checked_math_impl.h

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// Copyright 2017 The Chromium Authors
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
 
// Slightly adapted for inclusion in V8.
// Copyright 2025 the V8 project authors. All rights reserved.
 
#ifndef V8_BASE_NUMERICS_CHECKED_MATH_IMPL_H_
#define V8_BASE_NUMERICS_CHECKED_MATH_IMPL_H_
 
// IWYU pragma: private, include "src/base/numerics/checked_math.h"
 
#include <stdint.h>
 
#include <cmath>
#include <concepts>
#include <limits>
#include <type_traits>
 
#include "src/base/numerics/safe_conversions.h"
#include "src/base/numerics/safe_math_shared_impl.h"  // IWYU pragma: export
 
namespace v8::base {
namespace internal {
 
template <typename T>
constexpr bool CheckedAddImpl(T x, T y, T* result) {
  static_assert(std::integral<T>, "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.
  using UnsignedDst = typename std::make_unsigned<T>::type;
  using SignedDst = typename std::make_signed<T>::type;
  const UnsignedDst ux = static_cast<UnsignedDst>(x);
  const UnsignedDst uy = static_cast<UnsignedDst>(y);
  const UnsignedDst uresult = static_cast<UnsignedDst>(ux + uy);
  // Addition is valid if the sign of (x + y) is equal to either that of x or
  // that of y.
  if (std::is_signed_v<T>
          ? static_cast<SignedDst>((uresult ^ ux) & (uresult ^ uy)) < 0
          : uresult < uy) {  // Unsigned is either valid or underflow.
    return false;
  }
  *result = static_cast<T>(uresult);
  return true;
}
 
template <typename T, typename U>
struct CheckedAddOp {};
 
template <typename T, typename U>
  requires(std::integral<T> && std::integral<U>)
struct CheckedAddOp<T, U> {
  using result_type = MaxExponentPromotion<T, U>;
  template <typename V>
  static constexpr bool Do(T x, U y, V* result) {
    if constexpr (CheckedAddFastOp<T, U>::is_supported) {
      return CheckedAddFastOp<T, U>::Do(x, y, result);
    }
 
    // Double the underlying type up to a full machine word.
    using FastPromotion = FastIntegerArithmeticPromotion<T, U>;
    using Promotion =
        std::conditional_t<(kIntegerBitsPlusSign<FastPromotion> >
                            kIntegerBitsPlusSign<intptr_t>),
                           BigEnoughPromotion<T, U>, FastPromotion>;
    // 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.
    if (!IsValueInRangeForNumericType<Promotion>(x) ||
        !IsValueInRangeForNumericType<Promotion>(y)) [[unlikely]] {
      return false;
    }
 
    Promotion presult = {};
    bool is_valid = true;
    if constexpr (kIsIntegerArithmeticSafe<Promotion, T, U>) {
      presult = static_cast<Promotion>(x) + static_cast<Promotion>(y);
    } else {
      is_valid = CheckedAddImpl(static_cast<Promotion>(x),
                                static_cast<Promotion>(y), &presult);
    }
    if (!is_valid || !IsValueInRangeForNumericType<V>(presult)) {
      return false;
    }
    *result = static_cast<V>(presult);
    return true;
  }
};
 
template <typename T>
constexpr bool CheckedSubImpl(T x, T y, T* result) {
  static_assert(std::integral<T>, "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.
  using UnsignedDst = typename std::make_unsigned<T>::type;
  using SignedDst = typename std::make_signed<T>::type;
  const UnsignedDst ux = static_cast<UnsignedDst>(x);
  const UnsignedDst uy = static_cast<UnsignedDst>(y);
  const UnsignedDst uresult = static_cast<UnsignedDst>(ux - uy);
  // Subtraction is valid if either x and y have same sign, or (x-y) and x have
  // the same sign.
  if (std::is_signed_v<T>
          ? static_cast<SignedDst>((uresult ^ ux) & (ux ^ uy)) < 0
          : x < y) {
    return false;
  }
  *result = static_cast<T>(uresult);
  return true;
}
 
template <typename T, typename U>
struct CheckedSubOp {};
 
template <typename T, typename U>
  requires(std::integral<T> && std::integral<U>)
struct CheckedSubOp<T, U> {
  using result_type = MaxExponentPromotion<T, U>;
  template <typename V>
  static constexpr bool Do(T x, U y, V* result) {
    if constexpr (CheckedSubFastOp<T, U>::is_supported) {
      return CheckedSubFastOp<T, U>::Do(x, y, result);
    }
 
    // Double the underlying type up to a full machine word.
    using FastPromotion = FastIntegerArithmeticPromotion<T, U>;
    using Promotion =
        std::conditional_t<(kIntegerBitsPlusSign<FastPromotion> >
                            kIntegerBitsPlusSign<intptr_t>),
                           BigEnoughPromotion<T, U>, FastPromotion>;
    // 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.
    if (!IsValueInRangeForNumericType<Promotion>(x) ||
        !IsValueInRangeForNumericType<Promotion>(y)) [[unlikely]] {
      return false;
    }
 
    Promotion presult = {};
    bool is_valid = true;
    if constexpr (kIsIntegerArithmeticSafe<Promotion, T, U>) {
      presult = static_cast<Promotion>(x) - static_cast<Promotion>(y);
    } else {
      is_valid = CheckedSubImpl(static_cast<Promotion>(x),
                                static_cast<Promotion>(y), &presult);
    }
    if (!is_valid || !IsValueInRangeForNumericType<V>(presult)) {
      return false;
    }
    *result = static_cast<V>(presult);
    return true;
  }
};
 
template <typename T>
constexpr bool CheckedMulImpl(T x, T y, T* result) {
  static_assert(std::integral<T>, "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);
  const UnsignedDst uresult = static_cast<UnsignedDst>(ux * uy);
  const bool is_negative =
      std::is_signed_v<T> && static_cast<SignedDst>(x ^ y) < 0;
  // 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.
  if (uy > UnsignedDst(!std::is_signed_v<T> || is_negative) &&
      ux > (std::numeric_limits<T>::max() + UnsignedDst(is_negative)) / uy) {
    return false;
  }
  *result = static_cast<T>(is_negative ? 0 - uresult : uresult);
  return true;
}
 
template <typename T, typename U>
struct CheckedMulOp {};
 
template <typename T, typename U>
  requires(std::integral<T> && std::integral<U>)
struct CheckedMulOp<T, U> {
  using result_type = MaxExponentPromotion<T, U>;
  template <typename V>
  static constexpr bool Do(T x, U y, V* result) {
    if constexpr (CheckedMulFastOp<T, U>::is_supported) {
      return CheckedMulFastOp<T, U>::Do(x, y, result);
    }
 
    using Promotion = FastIntegerArithmeticPromotion<T, U>;
    // Verify the destination type can hold the result (always true for 0).
    if ((!IsValueInRangeForNumericType<Promotion>(x) ||
         !IsValueInRangeForNumericType<Promotion>(y)) &&
        x && y) [[unlikely]] {
      return false;
    }
 
    Promotion presult = {};
    bool is_valid = true;
    if constexpr (CheckedMulFastOp<Promotion, Promotion>::is_supported) {
      // The fast op may be available with the promoted type.
      // The casts here are safe because of the "value in range" conditional
      // above.
      is_valid = CheckedMulFastOp<Promotion, Promotion>::Do(
          static_cast<Promotion>(x), static_cast<Promotion>(y), &presult);
    } else if constexpr (kIsIntegerArithmeticSafe<Promotion, T, U>) {
      presult = static_cast<Promotion>(x) * static_cast<Promotion>(y);
    } else {
      is_valid = CheckedMulImpl(static_cast<Promotion>(x),
                                static_cast<Promotion>(y), &presult);
    }
    if (!is_valid || !IsValueInRangeForNumericType<V>(presult)) {
      return false;
    }
    *result = static_cast<V>(presult);
    return true;
  }
};
 
// Division just requires a check for a zero denominator or an invalid negation
// on signed min/-1.
template <typename T, typename U>
struct CheckedDivOp {};
 
template <typename T, typename U>
  requires(std::integral<T> && std::integral<U>)
struct CheckedDivOp<T, U> {
  using result_type = MaxExponentPromotion<T, U>;
  template <typename V>
  static constexpr bool Do(T x, U y, V* result) {
    if (!y) [[unlikely]] {
      return false;
    }
 
    // The overflow check can be compiled away if we don't have the exact
    // combination of types needed to trigger this case.
    using Promotion = BigEnoughPromotion<T, U>;
    if (std::is_signed_v<T> && std::is_signed_v<U> &&
        kIsTypeInRangeForNumericType<T, Promotion> &&
        static_cast<Promotion>(x) == std::numeric_limits<Promotion>::lowest() &&
        y == static_cast<U>(-1)) [[unlikely]] {
      return false;
    }
 
    // This branch always compiles away if the above branch wasn't removed.
    if ((!IsValueInRangeForNumericType<Promotion>(x) ||
         !IsValueInRangeForNumericType<Promotion>(y)) &&
        x) [[unlikely]] {
      return false;
    }
 
    const Promotion presult = Promotion(x) / Promotion(y);
    if (!IsValueInRangeForNumericType<V>(presult)) {
      return false;
    }
    *result = static_cast<V>(presult);
    return true;
  }
};
 
template <typename T, typename U>
struct CheckedModOp {};
 
template <typename T, typename U>
  requires(std::integral<T> && std::integral<U>)
struct CheckedModOp<T, U> {
  using result_type = MaxExponentPromotion<T, U>;
  template <typename V>
  static constexpr bool Do(T x, U y, V* result) {
    if (!y) [[unlikely]] {
      return false;
    }
 
    using Promotion = BigEnoughPromotion<T, U>;
    if (std::is_signed_v<T> && std::is_signed_v<U> &&
        kIsTypeInRangeForNumericType<T, Promotion> &&
        static_cast<Promotion>(x) == std::numeric_limits<Promotion>::lowest() &&
        y == static_cast<U>(-1)) [[unlikely]] {
      *result = 0;
      return true;
    }
 
    const Promotion presult =
        static_cast<Promotion>(x) % static_cast<Promotion>(y);
    if (!IsValueInRangeForNumericType<V>(presult)) {
      return false;
    }
    *result = static_cast<Promotion>(presult);
    return true;
  }
};
 
template <typename T, typename U>
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>
  requires(std::integral<T> && std::integral<U>)
struct CheckedLshOp<T, U> {
  using result_type = T;
  template <typename V>
  static constexpr bool Do(T x, U shift, V* result) {
    // Disallow negative numbers and verify the shift is in bounds.
    if (!IsValueNegative(x) &&
        as_unsigned(shift) < as_unsigned(std::numeric_limits<T>::digits))
        [[likely]] {
      // Shift as unsigned to avoid undefined behavior.
      *result = static_cast<V>(as_unsigned(x) << shift);
      // If the shift can be reversed, we know it was valid.
      return *result >> shift == x;
    }
 
    // Handle the legal corner-case of a full-width signed shift of zero.
    if (!std::is_signed_v<T> || x ||
        as_unsigned(shift) != as_unsigned(std::numeric_limits<T>::digits)) {
      return false;
    }
    *result = 0;
    return true;
  }
};
 
template <typename T, typename U>
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>
  requires(std::integral<T> && std::integral<U>)
struct CheckedRshOp<T, U> {
  using result_type = T;
  template <typename V>
  static constexpr bool Do(T x, U shift, V* result) {
    // Use sign conversion to push negative values out of range.
    if (as_unsigned(shift) >= kIntegerBitsPlusSign<T>) [[unlikely]] {
      return false;
    }
 
    const T tmp = x >> shift;
    if (!IsValueInRangeForNumericType<V>(tmp)) {
      return false;
    }
    *result = static_cast<V>(tmp);
    return true;
  }
};
 
template <typename T, typename U>
struct CheckedAndOp {};
 
// For simplicity we support only unsigned integer results.
template <typename T, typename U>
  requires(std::integral<T> && std::integral<U>)
struct CheckedAndOp<T, U> {
  using result_type = std::make_unsigned_t<MaxExponentPromotion<T, U>>;
  template <typename V>
  static constexpr bool Do(T x, U y, V* result) {
    const result_type tmp =
        static_cast<result_type>(x) & static_cast<result_type>(y);
    if (!IsValueInRangeForNumericType<V>(tmp)) {
      return false;
    }
    *result = static_cast<V>(tmp);
    return true;
  }
};
 
template <typename T, typename U>
struct CheckedOrOp {};
 
// For simplicity we support only unsigned integers.
template <typename T, typename U>
  requires(std::integral<T> && std::integral<U>)
struct CheckedOrOp<T, U> {
  using result_type = std::make_unsigned_t<MaxExponentPromotion<T, U>>;
  template <typename V>
  static constexpr bool Do(T x, U y, V* result) {
    const result_type tmp =
        static_cast<result_type>(x) | static_cast<result_type>(y);
    if (!IsValueInRangeForNumericType<V>(tmp)) {
      return false;
    }
    *result = static_cast<V>(tmp);
    return true;
  }
};
 
template <typename T, typename U>
struct CheckedXorOp {};
 
// For simplicity we support only unsigned integers.
template <typename T, typename U>
  requires(std::integral<T> && std::integral<U>)
struct CheckedXorOp<T, U> {
  using result_type = std::make_unsigned_t<MaxExponentPromotion<T, U>>;
  template <typename V>
  static constexpr bool Do(T x, U y, V* result) {
    const result_type tmp =
        static_cast<result_type>(x) ^ static_cast<result_type>(y);
    if (!IsValueInRangeForNumericType<V>(tmp)) {
      return false;
    }
    *result = static_cast<V>(tmp);
    return true;
  }
};
 
// 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>
struct CheckedMaxOp {};
 
template <typename T, typename U>
  requires(std::is_arithmetic_v<T> && std::is_arithmetic_v<U>)
struct CheckedMaxOp<T, U> {
  using result_type = MaxExponentPromotion<T, U>;
  template <typename V>
  static constexpr bool Do(T x, U y, V* result) {
    const result_type tmp = IsGreater<T, U>::Test(x, y)
                                ? static_cast<result_type>(x)
                                : static_cast<result_type>(y);
    if (!IsValueInRangeForNumericType<V>(tmp)) {
      return false;
    }
    *result = static_cast<V>(tmp);
    return true;
  }
};
 
// 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>
struct CheckedMinOp {};
 
template <typename T, typename U>
  requires(std::is_arithmetic_v<T> && std::is_arithmetic_v<U>)
struct CheckedMinOp<T, U> {
  using result_type = LowestValuePromotion<T, U>;
  template <typename V>
  static constexpr bool Do(T x, U y, V* result) {
    const result_type tmp = IsLess<T, U>::Test(x, y)
                                ? static_cast<result_type>(x)
                                : static_cast<result_type>(y);
    if (!IsValueInRangeForNumericType<V>(tmp)) {
      return false;
    }
    *result = static_cast<V>(tmp);
    return true;
  }
};
 
// 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>                                \
    requires(std::floating_point<T> || std::floating_point<U>)     \
  struct Checked##NAME##Op<T, U> {                                 \
    using result_type = MaxExponentPromotion<T, U>;                \
    template <typename V>                                          \
    static constexpr bool Do(T x, U y, V* result) {                \
      const result_type presult = x OP y;                          \
      if (!IsValueInRangeForNumericType<V>(presult)) return false; \
      *result = static_cast<V>(presult);                           \
      return true;                                                 \
    }                                                              \
  };
 
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
 
// 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::integral<NumericType>
          ? NUMERIC_INTEGER
          : (std::floating_point<NumericType> ? 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> {
 public:
  template <typename Src = int>
  constexpr explicit CheckedNumericState(Src value = 0, bool is_valid = true)
      : is_valid_(is_valid && IsValueInRangeForNumericType<T>(value)),
        value_(WellDefinedConversionOrZero(value, is_valid_)) {
    static_assert(std::is_arithmetic_v<Src>, "Argument must be numeric.");
  }
 
  template <typename Src>
  constexpr CheckedNumericState(const CheckedNumericState<Src>& rhs)
      : CheckedNumericState(rhs.value(), rhs.is_valid()) {}
 
  constexpr bool is_valid() const { return is_valid_; }
 
  constexpr T value() const { return value_; }
 
 private:
  // Ensures that a type conversion does not trigger undefined behavior.
  template <typename Src>
  static constexpr T WellDefinedConversionOrZero(Src value, bool is_valid) {
    return (std::integral<UnderlyingType<Src>> || is_valid)
               ? static_cast<T>(value)
               : 0;
  }
 
  // is_valid_ precedes value_ because member initializers in the constructors
  // are evaluated in field order, and is_valid_ must be read when initializing
  // value_.
  bool is_valid_;
  T value_;
};
 
// Floating points maintain their own validity, but need translation wrappers.
template <typename T>
class CheckedNumericState<T, NUMERIC_FLOATING> {
 public:
  template <typename Src = double>
  constexpr explicit CheckedNumericState(Src value = 0.0, bool is_valid = true)
      : value_(WellDefinedConversionOrNaN(
            value, is_valid && IsValueInRangeForNumericType<T>(value))) {}
 
  template <typename Src>
  constexpr CheckedNumericState(const CheckedNumericState<Src>& rhs)
      : CheckedNumericState(rhs.value(), rhs.is_valid()) {}
 
  constexpr bool is_valid() const {
    // Written this way because std::isfinite is not constexpr before C++23.
    // TODO(C++23): Use `std::isfinite()` unconditionally.
    return std::is_constant_evaluated()
               ? value_ <= std::numeric_limits<T>::max() &&
                     value_ >= std::numeric_limits<T>::lowest()
               : std::isfinite(value_);
  }
 
  constexpr T value() const { return value_; }
 
 private:
  // Ensures that a type conversion does not trigger undefined behavior.
  template <typename Src>
  static constexpr T WellDefinedConversionOrNaN(Src value, bool is_valid) {
    return (kStaticDstRangeRelationToSrcRange<T, UnderlyingType<Src>> ==
                NumericRangeRepresentation::kContained ||
            is_valid)
               ? static_cast<T>(value)
               : std::numeric_limits<T>::quiet_NaN();
  }
 
  T value_;
};
 
}  // namespace internal
}  // namespace v8::base
 
#endif  // V8_BASE_NUMERICS_CHECKED_MATH_IMPL_H_