xref: /aosp_15_r20/external/angle/src/common/base/anglebase/numerics/safe_conversions_impl.h (revision 8975f5c5ed3d1c378011245431ada316dfb6f244)

// 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 <stdint.h>

#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 angle
{
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());
        bool ge_zero    = false;
        // Converting floating-point to integer will discard fractional part, so
        // values in (-1.0, -0.0) will truncate to 0 and fit in Dst.
        if (std::is_floating_point<Src>::value)
        {
            ge_zero = value > Src(-1);
        }
        else
        {
            ge_zero = value >= Src(0);
        }
        return RangeCheck(
            ge_zero && (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
}  // namespace angle

#endif  // BASE_NUMERICS_SAFE_CONVERSIONS_IMPL_H_