Update safe numerics package to get bitwise ops

third_party/base/numerics/safe_math_impl.h

Index: third_party/base/numerics/safe_math_impl.h
diff --git a/third_party/base/numerics/safe_math_impl.h b/third_party/base/numerics/safe_math_impl.h
index f950f5d517e107248596bc23ca832f4d107803e9..5ad79ce1923dadb69971e407298baab3717dc060 100644
--- a/third_party/base/numerics/safe_math_impl.h
+++ b/third_party/base/numerics/safe_math_impl.h
@@ -14,7 +14,6 @@
 #include <limits>
 #include <type_traits>
 
-#include "third_party/base/macros.h"
 #include "third_party/base/numerics/safe_conversions.h"
 
 namespace pdfium {
@@ -25,355 +24,486 @@ namespace internal {
 // but it may not be fast. This code could be split based on
 // platform/architecture and replaced with potentially faster implementations.
 
-// Integer promotion templates used by the portable checked integer arithmetic.
-template <size_t Size, bool IsSigned>
-struct IntegerForSizeAndSign;
-template <>
-struct IntegerForSizeAndSign<1, true> {
-  typedef int8_t type;
-};
-template <>
-struct IntegerForSizeAndSign<1, false> {
-  typedef uint8_t type;
-};
-template <>
-struct IntegerForSizeAndSign<2, true> {
-  typedef int16_t type;
-};
-template <>
-struct IntegerForSizeAndSign<2, false> {
-  typedef uint16_t type;
-};
-template <>
-struct IntegerForSizeAndSign<4, true> {
-  typedef int32_t type;
-};
-template <>
-struct IntegerForSizeAndSign<4, false> {
-  typedef uint32_t type;
-};
-template <>
-struct IntegerForSizeAndSign<8, true> {
-  typedef int64_t type;
-};
-template <>
-struct IntegerForSizeAndSign<8, false> {
-  typedef uint64_t type;
-};
-
-// 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).
-
-template <typename Integer>
-struct UnsignedIntegerForSize {
-  typedef typename std::enable_if<
-      std::numeric_limits<Integer>::is_integer,
-      typename IntegerForSizeAndSign<sizeof(Integer), false>::type>::type type;
-};
-
-template <typename Integer>
-struct SignedIntegerForSize {
-  typedef typename std::enable_if<
-      std::numeric_limits<Integer>::is_integer,
-      typename IntegerForSizeAndSign<sizeof(Integer), true>::type>::type type;
-};
-
-template <typename Integer>
-struct TwiceWiderInteger {
-  typedef typename std::enable_if<
-      std::numeric_limits<Integer>::is_integer,
-      typename IntegerForSizeAndSign<
-          sizeof(Integer) * 2,
-          std::numeric_limits<Integer>::is_signed>::type>::type type;
-};
-
-template <typename Integer>
-struct PositionOfSignBit {
-  static const typename std::enable_if<std::numeric_limits<Integer>::is_integer,
-                                       size_t>::type value =
-      CHAR_BIT * sizeof(Integer) - 1;
-};
-
 // This is used for UnsignedAbs, where we need to support floating-point
 // template instantiations even though we don't actually support the operations.
-// However, there is no corresponding implementation of e.g. CheckedUnsignedAbs,
+// However, there is no corresponding implementation of e.g. SafeUnsignedAbs,
 // so the float versions will not compile.
 template <typename Numeric,
-          bool IsInteger = std::numeric_limits<Numeric>::is_integer,
-          bool IsFloat = std::numeric_limits<Numeric>::is_iec559>
+          bool IsInteger = std::is_integral<Numeric>::value,
+          bool IsFloat = std::is_floating_point<Numeric>::value>
 struct UnsignedOrFloatForSize;
 
 template <typename Numeric>
 struct UnsignedOrFloatForSize<Numeric, true, false> {
-  typedef typename UnsignedIntegerForSize<Numeric>::type type;
+  using type = typename std::make_unsigned<Numeric>::type;
 };
 
 template <typename Numeric>
 struct UnsignedOrFloatForSize<Numeric, false, true> {
-  typedef Numeric type;
+  using type = Numeric;
 };
 
-// Helper templates for integer manipulations.
-
-template <typename T>
-constexpr bool HasSignBit(T x) {
-  // Cast to unsigned since right shift on signed is undefined.
-  return !!(static_cast<typename UnsignedIntegerForSize<T>::type>(x) >>
-            PositionOfSignBit<T>::value);
-}
-
-// This wrapper undoes the standard integer promotions.
-template <typename T>
-constexpr T BinaryComplement(T x) {
-  return static_cast<T>(~x);
-}
-
-// Here are the actual portable checked integer math implementations.
-// TODO(jschuh): Break this code out from the enable_if pattern and find a clean
-// way to coalesce things into the CheckedNumericState specializations below.
+// Probe for builtin math overflow support on Clang and version check on GCC.
+#if defined(__has_builtin)
+#define USE_OVERFLOW_BUILTINS (__has_builtin(__builtin_add_overflow))
+#elif defined(__GNUC__)
+#define USE_OVERFLOW_BUILTINS (__GNUC__ >= 5)
+#else
+#define USE_OVERFLOW_BUILTINS (0)
+#endif
 
 template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer, T>::type
-CheckedAdd(T x, T y, RangeConstraint* validity) {
+bool CheckedAddImpl(T x, T y, T* result) {
+  static_assert(std::is_integral<T>::value, "Type must be integral");
   // Since the value of x+y is undefined if we have a signed type, we compute
   // it using the unsigned type of the same size.
-  typedef typename UnsignedIntegerForSize<T>::type UnsignedDst;
+  using UnsignedDst = typename std::make_unsigned<T>::type;
+  using SignedDst = typename std::make_signed<T>::type;
   UnsignedDst ux = static_cast<UnsignedDst>(x);
   UnsignedDst uy = static_cast<UnsignedDst>(y);
   UnsignedDst uresult = static_cast<UnsignedDst>(ux + uy);
+  *result = static_cast<T>(uresult);
   // Addition is valid if the sign of (x + y) is equal to either that of x or
   // that of y.
-  if (std::numeric_limits<T>::is_signed) {
-    if (HasSignBit(BinaryComplement(
-            static_cast<UnsignedDst>((uresult ^ ux) & (uresult ^ uy))))) {
-      *validity = RANGE_VALID;
-    } else {  // Direction of wrap is inverse of result sign.
-      *validity = HasSignBit(uresult) ? RANGE_OVERFLOW : RANGE_UNDERFLOW;
+  return (std::is_signed<T>::value)
+             ? static_cast<SignedDst>((uresult ^ ux) & (uresult ^ uy)) >= 0
+             : uresult >= uy;  // Unsigned is either valid or underflow.
+}
+
+template <typename T, typename U, class Enable = void>
+struct CheckedAddOp {};
+
+template <typename T, typename U>
+struct CheckedAddOp<T,
+                    U,
+                    typename std::enable_if<std::is_integral<T>::value &&
+                                            std::is_integral<U>::value>::type> {
+  using result_type = typename MaxExponentPromotion<T, U>::type;
+  template <typename V>
+  static bool Do(T x, U y, V* result) {
+#if USE_OVERFLOW_BUILTINS
+    return !__builtin_add_overflow(x, y, result);
+#else
+    using Promotion = typename BigEnoughPromotion<T, U>::type;
+    Promotion presult;
+    // Fail if either operand is out of range for the promoted type.
+    // TODO(jschuh): This could be made to work for a broader range of values.
+    bool is_valid = IsValueInRangeForNumericType<Promotion>(x) &&
+                    IsValueInRangeForNumericType<Promotion>(y);
+
+    if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
+      presult = static_cast<Promotion>(x) + static_cast<Promotion>(y);
+    } else {
+      is_valid &= CheckedAddImpl(static_cast<Promotion>(x),
+                                 static_cast<Promotion>(y), &presult);
     }
-  } else {  // Unsigned is either valid or overflow.
-    *validity = BinaryComplement(x) >= y ? RANGE_VALID : RANGE_OVERFLOW;
+    *result = static_cast<V>(presult);
+    return is_valid && IsValueInRangeForNumericType<V>(presult);
+#endif
   }
-  return static_cast<T>(uresult);
-}
+};
 
 template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer, T>::type
-CheckedSub(T x, T y, RangeConstraint* validity) {
+bool CheckedSubImpl(T x, T y, T* result) {
+  static_assert(std::is_integral<T>::value, "Type must be integral");
   // Since the value of x+y is undefined if we have a signed type, we compute
   // it using the unsigned type of the same size.
-  typedef typename UnsignedIntegerForSize<T>::type UnsignedDst;
+  using UnsignedDst = typename std::make_unsigned<T>::type;
+  using SignedDst = typename std::make_signed<T>::type;
   UnsignedDst ux = static_cast<UnsignedDst>(x);
   UnsignedDst uy = static_cast<UnsignedDst>(y);
   UnsignedDst uresult = static_cast<UnsignedDst>(ux - uy);
+  *result = static_cast<T>(uresult);
   // Subtraction is valid if either x and y have same sign, or (x-y) and x have
   // the same sign.
-  if (std::numeric_limits<T>::is_signed) {
-    if (HasSignBit(BinaryComplement(
-            static_cast<UnsignedDst>((uresult ^ ux) & (ux ^ uy))))) {
-      *validity = RANGE_VALID;
-    } else {  // Direction of wrap is inverse of result sign.
-      *validity = HasSignBit(uresult) ? RANGE_OVERFLOW : RANGE_UNDERFLOW;
+  return (std::is_signed<T>::value)
+             ? static_cast<SignedDst>((uresult ^ ux) & (ux ^ uy)) >= 0
+             : x >= y;
+}
+
+template <typename T, typename U, class Enable = void>
+struct CheckedSubOp {};
+
+template <typename T, typename U>
+struct CheckedSubOp<T,
+                    U,
+                    typename std::enable_if<std::is_integral<T>::value &&
+                                            std::is_integral<U>::value>::type> {
+  using result_type = typename MaxExponentPromotion<T, U>::type;
+  template <typename V>
+  static bool Do(T x, U y, V* result) {
+#if USE_OVERFLOW_BUILTINS
+    return !__builtin_sub_overflow(x, y, result);
+#else
+    using Promotion = typename BigEnoughPromotion<T, U>::type;
+    Promotion presult;
+    // Fail if either operand is out of range for the promoted type.
+    // TODO(jschuh): This could be made to work for a broader range of values.
+    bool is_valid = IsValueInRangeForNumericType<Promotion>(x) &&
+                    IsValueInRangeForNumericType<Promotion>(y);
+
+    if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
+      presult = static_cast<Promotion>(x) - static_cast<Promotion>(y);
+    } else {
+      is_valid &= CheckedSubImpl(static_cast<Promotion>(x),
+                                 static_cast<Promotion>(y), &presult);
     }
-  } else {  // Unsigned is either valid or underflow.
-    *validity = x >= y ? RANGE_VALID : RANGE_UNDERFLOW;
+    *result = static_cast<V>(presult);
+    return is_valid && IsValueInRangeForNumericType<V>(presult);
+#endif
   }
-  return static_cast<T>(uresult);
-}
+};
 
-// Integer multiplication is a bit complicated. In the fast case we just
-// we just promote to a twice wider type, and range check the result. In the
-// slow case we need to manually check that the result won't be truncated by
-// checking with division against the appropriate bound.
 template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            sizeof(T) * 2 <= sizeof(uintmax_t),
-                        T>::type
-CheckedMul(T x, T y, RangeConstraint* validity) {
-  typedef typename TwiceWiderInteger<T>::type IntermediateType;
-  IntermediateType tmp =
-      static_cast<IntermediateType>(x) * static_cast<IntermediateType>(y);
-  *validity = DstRangeRelationToSrcRange<T>(tmp);
-  return static_cast<T>(tmp);
+bool CheckedMulImpl(T x, T y, T* result) {
+  static_assert(std::is_integral<T>::value, "Type must be integral");
+  // Since the value of x*y is potentially undefined if we have a signed type,
+  // we compute it using the unsigned type of the same size.
+  using UnsignedDst = typename std::make_unsigned<T>::type;
+  using SignedDst = typename std::make_signed<T>::type;
+  const UnsignedDst ux = SafeUnsignedAbs(x);
+  const UnsignedDst uy = SafeUnsignedAbs(y);
+  UnsignedDst uresult = static_cast<UnsignedDst>(ux * uy);
+  const bool is_negative =
+      std::is_signed<T>::value && static_cast<SignedDst>(x ^ y) < 0;
+  *result = is_negative ? 0 - uresult : uresult;
+  // We have a fast out for unsigned identity or zero on the second operand.
+  // After that it's an unsigned overflow check on the absolute value, with
+  // a +1 bound for a negative result.
+  return uy <= UnsignedDst(!std::is_signed<T>::value || is_negative) ||
+         ux <= (std::numeric_limits<T>::max() + UnsignedDst(is_negative)) / uy;
 }
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            std::numeric_limits<T>::is_signed &&
-                            (sizeof(T) * 2 > sizeof(uintmax_t)),
-                        T>::type
-CheckedMul(T x, T y, RangeConstraint* validity) {
-  // If either side is zero then the result will be zero.
-  if (!x || !y) {
-    *validity = RANGE_VALID;
-    return static_cast<T>(0);
-  }
-  if (x > 0) {
-    if (y > 0) {
-      *validity =
-          x <= std::numeric_limits<T>::max() / y ? RANGE_VALID : RANGE_OVERFLOW;
+template <typename T, typename U, class Enable = void>
+struct CheckedMulOp {};
+
+template <typename T, typename U>
+struct CheckedMulOp<T,
+                    U,
+                    typename std::enable_if<std::is_integral<T>::value &&
+                                            std::is_integral<U>::value>::type> {
+  using result_type = typename MaxExponentPromotion<T, U>::type;
+  template <typename V>
+  static bool Do(T x, U y, V* result) {
+#if USE_OVERFLOW_BUILTINS
+#if defined(__clang__)
+    // TODO(jschuh): Get the Clang runtime library issues sorted out so we can
+    // support full-width, mixed-sign multiply builtins.
+    // https://crbug.com/613003
+    static const bool kUseMaxInt =
+        // Narrower type than uintptr_t is always safe.
+        std::numeric_limits<__typeof__(x * y)>::digits <
+            std::numeric_limits<intptr_t>::digits ||
+        // Safe for intptr_t and uintptr_t if the sign matches.
+        (IntegerBitsPlusSign<__typeof__(x * y)>::value ==
+             IntegerBitsPlusSign<intptr_t>::value &&
+         std::is_signed<T>::value == std::is_signed<U>::value);
+#else
+    static const bool kUseMaxInt = true;
+#endif
+    if (kUseMaxInt)
+      return !__builtin_mul_overflow(x, y, result);
+#endif
+    using Promotion = typename FastIntegerArithmeticPromotion<T, U>::type;
+    Promotion presult;
+    // Fail if either operand is out of range for the promoted type.
+    // TODO(jschuh): This could be made to work for a broader range of values.
+    bool is_valid = IsValueInRangeForNumericType<Promotion>(x) &&
+                    IsValueInRangeForNumericType<Promotion>(y);
+
+    if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
+      presult = static_cast<Promotion>(x) * static_cast<Promotion>(y);
     } else {
-      *validity = y >= std::numeric_limits<T>::min() / x ? RANGE_VALID
-                                                         : RANGE_UNDERFLOW;
-    }
-  } else {
-    if (y > 0) {
-      *validity = x >= std::numeric_limits<T>::min() / y ? RANGE_VALID
-                                                         : RANGE_UNDERFLOW;
-    } else {
-      *validity =
-          y >= std::numeric_limits<T>::max() / x ? RANGE_VALID : RANGE_OVERFLOW;
+      is_valid &= CheckedMulImpl(static_cast<Promotion>(x),
+                                 static_cast<Promotion>(y), &presult);
     }
+    *result = static_cast<V>(presult);
+    return is_valid && IsValueInRangeForNumericType<V>(presult);
   }
-  return static_cast<T>(*validity == RANGE_VALID ? x * y : 0);
-}
+};
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            !std::numeric_limits<T>::is_signed &&
-                            (sizeof(T) * 2 > sizeof(uintmax_t)),
-                        T>::type
-CheckedMul(T x, T y, RangeConstraint* validity) {
-  *validity = (y == 0 || x <= std::numeric_limits<T>::max() / y)
-                  ? RANGE_VALID
-                  : RANGE_OVERFLOW;
-  return static_cast<T>(*validity == RANGE_VALID ? x * y : 0);
-}
+// Avoid poluting the namespace once we're done with the macro.
+#undef USE_OVERFLOW_BUILTINS
 
 // Division just requires a check for a zero denominator or an invalid negation
 // on signed min/-1.
 template <typename T>
-T CheckedDiv(T x,
-             T y,
-             RangeConstraint* validity,
-             typename std::enable_if<std::numeric_limits<T>::is_integer,
-                                     int>::type = 0) {
-  if (y == 0) {
-    *validity = RANGE_INVALID;
-    return static_cast<T>(0);
-  }
-  if (std::numeric_limits<T>::is_signed && x == std::numeric_limits<T>::min() &&
-      y == static_cast<T>(-1)) {
-    *validity = RANGE_OVERFLOW;
-    return std::numeric_limits<T>::min();
+bool CheckedDivImpl(T x, T y, T* result) {
+  static_assert(std::is_integral<T>::value, "Type must be integral");
+  if (y && (!std::is_signed<T>::value ||
+            x != std::numeric_limits<T>::lowest() || y != static_cast<T>(-1))) {
+    *result = x / y;
+    return true;
   }
-
-  *validity = RANGE_VALID;
-  return static_cast<T>(x / y);
+  return false;
 }
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            std::numeric_limits<T>::is_signed,
-                        T>::type
-CheckedMod(T x, T y, RangeConstraint* validity) {
-  *validity = y > 0 ? RANGE_VALID : RANGE_INVALID;
-  return static_cast<T>(*validity == RANGE_VALID ? x % y : 0);
-}
+template <typename T, typename U, class Enable = void>
+struct CheckedDivOp {};
+
+template <typename T, typename U>
+struct CheckedDivOp<T,
+                    U,
+                    typename std::enable_if<std::is_integral<T>::value &&
+                                            std::is_integral<U>::value>::type> {
+  using result_type = typename MaxExponentPromotion<T, U>::type;
+  template <typename V>
+  static bool Do(T x, U y, V* result) {
+    using Promotion = typename BigEnoughPromotion<T, U>::type;
+    Promotion presult;
+    // Fail if either operand is out of range for the promoted type.
+    // TODO(jschuh): This could be made to work for a broader range of values.
+    bool is_valid = IsValueInRangeForNumericType<Promotion>(x) &&
+                    IsValueInRangeForNumericType<Promotion>(y);
+    is_valid &= CheckedDivImpl(static_cast<Promotion>(x),
+                               static_cast<Promotion>(y), &presult);
+    *result = static_cast<V>(presult);
+    return is_valid && IsValueInRangeForNumericType<V>(presult);
+  }
+};
 
 template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            !std::numeric_limits<T>::is_signed,
-                        T>::type
-CheckedMod(T x, T y, RangeConstraint* validity) {
-  *validity = y != 0 ? RANGE_VALID : RANGE_INVALID;
-  return static_cast<T>(*validity == RANGE_VALID ? x % y : 0);
+bool CheckedModImpl(T x, T y, T* result) {
+  static_assert(std::is_integral<T>::value, "Type must be integral");
+  if (y > 0) {
+    *result = static_cast<T>(x % y);
+    return true;
+  }
+  return false;
 }
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            std::numeric_limits<T>::is_signed,
-                        T>::type
-CheckedNeg(T value, RangeConstraint* validity) {
-  *validity =
-      value != std::numeric_limits<T>::min() ? RANGE_VALID : RANGE_OVERFLOW;
-  // The negation of signed min is min, so catch that one.
-  return static_cast<T>(*validity == RANGE_VALID ? -value : 0);
-}
+template <typename T, typename U, class Enable = void>
+struct CheckedModOp {};
+
+template <typename T, typename U>
+struct CheckedModOp<T,
+                    U,
+                    typename std::enable_if<std::is_integral<T>::value &&
+                                            std::is_integral<U>::value>::type> {
+  using result_type = typename MaxExponentPromotion<T, U>::type;
+  template <typename V>
+  static bool Do(T x, U y, V* result) {
+    using Promotion = typename BigEnoughPromotion<T, U>::type;
+    Promotion presult;
+    bool is_valid = CheckedModImpl(static_cast<Promotion>(x),
+                                   static_cast<Promotion>(y), &presult);
+    *result = static_cast<V>(presult);
+    return is_valid && IsValueInRangeForNumericType<V>(presult);
+  }
+};
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            !std::numeric_limits<T>::is_signed,
-                        T>::type
-CheckedNeg(T value, RangeConstraint* validity) {
-  // The only legal unsigned negation is zero.
-  *validity = value ? RANGE_UNDERFLOW : RANGE_VALID;
-  return static_cast<T>(
-      *validity == RANGE_VALID
-          ? -static_cast<typename SignedIntegerForSize<T>::type>(value)
-          : 0);
-}
+template <typename T, typename U, class Enable = void>
+struct CheckedLshOp {};
+
+// Left shift. Shifts less than 0 or greater than or equal to the number
+// of bits in the promoted type are undefined. Shifts of negative values
+// are undefined. Otherwise it is defined when the result fits.
+template <typename T, typename U>
+struct CheckedLshOp<T,
+                    U,
+                    typename std::enable_if<std::is_integral<T>::value &&
+                                            std::is_integral<U>::value>::type> {
+  using result_type = T;
+  template <typename V>
+  static bool Do(T x, U shift, V* result) {
+    using ShiftType = typename std::make_unsigned<T>::type;
+    static const ShiftType kBitWidth = IntegerBitsPlusSign<T>::value;
+    const ShiftType real_shift = static_cast<ShiftType>(shift);
+    // Signed shift is not legal on negative values.
+    if (!IsValueNegative(x) && real_shift < kBitWidth) {
+      // Just use a multiplication because it's easy.
+      // TODO(jschuh): This could probably be made more efficient.
+      if (!std::is_signed<T>::value || real_shift != kBitWidth - 1)
+        return CheckedMulOp<T, T>::Do(x, static_cast<T>(1) << shift, result);
+      return !x;  // Special case zero for a full width signed shift.
+    }
+    return false;
+  }
+};
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            std::numeric_limits<T>::is_signed,
-                        T>::type
-CheckedAbs(T value, RangeConstraint* validity) {
-  *validity =
-      value != std::numeric_limits<T>::min() ? RANGE_VALID : RANGE_OVERFLOW;
-  return static_cast<T>(*validity == RANGE_VALID ? std::abs(value) : 0);
-}
+template <typename T, typename U, class Enable = void>
+struct CheckedRshOp {};
+
+// Right shift. Shifts less than 0 or greater than or equal to the number
+// of bits in the promoted type are undefined. Otherwise, it is always defined,
+// but a right shift of a negative value is implementation-dependent.
+template <typename T, typename U>
+struct CheckedRshOp<T,
+                    U,
+                    typename std::enable_if<std::is_integral<T>::value &&
+                                            std::is_integral<U>::value>::type> {
+  using result_type = T;
+  template <typename V = result_type>
+  static bool Do(T x, U shift, V* result) {
+    // Use the type conversion push negative values out of range.
+    using ShiftType = typename std::make_unsigned<T>::type;
+    if (static_cast<ShiftType>(shift) < IntegerBitsPlusSign<T>::value) {
+      T tmp = x >> shift;
+      *result = static_cast<V>(tmp);
+      return IsValueInRangeForNumericType<V>(tmp);
+    }
+    return false;
+  }
+};
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            !std::numeric_limits<T>::is_signed,
-                        T>::type
-CheckedAbs(T value, RangeConstraint* validity) {
-  // T is unsigned, so |value| must already be positive.
-  *validity = RANGE_VALID;
-  return value;
-}
+template <typename T, typename U, class Enable = void>
+struct CheckedAndOp {};
+
+// For simplicity we support only unsigned integer results.
+template <typename T, typename U>
+struct CheckedAndOp<T,
+                    U,
+                    typename std::enable_if<std::is_integral<T>::value &&
+                                            std::is_integral<U>::value>::type> {
+  using result_type = typename std::make_unsigned<
+      typename MaxExponentPromotion<T, U>::type>::type;
+  template <typename V = result_type>
+  static bool Do(T x, U y, V* result) {
+    result_type tmp = static_cast<result_type>(x) & static_cast<result_type>(y);
+    *result = static_cast<V>(tmp);
+    return IsValueInRangeForNumericType<V>(tmp);
+  }
+};
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            std::numeric_limits<T>::is_signed,
-                        typename UnsignedIntegerForSize<T>::type>::type
-CheckedUnsignedAbs(T value) {
-  typedef typename UnsignedIntegerForSize<T>::type UnsignedT;
-  return value == std::numeric_limits<T>::min()
-             ? static_cast<UnsignedT>(std::numeric_limits<T>::max()) + 1
-             : static_cast<UnsignedT>(std::abs(value));
-}
+template <typename T, typename U, class Enable = void>
+struct CheckedOrOp {};
+
+// For simplicity we support only unsigned integers.
+template <typename T, typename U>
+struct CheckedOrOp<T,
+                   U,
+                   typename std::enable_if<std::is_integral<T>::value &&
+                                           std::is_integral<U>::value>::type> {
+  using result_type = typename std::make_unsigned<
+      typename MaxExponentPromotion<T, U>::type>::type;
+  template <typename V = result_type>
+  static bool Do(T x, U y, V* result) {
+    result_type tmp = static_cast<result_type>(x) | static_cast<result_type>(y);
+    *result = static_cast<V>(tmp);
+    return IsValueInRangeForNumericType<V>(tmp);
+  }
+};
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_integer &&
-                            !std::numeric_limits<T>::is_signed,
-                        T>::type
-CheckedUnsignedAbs(T value) {
-  // T is unsigned, so |value| must already be positive.
-  return static_cast<T>(value);
-}
+template <typename T, typename U, class Enable = void>
+struct CheckedXorOp {};
+
+// For simplicity we support only unsigned integers.
+template <typename T, typename U>
+struct CheckedXorOp<T,
+                    U,
+                    typename std::enable_if<std::is_integral<T>::value &&
+                                            std::is_integral<U>::value>::type> {
+  using result_type = typename std::make_unsigned<
+      typename MaxExponentPromotion<T, U>::type>::type;
+  template <typename V = result_type>
+  static bool Do(T x, U y, V* result) {
+    result_type tmp = static_cast<result_type>(x) ^ static_cast<result_type>(y);
+    *result = static_cast<V>(tmp);
+    return IsValueInRangeForNumericType<V>(tmp);
+  }
+};
 
-// These are the floating point stubs that the compiler needs to see. Only the
-// negation operation is ever called.
-#define BASE_FLOAT_ARITHMETIC_STUBS(NAME)                             \
-  template <typename T>                                               \
-  typename std::enable_if<std::numeric_limits<T>::is_iec559, T>::type \
-      Checked##NAME(T, T, RangeConstraint*) {                         \
-    NOTREACHED();                                                     \
-    return static_cast<T>(0);                                         \
+// Max doesn't really need to be implemented this way because it can't fail,
+// but it makes the code much cleaner to use the MathOp wrappers.
+template <typename T, typename U, class Enable = void>
+struct CheckedMaxOp {};
+
+template <typename T, typename U>
+struct CheckedMaxOp<
+    T,
+    U,
+    typename std::enable_if<std::is_arithmetic<T>::value &&
+                            std::is_arithmetic<U>::value>::type> {
+  using result_type = typename MaxExponentPromotion<T, U>::type;
+  template <typename V = result_type>
+  static bool Do(T x, U y, V* result) {
+    *result = IsGreater<T, U>::Test(x, y) ? static_cast<result_type>(x)
+                                          : static_cast<result_type>(y);
+    return true;
   }
+};
 
-BASE_FLOAT_ARITHMETIC_STUBS(Add)
-BASE_FLOAT_ARITHMETIC_STUBS(Sub)
-BASE_FLOAT_ARITHMETIC_STUBS(Mul)
-BASE_FLOAT_ARITHMETIC_STUBS(Div)
-BASE_FLOAT_ARITHMETIC_STUBS(Mod)
+// Min doesn't really need to be implemented this way because it can't fail,
+// but it makes the code much cleaner to use the MathOp wrappers.
+template <typename T, typename U, class Enable = void>
+struct CheckedMinOp {};
+
+template <typename T, typename U>
+struct CheckedMinOp<
+    T,
+    U,
+    typename std::enable_if<std::is_arithmetic<T>::value &&
+                            std::is_arithmetic<U>::value>::type> {
+  using result_type = typename LowestValuePromotion<T, U>::type;
+  template <typename V = result_type>
+  static bool Do(T x, U y, V* result) {
+    *result = IsLess<T, U>::Test(x, y) ? static_cast<result_type>(x)
+                                       : static_cast<result_type>(y);
+    return true;
+  }
+};
 
-#undef BASE_FLOAT_ARITHMETIC_STUBS
+// This is just boilerplate that wraps the standard floating point arithmetic.
+// A macro isn't the nicest solution, but it beats rewriting these repeatedly.
+#define BASE_FLOAT_ARITHMETIC_OPS(NAME, OP)                                    \
+  template <typename T, typename U>                                            \
+  struct Checked##NAME##Op<                                                    \
+      T, U, typename std::enable_if<std::is_floating_point<T>::value ||        \
+                                    std::is_floating_point<U>::value>::type> { \
+    using result_type = typename MaxExponentPromotion<T, U>::type;             \
+    template <typename V>                                                      \
+    static bool Do(T x, U y, V* result) {                                      \
+      using Promotion = typename MaxExponentPromotion<T, U>::type;             \
+      Promotion presult = x OP y;                                              \
+      *result = static_cast<V>(presult);                                       \
+      return IsValueInRangeForNumericType<V>(presult);                         \
+    }                                                                          \
+  };
+
+BASE_FLOAT_ARITHMETIC_OPS(Add, +)
+BASE_FLOAT_ARITHMETIC_OPS(Sub, -)
+BASE_FLOAT_ARITHMETIC_OPS(Mul, *)
+BASE_FLOAT_ARITHMETIC_OPS(Div, /)
+
+#undef BASE_FLOAT_ARITHMETIC_OPS
+
+// Wrap the unary operations to allow SFINAE when instantiating integrals versus
+// floating points. These don't perform any overflow checking. Rather, they
+// exhibit well-defined overflow semantics and rely on the caller to detect
+// if an overflow occured.
+
+template <typename T,
+          typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
+constexpr T NegateWrapper(T value) {
+  using UnsignedT = typename std::make_unsigned<T>::type;
+  // This will compile to a NEG on Intel, and is normal negation on ARM.
+  return static_cast<T>(UnsignedT(0) - static_cast<UnsignedT>(value));
+}
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_iec559, T>::type CheckedNeg(
-    T value,
-    RangeConstraint*) {
-  return static_cast<T>(-value);
+template <
+    typename T,
+    typename std::enable_if<std::is_floating_point<T>::value>::type* = nullptr>
+constexpr T NegateWrapper(T value) {
+  return -value;
 }
 
-template <typename T>
-typename std::enable_if<std::numeric_limits<T>::is_iec559, T>::type CheckedAbs(
-    T value,
-    RangeConstraint*) {
-  return static_cast<T>(std::abs(value));
+template <typename T,
+          typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
+constexpr typename std::make_unsigned<T>::type InvertWrapper(T value) {
+  return ~value;
+}
+
+template <typename T,
+          typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
+constexpr T AbsWrapper(T value) {
+  return static_cast<T>(SafeUnsignedAbs(value));
+}
+
+template <
+    typename T,
+    typename std::enable_if<std::is_floating_point<T>::value>::type* = nullptr>
+constexpr T AbsWrapper(T value) {
+  return value < 0 ? -value : value;
 }
 
 // Floats carry around their validity state with them, but integers do not. So,
@@ -388,10 +518,10 @@ enum NumericRepresentation {
 template <typename NumericType>
 struct GetNumericRepresentation {
   static const NumericRepresentation value =
-      std::numeric_limits<NumericType>::is_integer
+      std::is_integral<NumericType>::value
           ? NUMERIC_INTEGER
-          : (std::numeric_limits<NumericType>::is_iec559 ? NUMERIC_FLOATING
-                                                         : NUMERIC_UNKNOWN);
+          : (std::is_floating_point<NumericType>::value ? NUMERIC_FLOATING
+                                                        : NUMERIC_UNKNOWN);
 };
 
 template <typename T, NumericRepresentation type =
@@ -402,41 +532,48 @@ class CheckedNumericState {};
 template <typename T>
 class CheckedNumericState<T, NUMERIC_INTEGER> {
  private:
+  // is_valid_ precedes value_ because member intializers in the constructors
+  // are evaluated in field order, and is_valid_ must be read when initializing
+  // value_.
+  bool is_valid_;
   T value_;
-  RangeConstraint validity_ : CHAR_BIT;  // Actually requires only two bits.
+
+  // Ensures that a type conversion does not trigger undefined behavior.
+  template <typename Src>
+  static constexpr T WellDefinedConversionOrZero(const Src value,
+                                                 const bool is_valid) {
+    using SrcType = typename internal::UnderlyingType<Src>::type;
+    return (std::is_integral<SrcType>::value || is_valid)
+               ? static_cast<T>(value)
+               : static_cast<T>(0);
+  }
 
  public:
   template <typename Src, NumericRepresentation type>
   friend class CheckedNumericState;
 
-  CheckedNumericState() : value_(0), validity_(RANGE_VALID) {}
+  constexpr CheckedNumericState() : is_valid_(true), value_(0) {}
 
   template <typename Src>
-  CheckedNumericState(Src value, RangeConstraint validity)
-      : value_(static_cast<T>(value)),
-        validity_(GetRangeConstraint(validity |
-                                     DstRangeRelationToSrcRange<T>(value))) {
-    static_assert(std::numeric_limits<Src>::is_specialized,
-                  "Argument must be numeric.");
+  constexpr CheckedNumericState(Src value, bool is_valid)
+      : is_valid_(is_valid && IsValueInRangeForNumericType<T>(value)),
+        value_(WellDefinedConversionOrZero(value, is_valid_)) {
+    static_assert(std::is_arithmetic<Src>::value, "Argument must be numeric.");
   }
 
   // Copy constructor.
   template <typename Src>
-  CheckedNumericState(const CheckedNumericState<Src>& rhs)
-      : value_(static_cast<T>(rhs.value())),
-        validity_(GetRangeConstraint(
-            rhs.validity() | DstRangeRelationToSrcRange<T>(rhs.value()))) {}
+  constexpr CheckedNumericState(const CheckedNumericState<Src>& rhs)
+      : is_valid_(rhs.IsValid()),
+        value_(WellDefinedConversionOrZero(rhs.value(), is_valid_)) {}
 
   template <typename Src>
-  explicit CheckedNumericState(
-      Src value,
-      typename std::enable_if<std::numeric_limits<Src>::is_specialized,
-                              int>::type = 0)
-      : value_(static_cast<T>(value)),
-        validity_(DstRangeRelationToSrcRange<T>(value)) {}
-
-  RangeConstraint validity() const { return validity_; }
-  T value() const { return value_; }
+  constexpr explicit CheckedNumericState(Src value)
+      : is_valid_(IsValueInRangeForNumericType<T>(value)),
+        value_(WellDefinedConversionOrZero(value, is_valid_)) {}
+
+  constexpr bool is_valid() const { return is_valid_; }
+  constexpr T value() const { return value_; }
 };
 
 // Floating points maintain their own validity, but need translation wrappers.
@@ -445,94 +582,58 @@ class CheckedNumericState<T, NUMERIC_FLOATING> {
  private:
   T value_;
 
+  // Ensures that a type conversion does not trigger undefined behavior.
+  template <typename Src>
+  static constexpr T WellDefinedConversionOrNaN(const Src value,
+                                                const bool is_valid) {
+    using SrcType = typename internal::UnderlyingType<Src>::type;
+    return (StaticDstRangeRelationToSrcRange<T, SrcType>::value ==
+                NUMERIC_RANGE_CONTAINED ||
+            is_valid)
+               ? static_cast<T>(value)
+               : std::numeric_limits<T>::quiet_NaN();
+  }
+
  public:
   template <typename Src, NumericRepresentation type>
   friend class CheckedNumericState;
 
-  CheckedNumericState() : value_(0.0) {}
+  constexpr CheckedNumericState() : value_(0.0) {}
 
   template <typename Src>
-  CheckedNumericState(
-      Src value,
-      RangeConstraint validity,
-      typename std::enable_if<std::numeric_limits<Src>::is_integer, int>::type =
-          0) {
-    switch (DstRangeRelationToSrcRange<T>(value)) {
-      case RANGE_VALID:
-        value_ = static_cast<T>(value);
-        break;
-
-      case RANGE_UNDERFLOW:
-        value_ = -std::numeric_limits<T>::infinity();
-        break;
-
-      case RANGE_OVERFLOW:
-        value_ = std::numeric_limits<T>::infinity();
-        break;
-
-      case RANGE_INVALID:
-        value_ = std::numeric_limits<T>::quiet_NaN();
-        break;
-
-      default:
-        NOTREACHED();
-    }
-  }
+  constexpr CheckedNumericState(Src value, bool is_valid)
+      : value_(WellDefinedConversionOrNaN(value, is_valid)) {}
 
   template <typename Src>
-  explicit CheckedNumericState(
-      Src value,
-      typename std::enable_if<std::numeric_limits<Src>::is_specialized,
-                              int>::type = 0)
-      : value_(static_cast<T>(value)) {}
+  constexpr explicit CheckedNumericState(Src value)
+      : value_(WellDefinedConversionOrNaN(
+            value,
+            IsValueInRangeForNumericType<T>(value))) {}
 
   // Copy constructor.
   template <typename Src>
-  CheckedNumericState(const CheckedNumericState<Src>& rhs)
-      : value_(static_cast<T>(rhs.value())) {}
-
-  RangeConstraint validity() const {
-    return GetRangeConstraint(value_ <= std::numeric_limits<T>::max(),
-                              value_ >= -std::numeric_limits<T>::max());
+  constexpr CheckedNumericState(const CheckedNumericState<Src>& rhs)
+      : value_(WellDefinedConversionOrNaN(
+            rhs.value(),
+            rhs.is_valid() && IsValueInRangeForNumericType<T>(rhs.value()))) {}
+
+  constexpr bool is_valid() const {
+    // Written this way because std::isfinite is not reliably constexpr.
+    // TODO(jschuh): Fix this if the libraries ever get fixed.
+    return value_ <= std::numeric_limits<T>::max() &&
+           value_ >= std::numeric_limits<T>::lowest();
   }
-  T value() const { return value_; }
-};
-
-// For integers less than 128-bit and floats 32-bit or larger, we have the type
-// with the larger maximum exponent take precedence.
-enum ArithmeticPromotionCategory { LEFT_PROMOTION, RIGHT_PROMOTION };
-
-template <typename Lhs,
-          typename Rhs = Lhs,
-          ArithmeticPromotionCategory Promotion =
-              (MaxExponent<Lhs>::value > MaxExponent<Rhs>::value)
-                  ? LEFT_PROMOTION
-                  : RIGHT_PROMOTION>
-struct ArithmeticPromotion;
-
-template <typename Lhs, typename Rhs>
-struct ArithmeticPromotion<Lhs, Rhs, LEFT_PROMOTION> {
-  typedef Lhs type;
-};
-
-template <typename Lhs, typename Rhs>
-struct ArithmeticPromotion<Lhs, Rhs, RIGHT_PROMOTION> {
-  typedef Rhs type;
+  constexpr T value() const { return value_; }
 };
 
-// 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>
-struct IsIntegerArithmeticSafe {
-  static const bool value = !std::numeric_limits<T>::is_iec559 &&
-                            StaticDstRangeRelationToSrcRange<T, Lhs>::value ==
-                                NUMERIC_RANGE_CONTAINED &&
-                            sizeof(T) >= (2 * sizeof(Lhs)) &&
-                            StaticDstRangeRelationToSrcRange<T, Rhs>::value !=
-                                NUMERIC_RANGE_CONTAINED &&
-                            sizeof(T) >= (2 * sizeof(Rhs));
+template <template <typename, typename, typename> class M,
+          typename L,
+          typename R>
+struct MathWrapper {
+  using math = M<typename UnderlyingType<L>::type,
+                 typename UnderlyingType<R>::type,
+                 void>;
+  using type = typename math::result_type;
 };
 
 }  // namespace internal