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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
/*
* 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);
// 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:
//
// 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
* 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 */