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// Copyright 2017 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_CHECKED_MATH_IMPL_H_
#define BASE_NUMERICS_CHECKED_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"
#include "base/numerics/safe_math_shared_impl.h"
namespace base {
namespace internal {
template <typename T>
constexpr bool CheckedAddImpl(T x, T y, T* result) {
static_assert(std::is_integral<T>::value, "Type must be integral");
// 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.
using UnsignedDst = typename std::make_unsigned<T>::type;
using SignedDst = typename std::make_signed<T>::type;
UnsignedDst ux = static_cast<UnsignedDst>(x);
UnsignedDst uy = static_cast<UnsignedDst>(y);
UnsignedDst uresult = static_cast<UnsignedDst>(ux + uy);
*result = static_cast<T>(uresult);
// Addition is valid if the sign of (x + y) is equal to either that of x or
// that of y.
return (std::is_signed<T>::value)
? static_cast<SignedDst>((uresult ^ ux) & (uresult ^ uy)) >= 0
: uresult >= uy; // Unsigned is either valid or underflow.
}
template <typename T, typename U, class Enable = void>
struct CheckedAddOp {};
template <typename T, typename U>
struct CheckedAddOp<T,
U,
typename std::enable_if<std::is_integral<T>::value &&
std::is_integral<U>::value>::type> {
using result_type = typename MaxExponentPromotion<T, U>::type;
template <typename V>
static constexpr bool Do(T x, U y, V* result) {
// TODO(jschuh) Make this "constexpr if" once we're C++17.
if (CheckedAddFastOp<T, U>::is_supported)
return CheckedAddFastOp<T, U>::Do(x, y, result);
// Double the underlying type up to a full machine word.
using FastPromotion = typename FastIntegerArithmeticPromotion<T, U>::type;
using Promotion =
typename std::conditional<(IntegerBitsPlusSign<FastPromotion>::value >
IntegerBitsPlusSign<intptr_t>::value),
typename BigEnoughPromotion<T, U>::type,
FastPromotion>::type;
// Fail if either operand is out of range for the promoted type.
// TODO(jschuh): This could be made to work for a broader range of values.
if (BASE_NUMERICS_UNLIKELY(!IsValueInRangeForNumericType<Promotion>(x) ||
!IsValueInRangeForNumericType<Promotion>(y))) {
return false;
}
Promotion presult = {};
bool is_valid = true;
if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
presult = static_cast<Promotion>(x) + static_cast<Promotion>(y);
} else {
is_valid = CheckedAddImpl(static_cast<Promotion>(x),
static_cast<Promotion>(y), &presult);
}
*result = static_cast<V>(presult);
return is_valid && IsValueInRangeForNumericType<V>(presult);
}
};
template <typename T>
constexpr bool CheckedSubImpl(T x, T y, T* result) {
static_assert(std::is_integral<T>::value, "Type must be integral");
// 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.
using UnsignedDst = typename std::make_unsigned<T>::type;
using SignedDst = typename std::make_signed<T>::type;
UnsignedDst ux = static_cast<UnsignedDst>(x);
UnsignedDst uy = static_cast<UnsignedDst>(y);
UnsignedDst uresult = static_cast<UnsignedDst>(ux - uy);
*result = static_cast<T>(uresult);
// Subtraction is valid if either x and y have same sign, or (x-y) and x have
// the same sign.
return (std::is_signed<T>::value)
? static_cast<SignedDst>((uresult ^ ux) & (ux ^ uy)) >= 0
: x >= y;
}
template <typename T, typename U, class Enable = void>
struct CheckedSubOp {};
template <typename T, typename U>
struct CheckedSubOp<T,
U,
typename std::enable_if<std::is_integral<T>::value &&
std::is_integral<U>::value>::type> {
using result_type = typename MaxExponentPromotion<T, U>::type;
template <typename V>
static constexpr bool Do(T x, U y, V* result) {
// TODO(jschuh) Make this "constexpr if" once we're C++17.
if (CheckedSubFastOp<T, U>::is_supported)
return CheckedSubFastOp<T, U>::Do(x, y, result);
// Double the underlying type up to a full machine word.
using FastPromotion = typename FastIntegerArithmeticPromotion<T, U>::type;
using Promotion =
typename std::conditional<(IntegerBitsPlusSign<FastPromotion>::value >
IntegerBitsPlusSign<intptr_t>::value),
typename BigEnoughPromotion<T, U>::type,
FastPromotion>::type;
// Fail if either operand is out of range for the promoted type.
// TODO(jschuh): This could be made to work for a broader range of values.
if (BASE_NUMERICS_UNLIKELY(!IsValueInRangeForNumericType<Promotion>(x) ||
!IsValueInRangeForNumericType<Promotion>(y))) {
return false;
}
Promotion presult = {};
bool is_valid = true;
if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
presult = static_cast<Promotion>(x) - static_cast<Promotion>(y);
} else {
is_valid = CheckedSubImpl(static_cast<Promotion>(x),
static_cast<Promotion>(y), &presult);
}
*result = static_cast<V>(presult);
return is_valid && IsValueInRangeForNumericType<V>(presult);
}
};
template <typename T>
constexpr bool CheckedMulImpl(T x, T y, T* result) {
static_assert(std::is_integral<T>::value, "Type must be integral");
// Since the value of x*y is potentially undefined if we have a signed type,
// we compute it using the unsigned type of the same size.
using UnsignedDst = typename std::make_unsigned<T>::type;
using SignedDst = typename std::make_signed<T>::type;
const UnsignedDst ux = SafeUnsignedAbs(x);
const UnsignedDst uy = SafeUnsignedAbs(y);
UnsignedDst uresult = static_cast<UnsignedDst>(ux * uy);
const bool is_negative =
std::is_signed<T>::value && static_cast<SignedDst>(x ^ y) < 0;
*result = is_negative ? 0 - uresult : uresult;
// We have a fast out for unsigned identity or zero on the second operand.
// After that it's an unsigned overflow check on the absolute value, with
// a +1 bound for a negative result.
return uy <= UnsignedDst(!std::is_signed<T>::value || is_negative) ||
ux <= (std::numeric_limits<T>::max() + UnsignedDst(is_negative)) / uy;
}
template <typename T, typename U, class Enable = void>
struct CheckedMulOp {};
template <typename T, typename U>
struct CheckedMulOp<T,
U,
typename std::enable_if<std::is_integral<T>::value &&
std::is_integral<U>::value>::type> {
using result_type = typename MaxExponentPromotion<T, U>::type;
template <typename V>
static constexpr bool Do(T x, U y, V* result) {
// TODO(jschuh) Make this "constexpr if" once we're C++17.
if (CheckedMulFastOp<T, U>::is_supported)
return CheckedMulFastOp<T, U>::Do(x, y, result);
using Promotion = typename FastIntegerArithmeticPromotion<T, U>::type;
// Verify the destination type can hold the result (always true for 0).
if (BASE_NUMERICS_UNLIKELY((!IsValueInRangeForNumericType<Promotion>(x) ||
!IsValueInRangeForNumericType<Promotion>(y)) &&
x && y)) {
return false;
}
Promotion presult = {};
bool is_valid = true;
if (CheckedMulFastOp<Promotion, Promotion>::is_supported) {
// The fast op may be available with the promoted type.
is_valid = CheckedMulFastOp<Promotion, Promotion>::Do(x, y, &presult);
} else if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
presult = static_cast<Promotion>(x) * static_cast<Promotion>(y);
} else {
is_valid = CheckedMulImpl(static_cast<Promotion>(x),
static_cast<Promotion>(y), &presult);
}
*result = static_cast<V>(presult);
return is_valid && IsValueInRangeForNumericType<V>(presult);
}
};
// Division just requires a check for a zero denominator or an invalid negation
// on signed min/-1.
template <typename T, typename U, class Enable = void>
struct CheckedDivOp {};
template <typename T, typename U>
struct CheckedDivOp<T,
U,
typename std::enable_if<std::is_integral<T>::value &&
std::is_integral<U>::value>::type> {
using result_type = typename MaxExponentPromotion<T, U>::type;
template <typename V>
static constexpr bool Do(T x, U y, V* result) {
if (BASE_NUMERICS_UNLIKELY(!y))
return false;
// The overflow check can be compiled away if we don't have the exact
// combination of types needed to trigger this case.
using Promotion = typename BigEnoughPromotion<T, U>::type;
if (BASE_NUMERICS_UNLIKELY(
(std::is_signed<T>::value && std::is_signed<U>::value &&
IsTypeInRangeForNumericType<T, Promotion>::value &&
static_cast<Promotion>(x) ==
std::numeric_limits<Promotion>::lowest() &&
y == static_cast<U>(-1)))) {
return false;
}
// This branch always compiles away if the above branch wasn't removed.
if (BASE_NUMERICS_UNLIKELY((!IsValueInRangeForNumericType<Promotion>(x) ||
!IsValueInRangeForNumericType<Promotion>(y)) &&
x)) {
return false;
}
Promotion presult = Promotion(x) / Promotion(y);
*result = static_cast<V>(presult);
return IsValueInRangeForNumericType<V>(presult);
}
};
template <typename T, typename U, class Enable = void>
struct CheckedModOp {};
template <typename T, typename U>
struct CheckedModOp<T,
U,
typename std::enable_if<std::is_integral<T>::value &&
std::is_integral<U>::value>::type> {
using result_type = typename MaxExponentPromotion<T, U>::type;
template <typename V>
static constexpr bool Do(T x, U y, V* result) {
using Promotion = typename BigEnoughPromotion<T, U>::type;
if (BASE_NUMERICS_LIKELY(y)) {
Promotion presult = static_cast<Promotion>(x) % static_cast<Promotion>(y);
*result = static_cast<Promotion>(presult);
return IsValueInRangeForNumericType<V>(presult);
}
return false;
}
};
template <typename T, typename U, class Enable = void>
struct CheckedLshOp {};
// Left shift. Shifts less than 0 or greater than or equal to the number
// of bits in the promoted type are undefined. Shifts of negative values
// are undefined. Otherwise it is defined when the result fits.
template <typename T, typename U>
struct CheckedLshOp<T,
U,
typename std::enable_if<std::is_integral<T>::value &&
std::is_integral<U>::value>::type> {
using result_type = T;
template <typename V>
static constexpr bool Do(T x, U shift, V* result) {
// Disallow negative numbers and verify the shift is in bounds.
if (BASE_NUMERICS_LIKELY(!IsValueNegative(x) &&
as_unsigned(shift) <
as_unsigned(std::numeric_limits<T>::digits))) {
// Shift as unsigned to avoid undefined behavior.
*result = static_cast<V>(as_unsigned(x) << shift);
// If the shift can be reversed, we know it was valid.
return *result >> shift == x;
}
// Handle the legal corner-case of a full-width signed shift of zero.
return std::is_signed<T>::value && !x &&
as_unsigned(shift) == as_unsigned(std::numeric_limits<T>::digits);
}
};
template <typename T, typename U, class Enable = void>
struct CheckedRshOp {};
// Right shift. Shifts less than 0 or greater than or equal to the number
// of bits in the promoted type are undefined. Otherwise, it is always defined,
// but a right shift of a negative value is implementation-dependent.
template <typename T, typename U>
struct CheckedRshOp<T,
U,
typename std::enable_if<std::is_integral<T>::value &&
std::is_integral<U>::value>::type> {
using result_type = T;
template <typename V>
static bool Do(T x, U shift, V* result) {
// Use the type conversion push negative values out of range.
if (BASE_NUMERICS_LIKELY(as_unsigned(shift) <
IntegerBitsPlusSign<T>::value)) {
T tmp = x >> shift;
*result = static_cast<V>(tmp);
return IsValueInRangeForNumericType<V>(tmp);
}
return false;
}
};
template <typename T, typename U, class Enable = void>
struct CheckedAndOp {};
// For simplicity we support only unsigned integer results.
template <typename T, typename U>
struct CheckedAndOp<T,
U,
typename std::enable_if<std::is_integral<T>::value &&
std::is_integral<U>::value>::type> {
using result_type = typename std::make_unsigned<
typename MaxExponentPromotion<T, U>::type>::type;
template <typename V>
static constexpr bool Do(T x, U y, V* result) {
result_type tmp = static_cast<result_type>(x) & static_cast<result_type>(y);
*result = static_cast<V>(tmp);
return IsValueInRangeForNumericType<V>(tmp);
}
};
template <typename T, typename U, class Enable = void>
struct CheckedOrOp {};
// For simplicity we support only unsigned integers.
template <typename T, typename U>
struct CheckedOrOp<T,
U,
typename std::enable_if<std::is_integral<T>::value &&
std::is_integral<U>::value>::type> {
using result_type = typename std::make_unsigned<
typename MaxExponentPromotion<T, U>::type>::type;
template <typename V>
static constexpr bool Do(T x, U y, V* result) {
result_type tmp = static_cast<result_type>(x) | static_cast<result_type>(y);
*result = static_cast<V>(tmp);
return IsValueInRangeForNumericType<V>(tmp);
}
};
template <typename T, typename U, class Enable = void>
struct CheckedXorOp {};
// For simplicity we support only unsigned integers.
template <typename T, typename U>
struct CheckedXorOp<T,
U,
typename std::enable_if<std::is_integral<T>::value &&
std::is_integral<U>::value>::type> {
using result_type = typename std::make_unsigned<
typename MaxExponentPromotion<T, U>::type>::type;
template <typename V>
static constexpr bool Do(T x, U y, V* result) {
result_type tmp = static_cast<result_type>(x) ^ static_cast<result_type>(y);
*result = static_cast<V>(tmp);
return IsValueInRangeForNumericType<V>(tmp);
}
};
// Max doesn't really need to be implemented this way because it can't fail,
// but it makes the code much cleaner to use the MathOp wrappers.
template <typename T, typename U, class Enable = void>
struct CheckedMaxOp {};
template <typename T, typename U>
struct CheckedMaxOp<
T,
U,
typename std::enable_if<std::is_arithmetic<T>::value &&
std::is_arithmetic<U>::value>::type> {
using result_type = typename MaxExponentPromotion<T, U>::type;
template <typename V>
static constexpr bool Do(T x, U y, V* result) {
result_type tmp = IsGreater<T, U>::Test(x, y) ? static_cast<result_type>(x)
: static_cast<result_type>(y);
*result = static_cast<V>(tmp);
return IsValueInRangeForNumericType<V>(tmp);
}
};
// Min doesn't really need to be implemented this way because it can't fail,
// but it makes the code much cleaner to use the MathOp wrappers.
template <typename T, typename U, class Enable = void>
struct CheckedMinOp {};
template <typename T, typename U>
struct CheckedMinOp<
T,
U,
typename std::enable_if<std::is_arithmetic<T>::value &&
std::is_arithmetic<U>::value>::type> {
using result_type = typename LowestValuePromotion<T, U>::type;
template <typename V>
static constexpr bool Do(T x, U y, V* result) {
result_type tmp = IsLess<T, U>::Test(x, y) ? static_cast<result_type>(x)
: static_cast<result_type>(y);
*result = static_cast<V>(tmp);
return IsValueInRangeForNumericType<V>(tmp);
}
};
// This is just boilerplate that wraps the standard floating point arithmetic.
// A macro isn't the nicest solution, but it beats rewriting these repeatedly.
#define BASE_FLOAT_ARITHMETIC_OPS(NAME, OP) \
template <typename T, typename U> \
struct Checked##NAME##Op< \
T, U, \
typename std::enable_if<std::is_floating_point<T>::value || \
std::is_floating_point<U>::value>::type> { \
using result_type = typename MaxExponentPromotion<T, U>::type; \
template <typename V> \
static constexpr bool Do(T x, U y, V* result) { \
using Promotion = typename MaxExponentPromotion<T, U>::type; \
Promotion presult = x OP y; \
*result = static_cast<V>(presult); \
return IsValueInRangeForNumericType<V>(presult); \
} \
};
BASE_FLOAT_ARITHMETIC_OPS(Add, +)
BASE_FLOAT_ARITHMETIC_OPS(Sub, -)
BASE_FLOAT_ARITHMETIC_OPS(Mul, *)
BASE_FLOAT_ARITHMETIC_OPS(Div, /)
#undef BASE_FLOAT_ARITHMETIC_OPS
// 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::is_integral<NumericType>::value
? NUMERIC_INTEGER
: (std::is_floating_point<NumericType>::value ? 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:
// is_valid_ precedes value_ because member intializers in the constructors
// are evaluated in field order, and is_valid_ must be read when initializing
// value_.
bool is_valid_;
T value_;
// Ensures that a type conversion does not trigger undefined behavior.
template <typename Src>
static constexpr T WellDefinedConversionOrZero(const Src value,
const bool is_valid) {
using SrcType = typename internal::UnderlyingType<Src>::type;
return (std::is_integral<SrcType>::value || is_valid)
? static_cast<T>(value)
: static_cast<T>(0);
}
public:
template <typename Src, NumericRepresentation type>
friend class CheckedNumericState;
constexpr CheckedNumericState() : is_valid_(true), value_(0) {}
template <typename Src>
constexpr CheckedNumericState(Src value, bool is_valid)
: is_valid_(is_valid && IsValueInRangeForNumericType<T>(value)),
value_(WellDefinedConversionOrZero(value, is_valid_)) {
static_assert(std::is_arithmetic<Src>::value, "Argument must be numeric.");
}
// Copy constructor.
template <typename Src>
constexpr CheckedNumericState(const CheckedNumericState<Src>& rhs)
: is_valid_(rhs.IsValid()),
value_(WellDefinedConversionOrZero(rhs.value(), is_valid_)) {}
template <typename Src>
constexpr explicit CheckedNumericState(Src value)
: is_valid_(IsValueInRangeForNumericType<T>(value)),
value_(WellDefinedConversionOrZero(value, is_valid_)) {}
constexpr bool is_valid() const { return is_valid_; }
constexpr 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_;
// Ensures that a type conversion does not trigger undefined behavior.
template <typename Src>
static constexpr T WellDefinedConversionOrNaN(const Src value,
const bool is_valid) {
using SrcType = typename internal::UnderlyingType<Src>::type;
return (StaticDstRangeRelationToSrcRange<T, SrcType>::value ==
NUMERIC_RANGE_CONTAINED ||
is_valid)
? static_cast<T>(value)
: std::numeric_limits<T>::quiet_NaN();
}
public:
template <typename Src, NumericRepresentation type>
friend class CheckedNumericState;
constexpr CheckedNumericState() : value_(0.0) {}
template <typename Src>
constexpr CheckedNumericState(Src value, bool is_valid)
: value_(WellDefinedConversionOrNaN(value, is_valid)) {}
template <typename Src>
constexpr explicit CheckedNumericState(Src value)
: value_(WellDefinedConversionOrNaN(
value,
IsValueInRangeForNumericType<T>(value))) {}
// Copy constructor.
template <typename Src>
constexpr CheckedNumericState(const CheckedNumericState<Src>& rhs)
: value_(WellDefinedConversionOrNaN(
rhs.value(),
rhs.is_valid() && IsValueInRangeForNumericType<T>(rhs.value()))) {}
constexpr bool is_valid() const {
// Written this way because std::isfinite is not reliably constexpr.
return MustTreatAsConstexpr(value_)
? value_ <= std::numeric_limits<T>::max() &&
value_ >= std::numeric_limits<T>::lowest()
: std::isfinite(value_);
}
constexpr T value() const { return value_; }
};
} // namespace internal
} // namespace base
#endif // BASE_NUMERICS_CHECKED_MATH_IMPL_H_