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// Copyright 2014 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_SAFE_MATH_IMPL_H_
#define BASE_NUMERICS_SAFE_MATH_IMPL_H_
#include <stddef.h>
#include <stdint.h>
#include <climits>
#include <cmath>
#include <cstdlib>
#include <limits>
#include <type_traits>
#include "base/numerics/safe_conversions.h"
namespace base {
namespace internal {
// Everything from here up to the floating point operations is portable C++,
// but it may not be fast. This code could be split based on
// platform/architecture and replaced with potentially faster implementations.
// Integer promotion templates used by the portable checked integer arithmetic.
template <size_t Size, bool IsSigned>
struct IntegerForSizeAndSign;
template <>
struct IntegerForSizeAndSign<1, true> {
typedef int8_t type;
};
template <>
struct IntegerForSizeAndSign<1, false> {
typedef uint8_t type;
};
template <>
struct IntegerForSizeAndSign<2, true> {
typedef int16_t type;
};
template <>
struct IntegerForSizeAndSign<2, false> {
typedef uint16_t type;
};
template <>
struct IntegerForSizeAndSign<4, true> {
typedef int32_t type;
};
template <>
struct IntegerForSizeAndSign<4, false> {
typedef uint32_t type;
};
template <>
struct IntegerForSizeAndSign<8, true> {
typedef int64_t type;
};
template <>
struct IntegerForSizeAndSign<8, false> {
typedef uint64_t type;
};
// WARNING: We have no IntegerForSizeAndSign<16, *>. If we ever add one to
// support 128-bit math, then the ArithmeticPromotion template below will need
// to be updated (or more likely replaced with a decltype expression).
template <typename Integer>
struct UnsignedIntegerForSize {
typedef typename std::enable_if<
std::numeric_limits<Integer>::is_integer,
typename IntegerForSizeAndSign<sizeof(Integer), false>::type>::type type;
};
template <typename Integer>
struct SignedIntegerForSize {
typedef typename std::enable_if<
std::numeric_limits<Integer>::is_integer,
typename IntegerForSizeAndSign<sizeof(Integer), true>::type>::type type;
};
template <typename Integer>
struct TwiceWiderInteger {
typedef typename std::enable_if<
std::numeric_limits<Integer>::is_integer,
typename IntegerForSizeAndSign<
sizeof(Integer) * 2,
std::numeric_limits<Integer>::is_signed>::type>::type type;
};
template <typename Integer>
struct PositionOfSignBit {
static const typename std::enable_if<std::numeric_limits<Integer>::is_integer,
size_t>::type value =
CHAR_BIT * sizeof(Integer) - 1;
};
// This is used for UnsignedAbs, where we need to support floating-point
// template instantiations even though we don't actually support the operations.
// However, there is no corresponding implementation of e.g. CheckedUnsignedAbs,
// so the float versions will not compile.
template <typename Numeric,
bool IsInteger = std::numeric_limits<Numeric>::is_integer,
bool IsFloat = std::numeric_limits<Numeric>::is_iec559>
struct UnsignedOrFloatForSize;
template <typename Numeric>
struct UnsignedOrFloatForSize<Numeric, true, false> {
typedef typename UnsignedIntegerForSize<Numeric>::type type;
};
template <typename Numeric>
struct UnsignedOrFloatForSize<Numeric, false, true> {
typedef Numeric type;
};
// Helper templates for integer manipulations.
template <typename T>
constexpr bool HasSignBit(T x) {
// Cast to unsigned since right shift on signed is undefined.
return !!(static_cast<typename UnsignedIntegerForSize<T>::type>(x) >>
PositionOfSignBit<T>::value);
}
// This wrapper undoes the standard integer promotions.
template <typename T>
constexpr T BinaryComplement(T x) {
return static_cast<T>(~x);
}
// Here are the actual portable checked integer math implementations.
// TODO(jschuh): Break this code out from the enable_if pattern and find a clean
// way to coalesce things into the CheckedNumericState specializations below.
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer, T>::type
CheckedAdd(T x, T y, RangeConstraint* validity) {
// 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.
typedef typename UnsignedIntegerForSize<T>::type UnsignedDst;
UnsignedDst ux = static_cast<UnsignedDst>(x);
UnsignedDst uy = static_cast<UnsignedDst>(y);
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::numeric_limits<T>::is_signed) {
if (HasSignBit(BinaryComplement(
static_cast<UnsignedDst>((uresult ^ ux) & (uresult ^ uy))))) {
*validity = RANGE_VALID;
} else { // Direction of wrap is inverse of result sign.
*validity = HasSignBit(uresult) ? RANGE_OVERFLOW : RANGE_UNDERFLOW;
}
} else { // Unsigned is either valid or overflow.
*validity = BinaryComplement(x) >= y ? RANGE_VALID : RANGE_OVERFLOW;
}
return static_cast<T>(uresult);
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer, T>::type
CheckedSub(T x, T y, RangeConstraint* validity) {
// 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.
typedef typename UnsignedIntegerForSize<T>::type UnsignedDst;
UnsignedDst ux = static_cast<UnsignedDst>(x);
UnsignedDst uy = static_cast<UnsignedDst>(y);
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::numeric_limits<T>::is_signed) {
if (HasSignBit(BinaryComplement(
static_cast<UnsignedDst>((uresult ^ ux) & (ux ^ uy))))) {
*validity = RANGE_VALID;
} else { // Direction of wrap is inverse of result sign.
*validity = HasSignBit(uresult) ? RANGE_OVERFLOW : RANGE_UNDERFLOW;
}
} else { // Unsigned is either valid or underflow.
*validity = x >= y ? RANGE_VALID : RANGE_UNDERFLOW;
}
return static_cast<T>(uresult);
}
// Integer multiplication is a bit complicated. In the fast case we just
// we just promote to a twice wider type, and range check the result. In the
// slow case we need to manually check that the result won't be truncated by
// checking with division against the appropriate bound.
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
sizeof(T) * 2 <= sizeof(uintmax_t),
T>::type
CheckedMul(T x, T y, RangeConstraint* validity) {
typedef typename TwiceWiderInteger<T>::type IntermediateType;
IntermediateType tmp =
static_cast<IntermediateType>(x) * static_cast<IntermediateType>(y);
*validity = DstRangeRelationToSrcRange<T>(tmp);
return static_cast<T>(tmp);
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
std::numeric_limits<T>::is_signed &&
(sizeof(T) * 2 > sizeof(uintmax_t)),
T>::type
CheckedMul(T x, T y, RangeConstraint* validity) {
// If either side is zero then the result will be zero.
if (!x || !y) {
*validity = RANGE_VALID;
return static_cast<T>(0);
} else if (x > 0) {
if (y > 0)
*validity =
x <= std::numeric_limits<T>::max() / y ? RANGE_VALID : RANGE_OVERFLOW;
else
*validity = y >= std::numeric_limits<T>::min() / x ? RANGE_VALID
: RANGE_UNDERFLOW;
} else {
if (y > 0)
*validity = x >= std::numeric_limits<T>::min() / y ? RANGE_VALID
: RANGE_UNDERFLOW;
else
*validity =
y >= std::numeric_limits<T>::max() / x ? RANGE_VALID : RANGE_OVERFLOW;
}
return static_cast<T>(*validity == RANGE_VALID ? x * y : 0);
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T>::is_signed &&
(sizeof(T) * 2 > sizeof(uintmax_t)),
T>::type
CheckedMul(T x, T y, RangeConstraint* validity) {
*validity = (y == 0 || x <= std::numeric_limits<T>::max() / y)
? RANGE_VALID
: RANGE_OVERFLOW;
return static_cast<T>(*validity == RANGE_VALID ? x * y : 0);
}
// Division just requires a check for an invalid negation on signed min/-1.
template <typename T>
T CheckedDiv(T x,
T y,
RangeConstraint* validity,
typename std::enable_if<std::numeric_limits<T>::is_integer,
int>::type = 0) {
if (std::numeric_limits<T>::is_signed && x == std::numeric_limits<T>::min() &&
y == static_cast<T>(-1)) {
*validity = RANGE_OVERFLOW;
return std::numeric_limits<T>::min();
}
*validity = RANGE_VALID;
return static_cast<T>(x / y);
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
std::numeric_limits<T>::is_signed,
T>::type
CheckedMod(T x, T y, RangeConstraint* validity) {
*validity = y > 0 ? RANGE_VALID : RANGE_INVALID;
return static_cast<T>(*validity == RANGE_VALID ? x % y: 0);
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T>::is_signed,
T>::type
CheckedMod(T x, T y, RangeConstraint* validity) {
*validity = RANGE_VALID;
return static_cast<T>(x % y);
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
std::numeric_limits<T>::is_signed,
T>::type
CheckedNeg(T value, RangeConstraint* validity) {
*validity =
value != std::numeric_limits<T>::min() ? RANGE_VALID : RANGE_OVERFLOW;
// The negation of signed min is min, so catch that one.
return static_cast<T>(*validity == RANGE_VALID ? -value : 0);
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T>::is_signed,
T>::type
CheckedNeg(T value, RangeConstraint* validity) {
// The only legal unsigned negation is zero.
*validity = value ? RANGE_UNDERFLOW : RANGE_VALID;
return static_cast<T>(*validity == RANGE_VALID ?
-static_cast<typename SignedIntegerForSize<T>::type>(value) : 0);
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
std::numeric_limits<T>::is_signed,
T>::type
CheckedAbs(T value, RangeConstraint* validity) {
*validity =
value != std::numeric_limits<T>::min() ? RANGE_VALID : RANGE_OVERFLOW;
return static_cast<T>(*validity == RANGE_VALID ? std::abs(value) : 0);
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T>::is_signed,
T>::type
CheckedAbs(T value, RangeConstraint* validity) {
// T is unsigned, so |value| must already be positive.
*validity = RANGE_VALID;
return value;
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
std::numeric_limits<T>::is_signed,
typename UnsignedIntegerForSize<T>::type>::type
CheckedUnsignedAbs(T value) {
typedef typename UnsignedIntegerForSize<T>::type UnsignedT;
return value == std::numeric_limits<T>::min()
? static_cast<UnsignedT>(std::numeric_limits<T>::max()) + 1
: static_cast<UnsignedT>(std::abs(value));
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T>::is_signed,
T>::type
CheckedUnsignedAbs(T value) {
// T is unsigned, so |value| must already be positive.
return static_cast<T>(value);
}
// These are the floating point stubs that the compiler needs to see. Only the
// negation operation is ever called.
#define BASE_FLOAT_ARITHMETIC_STUBS(NAME) \
template <typename T> \
typename std::enable_if<std::numeric_limits<T>::is_iec559, T>::type \
Checked##NAME(T, T, RangeConstraint*) { \
NOTREACHED(); \
return static_cast<T>(0); \
}
BASE_FLOAT_ARITHMETIC_STUBS(Add)
BASE_FLOAT_ARITHMETIC_STUBS(Sub)
BASE_FLOAT_ARITHMETIC_STUBS(Mul)
BASE_FLOAT_ARITHMETIC_STUBS(Div)
BASE_FLOAT_ARITHMETIC_STUBS(Mod)
#undef BASE_FLOAT_ARITHMETIC_STUBS
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_iec559, T>::type CheckedNeg(
T value,
RangeConstraint*) {
return static_cast<T>(-value);
}
template <typename T>
typename std::enable_if<std::numeric_limits<T>::is_iec559, T>::type CheckedAbs(
T value,
RangeConstraint*) {
return static_cast<T>(std::abs(value));
}
// 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::numeric_limits<NumericType>::is_integer
? NUMERIC_INTEGER
: (std::numeric_limits<NumericType>::is_iec559 ? 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> {
private:
T value_;
RangeConstraint validity_ : CHAR_BIT; // Actually requires only two bits.
public:
template <typename Src, NumericRepresentation type>
friend class CheckedNumericState;
CheckedNumericState() : value_(0), validity_(RANGE_VALID) {}
template <typename Src>
CheckedNumericState(Src value, RangeConstraint validity)
: value_(static_cast<T>(value)),
validity_(GetRangeConstraint(validity |
DstRangeRelationToSrcRange<T>(value))) {
static_assert(std::numeric_limits<Src>::is_specialized,
"Argument must be numeric.");
}
// Copy constructor.
template <typename Src>
CheckedNumericState(const CheckedNumericState<Src>& rhs)
: value_(static_cast<T>(rhs.value())),
validity_(GetRangeConstraint(
rhs.validity() | DstRangeRelationToSrcRange<T>(rhs.value()))) {}
template <typename Src>
explicit CheckedNumericState(
Src value,
typename std::enable_if<std::numeric_limits<Src>::is_specialized,
int>::type = 0)
: value_(static_cast<T>(value)),
validity_(DstRangeRelationToSrcRange<T>(value)) {}
RangeConstraint validity() const { return validity_; }
T value() const { return value_; }
};
// Floating points maintain their own validity, but need translation wrappers.
template <typename T>
class CheckedNumericState<T, NUMERIC_FLOATING> {
private:
T value_;
public:
template <typename Src, NumericRepresentation type>
friend class CheckedNumericState;
CheckedNumericState() : value_(0.0) {}
template <typename Src>
CheckedNumericState(
Src value,
RangeConstraint validity,
typename std::enable_if<std::numeric_limits<Src>::is_integer, int>::type =
0) {
switch (DstRangeRelationToSrcRange<T>(value)) {
case RANGE_VALID:
value_ = static_cast<T>(value);
break;
case RANGE_UNDERFLOW:
value_ = -std::numeric_limits<T>::infinity();
break;
case RANGE_OVERFLOW:
value_ = std::numeric_limits<T>::infinity();
break;
case RANGE_INVALID:
value_ = std::numeric_limits<T>::quiet_NaN();
break;
default:
NOTREACHED();
}
}
template <typename Src>
explicit CheckedNumericState(
Src value,
typename std::enable_if<std::numeric_limits<Src>::is_specialized,
int>::type = 0)
: value_(static_cast<T>(value)) {}
// Copy constructor.
template <typename Src>
CheckedNumericState(const CheckedNumericState<Src>& rhs)
: value_(static_cast<T>(rhs.value())) {}
RangeConstraint validity() const {
return GetRangeConstraint(value_ <= std::numeric_limits<T>::max(),
value_ >= -std::numeric_limits<T>::max());
}
T value() const { return value_; }
};
// For integers less than 128-bit and floats 32-bit or larger, we have the type
// with the larger maximum exponent take precedence.
enum ArithmeticPromotionCategory { LEFT_PROMOTION, RIGHT_PROMOTION };
template <typename Lhs,
typename Rhs = Lhs,
ArithmeticPromotionCategory Promotion =
(MaxExponent<Lhs>::value > MaxExponent<Rhs>::value)
? LEFT_PROMOTION
: RIGHT_PROMOTION>
struct ArithmeticPromotion;
template <typename Lhs, typename Rhs>
struct ArithmeticPromotion<Lhs, Rhs, LEFT_PROMOTION> {
typedef Lhs type;
};
template <typename Lhs, typename Rhs>
struct ArithmeticPromotion<Lhs, Rhs, RIGHT_PROMOTION> {
typedef Rhs type;
};
// We can statically check if operations on the provided types can wrap, so we
// can skip the checked operations if they're not needed. So, for an integer we
// care if the destination type preserves the sign and is twice the width of
// the source.
template <typename T, typename Lhs, typename Rhs>
struct IsIntegerArithmeticSafe {
static const bool value = !std::numeric_limits<T>::is_iec559 &&
StaticDstRangeRelationToSrcRange<T, Lhs>::value ==
NUMERIC_RANGE_CONTAINED &&
sizeof(T) >= (2 * sizeof(Lhs)) &&
StaticDstRangeRelationToSrcRange<T, Rhs>::value !=
NUMERIC_RANGE_CONTAINED &&
sizeof(T) >= (2 * sizeof(Rhs));
};
} // namespace internal
} // namespace base
#endif // BASE_NUMERICS_SAFE_MATH_IMPL_H_