/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */ /* vim: set ts=8 sts=2 et sw=2 tw=80: */ /* This Source Code Form is subject to the terms of the Mozilla Public * License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/* * Math operations that implement wraparound semantics on overflow or underflow. * * While in some cases (but not all of them!) plain old C++ operators and casts * will behave just like these functions, there are three reasons you should use * these functions: * * 1) These functions make *explicit* the desire for and dependence upon * wraparound semantics, just as Rust's i32::wrapping_add and similar * functions explicitly produce wraparound in Rust. * 2) They implement this functionality *safely*, without invoking signed * integer overflow that has undefined behavior in C++. * 3) They play nice with compiler-based integer-overflow sanitizers (see * build/moz.configure/toolchain.configure), that in appropriately * configured builds verify at runtime that integral arithmetic doesn't * overflow.
*/
template <typename UnsignedType> struct WrapToSignedHelper {
static_assert(std::is_unsigned_v<UnsignedType>, "WrapToSigned must be passed an unsigned type");
using SignedType = std::make_signed_t<UnsignedType>;
// Overflow-correctness was proven in bug 1432646 and is explained in the // comment below. This function is very hot, both at compile time and // runtime, so disable all overflow checking in it.
MOZ_NO_SANITIZE_UNSIGNED_OVERFLOW
MOZ_NO_SANITIZE_SIGNED_OVERFLOW static constexpr SignedType compute(
UnsignedType aValue) { // This algorithm was originally provided here: // https://stackoverflow.com/questions/13150449/efficient-unsigned-to-signed-cast-avoiding-implementation-defined-behavior // // If the value is in the non-negative signed range, just cast. // // If the value will be negative, compute its delta from the first number // past the max signed integer, then add that to the minimum signed value. // // At the low end: if |u| is the maximum signed value plus one, then it has // the same mathematical value as |MinValue| cast to unsigned form. The // delta is zero, so the signed form of |u| is |MinValue| -- exactly the // result of adding zero delta to |MinValue|. // // At the high end: if |u| is the maximum *unsigned* value, then it has all // bits set. |MinValue| cast to unsigned form is purely the high bit set. // So the delta is all bits but high set -- exactly |MaxValue|. And as // |MinValue = -MaxValue - 1|, we have |MaxValue + (-MaxValue - 1)| to // equal -1. // // Thus the delta below is in signed range, the corresponding cast is safe, // and this computation produces values spanning [MinValue, 0): exactly the // desired range of all negative signed integers. return (aValue <= MaxValueUnsigned)
? static_cast<SignedType>(aValue)
: static_cast<SignedType>(aValue - MinValueUnsigned) + MinValue;
}
};
} // namespace detail
/** * Convert an unsigned value to signed, if necessary wrapping around. * * This is the behavior normal C++ casting will perform in most implementations * these days -- but this function makes explicit that such conversion is * happening.
*/ template <typename UnsignedType>
constexpr typename detail::WrapToSignedHelper<UnsignedType>::SignedType
WrapToSigned(UnsignedType aValue) { return detail::WrapToSignedHelper<UnsignedType>::compute(aValue);
}
namespace detail {
template <typename T>
constexpr T ToResult(std::make_unsigned_t<T> aUnsigned) { // We could *always* return WrapToSigned and rely on unsigned conversion to // undo the wrapping when |T| is unsigned, but this seems clearer. return std::is_signed_v<T> ? WrapToSigned(aUnsigned) : aUnsigned;
}
public:
MOZ_NO_SANITIZE_UNSIGNED_OVERFLOW static constexpr T compute(T aX, T aY) { return ToResult<T>(static_cast<UnsignedT>(aX) + static_cast<UnsignedT>(aY));
}
};
} // namespace detail
/** * Add two integers of the same type and return the result converted to that * type using wraparound semantics, without triggering overflow sanitizers. * * For N-bit unsigned integer types, this is equivalent to adding the two * numbers, then taking the result mod 2**N: * * WrappingAdd(uint32_t(42), uint32_t(17)) is 59 (59 mod 2**32); * WrappingAdd(uint8_t(240), uint8_t(20)) is 4 (260 mod 2**8). * * Unsigned WrappingAdd acts exactly like C++ unsigned addition. * * For N-bit signed integer types, this is equivalent to adding the two numbers * wrapped to unsigned, then wrapping the sum mod 2**N to the signed range: * * WrappingAdd(int16_t(32767), int16_t(3)) is * -32766 ((32770 mod 2**16) - 2**16); * WrappingAdd(int8_t(-128), int8_t(-128)) is * 0 (256 mod 2**8); * WrappingAdd(int32_t(-42), int32_t(-17)) is * -59 ((8589934533 mod 2**32) - 2**32). * * There's no equivalent to this operation in C++, as C++ signed addition that * overflows has undefined behavior. But it's how such addition *tends* to * behave with most compilers, unless an optimization or similar -- quite * permissibly -- triggers different behavior.
*/ template <typename T>
constexpr T WrappingAdd(T aX, T aY) { return detail::WrappingAddHelper<T>::compute(aX, aY);
}
public:
MOZ_NO_SANITIZE_UNSIGNED_OVERFLOW static constexpr T compute(T aX, T aY) { return ToResult<T>(static_cast<UnsignedT>(aX) - static_cast<UnsignedT>(aY));
}
};
} // namespace detail
/** * Subtract two integers of the same type and return the result converted to * that type using wraparound semantics, without triggering overflow sanitizers. * * For N-bit unsigned integer types, this is equivalent to subtracting the two * numbers, then taking the result mod 2**N: * * WrappingSubtract(uint32_t(42), uint32_t(17)) is 29 (29 mod 2**32); * WrappingSubtract(uint8_t(5), uint8_t(20)) is 241 (-15 mod 2**8). * * Unsigned WrappingSubtract acts exactly like C++ unsigned subtraction. * * For N-bit signed integer types, this is equivalent to subtracting the two * numbers wrapped to unsigned, then wrapping the difference mod 2**N to the * signed range: * * WrappingSubtract(int16_t(32767), int16_t(-5)) is -32764 ((32772 mod 2**16) * - 2**16); WrappingSubtract(int8_t(-128), int8_t(127)) is 1 (-255 mod 2**8); * WrappingSubtract(int32_t(-17), int32_t(-42)) is 25 (25 mod 2**32). * * There's no equivalent to this operation in C++, as C++ signed subtraction * that overflows has undefined behavior. But it's how such subtraction *tends* * to behave with most compilers, unless an optimization or similar -- quite * permissibly -- triggers different behavior.
*/ template <typename T>
constexpr T WrappingSubtract(T aX, T aY) { return detail::WrappingSubtractHelper<T>::compute(aX, aY);
}
public:
MOZ_NO_SANITIZE_UNSIGNED_OVERFLOW static constexpr T compute(T aX, T aY) { // Begin with |1U| to ensure the overall operation chain is never promoted // to signed integer operations that might have *signed* integer overflow. return ToResult<T>(static_cast<UnsignedT>(1U * static_cast<UnsignedT>(aX) * static_cast<UnsignedT>(aY)));
}
};
} // namespace detail
/** * Multiply two integers of the same type and return the result converted to * that type using wraparound semantics, without triggering overflow sanitizers. * * For N-bit unsigned integer types, this is equivalent to multiplying the two * numbers, then taking the result mod 2**N: * * WrappingMultiply(uint32_t(42), uint32_t(17)) is 714 (714 mod 2**32); * WrappingMultiply(uint8_t(16), uint8_t(24)) is 128 (384 mod 2**8); * WrappingMultiply(uint16_t(3), uint16_t(32768)) is 32768 (98304 mod 2*16). * * Unsigned WrappingMultiply is *not* identical to C++ multiplication: with most * compilers, in rare cases uint16_t*uint16_t can invoke *signed* integer * overflow having undefined behavior! http://kqueue.org/blog/2013/09/17/cltq/ * has the grody details. (Some compilers do this for uint32_t, not uint16_t.) * So it's especially important to use WrappingMultiply for wraparound math with * uint16_t. That quirk aside, this function acts like you *thought* C++ * unsigned multiplication always worked. * * For N-bit signed integer types, this is equivalent to multiplying the two * numbers wrapped to unsigned, then wrapping the product mod 2**N to the signed * range: * * WrappingMultiply(int16_t(-456), int16_t(123)) is * 9448 ((-56088 mod 2**16) + 2**16); * WrappingMultiply(int32_t(-7), int32_t(-9)) is 63 (63 mod 2**32); * WrappingMultiply(int8_t(16), int8_t(24)) is -128 ((384 mod 2**8) - 2**8); * WrappingMultiply(int8_t(16), int8_t(255)) is -16 ((4080 mod 2**8) - 2**8). * * There's no equivalent to this operation in C++, as C++ signed * multiplication that overflows has undefined behavior. But it's how such * multiplication *tends* to behave with most compilers, unless an optimization * or similar -- quite permissibly -- triggers different behavior.
*/ template <typename T>
constexpr T WrappingMultiply(T aX, T aY) { return detail::WrappingMultiplyHelper<T>::compute(aX, aY);
}
} /* namespace mozilla */
#endif/* mozilla_WrappingOperations_h */
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