safe_conversions_impl.h

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// Copyright 2014 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
 
#ifndef BASE_NUMERICS_SAFE_CONVERSIONS_IMPL_H_
#define BASE_NUMERICS_SAFE_CONVERSIONS_IMPL_H_
 
#include <cstdint>
#include <limits>
#include <type_traits>
 
#if defined(__GNUC__) || defined(__clang__)
#define BASE_NUMERICS_LIKELY(x) __builtin_expect(!!(x), 1)
#define BASE_NUMERICS_UNLIKELY(x) __builtin_expect(!!(x), 0)
#else
#define BASE_NUMERICS_LIKELY(x) (x)
#define BASE_NUMERICS_UNLIKELY(x) (x)
#endif
 
namespace base {
namespace internal {
 
// The std library doesn't provide a binary max_exponent for integers, however
// we can compute an analog using std::numeric_limits<>::digits.
template <typename NumericType>
struct MaxExponent {
  static const int value = std::is_floating_point<NumericType>::value
                               ? std::numeric_limits<NumericType>::max_exponent
                               : std::numeric_limits<NumericType>::digits + 1;
};
 
// The number of bits (including the sign) in an integer. Eliminates sizeof
// hacks.
template <typename NumericType>
struct IntegerBitsPlusSign {
  static const int value = std::numeric_limits<NumericType>::digits +
                           std::is_signed<NumericType>::value;
};
 
// Helper templates for integer manipulations.
 
template <typename Integer>
struct PositionOfSignBit {
  static const size_t value = IntegerBitsPlusSign<Integer>::value - 1;
};
 
// Determines if a numeric value is negative without throwing compiler
// warnings on: unsigned(value) < 0.
template <typename T,
          typename std::enable_if<std::is_signed<T>::value>::type* = nullptr>
constexpr bool IsValueNegative(T value) {
  static_assert(std::is_arithmetic<T>::value, "Argument must be numeric.");
  return value < 0;
}
 
template <typename T,
          typename std::enable_if<!std::is_signed<T>::value>::type* = nullptr>
constexpr bool IsValueNegative(T) {
  static_assert(std::is_arithmetic<T>::value, "Argument must be numeric.");
  return false;
}
 
// This performs a fast negation, returning a signed value. It works on unsigned
// arguments, but probably doesn't do what you want for any unsigned value
// larger than max / 2 + 1 (i.e. signed min cast to unsigned).
template <typename T>
constexpr typename std::make_signed<T>::type ConditionalNegate(
    T x,
    bool is_negative) {
  static_assert(std::is_integral<T>::value, "Type must be integral");
  using SignedT = typename std::make_signed<T>::type;
  using UnsignedT = typename std::make_unsigned<T>::type;
  return static_cast<SignedT>(
      (static_cast<UnsignedT>(x) ^ -SignedT(is_negative)) + is_negative);
}
 
// This performs a safe, absolute value via unsigned overflow.
template <typename T>
constexpr typename std::make_unsigned<T>::type SafeUnsignedAbs(T value) {
  static_assert(std::is_integral<T>::value, "Type must be integral");
  using UnsignedT = typename std::make_unsigned<T>::type;
  return IsValueNegative(value)
             ? static_cast<UnsignedT>(0u - static_cast<UnsignedT>(value))
             : static_cast<UnsignedT>(value);
}
 
// This allows us to switch paths on known compile-time constants.
#if defined(__clang__) || defined(__GNUC__)
constexpr bool CanDetectCompileTimeConstant() {
  return true;
}
template <typename T>
constexpr bool IsCompileTimeConstant(const T v) {
  return __builtin_constant_p(v);
}
#else
constexpr bool CanDetectCompileTimeConstant() {
  return false;
}
template <typename T>
constexpr bool IsCompileTimeConstant(const T) {
  return false;
}
#endif
template <typename T>
constexpr bool MustTreatAsConstexpr(const T v) {
  // Either we can't detect a compile-time constant, and must always use the
  // constexpr path, or we know we have a compile-time constant.
  return !CanDetectCompileTimeConstant() || IsCompileTimeConstant(v);
}
 
// Forces a crash, like a CHECK(false). Used for numeric boundary errors.
// Also used in a constexpr template to trigger a compilation failure on
// an error condition.
struct CheckOnFailure {
  template <typename T>
  static T HandleFailure() {
#if defined(_MSC_VER)
    __debugbreak();
#elif defined(__GNUC__) || defined(__clang__)
    __builtin_trap();
#else
    ((void)(*(volatile char*)0 = 0));
#endif
    return T();
  }
};
 
enum IntegerRepresentation {
  INTEGER_REPRESENTATION_UNSIGNED,
  INTEGER_REPRESENTATION_SIGNED
};
 
// A range for a given nunmeric Src type is contained for a given numeric Dst
// type if both numeric_limits<Src>::max() <= numeric_limits<Dst>::max() and
// numeric_limits<Src>::lowest() >= numeric_limits<Dst>::lowest() are true.
// We implement this as template specializations rather than simple static
// comparisons to ensure type correctness in our comparisons.
enum NumericRangeRepresentation {
  NUMERIC_RANGE_NOT_CONTAINED,
  NUMERIC_RANGE_CONTAINED
};
 
// Helper templates to statically determine if our destination type can contain
// maximum and minimum values represented by the source type.
 
template <typename Dst,
          typename Src,
          IntegerRepresentation DstSign = std::is_signed<Dst>::value
                                              ? INTEGER_REPRESENTATION_SIGNED
                                              : INTEGER_REPRESENTATION_UNSIGNED,
          IntegerRepresentation SrcSign = std::is_signed<Src>::value
                                              ? INTEGER_REPRESENTATION_SIGNED
                                              : INTEGER_REPRESENTATION_UNSIGNED>
struct StaticDstRangeRelationToSrcRange;
 
// Same sign: Dst is guaranteed to contain Src only if its range is equal or
// larger.
template <typename Dst, typename Src, IntegerRepresentation Sign>
struct StaticDstRangeRelationToSrcRange<Dst, Src, Sign, Sign> {
  static const NumericRangeRepresentation value =
      MaxExponent<Dst>::value >= MaxExponent<Src>::value
          ? NUMERIC_RANGE_CONTAINED
          : NUMERIC_RANGE_NOT_CONTAINED;
};
 
// Unsigned to signed: Dst is guaranteed to contain source only if its range is
// larger.
template <typename Dst, typename Src>
struct StaticDstRangeRelationToSrcRange<Dst,
                                        Src,
                                        INTEGER_REPRESENTATION_SIGNED,
                                        INTEGER_REPRESENTATION_UNSIGNED> {
  static const NumericRangeRepresentation value =
      MaxExponent<Dst>::value > MaxExponent<Src>::value
          ? NUMERIC_RANGE_CONTAINED
          : NUMERIC_RANGE_NOT_CONTAINED;
};
 
// Signed to unsigned: Dst cannot be statically determined to contain Src.
template <typename Dst, typename Src>
struct StaticDstRangeRelationToSrcRange<Dst,
                                        Src,
                                        INTEGER_REPRESENTATION_UNSIGNED,
                                        INTEGER_REPRESENTATION_SIGNED> {
  static const NumericRangeRepresentation value = NUMERIC_RANGE_NOT_CONTAINED;
};
 
// This class wraps the range constraints as separate booleans so the compiler
// can identify constants and eliminate unused code paths.
class RangeCheck {
 public:
  constexpr RangeCheck(bool is_in_lower_bound, bool is_in_upper_bound)
      : is_underflow_(!is_in_lower_bound), is_overflow_(!is_in_upper_bound) {}
  constexpr RangeCheck() : is_underflow_(0), is_overflow_(0) {}
  constexpr bool IsValid() const { return !is_overflow_ && !is_underflow_; }
  constexpr bool IsInvalid() const { return is_overflow_ && is_underflow_; }
  constexpr bool IsOverflow() const { return is_overflow_ && !is_underflow_; }
  constexpr bool IsUnderflow() const { return !is_overflow_ && is_underflow_; }
  constexpr bool IsOverflowFlagSet() const { return is_overflow_; }
  constexpr bool IsUnderflowFlagSet() const { return is_underflow_; }
  constexpr bool operator==(const RangeCheck rhs) const {
    return is_underflow_ == rhs.is_underflow_ &&
           is_overflow_ == rhs.is_overflow_;
  }
  constexpr bool operator!=(const RangeCheck rhs) const {
    return !(*this == rhs);
  }
 
 private:
  // Do not change the order of these member variables. The integral conversion
  // optimization depends on this exact order.
  const bool is_underflow_;
  const bool is_overflow_;
};
 
// The following helper template addresses a corner case in range checks for
// conversion from a floating-point type to an integral type of smaller range
// but larger precision (e.g. float -> unsigned). The problem is as follows:
//   1. Integral maximum is always one less than a power of two, so it must be
//      truncated to fit the mantissa of the floating point. The direction of
//      rounding is implementation defined, but by default it's always IEEE
//      floats, which round to nearest and thus result in a value of larger
//      magnitude than the integral value.
//      Example: float f = UINT_MAX; // f is 4294967296f but UINT_MAX
//                                   // is 4294967295u.
//   2. If the floating point value is equal to the promoted integral maximum
//      value, a range check will erroneously pass.
//      Example: (4294967296f <= 4294967295u) // This is true due to a precision
//                                            // loss in rounding up to float.
//   3. When the floating point value is then converted to an integral, the
//      resulting value is out of range for the target integral type and
//      thus is implementation defined.
//      Example: unsigned u = (float)INT_MAX; // u will typically overflow to 0.
// To fix this bug we manually truncate the maximum value when the destination
// type is an integral of larger precision than the source floating-point type,
// such that the resulting maximum is represented exactly as a floating point.
template <typename Dst, typename Src, template <typename> class Bounds>
struct NarrowingRange {
  using SrcLimits = std::numeric_limits<Src>;
  using DstLimits = typename std::numeric_limits<Dst>;
 
  // Computes the mask required to make an accurate comparison between types.
  static const int kShift =
      (MaxExponent<Src>::value > MaxExponent<Dst>::value &&
       SrcLimits::digits < DstLimits::digits)
          ? (DstLimits::digits - SrcLimits::digits)
          : 0;
  template <
      typename T,
      typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
 
  // Masks out the integer bits that are beyond the precision of the
  // intermediate type used for comparison.
  static constexpr T Adjust(T value) {
    static_assert(std::is_same<T, Dst>::value, "");
    static_assert(kShift < DstLimits::digits, "");
    return static_cast<T>(
        ConditionalNegate(SafeUnsignedAbs(value) & ~((T(1) << kShift) - T(1)),
                          IsValueNegative(value)));
  }
 
  template <typename T,
            typename std::enable_if<std::is_floating_point<T>::value>::type* =
                nullptr>
  static constexpr T Adjust(T value) {
    static_assert(std::is_same<T, Dst>::value, "");
    static_assert(kShift == 0, "");
    return value;
  }
 
  static constexpr Dst max() { return Adjust(Bounds<Dst>::max()); }
  static constexpr Dst lowest() { return Adjust(Bounds<Dst>::lowest()); }
};
 
template <typename Dst,
          typename Src,
          template <typename>
          class Bounds,
          IntegerRepresentation DstSign = std::is_signed<Dst>::value
                                              ? INTEGER_REPRESENTATION_SIGNED
                                              : INTEGER_REPRESENTATION_UNSIGNED,
          IntegerRepresentation SrcSign = std::is_signed<Src>::value
                                              ? INTEGER_REPRESENTATION_SIGNED
                                              : INTEGER_REPRESENTATION_UNSIGNED,
          NumericRangeRepresentation DstRange =
              StaticDstRangeRelationToSrcRange<Dst, Src>::value>
struct DstRangeRelationToSrcRangeImpl;
 
// The following templates are for ranges that must be verified at runtime. We
// split it into checks based on signedness to avoid confusing casts and
// compiler warnings on signed an unsigned comparisons.
 
// Same sign narrowing: The range is contained for normal limits.
template <typename Dst,
          typename Src,
          template <typename>
          class Bounds,
          IntegerRepresentation DstSign,
          IntegerRepresentation SrcSign>
struct DstRangeRelationToSrcRangeImpl<Dst,
                                      Src,
                                      Bounds,
                                      DstSign,
                                      SrcSign,
                                      NUMERIC_RANGE_CONTAINED> {
  static constexpr RangeCheck Check(Src value) {
    using SrcLimits = std::numeric_limits<Src>;
    using DstLimits = NarrowingRange<Dst, Src, Bounds>;
    return RangeCheck(
        static_cast<Dst>(SrcLimits::lowest()) >= DstLimits::lowest() ||
            static_cast<Dst>(value) >= DstLimits::lowest(),
        static_cast<Dst>(SrcLimits::max()) <= DstLimits::max() ||
            static_cast<Dst>(value) <= DstLimits::max());
  }
};
 
// Signed to signed narrowing: Both the upper and lower boundaries may be
// exceeded for standard limits.
template <typename Dst, typename Src, template <typename> class Bounds>
struct DstRangeRelationToSrcRangeImpl<Dst,
                                      Src,
                                      Bounds,
                                      INTEGER_REPRESENTATION_SIGNED,
                                      INTEGER_REPRESENTATION_SIGNED,
                                      NUMERIC_RANGE_NOT_CONTAINED> {
  static constexpr RangeCheck Check(Src value) {
    using DstLimits = NarrowingRange<Dst, Src, Bounds>;
    return RangeCheck(value >= DstLimits::lowest(), value <= DstLimits::max());
  }
};
 
// Unsigned to unsigned narrowing: Only the upper bound can be exceeded for
// standard limits.
template <typename Dst, typename Src, template <typename> class Bounds>
struct DstRangeRelationToSrcRangeImpl<Dst,
                                      Src,
                                      Bounds,
                                      INTEGER_REPRESENTATION_UNSIGNED,
                                      INTEGER_REPRESENTATION_UNSIGNED,
                                      NUMERIC_RANGE_NOT_CONTAINED> {
  static constexpr RangeCheck Check(Src value) {
    using DstLimits = NarrowingRange<Dst, Src, Bounds>;
    return RangeCheck(
        DstLimits::lowest() == Dst(0) || value >= DstLimits::lowest(),
        value <= DstLimits::max());
  }
};
 
// Unsigned to signed: Only the upper bound can be exceeded for standard limits.
template <typename Dst, typename Src, template <typename> class Bounds>
struct DstRangeRelationToSrcRangeImpl<Dst,
                                      Src,
                                      Bounds,
                                      INTEGER_REPRESENTATION_SIGNED,
                                      INTEGER_REPRESENTATION_UNSIGNED,
                                      NUMERIC_RANGE_NOT_CONTAINED> {
  static constexpr RangeCheck Check(Src value) {
    using DstLimits = NarrowingRange<Dst, Src, Bounds>;
    using Promotion = decltype(Src() + Dst());
    return RangeCheck(DstLimits::lowest() <= Dst(0) ||
                          static_cast<Promotion>(value) >=
                              static_cast<Promotion>(DstLimits::lowest()),
                      static_cast<Promotion>(value) <=
                          static_cast<Promotion>(DstLimits::max()));
  }
};
 
// Signed to unsigned: The upper boundary may be exceeded for a narrower Dst,
// and any negative value exceeds the lower boundary for standard limits.
template <typename Dst, typename Src, template <typename> class Bounds>
struct DstRangeRelationToSrcRangeImpl<Dst,
                                      Src,
                                      Bounds,
                                      INTEGER_REPRESENTATION_UNSIGNED,
                                      INTEGER_REPRESENTATION_SIGNED,
                                      NUMERIC_RANGE_NOT_CONTAINED> {
  static constexpr RangeCheck Check(Src value) {
    using SrcLimits = std::numeric_limits<Src>;
    using DstLimits = NarrowingRange<Dst, Src, Bounds>;
    using Promotion = decltype(Src() + Dst());
    return RangeCheck(
        value >= Src(0) && (DstLimits::lowest() == 0 ||
                            static_cast<Dst>(value) >= DstLimits::lowest()),
        static_cast<Promotion>(SrcLimits::max()) <=
                static_cast<Promotion>(DstLimits::max()) ||
            static_cast<Promotion>(value) <=
                static_cast<Promotion>(DstLimits::max()));
  }
};
 
// Simple wrapper for statically checking if a type's range is contained.
template <typename Dst, typename Src>
struct IsTypeInRangeForNumericType {
  static const bool value = StaticDstRangeRelationToSrcRange<Dst, Src>::value ==
                            NUMERIC_RANGE_CONTAINED;
};
 
template <typename Dst,
          template <typename> class Bounds = std::numeric_limits,
          typename Src>
constexpr RangeCheck DstRangeRelationToSrcRange(Src value) {
  static_assert(std::is_arithmetic<Src>::value, "Argument must be numeric.");
  static_assert(std::is_arithmetic<Dst>::value, "Result must be numeric.");
  static_assert(Bounds<Dst>::lowest() < Bounds<Dst>::max(), "");
  return DstRangeRelationToSrcRangeImpl<Dst, Src, Bounds>::Check(value);
}
 
// Integer promotion templates used by the portable checked integer arithmetic.
template <size_t Size, bool IsSigned>
struct IntegerForDigitsAndSign;
 
#define INTEGER_FOR_DIGITS_AND_SIGN(I)                          \
  template <>                                                   \
  struct IntegerForDigitsAndSign<IntegerBitsPlusSign<I>::value, \
                                 std::is_signed<I>::value> {    \
    using type = I;                                             \
  }
 
INTEGER_FOR_DIGITS_AND_SIGN(int8_t);
INTEGER_FOR_DIGITS_AND_SIGN(uint8_t);
INTEGER_FOR_DIGITS_AND_SIGN(int16_t);
INTEGER_FOR_DIGITS_AND_SIGN(uint16_t);
INTEGER_FOR_DIGITS_AND_SIGN(int32_t);
INTEGER_FOR_DIGITS_AND_SIGN(uint32_t);
INTEGER_FOR_DIGITS_AND_SIGN(int64_t);
INTEGER_FOR_DIGITS_AND_SIGN(uint64_t);
#undef INTEGER_FOR_DIGITS_AND_SIGN
 
// WARNING: We have no IntegerForSizeAndSign<16, *>. If we ever add one to
// support 128-bit math, then the ArithmeticPromotion template below will need
// to be updated (or more likely replaced with a decltype expression).
static_assert(IntegerBitsPlusSign<intmax_t>::value == 64,
              "Max integer size not supported for this toolchain.");
 
template <typename Integer, bool IsSigned = std::is_signed<Integer>::value>
struct TwiceWiderInteger {
  using type =
      typename IntegerForDigitsAndSign<IntegerBitsPlusSign<Integer>::value * 2,
                                       IsSigned>::type;
};
 
enum ArithmeticPromotionCategory {
  LEFT_PROMOTION,  // Use the type of the left-hand argument.
  RIGHT_PROMOTION  // Use the type of the right-hand argument.
};
 
// Determines the type that can represent the largest positive value.
template <typename Lhs,
          typename Rhs,
          ArithmeticPromotionCategory Promotion =
              (MaxExponent<Lhs>::value > MaxExponent<Rhs>::value)
                  ? LEFT_PROMOTION
                  : RIGHT_PROMOTION>
struct MaxExponentPromotion;
 
template <typename Lhs, typename Rhs>
struct MaxExponentPromotion<Lhs, Rhs, LEFT_PROMOTION> {
  using type = Lhs;
};
 
template <typename Lhs, typename Rhs>
struct MaxExponentPromotion<Lhs, Rhs, RIGHT_PROMOTION> {
  using type = Rhs;
};
 
// Determines the type that can represent the lowest arithmetic value.
template <typename Lhs,
          typename Rhs,
          ArithmeticPromotionCategory Promotion =
              std::is_signed<Lhs>::value
                  ? (std::is_signed<Rhs>::value
                         ? (MaxExponent<Lhs>::value > MaxExponent<Rhs>::value
                                ? LEFT_PROMOTION
                                : RIGHT_PROMOTION)
                         : LEFT_PROMOTION)
                  : (std::is_signed<Rhs>::value
                         ? RIGHT_PROMOTION
                         : (MaxExponent<Lhs>::value < MaxExponent<Rhs>::value
                                ? LEFT_PROMOTION
                                : RIGHT_PROMOTION))>
struct LowestValuePromotion;
 
template <typename Lhs, typename Rhs>
struct LowestValuePromotion<Lhs, Rhs, LEFT_PROMOTION> {
  using type = Lhs;
};
 
template <typename Lhs, typename Rhs>
struct LowestValuePromotion<Lhs, Rhs, RIGHT_PROMOTION> {
  using type = Rhs;
};
 
// Determines the type that is best able to represent an arithmetic result.
template <
    typename Lhs,
    typename Rhs = Lhs,
    bool is_intmax_type =
        std::is_integral<typename MaxExponentPromotion<Lhs, Rhs>::type>::value&&
            IntegerBitsPlusSign<typename MaxExponentPromotion<Lhs, Rhs>::type>::
                value == IntegerBitsPlusSign<intmax_t>::value,
    bool is_max_exponent =
        StaticDstRangeRelationToSrcRange<
            typename MaxExponentPromotion<Lhs, Rhs>::type,
            Lhs>::value ==
        NUMERIC_RANGE_CONTAINED&& StaticDstRangeRelationToSrcRange<
            typename MaxExponentPromotion<Lhs, Rhs>::type,
            Rhs>::value == NUMERIC_RANGE_CONTAINED>
struct BigEnoughPromotion;
 
// The side with the max exponent is big enough.
template <typename Lhs, typename Rhs, bool is_intmax_type>
struct BigEnoughPromotion<Lhs, Rhs, is_intmax_type, true> {
  using type = typename MaxExponentPromotion<Lhs, Rhs>::type;
  static const bool is_contained = true;
};
 
// We can use a twice wider type to fit.
template <typename Lhs, typename Rhs>
struct BigEnoughPromotion<Lhs, Rhs, false, false> {
  using type =
      typename TwiceWiderInteger<typename MaxExponentPromotion<Lhs, Rhs>::type,
                                 std::is_signed<Lhs>::value ||
                                     std::is_signed<Rhs>::value>::type;
  static const bool is_contained = true;
};
 
// No type is large enough.
template <typename Lhs, typename Rhs>
struct BigEnoughPromotion<Lhs, Rhs, true, false> {
  using type = typename MaxExponentPromotion<Lhs, Rhs>::type;
  static const bool is_contained = false;
};
 
// We can statically check if operations on the provided types can wrap, so we
// can skip the checked operations if they're not needed. So, for an integer we
// care if the destination type preserves the sign and is twice the width of
// the source.
template <typename T, typename Lhs, typename Rhs = Lhs>
struct IsIntegerArithmeticSafe {
  static const bool value =
      !std::is_floating_point<T>::value &&
      !std::is_floating_point<Lhs>::value &&
      !std::is_floating_point<Rhs>::value &&
      std::is_signed<T>::value >= std::is_signed<Lhs>::value &&
      IntegerBitsPlusSign<T>::value >= (2 * IntegerBitsPlusSign<Lhs>::value) &&
      std::is_signed<T>::value >= std::is_signed<Rhs>::value &&
      IntegerBitsPlusSign<T>::value >= (2 * IntegerBitsPlusSign<Rhs>::value);
};
 
// Promotes to a type that can represent any possible result of a binary
// arithmetic operation with the source types.
template <typename Lhs,
          typename Rhs,
          bool is_promotion_possible = IsIntegerArithmeticSafe<
              typename std::conditional<std::is_signed<Lhs>::value ||
                                            std::is_signed<Rhs>::value,
                                        intmax_t,
                                        uintmax_t>::type,
              typename MaxExponentPromotion<Lhs, Rhs>::type>::value>
struct FastIntegerArithmeticPromotion;
 
template <typename Lhs, typename Rhs>
struct FastIntegerArithmeticPromotion<Lhs, Rhs, true> {
  using type =
      typename TwiceWiderInteger<typename MaxExponentPromotion<Lhs, Rhs>::type,
                                 std::is_signed<Lhs>::value ||
                                     std::is_signed<Rhs>::value>::type;
  static_assert(IsIntegerArithmeticSafe<type, Lhs, Rhs>::value, "");
  static const bool is_contained = true;
};
 
template <typename Lhs, typename Rhs>
struct FastIntegerArithmeticPromotion<Lhs, Rhs, false> {
  using type = typename BigEnoughPromotion<Lhs, Rhs>::type;
  static const bool is_contained = false;
};
 
// Extracts the underlying type from an enum.
template <typename T, bool is_enum = std::is_enum<T>::value>
struct ArithmeticOrUnderlyingEnum;
 
template <typename T>
struct ArithmeticOrUnderlyingEnum<T, true> {
  using type = typename std::underlying_type<T>::type;
  static const bool value = std::is_arithmetic<type>::value;
};
 
template <typename T>
struct ArithmeticOrUnderlyingEnum<T, false> {
  using type = T;
  static const bool value = std::is_arithmetic<type>::value;
};
 
// The following are helper templates used in the CheckedNumeric class.
template <typename T>
class CheckedNumeric;
 
template <typename T>
class ClampedNumeric;
 
template <typename T>
class StrictNumeric;
 
// Used to treat CheckedNumeric and arithmetic underlying types the same.
template <typename T>
struct UnderlyingType {
  using type = typename ArithmeticOrUnderlyingEnum<T>::type;
  static const bool is_numeric = std::is_arithmetic<type>::value;
  static const bool is_checked = false;
  static const bool is_clamped = false;
  static const bool is_strict = false;
};
 
template <typename T>
struct UnderlyingType<CheckedNumeric<T>> {
  using type = T;
  static const bool is_numeric = true;
  static const bool is_checked = true;
  static const bool is_clamped = false;
  static const bool is_strict = false;
};
 
template <typename T>
struct UnderlyingType<ClampedNumeric<T>> {
  using type = T;
  static const bool is_numeric = true;
  static const bool is_checked = false;
  static const bool is_clamped = true;
  static const bool is_strict = false;
};
 
template <typename T>
struct UnderlyingType<StrictNumeric<T>> {
  using type = T;
  static const bool is_numeric = true;
  static const bool is_checked = false;
  static const bool is_clamped = false;
  static const bool is_strict = true;
};
 
template <typename L, typename R>
struct IsCheckedOp {
  static const bool value =
      UnderlyingType<L>::is_numeric && UnderlyingType<R>::is_numeric &&
      (UnderlyingType<L>::is_checked || UnderlyingType<R>::is_checked);
};
 
template <typename L, typename R>
struct IsClampedOp {
  static const bool value =
      UnderlyingType<L>::is_numeric && UnderlyingType<R>::is_numeric &&
      (UnderlyingType<L>::is_clamped || UnderlyingType<R>::is_clamped) &&
      !(UnderlyingType<L>::is_checked || UnderlyingType<R>::is_checked);
};
 
template <typename L, typename R>
struct IsStrictOp {
  static const bool value =
      UnderlyingType<L>::is_numeric && UnderlyingType<R>::is_numeric &&
      (UnderlyingType<L>::is_strict || UnderlyingType<R>::is_strict) &&
      !(UnderlyingType<L>::is_checked || UnderlyingType<R>::is_checked) &&
      !(UnderlyingType<L>::is_clamped || UnderlyingType<R>::is_clamped);
};
 
// as_signed<> returns the supplied integral value (or integral castable
// Numeric template) cast as a signed integral of equivalent precision.
// I.e. it's mostly an alias for: static_cast<std::make_signed<T>::type>(t)
template <typename Src>
constexpr typename std::make_signed<
    typename base::internal::UnderlyingType<Src>::type>::type
as_signed(const Src value) {
  static_assert(std::is_integral<decltype(as_signed(value))>::value,
                "Argument must be a signed or unsigned integer type.");
  return static_cast<decltype(as_signed(value))>(value);
}
 
// as_unsigned<> returns the supplied integral value (or integral castable
// Numeric template) cast as an unsigned integral of equivalent precision.
// I.e. it's mostly an alias for: static_cast<std::make_unsigned<T>::type>(t)
template <typename Src>
constexpr typename std::make_unsigned<
    typename base::internal::UnderlyingType<Src>::type>::type
as_unsigned(const Src value) {
  static_assert(std::is_integral<decltype(as_unsigned(value))>::value,
                "Argument must be a signed or unsigned integer type.");
  return static_cast<decltype(as_unsigned(value))>(value);
}
 
template <typename L, typename R>
constexpr bool IsLessImpl(const L lhs,
                          const R rhs,
                          const RangeCheck l_range,
                          const RangeCheck r_range) {
  return l_range.IsUnderflow() || r_range.IsOverflow() ||
         (l_range == r_range && static_cast<decltype(lhs + rhs)>(lhs) <
                                    static_cast<decltype(lhs + rhs)>(rhs));
}
 
template <typename L, typename R>
struct IsLess {
  static_assert(std::is_arithmetic<L>::value && std::is_arithmetic<R>::value,
                "Types must be numeric.");
  static constexpr bool Test(const L lhs, const R rhs) {
    return IsLessImpl(lhs, rhs, DstRangeRelationToSrcRange<R>(lhs),
                      DstRangeRelationToSrcRange<L>(rhs));
  }
};
 
template <typename L, typename R>
constexpr bool IsLessOrEqualImpl(const L lhs,
                                 const R rhs,
                                 const RangeCheck l_range,
                                 const RangeCheck r_range) {
  return l_range.IsUnderflow() || r_range.IsOverflow() ||
         (l_range == r_range && static_cast<decltype(lhs + rhs)>(lhs) <=
                                    static_cast<decltype(lhs + rhs)>(rhs));
}
 
template <typename L, typename R>
struct IsLessOrEqual {
  static_assert(std::is_arithmetic<L>::value && std::is_arithmetic<R>::value,
                "Types must be numeric.");
  static constexpr bool Test(const L lhs, const R rhs) {
    return IsLessOrEqualImpl(lhs, rhs, DstRangeRelationToSrcRange<R>(lhs),
                             DstRangeRelationToSrcRange<L>(rhs));
  }
};
 
template <typename L, typename R>
constexpr bool IsGreaterImpl(const L lhs,
                             const R rhs,
                             const RangeCheck l_range,
                             const RangeCheck r_range) {
  return l_range.IsOverflow() || r_range.IsUnderflow() ||
         (l_range == r_range && static_cast<decltype(lhs + rhs)>(lhs) >
                                    static_cast<decltype(lhs + rhs)>(rhs));
}
 
template <typename L, typename R>
struct IsGreater {
  static_assert(std::is_arithmetic<L>::value && std::is_arithmetic<R>::value,
                "Types must be numeric.");
  static constexpr bool Test(const L lhs, const R rhs) {
    return IsGreaterImpl(lhs, rhs, DstRangeRelationToSrcRange<R>(lhs),
                         DstRangeRelationToSrcRange<L>(rhs));
  }
};
 
template <typename L, typename R>
constexpr bool IsGreaterOrEqualImpl(const L lhs,
                                    const R rhs,
                                    const RangeCheck l_range,
                                    const RangeCheck r_range) {
  return l_range.IsOverflow() || r_range.IsUnderflow() ||
         (l_range == r_range && static_cast<decltype(lhs + rhs)>(lhs) >=
                                    static_cast<decltype(lhs + rhs)>(rhs));
}
 
template <typename L, typename R>
struct IsGreaterOrEqual {
  static_assert(std::is_arithmetic<L>::value && std::is_arithmetic<R>::value,
                "Types must be numeric.");
  static constexpr bool Test(const L lhs, const R rhs) {
    return IsGreaterOrEqualImpl(lhs, rhs, DstRangeRelationToSrcRange<R>(lhs),
                                DstRangeRelationToSrcRange<L>(rhs));
  }
};
 
template <typename L, typename R>
struct IsEqual {
  static_assert(std::is_arithmetic<L>::value && std::is_arithmetic<R>::value,
                "Types must be numeric.");
  static constexpr bool Test(const L lhs, const R rhs) {
    return DstRangeRelationToSrcRange<R>(lhs) ==
               DstRangeRelationToSrcRange<L>(rhs) &&
           static_cast<decltype(lhs + rhs)>(lhs) ==
               static_cast<decltype(lhs + rhs)>(rhs);
  }
};
 
template <typename L, typename R>
struct IsNotEqual {
  static_assert(std::is_arithmetic<L>::value && std::is_arithmetic<R>::value,
                "Types must be numeric.");
  static constexpr bool Test(const L lhs, const R rhs) {
    return DstRangeRelationToSrcRange<R>(lhs) !=
               DstRangeRelationToSrcRange<L>(rhs) ||
           static_cast<decltype(lhs + rhs)>(lhs) !=
               static_cast<decltype(lhs + rhs)>(rhs);
  }
};
 
// These perform the actual math operations on the CheckedNumerics.
// Binary arithmetic operations.
template <template <typename, typename> class C, typename L, typename R>
constexpr bool SafeCompare(const L lhs, const R rhs) {
  static_assert(std::is_arithmetic<L>::value && std::is_arithmetic<R>::value,
                "Types must be numeric.");
  using Promotion = BigEnoughPromotion<L, R>;
  using BigType = typename Promotion::type;
  return Promotion::is_contained
             // Force to a larger type for speed if both are contained.
             ? C<BigType, BigType>::Test(
                   static_cast<BigType>(static_cast<L>(lhs)),
                   static_cast<BigType>(static_cast<R>(rhs)))
             // Let the template functions figure it out for mixed types.
             : C<L, R>::Test(lhs, rhs);
}
 
template <typename Dst, typename Src>
constexpr bool IsMaxInRangeForNumericType() {
  return IsGreaterOrEqual<Dst, Src>::Test(std::numeric_limits<Dst>::max(),
                                          std::numeric_limits<Src>::max());
}
 
template <typename Dst, typename Src>
constexpr bool IsMinInRangeForNumericType() {
  return IsLessOrEqual<Dst, Src>::Test(std::numeric_limits<Dst>::lowest(),
                                       std::numeric_limits<Src>::lowest());
}
 
template <typename Dst, typename Src>
constexpr Dst CommonMax() {
  return !IsMaxInRangeForNumericType<Dst, Src>()
             ? Dst(std::numeric_limits<Dst>::max())
             : Dst(std::numeric_limits<Src>::max());
}
 
template <typename Dst, typename Src>
constexpr Dst CommonMin() {
  return !IsMinInRangeForNumericType<Dst, Src>()
             ? Dst(std::numeric_limits<Dst>::lowest())
             : Dst(std::numeric_limits<Src>::lowest());
}
 
// This is a wrapper to generate return the max or min for a supplied type.
// If the argument is false, the returned value is the maximum. If true the
// returned value is the minimum.
template <typename Dst, typename Src = Dst>
constexpr Dst CommonMaxOrMin(bool is_min) {
  return is_min ? CommonMin<Dst, Src>() : CommonMax<Dst, Src>();
}
 
}  // namespace internal
}  // namespace base
 
#endif  // BASE_NUMERICS_SAFE_CONVERSIONS_IMPL_H_