Import Chromium base/numerics to resolve integer overflow.

We'll use this for integer overflows going forward.

BUG=382606
R=jam@chromium.org

Review URL: https://codereview.chromium.org/349363005

5 files changed, 1057 insertions, 0 deletions

diff --git a/third_party/numerics/OWNERS b/third_party/numerics/OWNERS
new file mode 100644
index 0000000000..f7816afe81
--- /dev/null
+++ b/third_party/numerics/OWNERS
@@ -0,0 +1,3 @@
+jschuh@chromium.org
+tsepez@chromium.org
+palmer@chromium.org
diff --git a/third_party/numerics/safe_conversions.h b/third_party/numerics/safe_conversions.h
new file mode 100644
index 0000000000..681dc0a9cc
--- /dev/null
+++ b/third_party/numerics/safe_conversions.h
@@ -0,0 +1,64 @@
+// 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_SAFE_CONVERSIONS_H_
+#define BASE_SAFE_CONVERSIONS_H_
+
+#include <limits>
+
+#include "../logging.h"
+#include "safe_conversions_impl.h"
+
+namespace base {
+
+// Convenience function that returns true if the supplied value is in range
+// for the destination type.
+template <typename Dst, typename Src>
+inline bool IsValueInRangeForNumericType(Src value) {
+  return internal::DstRangeRelationToSrcRange<Dst>(value) ==
+         internal::RANGE_VALID;
+}
+
+// checked_cast<> is analogous to static_cast<> for numeric types,
+// except that it CHECKs that the specified numeric conversion will not
+// overflow or underflow. NaN source will always trigger a CHECK.
+template <typename Dst, typename Src>
+inline Dst checked_cast(Src value) {
+  CHECK(IsValueInRangeForNumericType<Dst>(value));
+  return static_cast<Dst>(value);
+}
+
+// saturated_cast<> is analogous to static_cast<> for numeric types, except
+// that the specified numeric conversion will saturate rather than overflow or
+// underflow. NaN assignment to an integral will trigger a CHECK condition.
+template <typename Dst, typename Src>
+inline Dst saturated_cast(Src value) {
+  // Optimization for floating point values, which already saturate.
+  if (std::numeric_limits<Dst>::is_iec559)
+    return static_cast<Dst>(value);
+
+  switch (internal::DstRangeRelationToSrcRange<Dst>(value)) {
+    case internal::RANGE_VALID:
+      return static_cast<Dst>(value);
+
+    case internal::RANGE_UNDERFLOW:
+      return std::numeric_limits<Dst>::min();
+
+    case internal::RANGE_OVERFLOW:
+      return std::numeric_limits<Dst>::max();
+
+    // Should fail only on attempting to assign NaN to a saturated integer.
+    case internal::RANGE_INVALID:
+      CHECK(false);
+      return std::numeric_limits<Dst>::max();
+  }
+
+  NOTREACHED();
+  return static_cast<Dst>(value);
+}
+
+}  // namespace base
+
+#endif  // BASE_SAFE_CONVERSIONS_H_
+
diff --git a/third_party/numerics/safe_conversions_impl.h b/third_party/numerics/safe_conversions_impl.h
new file mode 100644
index 0000000000..a357e518d1
--- /dev/null
+++ b/third_party/numerics/safe_conversions_impl.h
@@ -0,0 +1,217 @@
+// 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_SAFE_CONVERSIONS_IMPL_H_
+#define BASE_SAFE_CONVERSIONS_IMPL_H_
+
+#include <limits>
+
+#include "../macros.h"
+#include "../template_util.h"
+
+namespace base {
+namespace internal {
+
+// The std library doesn't provide a binary max_exponent for integers, however
+// we can compute one by adding one to the number of non-sign bits. This allows
+// for accurate range comparisons between floating point and integer types.
+template <typename NumericType>
+struct MaxExponent {
+  static const int value = std::numeric_limits<NumericType>::is_iec559
+                               ? std::numeric_limits<NumericType>::max_exponent
+                               : (sizeof(NumericType) * 8 + 1 -
+                                  std::numeric_limits<NumericType>::is_signed);
+};
+
+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>::min() >= numeric_limits<Dst>::min() 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::numeric_limits<Dst>::is_signed
+                                            ? INTEGER_REPRESENTATION_SIGNED
+                                            : INTEGER_REPRESENTATION_UNSIGNED,
+    IntegerRepresentation SrcSign =
+        std::numeric_limits<Src>::is_signed
+            ? 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;
+};
+
+enum RangeConstraint {
+  RANGE_VALID = 0x0,  // Value can be represented by the destination type.
+  RANGE_UNDERFLOW = 0x1,  // Value would overflow.
+  RANGE_OVERFLOW = 0x2,  // Value would underflow.
+  RANGE_INVALID = RANGE_UNDERFLOW | RANGE_OVERFLOW  // Invalid (i.e. NaN).
+};
+
+// Helper function for coercing an int back to a RangeContraint.
+inline RangeConstraint GetRangeConstraint(int integer_range_constraint) {
+  assert(integer_range_constraint >= RANGE_VALID &&
+         integer_range_constraint <= RANGE_INVALID);
+  return static_cast<RangeConstraint>(integer_range_constraint);
+}
+
+// This function creates a RangeConstraint from an upper and lower bound
+// check by taking advantage of the fact that only NaN can be out of range in
+// both directions at once.
+inline RangeConstraint GetRangeConstraint(bool is_in_upper_bound,
+                                   bool is_in_lower_bound) {
+  return GetRangeConstraint((is_in_upper_bound ? 0 : RANGE_OVERFLOW) |
+                            (is_in_lower_bound ? 0 : RANGE_UNDERFLOW));
+}
+
+template <
+    typename Dst,
+    typename Src,
+    IntegerRepresentation DstSign = std::numeric_limits<Dst>::is_signed
+                                            ? INTEGER_REPRESENTATION_SIGNED
+                                            : INTEGER_REPRESENTATION_UNSIGNED,
+    IntegerRepresentation SrcSign = std::numeric_limits<Src>::is_signed
+                                            ? 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.
+
+// Dst range is statically determined to contain Src: Nothing to check.
+template <typename Dst,
+          typename Src,
+          IntegerRepresentation DstSign,
+          IntegerRepresentation SrcSign>
+struct DstRangeRelationToSrcRangeImpl<Dst,
+                                      Src,
+                                      DstSign,
+                                      SrcSign,
+                                      NUMERIC_RANGE_CONTAINED> {
+  static RangeConstraint Check(Src value) { return RANGE_VALID; }
+};
+
+// Signed to signed narrowing: Both the upper and lower boundaries may be
+// exceeded.
+template <typename Dst, typename Src>
+struct DstRangeRelationToSrcRangeImpl<Dst,
+                                      Src,
+                                      INTEGER_REPRESENTATION_SIGNED,
+                                      INTEGER_REPRESENTATION_SIGNED,
+                                      NUMERIC_RANGE_NOT_CONTAINED> {
+  static RangeConstraint Check(Src value) {
+    return std::numeric_limits<Dst>::is_iec559
+               ? GetRangeConstraint(value <= std::numeric_limits<Dst>::max(),
+                                    value >= -std::numeric_limits<Dst>::max())
+               : GetRangeConstraint(value <= std::numeric_limits<Dst>::max(),
+                                    value >= std::numeric_limits<Dst>::min());
+  }
+};
+
+// Unsigned to unsigned narrowing: Only the upper boundary can be exceeded.
+template <typename Dst, typename Src>
+struct DstRangeRelationToSrcRangeImpl<Dst,
+                                      Src,
+                                      INTEGER_REPRESENTATION_UNSIGNED,
+                                      INTEGER_REPRESENTATION_UNSIGNED,
+                                      NUMERIC_RANGE_NOT_CONTAINED> {
+  static RangeConstraint Check(Src value) {
+    return GetRangeConstraint(value <= std::numeric_limits<Dst>::max(), true);
+  }
+};
+
+// Unsigned to signed: The upper boundary may be exceeded.
+template <typename Dst, typename Src>
+struct DstRangeRelationToSrcRangeImpl<Dst,
+                                      Src,
+                                      INTEGER_REPRESENTATION_SIGNED,
+                                      INTEGER_REPRESENTATION_UNSIGNED,
+                                      NUMERIC_RANGE_NOT_CONTAINED> {
+  static RangeConstraint Check(Src value) {
+    return sizeof(Dst) > sizeof(Src)
+               ? RANGE_VALID
+               : GetRangeConstraint(
+                     value <= static_cast<Src>(std::numeric_limits<Dst>::max()),
+                     true);
+  }
+};
+
+// Signed to unsigned: The upper boundary may be exceeded for a narrower Dst,
+// and any negative value exceeds the lower boundary.
+template <typename Dst, typename Src>
+struct DstRangeRelationToSrcRangeImpl<Dst,
+                                      Src,
+                                      INTEGER_REPRESENTATION_UNSIGNED,
+                                      INTEGER_REPRESENTATION_SIGNED,
+                                      NUMERIC_RANGE_NOT_CONTAINED> {
+  static RangeConstraint Check(Src value) {
+    return (MaxExponent<Dst>::value >= MaxExponent<Src>::value)
+               ? GetRangeConstraint(true, value >= static_cast<Src>(0))
+               : GetRangeConstraint(
+                     value <= static_cast<Src>(std::numeric_limits<Dst>::max()),
+                     value >= static_cast<Src>(0));
+  }
+};
+
+template <typename Dst, typename Src>
+inline RangeConstraint DstRangeRelationToSrcRange(Src value) {
+  COMPILE_ASSERT(std::numeric_limits<Src>::is_specialized,
+                 argument_must_be_numeric);
+  COMPILE_ASSERT(std::numeric_limits<Dst>::is_specialized,
+                 result_must_be_numeric);
+  return DstRangeRelationToSrcRangeImpl<Dst, Src>::Check(value);
+}
+
+}  // namespace internal
+}  // namespace base
+
+#endif  // BASE_SAFE_CONVERSIONS_IMPL_H_
+
diff --git a/third_party/numerics/safe_math.h b/third_party/numerics/safe_math.h
new file mode 100644
index 0000000000..4b38ff2b1f
--- /dev/null
+++ b/third_party/numerics/safe_math.h
@@ -0,0 +1,271 @@
+// 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_SAFE_MATH_H_
+#define BASE_SAFE_MATH_H_
+
+#include "safe_math_impl.h"
+
+namespace base {
+
+namespace internal {
+
+// CheckedNumeric implements all the logic and operators for detecting integer
+// boundary conditions such as overflow, underflow, and invalid conversions.
+// The CheckedNumeric type implicitly converts from floating point and integer
+// data types, and contains overloads for basic arithmetic operations (i.e.: +,
+// -, *, /, %).
+//
+// The following methods convert from CheckedNumeric to standard numeric values:
+// IsValid() - Returns true if the underlying numeric value is valid (i.e. has
+//             has not wrapped and is not the result of an invalid conversion).
+// ValueOrDie() - Returns the underlying value. If the state is not valid this
+//                call will crash on a CHECK.
+// ValueOrDefault() - Returns the current value, or the supplied default if the
+//                    state is not valid.
+// ValueFloating() - Returns the underlying floating point value (valid only
+//                   only for floating point CheckedNumeric types).
+//
+// Bitwise operations are explicitly not supported, because correct
+// handling of some cases (e.g. sign manipulation) is ambiguous. Comparison
+// operations are explicitly not supported because they could result in a crash
+// on a CHECK condition. You should use patterns like the following for these
+// operations:
+// Bitwise operation:
+//     CheckedNumeric<int> checked_int = untrusted_input_value;
+//     int x = checked_int.ValueOrDefault(0) | kFlagValues;
+// Comparison:
+//   CheckedNumeric<size_t> checked_size;
+//   CheckedNumeric<int> checked_size = untrusted_input_value;
+//   checked_size = checked_size + HEADER LENGTH;
+//   if (checked_size.IsValid() && checked_size.ValueOrDie() < buffer_size)
+//     Do stuff...
+template <typename T>
+class CheckedNumeric {
+ public:
+  typedef T type;
+
+  CheckedNumeric() {}
+
+  // Copy constructor.
+  template <typename Src>
+  CheckedNumeric(const CheckedNumeric<Src>& rhs)
+      : state_(rhs.ValueUnsafe(), rhs.validity()) {}
+
+  template <typename Src>
+  CheckedNumeric(Src value, RangeConstraint validity)
+      : state_(value, validity) {}
+
+  // This is not an explicit constructor because we implicitly upgrade regular
+  // numerics to CheckedNumerics to make them easier to use.
+  template <typename Src>
+  CheckedNumeric(Src value)
+      : state_(value) {
+    COMPILE_ASSERT(std::numeric_limits<Src>::is_specialized,
+                   argument_must_be_numeric);
+  }
+
+  // IsValid() is the public API to test if a CheckedNumeric is currently valid.
+  bool IsValid() const { return validity() == RANGE_VALID; }
+
+  // ValueOrDie() The primary accessor for the underlying value. If the current
+  // state is not valid it will CHECK and crash.
+  T ValueOrDie() const {
+    CHECK(IsValid());
+    return state_.value();
+  }
+
+  // ValueOrDefault(T default_value) A convenience method that returns the
+  // current value if the state is valid, and the supplied default_value for
+  // any other state.
+  T ValueOrDefault(T default_value) const {
+    return IsValid() ? state_.value() : default_value;
+  }
+
+  // ValueFloating() - Since floating point values include their validity state,
+  // we provide an easy method for extracting them directly, without a risk of
+  // crashing on a CHECK.
+  T ValueFloating() const {
+    COMPILE_ASSERT(std::numeric_limits<T>::is_iec559, argument_must_be_float);
+    return CheckedNumeric<T>::cast(*this).ValueUnsafe();
+  }
+
+  // validity() - DO NOT USE THIS IN EXTERNAL CODE - It is public right now for
+  // tests and to avoid a big matrix of friend operator overloads. But the
+  // values it returns are likely to change in the future.
+  // Returns: current validity state (i.e. valid, overflow, underflow, nan).
+  // TODO(jschuh): crbug.com/332611 Figure out and implement semantics for
+  // saturation/wrapping so we can expose this state consistently and implement
+  // saturated arithmetic.
+  RangeConstraint validity() const { return state_.validity(); }
+
+  // ValueUnsafe() - DO NOT USE THIS IN EXTERNAL CODE - It is public right now
+  // for tests and to avoid a big matrix of friend operator overloads. But the
+  // values it returns are likely to change in the future.
+  // Returns: the raw numeric value, regardless of the current state.
+  // TODO(jschuh): crbug.com/332611 Figure out and implement semantics for
+  // saturation/wrapping so we can expose this state consistently and implement
+  // saturated arithmetic.
+  T ValueUnsafe() const { return state_.value(); }
+
+  // Prototypes for the supported arithmetic operator overloads.
+  template <typename Src> CheckedNumeric& operator+=(Src rhs);
+  template <typename Src> CheckedNumeric& operator-=(Src rhs);
+  template <typename Src> CheckedNumeric& operator*=(Src rhs);
+  template <typename Src> CheckedNumeric& operator/=(Src rhs);
+  template <typename Src> CheckedNumeric& operator%=(Src rhs);
+
+  CheckedNumeric operator-() const {
+    RangeConstraint validity;
+    T value = CheckedNeg(state_.value(), &validity);
+    // Negation is always valid for floating point.
+    if (std::numeric_limits<T>::is_iec559)
+      return CheckedNumeric<T>(value);
+
+    validity = GetRangeConstraint(state_.validity() | validity);
+    return CheckedNumeric<T>(value, validity);
+  }
+
+  CheckedNumeric Abs() const {
+    RangeConstraint validity;
+    T value = CheckedAbs(state_.value(), &validity);
+    // Absolute value is always valid for floating point.
+    if (std::numeric_limits<T>::is_iec559)
+      return CheckedNumeric<T>(value);
+
+    validity = GetRangeConstraint(state_.validity() | validity);
+    return CheckedNumeric<T>(value, validity);
+  }
+
+  CheckedNumeric& operator++() {
+    *this += 1;
+    return *this;
+  }
+
+  CheckedNumeric operator++(int) {
+    CheckedNumeric value = *this;
+    *this += 1;
+    return value;
+  }
+
+  CheckedNumeric& operator--() {
+    *this -= 1;
+    return *this;
+  }
+
+  CheckedNumeric operator--(int) {
+    CheckedNumeric value = *this;
+    *this -= 1;
+    return value;
+  }
+
+  // These static methods behave like a convenience cast operator targeting
+  // the desired CheckedNumeric type. As an optimization, a reference is
+  // returned when Src is the same type as T.
+  template <typename Src>
+  static CheckedNumeric<T> cast(
+      Src u,
+      typename enable_if<std::numeric_limits<Src>::is_specialized, int>::type =
+          0) {
+    return u;
+  }
+
+  template <typename Src>
+  static CheckedNumeric<T> cast(
+      const CheckedNumeric<Src>& u,
+      typename enable_if<!is_same<Src, T>::value, int>::type = 0) {
+    return u;
+  }
+
+  static const CheckedNumeric<T>& cast(const CheckedNumeric<T>& u) { return u; }
+
+ private:
+  CheckedNumericState<T> state_;
+};
+
+// This is the boilerplate for the standard arithmetic operator overloads. A
+// macro isn't the prettiest solution, but it beats rewriting these five times.
+// Some details worth noting are:
+//  * We apply the standard arithmetic promotions.
+//  * We skip range checks for floating points.
+//  * We skip range checks for destination integers with sufficient range.
+// TODO(jschuh): extract these out into templates.
+#define BASE_NUMERIC_ARITHMETIC_OPERATORS(NAME, OP, COMPOUND_OP)              \
+  /* Binary arithmetic operator for CheckedNumerics of the same type. */      \
+  template <typename T>                                                       \
+  CheckedNumeric<typename ArithmeticPromotion<T>::type> operator OP(          \
+      const CheckedNumeric<T>& lhs, const CheckedNumeric<T>& rhs) {           \
+    typedef typename ArithmeticPromotion<T>::type Promotion;                  \
+    /* Floating point always takes the fast path */                           \
+    if (std::numeric_limits<T>::is_iec559)                                    \
+      return CheckedNumeric<T>(lhs.ValueUnsafe() OP rhs.ValueUnsafe());       \
+    if (IsIntegerArithmeticSafe<Promotion, T, T>::value)                      \
+      return CheckedNumeric<Promotion>(                                       \
+          lhs.ValueUnsafe() OP rhs.ValueUnsafe(),                             \
+          GetRangeConstraint(rhs.validity() | lhs.validity()));               \
+    RangeConstraint validity = RANGE_VALID;                                   \
+    T result = Checked##NAME(static_cast<Promotion>(lhs.ValueUnsafe()),       \
+                             static_cast<Promotion>(rhs.ValueUnsafe()),       \
+                             &validity);                                      \
+    return CheckedNumeric<Promotion>(                                         \
+        result,                                                               \
+        GetRangeConstraint(validity | lhs.validity() | rhs.validity()));      \
+  }                                                                           \
+  /* Assignment arithmetic operator implementation from CheckedNumeric. */    \
+  template <typename T>                                                       \
+  template <typename Src>                                                     \
+  CheckedNumeric<T>& CheckedNumeric<T>::operator COMPOUND_OP(Src rhs) {       \
+    *this = CheckedNumeric<T>::cast(*this) OP CheckedNumeric<Src>::cast(rhs); \
+    return *this;                                                             \
+  }                                                                           \
+  /* Binary arithmetic operator for CheckedNumeric of different type. */      \
+  template <typename T, typename Src>                                         \
+  CheckedNumeric<typename ArithmeticPromotion<T, Src>::type> operator OP(     \
+      const CheckedNumeric<Src>& lhs, const CheckedNumeric<T>& rhs) {         \
+    typedef typename ArithmeticPromotion<T, Src>::type Promotion;             \
+    if (IsIntegerArithmeticSafe<Promotion, T, Src>::value)                    \
+      return CheckedNumeric<Promotion>(                                       \
+          lhs.ValueUnsafe() OP rhs.ValueUnsafe(),                             \
+          GetRangeConstraint(rhs.validity() | lhs.validity()));               \
+    return CheckedNumeric<Promotion>::cast(lhs)                               \
+        OP CheckedNumeric<Promotion>::cast(rhs);                              \
+  }                                                                           \
+  /* Binary arithmetic operator for left CheckedNumeric and right numeric. */ \
+  template <typename T, typename Src>                                         \
+  CheckedNumeric<typename ArithmeticPromotion<T, Src>::type> operator OP(     \
+      const CheckedNumeric<T>& lhs, Src rhs) {                                \
+    typedef typename ArithmeticPromotion<T, Src>::type Promotion;             \
+    if (IsIntegerArithmeticSafe<Promotion, T, Src>::value)                    \
+      return CheckedNumeric<Promotion>(lhs.ValueUnsafe() OP rhs,              \
+                                       lhs.validity());                       \
+    return CheckedNumeric<Promotion>::cast(lhs)                               \
+        OP CheckedNumeric<Promotion>::cast(rhs);                              \
+  }                                                                           \
+  /* Binary arithmetic operator for right numeric and left CheckedNumeric. */ \
+  template <typename T, typename Src>                                         \
+  CheckedNumeric<typename ArithmeticPromotion<T, Src>::type> operator OP(     \
+      Src lhs, const CheckedNumeric<T>& rhs) {                                \
+    typedef typename ArithmeticPromotion<T, Src>::type Promotion;             \
+    if (IsIntegerArithmeticSafe<Promotion, T, Src>::value)                    \
+      return CheckedNumeric<Promotion>(lhs OP rhs.ValueUnsafe(),              \
+                                       rhs.validity());                       \
+    return CheckedNumeric<Promotion>::cast(lhs)                               \
+        OP CheckedNumeric<Promotion>::cast(rhs);                              \
+  }
+
+BASE_NUMERIC_ARITHMETIC_OPERATORS(Add, +, += )
+BASE_NUMERIC_ARITHMETIC_OPERATORS(Sub, -, -= )
+BASE_NUMERIC_ARITHMETIC_OPERATORS(Mul, *, *= )
+BASE_NUMERIC_ARITHMETIC_OPERATORS(Div, /, /= )
+BASE_NUMERIC_ARITHMETIC_OPERATORS(Mod, %, %= )
+
+#undef BASE_NUMERIC_ARITHMETIC_OPERATORS
+
+}  // namespace internal
+
+using internal::CheckedNumeric;
+
+}  // namespace base
+
+#endif  // BASE_SAFE_MATH_H_
diff --git a/third_party/numerics/safe_math_impl.h b/third_party/numerics/safe_math_impl.h
new file mode 100644
index 0000000000..4bf59e64e0
--- /dev/null
+++ b/third_party/numerics/safe_math_impl.h
@@ -0,0 +1,502 @@
+// 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 SAFE_MATH_IMPL_H_
+#define SAFE_MATH_IMPL_H_
+
+#include <stdint.h>
+
+#include <cmath>
+#include <cstdlib>
+#include <limits>
+
+#include "../macros.h"
+#include "../template_util.h"
+#include "safe_conversions.h"
+
+namespace base {
+namespace internal {
+
+// Everything from here up to the floating point operations is portable C++,
+// 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 enable_if<
+      std::numeric_limits<Integer>::is_integer,
+      typename IntegerForSizeAndSign<sizeof(Integer), false>::type>::type type;
+};
+
+template <typename Integer>
+struct SignedIntegerForSize {
+  typedef typename enable_if<
+      std::numeric_limits<Integer>::is_integer,
+      typename IntegerForSizeAndSign<sizeof(Integer), true>::type>::type type;
+};
+
+template <typename Integer>
+struct TwiceWiderInteger {
+  typedef typename 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 enable_if<std::numeric_limits<Integer>::is_integer,
+                                  size_t>::type value = 8 * sizeof(Integer) - 1;
+};
+
+// Helper templates for integer manipulations.
+
+template <typename T>
+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>
+T BinaryComplement(T x) {
+  return ~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.
+
+template <typename T>
+typename enable_if<std::numeric_limits<T>::is_integer, T>::type
+CheckedAdd(T x, T y, RangeConstraint* validity) {
+  // 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;
+  UnsignedDst ux = static_cast<UnsignedDst>(x);
+  UnsignedDst uy = static_cast<UnsignedDst>(y);
+  UnsignedDst uresult = ux + uy;
+  // 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((uresult ^ ux) & (uresult ^ uy))))
+      *validity = RANGE_VALID;
+    else  // Direction of wrap is inverse of result sign.
+      *validity = HasSignBit(uresult) ? RANGE_OVERFLOW : RANGE_UNDERFLOW;
+
+  } else {  // Unsigned is either valid or overflow.
+    *validity = BinaryComplement(x) >= y ? RANGE_VALID : RANGE_OVERFLOW;
+  }
+  return static_cast<T>(uresult);
+}
+
+template <typename T>
+typename enable_if<std::numeric_limits<T>::is_integer, T>::type
+CheckedSub(T x, T y, RangeConstraint* validity) {
+  // 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;
+  UnsignedDst ux = static_cast<UnsignedDst>(x);
+  UnsignedDst uy = static_cast<UnsignedDst>(y);
+  UnsignedDst uresult = ux - uy;
+  // 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((uresult ^ ux) & (ux ^ uy))))
+      *validity = RANGE_VALID;
+    else  // Direction of wrap is inverse of result sign.
+      *validity = HasSignBit(uresult) ? RANGE_OVERFLOW : RANGE_UNDERFLOW;
+
+  } else {  // Unsigned is either valid or underflow.
+    *validity = x >= y ? RANGE_VALID : RANGE_UNDERFLOW;
+  }
+  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 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);
+}
+
+template <typename T>
+typename 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)) {
+    return RANGE_VALID;
+
+  } else if (x > 0) {
+    if (y > 0)
+      *validity =
+          x <= std::numeric_limits<T>::max() / y ? RANGE_VALID : RANGE_OVERFLOW;
+    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;
+  }
+
+  return x * y;
+}
+
+template <typename T>
+typename 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 x * y;
+}
+
+// Division just requires a check for an invalid negation on signed min/-1.
+template <typename T>
+T CheckedDiv(
+    T x,
+    T y,
+    RangeConstraint* validity,
+    typename enable_if<std::numeric_limits<T>::is_integer, int>::type = 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();
+  }
+
+  *validity = RANGE_VALID;
+  return x / y;
+}
+
+template <typename T>
+typename 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 x % y;
+}
+
+template <typename T>
+typename enable_if<
+    std::numeric_limits<T>::is_integer && !std::numeric_limits<T>::is_signed,
+    T>::type
+CheckedMod(T x, T y, RangeConstraint* validity) {
+  *validity = RANGE_VALID;
+  return x % y;
+}
+
+template <typename T>
+typename 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 -value;
+}
+
+template <typename T>
+typename 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>(
+      -static_cast<typename SignedIntegerForSize<T>::type>(value));
+}
+
+template <typename T>
+typename 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 std::abs(value);
+}
+
+template <typename T>
+typename enable_if<
+    std::numeric_limits<T>::is_integer && !std::numeric_limits<T>::is_signed,
+    T>::type
+CheckedAbs(T value, RangeConstraint* validity) {
+  // Absolute value of a positive is just its identiy.
+  *validity = RANGE_VALID;
+  return value;
+}
+
+// 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 enable_if<std::numeric_limits<T>::is_iec559, T>::type \
+  Checked##NAME(T, T, RangeConstraint*) {                        \
+    NOTREACHED();                                                \
+    return 0;                                                    \
+  }
+
+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)
+
+#undef BASE_FLOAT_ARITHMETIC_STUBS
+
+template <typename T>
+typename enable_if<std::numeric_limits<T>::is_iec559, T>::type CheckedNeg(
+    T value,
+    RangeConstraint*) {
+  return -value;
+}
+
+template <typename T>
+typename enable_if<std::numeric_limits<T>::is_iec559, T>::type CheckedAbs(
+    T value,
+    RangeConstraint*) {
+  return std::abs(value);
+}
+
+// Floats carry around their validity state with them, but integers do not. So,
+// we wrap the underlying value in a specialization in order to hide that detail
+// and expose an interface via accessors.
+enum NumericRepresentation {
+  NUMERIC_INTEGER,
+  NUMERIC_FLOATING,
+  NUMERIC_UNKNOWN
+};
+
+template <typename NumericType>
+struct GetNumericRepresentation {
+  static const NumericRepresentation value =
+      std::numeric_limits<NumericType>::is_integer
+          ? NUMERIC_INTEGER
+          : (std::numeric_limits<NumericType>::is_iec559 ? NUMERIC_FLOATING
+                                                         : NUMERIC_UNKNOWN);
+};
+
+template <typename T, NumericRepresentation type =
+                          GetNumericRepresentation<T>::value>
+class CheckedNumericState {};
+
+// Integrals require quite a bit of additional housekeeping to manage state.
+template <typename T>
+class CheckedNumericState<T, NUMERIC_INTEGER> {
+ private:
+  T value_;
+  RangeConstraint validity_;
+
+ public:
+  template <typename Src, NumericRepresentation type>
+  friend class CheckedNumericState;
+
+  CheckedNumericState() : value_(0), validity_(RANGE_VALID) {}
+
+  template <typename Src>
+  CheckedNumericState(Src value, RangeConstraint validity)
+      : value_(value),
+        validity_(GetRangeConstraint(validity |
+                                     DstRangeRelationToSrcRange<T>(value))) {
+    COMPILE_ASSERT(std::numeric_limits<Src>::is_specialized,
+                   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()))) {}
+
+  template <typename Src>
+  explicit CheckedNumericState(
+      Src value,
+      typename 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_; }
+};
+
+// Floating points maintain their own validity, but need translation wrappers.
+template <typename T>
+class CheckedNumericState<T, NUMERIC_FLOATING> {
+ private:
+  T value_;
+
+ public:
+  template <typename Src, NumericRepresentation type>
+  friend class CheckedNumericState;
+
+  CheckedNumericState() : value_(0.0) {}
+
+  template <typename Src>
+  CheckedNumericState(
+      Src value,
+      RangeConstraint validity,
+      typename 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();
+    }
+  }
+
+  template <typename Src>
+  explicit CheckedNumericState(
+      Src value,
+      typename enable_if<std::numeric_limits<Src>::is_specialized, int>::type =
+          0)
+      : value_(static_cast<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());
+  }
+  T value() const { return value_; }
+};
+
+// For integers less than 128-bit and floats 32-bit or larger, we can distil
+// C/C++ arithmetic promotions down to two simple rules:
+// 1. The type with the larger maximum exponent always takes precedence.
+// 2. The resulting type must be promoted to at least an int.
+// The following template specializations implement that promotion logic.
+enum ArithmeticPromotionCategory {
+  LEFT_PROMOTION,
+  RIGHT_PROMOTION,
+  DEFAULT_PROMOTION
+};
+
+template <typename Lhs,
+          typename Rhs = Lhs,
+          ArithmeticPromotionCategory Promotion =
+              (MaxExponent<Lhs>::value > MaxExponent<Rhs>::value)
+                  ? (MaxExponent<Lhs>::value > MaxExponent<int>::value
+                         ? LEFT_PROMOTION
+                         : DEFAULT_PROMOTION)
+                  : (MaxExponent<Rhs>::value > MaxExponent<int>::value
+                         ? RIGHT_PROMOTION
+                         : DEFAULT_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;
+};
+
+template <typename Lhs, typename Rhs>
+struct ArithmeticPromotion<Lhs, Rhs, DEFAULT_PROMOTION> {
+  typedef int type;
+};
+
+// 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));
+};
+
+}  // namespace internal
+}  // namespace base
+
+#endif  // SAFE_MATH_IMPL_H_