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Diffstat (limited to 'mfbt/WrappingOperations.h')
-rw-r--r-- | mfbt/WrappingOperations.h | 188 |
1 files changed, 188 insertions, 0 deletions
diff --git a/mfbt/WrappingOperations.h b/mfbt/WrappingOperations.h new file mode 100644 index 0000000000..c93626f653 --- /dev/null +++ b/mfbt/WrappingOperations.h @@ -0,0 +1,188 @@ +/* -*- 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 + * without performing C++ undefined behavior or tripping up compiler-based + * integer-overflow sanitizers. + */ + +#ifndef mozilla_WrappingOperations_h +#define mozilla_WrappingOperations_h + +#include "mozilla/Attributes.h" +#include "mozilla/TypeTraits.h" + +#include <limits.h> + +namespace mozilla { + +namespace detail { + +template<typename UnsignedType> +struct WrapToSignedHelper +{ + static_assert(mozilla::IsUnsigned<UnsignedType>::value, + "WrapToSigned must be passed an unsigned type"); + + using SignedType = typename mozilla::MakeSigned<UnsignedType>::Type; + + static constexpr SignedType MaxValue = + (UnsignedType(1) << (CHAR_BIT * sizeof(SignedType) - 1)) - 1; + static constexpr SignedType MinValue = -MaxValue - 1; + + static constexpr UnsignedType MinValueUnsigned = + static_cast<UnsignedType>(MinValue); + static constexpr UnsignedType MaxValueUnsigned = + static_cast<UnsignedType>(MaxValue); + + // 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> +inline constexpr typename detail::WrapToSignedHelper<UnsignedType>::SignedType +WrapToSigned(UnsignedType aValue) +{ + return detail::WrapToSignedHelper<UnsignedType>::compute(aValue); +} + +namespace detail { + +template<typename T> +struct WrappingMultiplyHelper +{ +private: + using UnsignedT = typename MakeUnsigned<T>::Type; + + MOZ_NO_SANITIZE_UNSIGNED_OVERFLOW + static UnsignedT + multiply(UnsignedT aX, UnsignedT aY) + { + // |mozilla::WrappingMultiply| isn't constexpr because MSVC warns about well- + // defined unsigned integer overflows that may happen here. + // https://msdn.microsoft.com/en-us/library/4kze989h.aspx And constexpr + // seems to cause the warning to be emitted at |WrappingMultiply| call *sites* + // instead of here, so these #pragmas are ineffective. + // + // https://stackoverflow.com/questions/37658794/integer-constant-overflow-warning-in-constexpr + // + // If/when MSVC fix this bug, we should make these functions constexpr. + + // Begin with |1U| to ensure the overall operation chain is never promoted + // to signed integer operations that might have *signed* integer overflow. + return static_cast<UnsignedT>(1U * aX * aY); + } + + static T + toResult(UnsignedT aX, UnsignedT aY) + { + // We could always return WrapToSigned and rely on unsigned conversion + // undoing the wrapping when |T| is unsigned, but this seems clearer. + return IsSigned<T>::value + ? WrapToSigned(multiply(aX, aY)) + : multiply(aX, aY); + } + +public: + MOZ_NO_SANITIZE_UNSIGNED_OVERFLOW + static T compute(T aX, T aY) + { + return toResult(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. This function: + * + * 1) makes explicit the desire for and dependence upon wraparound semantics, + * 2) provides wraparound semantics *safely* with no signed integer overflow + * that would have undefined behavior, and + * 3) won't trip up {,un}signed-integer overflow sanitizers (see + * build/autoconf/sanitize.m4) at runtime. + * + * 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). + * + * Use this function for any unsigned multiplication that can wrap (instead of + * normal C++ multiplication) to play nice with the sanitizers. But it's + * especially important to use it for uint16_t multiplication: in most compilers + * for uint16_t*uint16_t some operand values will trigger signed integer + * overflow with undefined behavior! http://kqueue.org/blog/2013/09/17/cltq/ + * has the grody details. Other than that one weird case, WrappingMultiply on + * unsigned types is the same as C++ multiplication. + * + * For N-bit signed integer types, this is equivalent to multiplying the two + * numbers wrapped to unsigned, taking the product mod 2**N, then wrapping that + * number 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 is no ready equivalent to this operation in C++, as applying C++ + * multiplication to signed integer types in ways that trigger overflow has + * undefined behavior. However, it's how multiplication *tends* to behave with + * most compilers in most situations, even though it's emphatically not required + * to do so. + */ +template<typename T> +inline T +WrappingMultiply(T aX, T aY) +{ + return detail::WrappingMultiplyHelper<T>::compute(aX, aY); +} + +} /* namespace mozilla */ + +#endif /* mozilla_WrappingOperations_h */ |