capnproto

units.h (46198B)

---

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