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+/* -*- 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/autoconf/sanitize.m4), that in appropriately configured builds
+ * verify at runtime that integral arithmetic doesn't overflow.
+ */
+
+#ifndef mozilla_WrappingOperations_h
+#define mozilla_WrappingOperations_h
+
+#include "mozilla/Attributes.h"
+
+#include <limits.h>
+#include <type_traits>
+
+namespace mozilla {
+
+namespace detail {
+
+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>;
+
+ 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>
+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;
+}
+
+template <typename T>
+struct WrappingAddHelper {
+ private:
+ using UnsignedT = std::make_unsigned_t<T>;
+
+ 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);
+}
+
+namespace detail {
+
+template <typename T>
+struct WrappingSubtractHelper {
+ private:
+ using UnsignedT = std::make_unsigned_t<T>;
+
+ 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);
+}
+
+namespace detail {
+
+template <typename T>
+struct WrappingMultiplyHelper {
+ private:
+ using UnsignedT = std::make_unsigned_t<T>;
+
+ 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 */