam@62: }
cannam@62: // We need to override min() between a Bounded and a constant since:
cannam@62: // 1) WiderType<> might choose BoundedConst over a 1-byte Bounded, which is wrong.
cannam@62: // 2) To clamp the bounds of the output type.
cannam@62: // 3) Same ternary operator typechecking issues.
cannam@62: 
cannam@62: // -------------------------------------------------------------------
cannam@62: 
cannam@62: template <uint64_t maxN, typename T>
cannam@62: class SafeUnwrapper {
cannam@62: public:
cannam@62:   inline explicit constexpr SafeUnwrapper(Bounded<maxN, T> value): value(value.unwrap()) {}
cannam@62: 
cannam@62:   template <typename U, typename = EnableIf<isIntegral<U>()>>
cannam@62:   inline constexpr operator U() const {
cannam@62:     static_assert(maxN <= U(maxValue), "possible truncation detected");
cannam@62:     return value;
cannam@62:   }
cannam@62: 
cannam@62:   inline constexpr operator bool() const {
cannam@62:     static_assert(maxN <= 1, "possible truncation detected");
cannam@62:     return value;
cannam@62:   }
cannam@62: 
cannam@62: private:
cannam@62:   T value;
cannam@62: };
cannam@62: 
cannam@62: template <uint64_t maxN, typename T>
cannam@62: inline constexpr SafeUnwrapper<maxN, T> unbound(Bounded<maxN, T> bounded) {
cannam@62:   // Unwraps the bounded value, returning a value that can be implicitly cast to any integer type.
cannam@62:   // If this implicit cast could truncate, a compile-time error will be raised.
cannam@62:   return SafeUnwrapper<maxN, T>(bounded);
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t value>
cannam@62: class SafeConstUnwrapper {
cannam@62: public:
cannam@62:   template <typename T, typename = EnableIf<isIntegral<T>()>>
cannam@62:   inline constexpr operator T() const {
cannam@62:     static_assert(value <= T(maxValue), "this operation will truncate");
cannam@62:     return value;
cannam@62:   }
cannam@62: 
cannam@62:   inline constexpr operator bool() const {
cannam@62:     static_assert(value <= 1, "this operation will truncate");
cannam@62:     return value;
cannam@62:   }
cannam@62: };
cannam@62: 
cannam@62: template <uint value>
cannam@62: inline constexpr SafeConstUnwrapper<value> unbound(BoundedConst<value>) {
cannam@62:   return SafeConstUnwrapper<value>();
cannam@62: }
cannam@62: 
cannam@62: template <typename T, typename U>
cannam@62: inline constexpr T unboundAs(U value) {
cannam@62:   return unbound(value);
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t requestedMax, uint64_t maxN, typename T>
cannam@62: inline constexpr T unboundMax(Bounded<maxN, T> value) {
cannam@62:   // Explicitly ungaurd expecting a value that is at most `maxN`.
cannam@62:   static_assert(maxN <= requestedMax, "possible overflow detected");
cannam@62:   return value.unwrap();
cannam@62: }
cannam@62: 
cannam@62: template <uint64_t requestedMax, uint value>
cannam@62: inline constexpr uint unboundMax(BoundedConst<value>) {
cannam@62:   // Explicitly ungaurd expecting a value that is at most `maxN`.
cannam@62:   static_assert(value <= requestedMax, "overflow detected");
cannam@62:   return value;
cannam@62: }
cannam@62: 
cannam@62: template <uint bits, typename T>
cannam@62: inline constexpr auto unboundMaxBits(T value) ->
cannam@62:     decltype(unboundMax<maxValueForBits<bits>()>(value)) {
cannam@62:   // Explicitly ungaurd expecting a value that fits into `bits` bits.
cannam@62:   return unboundMax<maxValueForBits<bits>()>(value);
cannam@62: }
cannam@62: 
cannam@62: #define OP(op) \
cannam@62: template <uint64_t maxN, typename T, typename U> \
cannam@62: inline constexpr auto operator op(T a, SafeUnwrapper<maxN, U> b) -> decltype(a op (T)b) { \
cannam@62:   return a op (AtLeastUInt<sizeof(T)*8>)b; \
cannam@62: } \
cannam@62: template <uint64_t maxN, typename T, typename U> \
cannam@62: inline constexpr auto operator op(SafeUnwrapper<maxN, U> b, T a) -> decltype((T)b op a) { \
cannam@62:   return (AtLeastUInt<sizeof(T)*8>)b op a; \
cannam@62: } \
cannam@62: template <uint64_t value, typename T> \
cannam@62: inline constexpr auto operator op(T a, SafeConstUnwrapper<value> b) -> decltype(a op (T)b) { \
cannam@62:   return a op (AtLeastUInt<sizeof(T)*8>)b; \
cannam@62: } \
cannam@62: template <uint64_t value, typename T> \
cannam@62: inline constexpr auto operator op(SafeConstUnwrapper<value> b, T a) -> decltype((T)b op a) { \
cannam@62:   return (AtLeastUInt<sizeof(T)*8>)b op a; \
cannam@62: }
cannam@62: 
cannam@62: OP(+)
cannam@62: OP(-)
cannam@62: OP(*)
cannam@62: OP(/)
cannam@62: OP(%)
cannam@62: OP(<<)
cannam@62: OP(>>)
cannam@62: OP(&)
cannam@62: OP(|)
cannam@62: OP(==)
cannam@62: OP(!=)
cannam@62: OP(<=)
cannam@62: OP(>=)
cannam@62: OP(<)
cannam@62: OP(>)
cannam@62: 
cannam@62: #undef OP
cannam@62: 
cannam@62: // -------------------------------------------------------------------
cannam@62: 
cannam@62: template <uint64_t maxN, typename T>
cannam@62: class Range<Bounded<maxN, T>> {
cannam@62: public:
cannam@62:   inline constexpr Range(Bounded<maxN, T> begin, Bounded<maxN, T> end)
cannam@62:       : inner(unbound(begin), unbound(end)) {}
cannam@62:   inline explicit constexpr Range(Bounded<maxN, T> end)
cannam@62:       : inner(unbound(end)) {}
cannam@62: 
cannam@62:   class Iterator {
cannam@62:   public:
cannam@62:     Iterator() = default;
cannam@62:     inline explicit Iterator(typename Range<T>::Iterator inner): inner(inner) {}
cannam@62: 
cannam@62:     inline Bounded<maxN, T> operator* () const { return Bounded<maxN, T>(*inner, unsafe); }
cannam@62:     inline Iterator& operator++() { ++inner; return *this; }
cannam@62: 
cannam@62:     inline bool operator==(const Iterator& other) const { return inner == other.inner; }
cannam@62:     inline bool operator!=(const Iterator& other) const { return inner != other.inner; }
cannam@62: 
cannam@62:   private:
cannam@62:     typename Range<T>::Iterator inner;
cannam@62:   };
cannam@62: 
cannam@62:   inline Iterator begin() const { return Iterator(inner.begin()); }
cannam@62:   inline Iterator end() const { return Iterator(inner.end()); }
cannam@62: 
cannam@62: private:
cannam@62:   Range<T> inner;
cannam@62: };
cannam@62: 
cannam@62: template <typename T, typename U>
cannam@62: class Range<Quantity<T, U>> {
cannam@62: public:
cannam@62:   inline constexpr Range(Quantity<T, U> begin, Quantity<T, U> end)
cannam@62:       : inner(begin / unit<Quantity<T, U>>(), end / unit<Quantity<T, U>>()) {}
cannam@62:   inline explicit constexpr Range(Quantity<T, U> end)
cannam@62:       : inner(end / unit<Quantity<T, U>>()) {}
cannam@62: 
cannam@62:   class Iterator {
cannam@62:   public:
cannam@62:     Iterator() = default;
cannam@62:     inline explicit Iterator(typename Range<T>::Iterator inner): inner(inner) {}
cannam@62: 
cannam@62:     inline Quantity<T, U> operator* () const { return *inner * unit<Quantity<T, U>>(); }
cannam@62:     inline Iterator& operator++() { ++inner; return *this; }
cannam@62: 
cannam@62:     inline bool operator==(const Iterator& other) const { return inner == other.inner; }
cannam@62:     inline bool operator!=(const Iterator& other) const { return inner != other.inner; }
cannam@62: 
cannam@62:   private:
cannam@62:     typename Range<T>::Iterator inner;
cannam@62:   };
cannam@62: 
cannam@62:   inline Iterator begin() const { return Iterator(inner.begin()); }
cannam@62:   inline Iterator end() const { return Iterator(inner.end()); }
cannam@62: 
cannam@62: private:
cannam@62:   Range<T> inner;
cannam@62: };
cannam@62: 
cannam@62: template <uint value>
cannam@62: inline constexpr Range<Bounded<value, uint>> zeroTo(BoundedConst<value> end) {
cannam@62:   return Range<Bounded<value, uint>>(end);
cannam@62: }
cannam@62: 
cannam@62: template <uint value, typename Unit>
cannam@62: inline constexpr Range<Quantity<Bounded<value, uint>, Unit>>
cannam@62:     zeroTo(Quantity<BoundedConst<value>, Unit> end) {
cannam@62:   return Range<Quantity<Bounded<value, uint>, Unit>>(end);
cannam@62: }
cannam@62: 
cannam@62: }  // namespace kj
cannam@62: 
cannam@62: #endif  // KJ_UNITS_H_