Update safe numerics package to get bitwise ops

Fix callers conventions to avoid ambiguity.
Fix bad bounds check unmasked by change.
Directly include headers no longer pulled in by numerics itself.

Review-Url: https://codereview.chromium.org/2640143003

1 files changed, 482 insertions, 381 deletions

diff --git a/third_party/base/numerics/safe_math_impl.h b/third_party/base/numerics/safe_math_impl.h
index f950f5d517..5ad79ce192 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