| // 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 <stddef.h> |
| #include <stdint.h> |
| |
| #include <climits> |
| #include <cmath> |
| #include <cstdlib> |
| #include <limits> |
| #include <type_traits> |
| |
| #include "anglebase/numerics/safe_conversions.h" |
| #include "anglebase/numerics/safe_math_shared_impl.h" |
| |
| namespace angle |
| { |
| namespace base |
| { |
| namespace internal |
| { |
| |
| template <typename T> |
| constexpr bool CheckedAddImpl(T x, T y, T *result) |
| { |
| static_assert(std::is_integral<T>::value, "Type must be integral"); |
| // Since the value of x+y is undefined if we have a signed type, we compute |
| // it using the unsigned type of the same size. |
| 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<T>::value ? 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, class Enable = void> |
| struct CheckedAddOp |
| {}; |
| |
| template <typename T, typename U> |
| struct CheckedAddOp< |
| T, |
| U, |
| typename std::enable_if<std::is_integral<T>::value && std::is_integral<U>::value>::type> |
| { |
| using result_type = typename MaxExponentPromotion<T, U>::type; |
| template <typename V> |
| static 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 = typename FastIntegerArithmeticPromotion<T, U>::type; |
| using Promotion = |
| typename std::conditional<(IntegerBitsPlusSign<FastPromotion>::value > |
| IntegerBitsPlusSign<intptr_t>::value), |
| typename BigEnoughPromotion<T, U>::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<Promotion>(x) || |
| !IsValueInRangeForNumericType<Promotion>(y))) |
| { |
| return false; |
| } |
| |
| Promotion presult = {}; |
| bool is_valid = true; |
| if constexpr (IsIntegerArithmeticSafe<Promotion, T, U>::value) |
| { |
| presult = static_cast<Promotion>(x) + static_cast<Promotion>(y); |
| } |
| else |
| { |
| is_valid = |
| CheckedAddImpl(static_cast<Promotion>(x), static_cast<Promotion>(y), &presult); |
| } |
| 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::is_integral<T>::value, "Type must be integral"); |
| // Since the value of x+y is undefined if we have a signed type, we compute |
| // it using the unsigned type of the same size. |
| 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<T>::value ? static_cast<SignedDst>((uresult ^ ux) & (ux ^ uy)) < 0 : x < y) |
| return false; |
| *result = static_cast<T>(uresult); |
| return true; |
| } |
| |
| template <typename T, typename U, class Enable = void> |
| struct CheckedSubOp |
| {}; |
| |
| template <typename T, typename U> |
| struct CheckedSubOp< |
| T, |
| U, |
| typename std::enable_if<std::is_integral<T>::value && std::is_integral<U>::value>::type> |
| { |
| using result_type = typename MaxExponentPromotion<T, U>::type; |
| template <typename V> |
| static 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 = typename FastIntegerArithmeticPromotion<T, U>::type; |
| using Promotion = |
| typename std::conditional<(IntegerBitsPlusSign<FastPromotion>::value > |
| IntegerBitsPlusSign<intptr_t>::value), |
| typename BigEnoughPromotion<T, U>::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<Promotion>(x) || |
| !IsValueInRangeForNumericType<Promotion>(y))) |
| { |
| return false; |
| } |
| |
| Promotion presult = {}; |
| bool is_valid = true; |
| if constexpr (IsIntegerArithmeticSafe<Promotion, T, U>::value) |
| { |
| presult = static_cast<Promotion>(x) - static_cast<Promotion>(y); |
| } |
| else |
| { |
| is_valid = |
| CheckedSubImpl(static_cast<Promotion>(x), static_cast<Promotion>(y), &presult); |
| } |
| 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::is_integral<T>::value, "Type must be integral"); |
| // Since the value of x*y is potentially undefined if we have a signed type, |
| // we compute it using the unsigned type of the same size. |
| using UnsignedDst = typename std::make_unsigned<T>::type; |
| using SignedDst = typename std::make_signed<T>::type; |
| const UnsignedDst ux = SafeUnsignedAbs(x); |
| const UnsignedDst uy = SafeUnsignedAbs(y); |
| const UnsignedDst uresult = static_cast<UnsignedDst>(ux * uy); |
| const bool is_negative = std::is_signed<T>::value && 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<T>::value || is_negative) && |
| ux > (std::numeric_limits<T>::max() + UnsignedDst(is_negative)) / uy) |
| return false; |
| *result = is_negative ? 0 - uresult : uresult; |
| return true; |
| } |
| |
| template <typename T, typename U, class Enable = void> |
| struct CheckedMulOp |
| {}; |
| |
| template <typename T, typename U> |
| struct CheckedMulOp< |
| T, |
| U, |
| typename std::enable_if<std::is_integral<T>::value && std::is_integral<U>::value>::type> |
| { |
| using result_type = typename MaxExponentPromotion<T, U>::type; |
| template <typename V> |
| static 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 = typename FastIntegerArithmeticPromotion<T, U>::type; |
| // Verify the destination type can hold the result (always true for 0). |
| if (BASE_NUMERICS_UNLIKELY((!IsValueInRangeForNumericType<Promotion>(x) || |
| !IsValueInRangeForNumericType<Promotion>(y)) && |
| x && y)) |
| { |
| 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. |
| is_valid = CheckedMulFastOp<Promotion, Promotion>::Do(x, y, &presult); |
| } |
| else if (IsIntegerArithmeticSafe<Promotion, T, U>::value) |
| { |
| 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, class Enable = void> |
| struct CheckedDivOp |
| {}; |
| |
| template <typename T, typename U> |
| struct CheckedDivOp< |
| T, |
| U, |
| typename std::enable_if<std::is_integral<T>::value && std::is_integral<U>::value>::type> |
| { |
| using result_type = typename MaxExponentPromotion<T, U>::type; |
| template <typename V> |
| static 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<T, U>::type; |
| if (BASE_NUMERICS_UNLIKELY( |
| (std::is_signed<T>::value && std::is_signed<U>::value && |
| IsTypeInRangeForNumericType<T, Promotion>::value && |
| static_cast<Promotion>(x) == std::numeric_limits<Promotion>::lowest() && |
| y == static_cast<U>(-1)))) |
| { |
| return false; |
| } |
| |
| // This branch always compiles away if the above branch wasn't removed. |
| if (BASE_NUMERICS_UNLIKELY((!IsValueInRangeForNumericType<Promotion>(x) || |
| !IsValueInRangeForNumericType<Promotion>(y)) && |
| x)) |
| { |
| 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, class Enable = void> |
| struct CheckedModOp |
| {}; |
| |
| template <typename T, typename U> |
| struct CheckedModOp< |
| T, |
| U, |
| typename std::enable_if<std::is_integral<T>::value && std::is_integral<U>::value>::type> |
| { |
| using result_type = typename MaxExponentPromotion<T, U>::type; |
| template <typename V> |
| static constexpr bool Do(T x, U y, V *result) |
| { |
| if (BASE_NUMERICS_UNLIKELY(!y)) |
| return false; |
| |
| using Promotion = typename BigEnoughPromotion<T, U>::type; |
| if (BASE_NUMERICS_UNLIKELY( |
| (std::is_signed<T>::value && std::is_signed<U>::value && |
| IsTypeInRangeForNumericType<T, Promotion>::value && |
| static_cast<Promotion>(x) == std::numeric_limits<Promotion>::lowest() && |
| y == static_cast<U>(-1)))) |
| { |
| *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, class Enable = void> |
| struct CheckedLshOp |
| {}; |
| |
| // Left shift. Shifts less than 0 or greater than or equal to the number |
| // of bits in the promoted type are undefined. Shifts of negative values |
| // are undefined. Otherwise it is defined when the result fits. |
| template <typename T, typename U> |
| struct CheckedLshOp< |
| T, |
| U, |
| typename std::enable_if<std::is_integral<T>::value && std::is_integral<U>::value>::type> |
| { |
| using result_type = T; |
| template <typename V> |
| static 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<T>::digits))) |
| { |
| // 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<T>::value || x || |
| as_unsigned(shift) != as_unsigned(std::numeric_limits<T>::digits)) |
| return false; |
| *result = 0; |
| return true; |
| } |
| }; |
| |
| template <typename T, typename U, class Enable = void> |
| struct CheckedRshOp |
| {}; |
| |
| // Right shift. Shifts less than 0 or greater than or equal to the number |
| // of bits in the promoted type are undefined. Otherwise, it is always defined, |
| // but a right shift of a negative value is implementation-dependent. |
| template <typename T, typename U> |
| struct CheckedRshOp< |
| T, |
| U, |
| typename std::enable_if<std::is_integral<T>::value && std::is_integral<U>::value>::type> |
| { |
| using result_type = T; |
| template <typename V> |
| static bool Do(T x, U shift, V *result) |
| { |
| // Use sign conversion to push negative values out of range. |
| if (BASE_NUMERICS_UNLIKELY(as_unsigned(shift) >= IntegerBitsPlusSign<T>::value)) |
| { |
| 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, class Enable = void> |
| struct CheckedAndOp |
| {}; |
| |
| // For simplicity we support only unsigned integer results. |
| template <typename T, typename U> |
| struct CheckedAndOp< |
| T, |
| U, |
| typename std::enable_if<std::is_integral<T>::value && std::is_integral<U>::value>::type> |
| { |
| using result_type = |
| typename std::make_unsigned<typename MaxExponentPromotion<T, U>::type>::type; |
| template <typename V> |
| 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, class Enable = void> |
| struct CheckedOrOp |
| {}; |
| |
| // For simplicity we support only unsigned integers. |
| template <typename T, typename U> |
| struct CheckedOrOp< |
| T, |
| U, |
| typename std::enable_if<std::is_integral<T>::value && std::is_integral<U>::value>::type> |
| { |
| using result_type = |
| typename std::make_unsigned<typename MaxExponentPromotion<T, U>::type>::type; |
| template <typename V> |
| 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, class Enable = void> |
| struct CheckedXorOp |
| {}; |
| |
| // For simplicity we support only unsigned integers. |
| template <typename T, typename U> |
| struct CheckedXorOp< |
| T, |
| U, |
| typename std::enable_if<std::is_integral<T>::value && std::is_integral<U>::value>::type> |
| { |
| using result_type = |
| typename std::make_unsigned<typename MaxExponentPromotion<T, U>::type>::type; |
| template <typename V> |
| 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, class Enable = void> |
| struct CheckedMaxOp |
| {}; |
| |
| template <typename T, typename U> |
| struct CheckedMaxOp< |
| T, |
| U, |
| typename std::enable_if<std::is_arithmetic<T>::value && std::is_arithmetic<U>::value>::type> |
| { |
| using result_type = typename MaxExponentPromotion<T, U>::type; |
| template <typename V> |
| 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, class Enable = void> |
| struct CheckedMinOp |
| {}; |
| |
| template <typename T, typename U> |
| struct CheckedMinOp< |
| T, |
| U, |
| typename std::enable_if<std::is_arithmetic<T>::value && std::is_arithmetic<U>::value>::type> |
| { |
| using result_type = typename LowestValuePromotion<T, U>::type; |
| template <typename V> |
| 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> \ |
| struct Checked##NAME##Op<T, U, \ |
| typename std::enable_if<std::is_floating_point<T>::value || \ |
| std::is_floating_point<U>::value>::type> \ |
| { \ |
| using result_type = typename MaxExponentPromotion<T, U>::type; \ |
| template <typename V> \ |
| static constexpr bool Do(T x, U y, V *result) \ |
| { \ |
| using Promotion = typename MaxExponentPromotion<T, U>::type; \ |
| const Promotion 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::is_integral<NumericType>::value |
| ? NUMERIC_INTEGER |
| : (std::is_floating_point<NumericType>::value ? 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<Src>::value, "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) |
| { |
| using SrcType = typename internal::UnderlyingType<Src>::type; |
| return (std::is_integral<SrcType>::value || is_valid) ? static_cast<T>(value) : 0; |
| } |
| |
| // 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_; |
| }; |
| |
| // 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 reliably constexpr. |
| return MustTreatAsConstexpr(value_) ? 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) |
| { |
| using SrcType = typename internal::UnderlyingType<Src>::type; |
| return (StaticDstRangeRelationToSrcRange<T, SrcType>::value == NUMERIC_RANGE_CONTAINED || |
| is_valid) |
| ? static_cast<T>(value) |
| : std::numeric_limits<T>::quiet_NaN(); |
| } |
| |
| T value_; |
| }; |
| |
| } // namespace internal |
| } // namespace base |
| } // namespace angle |
| |
| #endif // BASE_NUMERICS_CHECKED_MATH_IMPL_H_ |
