Add support for safe math operations in base/numerics

base/numerics/safe_math_impl.h

+// Copyright 2014 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#ifndef SAFE_MATH_IMPL_H_
+#define SAFE_MATH_IMPL_H_
+
+#include <stdint.h>
+
+#include <cmath>
+#include <cstdlib>
+#include <limits>
+
+#include "base/compiler_specific.h"
+#include "base/macros.h"
+#include "base/template_util.h"
+
+namespace base {
+namespace internal {
+
+using std::numeric_limits;
+
+// 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 {};

[awong, 2014/02/11 20:14:12]

Here and elsewhere, don't provide a definition for the template declaration if
it doesn't have semantics that make sense.

[jschuh, 2014/02/21 19:22:28]

Done.

+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;
+};
+// The ArithmeticPromotion template below will need to be updated (or more

[awong, 2014/02/11 20:14:12]

This looks like a TODO. Make it into a TODO?

Also add a newline before the comment so it's visually separated from the
specialization blob.

[jschuh, 2014/02/21 19:22:28]

We don't support 128-bit math today, so it's a warning. However, I will make it
explicitly such.

+// likely replaced with decltype) if we add support for 128-bit integers).
+
+template <typename Integer>
+struct UnsignedIntegerForSize {
+  typedef typename enable_if<

[awong, 2014/02/11 20:14:12]

Why do we need an enable_if here? Normally you use enable_ifs to remove
overloads that would become ambiguous when a template is instantiated with a
certain combinations of types. There doesn't seem to be any overloads here.

What compile error are you protecting again (or trying to ensure)?

[jschuh, 2014/02/21 19:22:28]

I'm preventing this:

  UnsignedIntegerForSize<float>::type

That would give you an uint32_t, which is very wrong.

+      numeric_limits<Integer>::is_integer,
+      typename IntegerForSizeAndSign<sizeof(Integer), false>::type>::type type;
+};
+
+template <typename Integer>
+struct SignedIntegerForSize {
+  typedef typename enable_if<
+      numeric_limits<Integer>::is_integer,
+      typename IntegerForSizeAndSign<sizeof(Integer), true>::type>::type type;
+};
+
+template <typename Integer>
+struct TwiceWiderInteger {
+  typedef typename enable_if<
+      numeric_limits<Integer>::is_integer,
+      typename IntegerForSizeAndSign<
+          sizeof(Integer) * 2,
+          numeric_limits<Integer>::is_signed>::type>::type type;
+};
+
+template <typename Integer>
+struct PositionOfSignBit {
+  static const typename enable_if<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 implementations.
+
+template <typename T>
+typename enable_if<numeric_limits<T>::is_integer, T>::type
+CheckedAdd(T x, T y, RangeCheckId* 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 (numeric_limits<T>::is_signed) {
+    if (HasSignBit(BinaryComplement((uresult ^ ux) & (uresult ^ uy))))
+      *validity = TYPE_VALID;
+    else  // Direction of wrap is inverse of result sign.
+      *validity = HasSignBit(uresult) ? TYPE_OVERFLOW : TYPE_UNDERFLOW;
+
+  } else {  // Unsigned is either valid or overflow.
+    *validity = BinaryComplement(x) >= y ? TYPE_VALID : TYPE_OVERFLOW;
+  }
+  return static_cast<T>(uresult);
+}
+
+template <typename T>
+typename enable_if<numeric_limits<T>::is_integer, T>::type
+CheckedSub(T x, T y, RangeCheckId* 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 (numeric_limits<T>::is_signed) {
+    if (HasSignBit(BinaryComplement((uresult ^ ux) & (ux ^ uy))))
+      *validity = TYPE_VALID;
+    else  // Direction of wrap is inverse of result sign.
+      *validity = HasSignBit(uresult) ? TYPE_OVERFLOW : TYPE_UNDERFLOW;
+
+  } else {  // Unsigned is either valid or underflow.
+    *validity = x >= y ? TYPE_VALID : TYPE_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<
+    numeric_limits<T>::is_integer && sizeof(T) * 2 <= sizeof(uintmax_t),
+    T>::type
+CheckedMul(T x, T y, RangeCheckId* validity) {
+  typedef typename TwiceWiderInteger<T>::type IntermediateType;
+  IntermediateType tmp =
+      static_cast<IntermediateType>(x) * static_cast<IntermediateType>(y);
+  *validity = RangeCheck<T>(tmp);
+  return static_cast<T>(tmp);
+}
+
+template <typename T>
+typename enable_if<numeric_limits<T>::is_integer&& numeric_limits<

[awong, 2014/02/11 20:14:12]

Yes...it's looking like you're using enable_if to force the template to not be
instantiable if the type is incorrect.

This seems better suited to a COMPILE_ASSERT().

[jschuh, 2014/02/21 19:22:28]

This is breaking out the specializations. Based on our discussion, I added a
TODO and will fix this when I coalesce the math primitives into
CheckedNumericState (which I've determined I need to do in order to easily
support integer saturation semantics).

+                       T>::is_signed&&(sizeof(T) * 2 > sizeof(uintmax_t)),
+                   T>::type
+CheckedMul(T x, T y, RangeCheckId* validity) {
+  // if either side is zero then the result will be zero.
+  if (!(x || y)) {
+    return TYPE_VALID;
+
+  } else if (x > 0) {
+    if (y > 0)
+      *validity =
+          x <= numeric_limits<T>::max() / y ? TYPE_VALID : TYPE_OVERFLOW;
+    else
+      *validity =
+          y >= numeric_limits<T>::min() / x ? TYPE_VALID : TYPE_UNDERFLOW;
+
+  } else {
+    if (y > 0)
+      *validity =
+          x >= numeric_limits<T>::min() / y ? TYPE_VALID : TYPE_UNDERFLOW;
+    else
+      *validity =
+          y >= numeric_limits<T>::max() / x ? TYPE_VALID : TYPE_OVERFLOW;
+  }
+
+  return x * y;
+}
+
+template <typename T>
+typename enable_if<numeric_limits<T>::is_integer &&
+                       !numeric_limits<T>::is_signed &&
+                       (sizeof(T) * 2 > sizeof(uintmax_t)),
+                   T>::type
+CheckedMul(T x, T y, RangeCheckId* validity) {
+  *validity = (y == 0 || x <= numeric_limits<T>::max() / y) ? TYPE_VALID
+                                                            : TYPE_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,
+             RangeCheckId* validity,
+             typename enable_if<numeric_limits<T>::is_integer, int>::type = 0) {
+  if (numeric_limits<T>::is_signed && x == numeric_limits<T>::min() &&
+      y == static_cast<T>(-1)) {
+    *validity = TYPE_OVERFLOW;
+    return numeric_limits<T>::min();
+  }
+
+  *validity = TYPE_VALID;
+  return x / y;
+}
+
+template <typename T>
+typename enable_if<numeric_limits<T>::is_integer&& numeric_limits<T>::is_signed,
+                   T>::type
+CheckedMod(T x, T y, RangeCheckId* validity) {
+  *validity = y > 0 ? TYPE_VALID : TYPE_INVALID;
+  return x % y;
+}
+
+template <typename T>
+typename enable_if<
+    numeric_limits<T>::is_integer && !numeric_limits<T>::is_signed,
+    T>::type
+CheckedMod(T x, T y, RangeCheckId* validity) {
+  *validity = TYPE_VALID;
+  return x % y;
+}
+
+template <typename T>
+typename enable_if<numeric_limits<T>::is_integer&& numeric_limits<T>::is_signed,
+                   T>::type
+CheckedNeg(T value, RangeCheckId* validity) {
+  *validity = value != numeric_limits<T>::min() ? TYPE_VALID : TYPE_OVERFLOW;
+  // The negation of signed min is min, so catch that one.
+  return -value;
+}
+
+template <typename T>
+typename enable_if<
+    numeric_limits<T>::is_integer && !numeric_limits<T>::is_signed,
+    T>::type
+CheckedNeg(T value, RangeCheckId* validity) {
+  // The only legal unsigned negation is zero.
+  *validity = value ? TYPE_UNDERFLOW : TYPE_VALID;
+  return static_cast<T>(
+      -static_cast<typename SignedIntegerForSize<T>::type>(value));
+}
+
+template <typename T>
+typename enable_if<numeric_limits<T>::is_integer&& numeric_limits<T>::is_signed,
+                   T>::type
+CheckedAbs(T value, RangeCheckId* validity) {
+  *validity = value != numeric_limits<T>::min() ? TYPE_VALID : TYPE_OVERFLOW;
+  return std::abs(value);
+}
+
+template <typename T>
+typename enable_if<
+    numeric_limits<T>::is_integer && !numeric_limits<T>::is_signed,
+    T>::type
+CheckedAbs(T value, RangeCheckId* validity) {
+  // Absolute value of a positive is just its identiy.
+  *validity = TYPE_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<numeric_limits<T>::is_iec559, T>::type Checked##NAME( \
+      T, T, RangeCheckId*) {                                               \
+    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<numeric_limits<T>::is_iec559, T>::type CheckedNeg(
+    T value,
+    RangeCheckId*) {
+  return -value;
+}
+
+template <typename T>
+typename enable_if<numeric_limits<T>::is_iec559, T>::type CheckedAbs(
+    T value,
+    RangeCheckId*) {
+  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 NumericTypeId { NUMERIC_INTEGER, NUMERIC_FLOATING, NUMERIC_UNKNOWN };
+
+template <typename NumericType>
+struct GetNumericTypeId {
+  static const NumericTypeId value =
+      numeric_limits<NumericType>::is_integer
+          ? NUMERIC_INTEGER
+          : (numeric_limits<NumericType>::is_iec559 ? NUMERIC_FLOATING
+                                                    : NUMERIC_UNKNOWN);
+};
+
+template <typename T, NumericTypeId type = GetNumericTypeId<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_;
+  RangeCheckId validity_;
+
+ public:
+  template <typename Src, NumericTypeId type>
+  friend class CheckedNumericState;
+
+  CheckedNumericState() : value_(0), validity_(TYPE_VALID) {}
+
+  template <typename Src>
+  CheckedNumericState(Src value, RangeCheckId validity)
+      : value_(value),
+        validity_(static_cast<RangeCheckId>(validity | RangeCheck<T>(value))) {
+    COMPILE_ASSERT(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_(static_cast<RangeCheckId>(rhs.validity() |
+                                            RangeCheck<T>(rhs.value()))) {}
+
+  template <typename Src>
+  explicit CheckedNumericState(
+      Src value,
+      typename enable_if<numeric_limits<Src>::is_specialized, int>::type = 0)
+      : value_(static_cast<T>(value)), validity_(RangeCheck<T>(value)) {}
+
+  RangeCheckId 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, NumericTypeId type>
+  friend class CheckedNumericState;
+
+  CheckedNumericState() : value_(0.0) {}
+
+  template <typename Src>
+  CheckedNumericState(
+      Src value,
+      RangeCheckId validity,
+      typename enable_if<numeric_limits<Src>::is_integer, int>::type = 0) {
+    switch (RangeCheck<T>(value)) {
+      case TYPE_VALID:
+        value_ = static_cast<T>(value);
+        break;
+
+      case TYPE_UNDERFLOW:
+        value_ = -numeric_limits<T>::infinity();
+        break;
+
+      case TYPE_OVERFLOW:
+        value_ = numeric_limits<T>::infinity();
+        break;
+
+      case TYPE_INVALID:
+        value_ = numeric_limits<T>::quiet_NaN();
+        break;
+
+      default:
+        NOTREACHED();
+    }
+  }
+
+  template <typename Src>
+  explicit CheckedNumericState(
+      Src value,
+      typename enable_if<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())) {}
+
+  RangeCheckId validity() const {
+    return BASE_NUMERIC_RANGE_CHECK_RESULT(value_ <= numeric_limits<T>::max(),
+                                           value_ >= -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 ArithmeticPromotionId {
+  LEFT_PROMOTION,
+  RIGHT_PROMOTION,
+  DEFAULT_PROMOTION
+};
+
+template <typename Lhs,
+          typename Rhs = Lhs,
+          ArithmeticPromotionId 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 = !numeric_limits<T>::is_iec559 &&
+                            StaticRangeCheck<T, Lhs>::value == CONTAINS_RANGE &&
+                            sizeof(T) >= (2 * sizeof(Lhs)) &&
+                            StaticRangeCheck<T, Rhs>::value != CONTAINS_RANGE &&
+                            sizeof(T) >= (2 * sizeof(Rhs));
+};
+
+}  // namespace internal
+}  // namespace base
+
+#endif  // SAFE_MATH_IMPL_H_