base/numerics/safe_conversions.h - gn - Git at Google

 // 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_H_
 #define BASE_NUMERICS_SAFE_CONVERSIONS_H_

 #include <stddef.h>

 #include <limits>
 #include <ostream>
 #include <type_traits>

 #include "base/numerics/safe_conversions_impl.h"

 #if !defined(__native_client__) && (defined(__ARMEL__) || defined(__arch64__))
 #include "base/numerics/safe_conversions_arm_impl.h"
 #define BASE_HAS_OPTIMIZED_SAFE_CONVERSIONS (1)
 #else
 #define BASE_HAS_OPTIMIZED_SAFE_CONVERSIONS (0)
 #endif

 namespace base {
 namespace internal {

 #if !BASE_HAS_OPTIMIZED_SAFE_CONVERSIONS
 template <typename Dst, typename Src>
 struct SaturateFastAsmOp {
   static const bool is_supported = false;
   static constexpr Dst Do(Src) {
     // Force a compile failure if instantiated.
     return CheckOnFailure::template HandleFailure<Dst>();
   }
 };
 #endif  // BASE_HAS_OPTIMIZED_SAFE_CONVERSIONS
 #undef BASE_HAS_OPTIMIZED_SAFE_CONVERSIONS

 // The following special case a few specific integer conversions where we can
 // eke out better performance than range checking.
 template <typename Dst, typename Src, typename Enable = void>
 struct IsValueInRangeFastOp {
   static const bool is_supported = false;
   static constexpr bool Do(Src value) {
     // Force a compile failure if instantiated.
     return CheckOnFailure::template HandleFailure<bool>();
   }
 };

 // Signed to signed range comparison.
 template <typename Dst, typename Src>
 struct IsValueInRangeFastOp<
     Dst,
     Src,
     typename std::enable_if<
         std::is_integral<Dst>::value && std::is_integral<Src>::value &&
         std::is_signed<Dst>::value && std::is_signed<Src>::value &&
         !IsTypeInRangeForNumericType<Dst, Src>::value>::type> {
   static const bool is_supported = true;

   static constexpr bool Do(Src value) {
     // Just downcast to the smaller type, sign extend it back to the original
     // type, and then see if it matches the original value.
     return value == static_cast<Dst>(value);
   }
 };

 // Signed to unsigned range comparison.
 template <typename Dst, typename Src>
 struct IsValueInRangeFastOp<
     Dst,
     Src,
     typename std::enable_if<
         std::is_integral<Dst>::value && std::is_integral<Src>::value &&
         !std::is_signed<Dst>::value && std::is_signed<Src>::value &&
         !IsTypeInRangeForNumericType<Dst, Src>::value>::type> {
   static const bool is_supported = true;

   static constexpr bool Do(Src value) {
     // We cast a signed as unsigned to overflow negative values to the top,
     // then compare against whichever maximum is smaller, as our upper bound.
     return as_unsigned(value) <= as_unsigned(CommonMax<Src, Dst>());
   }
 };

 // Convenience function that returns true if the supplied value is in range
 // for the destination type.
 template <typename Dst, typename Src>
 constexpr bool IsValueInRangeForNumericType(Src value) {
   using SrcType = typename internal::UnderlyingType<Src>::type;
   return internal::IsValueInRangeFastOp<Dst, SrcType>::is_supported
              ? internal::IsValueInRangeFastOp<Dst, SrcType>::Do(
                    static_cast<SrcType>(value))
              : internal::DstRangeRelationToSrcRange<Dst>(
                    static_cast<SrcType>(value))
                    .IsValid();
 }

 // checked_cast<> is analogous to static_cast<> for numeric types,
 // except that it CHECKs that the specified numeric conversion will not
 // overflow or underflow. NaN source will always trigger a CHECK.
 template <typename Dst,
           class CheckHandler = internal::CheckOnFailure,
           typename Src>
 constexpr Dst checked_cast(Src value) {
   // This throws a compile-time error on evaluating the constexpr if it can be
   // determined at compile-time as failing, otherwise it will CHECK at runtime.
   using SrcType = typename internal::UnderlyingType<Src>::type;
   return BASE_NUMERICS_LIKELY((IsValueInRangeForNumericType<Dst>(value)))
              ? static_cast<Dst>(static_cast<SrcType>(value))
              : CheckHandler::template HandleFailure<Dst>();
 }

 // Default boundaries for integral/float: max/infinity, lowest/-infinity, 0/NaN.
 // You may provide your own limits (e.g. to saturated_cast) so long as you
 // implement all of the static constexpr member functions in the class below.
 template <typename T>
 struct SaturationDefaultLimits : public std::numeric_limits<T> {
   static constexpr T NaN() {
     return std::numeric_limits<T>::has_quiet_NaN
                ? std::numeric_limits<T>::quiet_NaN()
                : T();
   }
   using std::numeric_limits<T>::max;
   static constexpr T Overflow() {
     return std::numeric_limits<T>::has_infinity
                ? std::numeric_limits<T>::infinity()
                : std::numeric_limits<T>::max();
   }
   using std::numeric_limits<T>::lowest;
   static constexpr T Underflow() {
     return std::numeric_limits<T>::has_infinity
                ? std::numeric_limits<T>::infinity() * -1
                : std::numeric_limits<T>::lowest();
   }
 };

 template <typename Dst, template <typename> class S, typename Src>
 constexpr Dst saturated_cast_impl(Src value, RangeCheck constraint) {
   // For some reason clang generates much better code when the branch is
   // structured exactly this way, rather than a sequence of checks.
   return !constraint.IsOverflowFlagSet()
              ? (!constraint.IsUnderflowFlagSet() ? static_cast<Dst>(value)
                                                  : S<Dst>::Underflow())
              // Skip this check for integral Src, which cannot be NaN.
              : (std::is_integral<Src>::value || !constraint.IsUnderflowFlagSet()
                     ? S<Dst>::Overflow()
                     : S<Dst>::NaN());
 }

 // We can reduce the number of conditions and get slightly better performance
 // for normal signed and unsigned integer ranges. And in the specific case of
 // Arm, we can use the optimized saturation instructions.
 template <typename Dst, typename Src, typename Enable = void>
 struct SaturateFastOp {
   static const bool is_supported = false;
   static constexpr Dst Do(Src value) {
     // Force a compile failure if instantiated.
     return CheckOnFailure::template HandleFailure<Dst>();
   }
 };

 template <typename Dst, typename Src>
 struct SaturateFastOp<
     Dst,
     Src,
     typename std::enable_if<std::is_integral<Src>::value &&
                             std::is_integral<Dst>::value>::type> {
   static const bool is_supported = true;
   static Dst Do(Src value) {
     if (SaturateFastAsmOp<Dst, Src>::is_supported)
       return SaturateFastAsmOp<Dst, Src>::Do(value);

     // The exact order of the following is structured to hit the correct
     // optimization heuristics across compilers. Do not change without
     // checking the emitted code.
     Dst saturated = CommonMaxOrMin<Dst, Src>(
         IsMaxInRangeForNumericType<Dst, Src>() ||
         (!IsMinInRangeForNumericType<Dst, Src>() && IsValueNegative(value)));
     return BASE_NUMERICS_LIKELY(IsValueInRangeForNumericType<Dst>(value))
                ? static_cast<Dst>(value)
                : saturated;
   }
 };

 // saturated_cast<> is analogous to static_cast<> for numeric types, except
 // that the specified numeric conversion will saturate by default rather than
 // overflow or underflow, and NaN assignment to an integral will return 0.
 // All boundary condition behaviors can be overriden with a custom handler.
 template <typename Dst,
           template <typename> class SaturationHandler = SaturationDefaultLimits,
           typename Src>
 constexpr Dst saturated_cast(Src value) {
   using SrcType = typename UnderlyingType<Src>::type;
   return !IsCompileTimeConstant(value) &&
                  SaturateFastOp<Dst, SrcType>::is_supported &&
                  std::is_same<SaturationHandler<Dst>,
                               SaturationDefaultLimits<Dst>>::value
              ? SaturateFastOp<Dst, SrcType>::Do(static_cast<SrcType>(value))
              : saturated_cast_impl<Dst, SaturationHandler, SrcType>(
                    static_cast<SrcType>(value),
                    DstRangeRelationToSrcRange<Dst, SaturationHandler, SrcType>(
                        static_cast<SrcType>(value)));
 }

 // strict_cast<> is analogous to static_cast<> for numeric types, except that
 // it will cause a compile failure if the destination type is not large enough
 // to contain any value in the source type. It performs no runtime checking.
 template <typename Dst, typename Src>
 constexpr Dst strict_cast(Src value) {
   using SrcType = typename UnderlyingType<Src>::type;
   static_assert(UnderlyingType<Src>::is_numeric, "Argument must be numeric.");
   static_assert(std::is_arithmetic<Dst>::value, "Result must be numeric.");

   // If you got here from a compiler error, it's because you tried to assign
   // from a source type to a destination type that has insufficient range.
   // The solution may be to change the destination type you're assigning to,
   // and use one large enough to represent the source.
   // Alternatively, you may be better served with the checked_cast<> or
   // saturated_cast<> template functions for your particular use case.
   static_assert(StaticDstRangeRelationToSrcRange<Dst, SrcType>::value ==
                     NUMERIC_RANGE_CONTAINED,
                 "The source type is out of range for the destination type. "
                 "Please see strict_cast<> comments for more information.");

   return static_cast<Dst>(static_cast<SrcType>(value));
 }

 // Some wrappers to statically check that a type is in range.
 template <typename Dst, typename Src, class Enable = void>
 struct IsNumericRangeContained {
   static const bool value = false;
 };

 template <typename Dst, typename Src>
 struct IsNumericRangeContained<
     Dst,
     Src,
     typename std::enable_if<ArithmeticOrUnderlyingEnum<Dst>::value &&
                             ArithmeticOrUnderlyingEnum<Src>::value>::type> {
   static const bool value = StaticDstRangeRelationToSrcRange<Dst, Src>::value ==
                             NUMERIC_RANGE_CONTAINED;
 };

 // StrictNumeric implements compile time range checking between numeric types by
 // wrapping assignment operations in a strict_cast. This class is intended to be
 // used for function arguments and return types, to ensure the destination type
 // can always contain the source type. This is essentially the same as enforcing
 // -Wconversion in gcc and C4302 warnings on MSVC, but it can be applied
 // incrementally at API boundaries, making it easier to convert code so that it
 // compiles cleanly with truncation warnings enabled.
 // This template should introduce no runtime overhead, but it also provides no
 // runtime checking of any of the associated mathematical operations. Use
 // CheckedNumeric for runtime range checks of the actual value being assigned.
 template <typename T>
 class StrictNumeric {
  public:
   using type = T;

   constexpr StrictNumeric() : value_(0) {}

   // Copy constructor.
   template <typename Src>
   constexpr StrictNumeric(const StrictNumeric<Src>& rhs)
       : value_(strict_cast<T>(rhs.value_)) {}

   // This is not an explicit constructor because we implicitly upgrade regular
   // numerics to StrictNumerics to make them easier to use.
   template <typename Src>
   constexpr StrictNumeric(Src value)  // NOLINT(runtime/explicit)
       : value_(strict_cast<T>(value)) {}

   // If you got here from a compiler error, it's because you tried to assign
   // from a source type to a destination type that has insufficient range.
   // The solution may be to change the destination type you're assigning to,
   // and use one large enough to represent the source.
   // If you're assigning from a CheckedNumeric<> class, you may be able to use
   // the AssignIfValid() member function, specify a narrower destination type to
   // the member value functions (e.g. val.template ValueOrDie<Dst>()), use one
   // of the value helper functions (e.g. ValueOrDieForType<Dst>(val)).
   // If you've encountered an _ambiguous overload_ you can use a static_cast<>
   // to explicitly cast the result to the destination type.
   // If none of that works, you may be better served with the checked_cast<> or
   // saturated_cast<> template functions for your particular use case.
   template <typename Dst,
             typename std::enable_if<
                 IsNumericRangeContained<Dst, T>::value>::type* = nullptr>
   constexpr operator Dst() const {
     return static_cast<typename ArithmeticOrUnderlyingEnum<Dst>::type>(value_);
   }

  private:
   const T value_;
 };

 // Convience wrapper returns a StrictNumeric from the provided arithmetic type.
 template <typename T>
 constexpr StrictNumeric<typename UnderlyingType<T>::type> MakeStrictNum(
     const T value) {
   return value;
 }

 // Overload the ostream output operator to make logging work nicely.
 template <typename T>
 std::ostream& operator<<(std::ostream& os, const StrictNumeric<T>& value) {
   os << static_cast<T>(value);
   return os;
 }

 #define BASE_NUMERIC_COMPARISON_OPERATORS(CLASS, NAME, OP)              \
   template <typename L, typename R,                                     \
             typename std::enable_if<                                    \
                 internal::Is##CLASS##Op<L, R>::value>::type* = nullptr> \
   constexpr bool operator OP(const L lhs, const R rhs) {                \
     return SafeCompare<NAME, typename UnderlyingType<L>::type,          \
                        typename UnderlyingType<R>::type>(lhs, rhs);     \
   }

 BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsLess, <);
 BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsLessOrEqual, <=);
 BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsGreater, >);
 BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsGreaterOrEqual, >=);
 BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsEqual, ==);
 BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsNotEqual, !=);

 };  // namespace internal

 using internal::as_signed;
 using internal::as_unsigned;
 using internal::checked_cast;
 using internal::IsTypeInRangeForNumericType;
 using internal::IsValueInRangeForNumericType;
 using internal::IsValueNegative;
 using internal::MakeStrictNum;
 using internal::SafeUnsignedAbs;
 using internal::saturated_cast;
 using internal::strict_cast;
 using internal::StrictNumeric;

 // Explicitly make a shorter size_t alias for convenience.
 using SizeT = StrictNumeric<size_t>;

 }  // namespace base

 #endif  // BASE_NUMERICS_SAFE_CONVERSIONS_H_
	// 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_H_
	#define BASE_NUMERICS_SAFE_CONVERSIONS_H_

	#include <stddef.h>

	#include <limits>
	#include <ostream>
	#include <type_traits>

	#include "base/numerics/safe_conversions_impl.h"

	#if !defined(__native_client__) && (defined(__ARMEL__) \|\| defined(__arch64__))
	#include "base/numerics/safe_conversions_arm_impl.h"
	#define BASE_HAS_OPTIMIZED_SAFE_CONVERSIONS (1)
	#else
	#define BASE_HAS_OPTIMIZED_SAFE_CONVERSIONS (0)
	#endif

	namespace base {
	namespace internal {

	#if !BASE_HAS_OPTIMIZED_SAFE_CONVERSIONS
	template <typename Dst, typename Src>
	struct SaturateFastAsmOp {
	static const bool is_supported = false;
	static constexpr Dst Do(Src) {
	// Force a compile failure if instantiated.
	return CheckOnFailure::template HandleFailure<Dst>();
	}
	};
	#endif // BASE_HAS_OPTIMIZED_SAFE_CONVERSIONS
	#undef BASE_HAS_OPTIMIZED_SAFE_CONVERSIONS

	// The following special case a few specific integer conversions where we can
	// eke out better performance than range checking.
	template <typename Dst, typename Src, typename Enable = void>
	struct IsValueInRangeFastOp {
	static const bool is_supported = false;
	static constexpr bool Do(Src value) {
	// Force a compile failure if instantiated.
	return CheckOnFailure::template HandleFailure<bool>();
	}
	};

	// Signed to signed range comparison.
	template <typename Dst, typename Src>
	struct IsValueInRangeFastOp<
	Dst,
	Src,
	typename std::enable_if<
	std::is_integral<Dst>::value && std::is_integral<Src>::value &&
	std::is_signed<Dst>::value && std::is_signed<Src>::value &&
	!IsTypeInRangeForNumericType<Dst, Src>::value>::type> {
	static const bool is_supported = true;

	static constexpr bool Do(Src value) {
	// Just downcast to the smaller type, sign extend it back to the original
	// type, and then see if it matches the original value.
	return value == static_cast<Dst>(value);
	}
	};

	// Signed to unsigned range comparison.
	template <typename Dst, typename Src>
	struct IsValueInRangeFastOp<
	Dst,
	Src,
	typename std::enable_if<
	std::is_integral<Dst>::value && std::is_integral<Src>::value &&
	!std::is_signed<Dst>::value && std::is_signed<Src>::value &&
	!IsTypeInRangeForNumericType<Dst, Src>::value>::type> {
	static const bool is_supported = true;

	static constexpr bool Do(Src value) {
	// We cast a signed as unsigned to overflow negative values to the top,
	// then compare against whichever maximum is smaller, as our upper bound.
	return as_unsigned(value) <= as_unsigned(CommonMax<Src, Dst>());
	}
	};

	// Convenience function that returns true if the supplied value is in range
	// for the destination type.
	template <typename Dst, typename Src>
	constexpr bool IsValueInRangeForNumericType(Src value) {
	using SrcType = typename internal::UnderlyingType<Src>::type;
	return internal::IsValueInRangeFastOp<Dst, SrcType>::is_supported
	? internal::IsValueInRangeFastOp<Dst, SrcType>::Do(
	static_cast<SrcType>(value))
	: internal::DstRangeRelationToSrcRange<Dst>(
	static_cast<SrcType>(value))
	.IsValid();
	}

	// checked_cast<> is analogous to static_cast<> for numeric types,
	// except that it CHECKs that the specified numeric conversion will not
	// overflow or underflow. NaN source will always trigger a CHECK.
	template <typename Dst,
	class CheckHandler = internal::CheckOnFailure,
	typename Src>
	constexpr Dst checked_cast(Src value) {
	// This throws a compile-time error on evaluating the constexpr if it can be
	// determined at compile-time as failing, otherwise it will CHECK at runtime.
	using SrcType = typename internal::UnderlyingType<Src>::type;
	return BASE_NUMERICS_LIKELY((IsValueInRangeForNumericType<Dst>(value)))
	? static_cast<Dst>(static_cast<SrcType>(value))
	: CheckHandler::template HandleFailure<Dst>();
	}

	// Default boundaries for integral/float: max/infinity, lowest/-infinity, 0/NaN.
	// You may provide your own limits (e.g. to saturated_cast) so long as you
	// implement all of the static constexpr member functions in the class below.
	template <typename T>
	struct SaturationDefaultLimits : public std::numeric_limits<T> {
	static constexpr T NaN() {
	return std::numeric_limits<T>::has_quiet_NaN
	? std::numeric_limits<T>::quiet_NaN()
	: T();
	}
	using std::numeric_limits<T>::max;
	static constexpr T Overflow() {
	return std::numeric_limits<T>::has_infinity
	? std::numeric_limits<T>::infinity()
	: std::numeric_limits<T>::max();
	}
	using std::numeric_limits<T>::lowest;
	static constexpr T Underflow() {
	return std::numeric_limits<T>::has_infinity
	? std::numeric_limits<T>::infinity() * -1
	: std::numeric_limits<T>::lowest();
	}
	};

	template <typename Dst, template <typename> class S, typename Src>
	constexpr Dst saturated_cast_impl(Src value, RangeCheck constraint) {
	// For some reason clang generates much better code when the branch is
	// structured exactly this way, rather than a sequence of checks.
	return !constraint.IsOverflowFlagSet()
	? (!constraint.IsUnderflowFlagSet() ? static_cast<Dst>(value)
	: S<Dst>::Underflow())
	// Skip this check for integral Src, which cannot be NaN.
	: (std::is_integral<Src>::value \|\| !constraint.IsUnderflowFlagSet()
	? S<Dst>::Overflow()
	: S<Dst>::NaN());
	}

	// We can reduce the number of conditions and get slightly better performance
	// for normal signed and unsigned integer ranges. And in the specific case of
	// Arm, we can use the optimized saturation instructions.
	template <typename Dst, typename Src, typename Enable = void>
	struct SaturateFastOp {
	static const bool is_supported = false;
	static constexpr Dst Do(Src value) {
	// Force a compile failure if instantiated.
	return CheckOnFailure::template HandleFailure<Dst>();
	}
	};

	template <typename Dst, typename Src>
	struct SaturateFastOp<
	Dst,
	Src,
	typename std::enable_if<std::is_integral<Src>::value &&
	std::is_integral<Dst>::value>::type> {
	static const bool is_supported = true;
	static Dst Do(Src value) {
	if (SaturateFastAsmOp<Dst, Src>::is_supported)
	return SaturateFastAsmOp<Dst, Src>::Do(value);

	// The exact order of the following is structured to hit the correct
	// optimization heuristics across compilers. Do not change without
	// checking the emitted code.
	Dst saturated = CommonMaxOrMin<Dst, Src>(
	IsMaxInRangeForNumericType<Dst, Src>() \|\|
	(!IsMinInRangeForNumericType<Dst, Src>() && IsValueNegative(value)));
	return BASE_NUMERICS_LIKELY(IsValueInRangeForNumericType<Dst>(value))
	? static_cast<Dst>(value)
	: saturated;
	}
	};

	// saturated_cast<> is analogous to static_cast<> for numeric types, except
	// that the specified numeric conversion will saturate by default rather than
	// overflow or underflow, and NaN assignment to an integral will return 0.
	// All boundary condition behaviors can be overriden with a custom handler.
	template <typename Dst,
	template <typename> class SaturationHandler = SaturationDefaultLimits,
	typename Src>
	constexpr Dst saturated_cast(Src value) {
	using SrcType = typename UnderlyingType<Src>::type;
	return !IsCompileTimeConstant(value) &&
	SaturateFastOp<Dst, SrcType>::is_supported &&
	std::is_same<SaturationHandler<Dst>,
	SaturationDefaultLimits<Dst>>::value
	? SaturateFastOp<Dst, SrcType>::Do(static_cast<SrcType>(value))
	: saturated_cast_impl<Dst, SaturationHandler, SrcType>(
	static_cast<SrcType>(value),
	DstRangeRelationToSrcRange<Dst, SaturationHandler, SrcType>(
	static_cast<SrcType>(value)));
	}

	// strict_cast<> is analogous to static_cast<> for numeric types, except that
	// it will cause a compile failure if the destination type is not large enough
	// to contain any value in the source type. It performs no runtime checking.
	template <typename Dst, typename Src>
	constexpr Dst strict_cast(Src value) {
	using SrcType = typename UnderlyingType<Src>::type;
	static_assert(UnderlyingType<Src>::is_numeric, "Argument must be numeric.");
	static_assert(std::is_arithmetic<Dst>::value, "Result must be numeric.");

	// If you got here from a compiler error, it's because you tried to assign
	// from a source type to a destination type that has insufficient range.
	// The solution may be to change the destination type you're assigning to,
	// and use one large enough to represent the source.
	// Alternatively, you may be better served with the checked_cast<> or
	// saturated_cast<> template functions for your particular use case.
	static_assert(StaticDstRangeRelationToSrcRange<Dst, SrcType>::value ==
	NUMERIC_RANGE_CONTAINED,
	"The source type is out of range for the destination type. "
	"Please see strict_cast<> comments for more information.");

	return static_cast<Dst>(static_cast<SrcType>(value));
	}

	// Some wrappers to statically check that a type is in range.
	template <typename Dst, typename Src, class Enable = void>
	struct IsNumericRangeContained {
	static const bool value = false;
	};

	template <typename Dst, typename Src>
	struct IsNumericRangeContained<
	Dst,
	Src,
	typename std::enable_if<ArithmeticOrUnderlyingEnum<Dst>::value &&
	ArithmeticOrUnderlyingEnum<Src>::value>::type> {
	static const bool value = StaticDstRangeRelationToSrcRange<Dst, Src>::value ==
	NUMERIC_RANGE_CONTAINED;
	};

	// StrictNumeric implements compile time range checking between numeric types by
	// wrapping assignment operations in a strict_cast. This class is intended to be
	// used for function arguments and return types, to ensure the destination type
	// can always contain the source type. This is essentially the same as enforcing
	// -Wconversion in gcc and C4302 warnings on MSVC, but it can be applied
	// incrementally at API boundaries, making it easier to convert code so that it
	// compiles cleanly with truncation warnings enabled.
	// This template should introduce no runtime overhead, but it also provides no
	// runtime checking of any of the associated mathematical operations. Use
	// CheckedNumeric for runtime range checks of the actual value being assigned.
	template <typename T>
	class StrictNumeric {
	public:
	using type = T;

	constexpr StrictNumeric() : value_(0) {}

	// Copy constructor.
	template <typename Src>
	constexpr StrictNumeric(const StrictNumeric<Src>& rhs)
	: value_(strict_cast<T>(rhs.value_)) {}

	// This is not an explicit constructor because we implicitly upgrade regular
	// numerics to StrictNumerics to make them easier to use.
	template <typename Src>
	constexpr StrictNumeric(Src value) // NOLINT(runtime/explicit)
	: value_(strict_cast<T>(value)) {}

	// If you got here from a compiler error, it's because you tried to assign
	// from a source type to a destination type that has insufficient range.
	// The solution may be to change the destination type you're assigning to,
	// and use one large enough to represent the source.
	// If you're assigning from a CheckedNumeric<> class, you may be able to use
	// the AssignIfValid() member function, specify a narrower destination type to
	// the member value functions (e.g. val.template ValueOrDie<Dst>()), use one
	// of the value helper functions (e.g. ValueOrDieForType<Dst>(val)).
	// If you've encountered an _ambiguous overload_ you can use a static_cast<>
	// to explicitly cast the result to the destination type.
	// If none of that works, you may be better served with the checked_cast<> or
	// saturated_cast<> template functions for your particular use case.
	template <typename Dst,
	typename std::enable_if<
	IsNumericRangeContained<Dst, T>::value>::type* = nullptr>
	constexpr operator Dst() const {
	return static_cast<typename ArithmeticOrUnderlyingEnum<Dst>::type>(value_);
	}

	private:
	const T value_;
	};

	// Convience wrapper returns a StrictNumeric from the provided arithmetic type.
	template <typename T>
	constexpr StrictNumeric<typename UnderlyingType<T>::type> MakeStrictNum(
	const T value) {
	return value;
	}

	// Overload the ostream output operator to make logging work nicely.
	template <typename T>
	std::ostream& operator<<(std::ostream& os, const StrictNumeric<T>& value) {
	os << static_cast<T>(value);
	return os;
	}

	#define BASE_NUMERIC_COMPARISON_OPERATORS(CLASS, NAME, OP) \
	template <typename L, typename R, \
	typename std::enable_if< \
	internal::Is##CLASS##Op<L, R>::value>::type* = nullptr> \
	constexpr bool operator OP(const L lhs, const R rhs) { \
	return SafeCompare<NAME, typename UnderlyingType<L>::type, \
	typename UnderlyingType<R>::type>(lhs, rhs); \
	}

	BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsLess, <);
	BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsLessOrEqual, <=);
	BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsGreater, >);
	BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsGreaterOrEqual, >=);
	BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsEqual, ==);
	BASE_NUMERIC_COMPARISON_OPERATORS(Strict, IsNotEqual, !=);

	}; // namespace internal

	using internal::as_signed;
	using internal::as_unsigned;
	using internal::checked_cast;
	using internal::IsTypeInRangeForNumericType;
	using internal::IsValueInRangeForNumericType;
	using internal::IsValueNegative;
	using internal::MakeStrictNum;
	using internal::SafeUnsignedAbs;
	using internal::saturated_cast;
	using internal::strict_cast;
	using internal::StrictNumeric;

	// Explicitly make a shorter size_t alias for convenience.
	using SizeT = StrictNumeric<size_t>;

	} // namespace base

	#endif // BASE_NUMERICS_SAFE_CONVERSIONS_H_