blob: e083389ebf38e3bee53eb1705af05b988da4e315 [file] [log] [blame]
 // Copyright 2017 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_NUMERICS_CHECKED_MATH_IMPL_H_ #define BASE_NUMERICS_CHECKED_MATH_IMPL_H_ #include #include #include #include #include #include #include #include "base/numerics/safe_conversions.h" #include "base/numerics/safe_math_shared_impl.h" namespace base { namespace internal { template constexpr bool CheckedAddImpl(T x, T y, T* result) { static_assert(std::is_integral::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. using UnsignedDst = typename std::make_unsigned::type; using SignedDst = typename std::make_signed::type; UnsignedDst ux = static_cast(x); UnsignedDst uy = static_cast(y); UnsignedDst uresult = static_cast(ux + uy); *result = static_cast(uresult); // Addition is valid if the sign of (x + y) is equal to either that of x or // that of y. return (std::is_signed::value) ? static_cast((uresult ^ ux) & (uresult ^ uy)) >= 0 : uresult >= uy; // Unsigned is either valid or underflow. } template struct CheckedAddOp {}; template struct CheckedAddOp::value && std::is_integral::value>::type> { using result_type = typename MaxExponentPromotion::type; template static constexpr bool Do(T x, U y, V* result) { // TODO(jschuh) Make this "constexpr if" once we're C++17. if (CheckedAddFastOp::is_supported) return CheckedAddFastOp::Do(x, y, result); // Double the underlying type up to a full machine word. using FastPromotion = typename FastIntegerArithmeticPromotion::type; using Promotion = typename std::conditional<(IntegerBitsPlusSign::value > IntegerBitsPlusSign::value), typename BigEnoughPromotion::type, FastPromotion>::type; // 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 (BASE_NUMERICS_UNLIKELY(!IsValueInRangeForNumericType(x) || !IsValueInRangeForNumericType(y))) { return false; } Promotion presult = {}; bool is_valid = true; if (IsIntegerArithmeticSafe::value) { presult = static_cast(x) + static_cast(y); } else { is_valid = CheckedAddImpl(static_cast(x), static_cast(y), &presult); } *result = static_cast(presult); return is_valid && IsValueInRangeForNumericType(presult); } }; template constexpr bool CheckedSubImpl(T x, T y, T* result) { static_assert(std::is_integral::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. using UnsignedDst = typename std::make_unsigned::type; using SignedDst = typename std::make_signed::type; UnsignedDst ux = static_cast(x); UnsignedDst uy = static_cast(y); UnsignedDst uresult = static_cast(ux - uy); *result = static_cast(uresult); // Subtraction is valid if either x and y have same sign, or (x-y) and x have // the same sign. return (std::is_signed::value) ? static_cast((uresult ^ ux) & (ux ^ uy)) >= 0 : x >= y; } template struct CheckedSubOp {}; template struct CheckedSubOp::value && std::is_integral::value>::type> { using result_type = typename MaxExponentPromotion::type; template static constexpr bool Do(T x, U y, V* result) { // TODO(jschuh) Make this "constexpr if" once we're C++17. if (CheckedSubFastOp::is_supported) return CheckedSubFastOp::Do(x, y, result); // Double the underlying type up to a full machine word. using FastPromotion = typename FastIntegerArithmeticPromotion::type; using Promotion = typename std::conditional<(IntegerBitsPlusSign::value > IntegerBitsPlusSign::value), typename BigEnoughPromotion::type, FastPromotion>::type; // 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 (BASE_NUMERICS_UNLIKELY(!IsValueInRangeForNumericType(x) || !IsValueInRangeForNumericType(y))) { return false; } Promotion presult = {}; bool is_valid = true; if (IsIntegerArithmeticSafe::value) { presult = static_cast(x) - static_cast(y); } else { is_valid = CheckedSubImpl(static_cast(x), static_cast(y), &presult); } *result = static_cast(presult); return is_valid && IsValueInRangeForNumericType(presult); } }; template constexpr bool CheckedMulImpl(T x, T y, T* result) { static_assert(std::is_integral::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::type; using SignedDst = typename std::make_signed::type; const UnsignedDst ux = SafeUnsignedAbs(x); const UnsignedDst uy = SafeUnsignedAbs(y); UnsignedDst uresult = static_cast(ux * uy); const bool is_negative = std::is_signed::value && static_cast(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::value || is_negative) || ux <= (std::numeric_limits::max() + UnsignedDst(is_negative)) / uy; } template struct CheckedMulOp {}; template struct CheckedMulOp::value && std::is_integral::value>::type> { using result_type = typename MaxExponentPromotion::type; template static constexpr bool Do(T x, U y, V* result) { // TODO(jschuh) Make this "constexpr if" once we're C++17. if (CheckedMulFastOp::is_supported) return CheckedMulFastOp::Do(x, y, result); using Promotion = typename FastIntegerArithmeticPromotion::type; // Verify the destination type can hold the result (always true for 0). if (BASE_NUMERICS_UNLIKELY((!IsValueInRangeForNumericType(x) || !IsValueInRangeForNumericType(y)) && x && y)) { return false; } Promotion presult = {}; bool is_valid = true; if (CheckedMulFastOp::is_supported) { // The fast op may be available with the promoted type. is_valid = CheckedMulFastOp::Do(x, y, &presult); } else if (IsIntegerArithmeticSafe::value) { presult = static_cast(x) * static_cast(y); } else { is_valid = CheckedMulImpl(static_cast(x), static_cast(y), &presult); } *result = static_cast(presult); return is_valid && IsValueInRangeForNumericType(presult); } }; // Division just requires a check for a zero denominator or an invalid negation // on signed min/-1. template struct CheckedDivOp {}; template struct CheckedDivOp::value && std::is_integral::value>::type> { using result_type = typename MaxExponentPromotion::type; template static constexpr bool Do(T x, U y, V* result) { if (BASE_NUMERICS_UNLIKELY(!y)) 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 = typename BigEnoughPromotion::type; if (BASE_NUMERICS_UNLIKELY( (std::is_signed::value && std::is_signed::value && IsTypeInRangeForNumericType::value && static_cast(x) == std::numeric_limits::lowest() && y == static_cast(-1)))) { return false; } // This branch always compiles away if the above branch wasn't removed. if (BASE_NUMERICS_UNLIKELY((!IsValueInRangeForNumericType(x) || !IsValueInRangeForNumericType(y)) && x)) { return false; } Promotion presult = Promotion(x) / Promotion(y); *result = static_cast(presult); return IsValueInRangeForNumericType(presult); } }; template struct CheckedModOp {}; template struct CheckedModOp::value && std::is_integral::value>::type> { using result_type = typename MaxExponentPromotion::type; template static constexpr bool Do(T x, U y, V* result) { using Promotion = typename BigEnoughPromotion::type; if (BASE_NUMERICS_LIKELY(y)) { Promotion presult = static_cast(x) % static_cast(y); *result = static_cast(presult); return IsValueInRangeForNumericType(presult); } return false; } }; template 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 struct CheckedLshOp::value && std::is_integral::value>::type> { using result_type = T; template static constexpr bool Do(T x, U shift, V* result) { // Disallow negative numbers and verify the shift is in bounds. if (BASE_NUMERICS_LIKELY(!IsValueNegative(x) && as_unsigned(shift) < as_unsigned(std::numeric_limits::digits))) { // Shift as unsigned to avoid undefined behavior. *result = static_cast(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. return std::is_signed::value && !x && as_unsigned(shift) == as_unsigned(std::numeric_limits::digits); } }; template 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 struct CheckedRshOp::value && std::is_integral::value>::type> { using result_type = T; template static bool Do(T x, U shift, V* result) { // Use the type conversion push negative values out of range. if (BASE_NUMERICS_LIKELY(as_unsigned(shift) < IntegerBitsPlusSign::value)) { T tmp = x >> shift; *result = static_cast(tmp); return IsValueInRangeForNumericType(tmp); } return false; } }; template struct CheckedAndOp {}; // For simplicity we support only unsigned integer results. template struct CheckedAndOp::value && std::is_integral::value>::type> { using result_type = typename std::make_unsigned< typename MaxExponentPromotion::type>::type; template static constexpr bool Do(T x, U y, V* result) { result_type tmp = static_cast(x) & static_cast(y); *result = static_cast(tmp); return IsValueInRangeForNumericType(tmp); } }; template struct CheckedOrOp {}; // For simplicity we support only unsigned integers. template struct CheckedOrOp::value && std::is_integral::value>::type> { using result_type = typename std::make_unsigned< typename MaxExponentPromotion::type>::type; template static constexpr bool Do(T x, U y, V* result) { result_type tmp = static_cast(x) | static_cast(y); *result = static_cast(tmp); return IsValueInRangeForNumericType(tmp); } }; template struct CheckedXorOp {}; // For simplicity we support only unsigned integers. template struct CheckedXorOp::value && std::is_integral::value>::type> { using result_type = typename std::make_unsigned< typename MaxExponentPromotion::type>::type; template static constexpr bool Do(T x, U y, V* result) { result_type tmp = static_cast(x) ^ static_cast(y); *result = static_cast(tmp); return IsValueInRangeForNumericType(tmp); } }; // 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 struct CheckedMaxOp {}; template struct CheckedMaxOp< T, U, typename std::enable_if::value && std::is_arithmetic::value>::type> { using result_type = typename MaxExponentPromotion::type; template static constexpr bool Do(T x, U y, V* result) { result_type tmp = IsGreater::Test(x, y) ? static_cast(x) : static_cast(y); *result = static_cast(tmp); return IsValueInRangeForNumericType(tmp); } }; // 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 struct CheckedMinOp {}; template struct CheckedMinOp< T, U, typename std::enable_if::value && std::is_arithmetic::value>::type> { using result_type = typename LowestValuePromotion::type; template static constexpr bool Do(T x, U y, V* result) { result_type tmp = IsLess::Test(x, y) ? static_cast(x) : static_cast(y); *result = static_cast(tmp); return IsValueInRangeForNumericType(tmp); } }; // 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 \ struct Checked##NAME##Op< \ T, U, \ typename std::enable_if::value || \ std::is_floating_point::value>::type> { \ using result_type = typename MaxExponentPromotion::type; \ template \ static constexpr bool Do(T x, U y, V* result) { \ using Promotion = typename MaxExponentPromotion::type; \ Promotion presult = x OP y; \ *result = static_cast(presult); \ return IsValueInRangeForNumericType(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 // 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 struct GetNumericRepresentation { static const NumericRepresentation value = std::is_integral::value ? NUMERIC_INTEGER : (std::is_floating_point::value ? NUMERIC_FLOATING : NUMERIC_UNKNOWN); }; template ::value> class CheckedNumericState {}; // Integrals require quite a bit of additional housekeeping to manage state. template class CheckedNumericState { 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_; // Ensures that a type conversion does not trigger undefined behavior. template static constexpr T WellDefinedConversionOrZero(const Src value, const bool is_valid) { using SrcType = typename internal::UnderlyingType::type; return (std::is_integral::value || is_valid) ? static_cast(value) : static_cast(0); } public: template friend class CheckedNumericState; constexpr CheckedNumericState() : is_valid_(true), value_(0) {} template constexpr CheckedNumericState(Src value, bool is_valid) : is_valid_(is_valid && IsValueInRangeForNumericType(value)), value_(WellDefinedConversionOrZero(value, is_valid_)) { static_assert(std::is_arithmetic::value, "Argument must be numeric."); } // Copy constructor. template constexpr CheckedNumericState(const CheckedNumericState& rhs) : is_valid_(rhs.IsValid()), value_(WellDefinedConversionOrZero(rhs.value(), is_valid_)) {} template constexpr explicit CheckedNumericState(Src value) : is_valid_(IsValueInRangeForNumericType(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. template class CheckedNumericState { private: T value_; // Ensures that a type conversion does not trigger undefined behavior. template static constexpr T WellDefinedConversionOrNaN(const Src value, const bool is_valid) { using SrcType = typename internal::UnderlyingType::type; return (StaticDstRangeRelationToSrcRange::value == NUMERIC_RANGE_CONTAINED || is_valid) ? static_cast(value) : std::numeric_limits::quiet_NaN(); } public: template friend class CheckedNumericState; constexpr CheckedNumericState() : value_(0.0) {} template constexpr CheckedNumericState(Src value, bool is_valid) : value_(WellDefinedConversionOrNaN(value, is_valid)) {} template constexpr explicit CheckedNumericState(Src value) : value_(WellDefinedConversionOrNaN( value, IsValueInRangeForNumericType(value))) {} // Copy constructor. template constexpr CheckedNumericState(const CheckedNumericState& rhs) : value_(WellDefinedConversionOrNaN( rhs.value(), rhs.is_valid() && IsValueInRangeForNumericType(rhs.value()))) {} constexpr bool is_valid() const { // Written this way because std::isfinite is not reliably constexpr. return MustTreatAsConstexpr(value_) ? value_ <= std::numeric_limits::max() && value_ >= std::numeric_limits::lowest() : std::isfinite(value_); } constexpr T value() const { return value_; } }; } // namespace internal } // namespace base #endif // BASE_NUMERICS_CHECKED_MATH_IMPL_H_