// 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_CONVERSIONS_IMPL_H_
#define BASE_NUMERICS_SAFE_CONVERSIONS_IMPL_H_
#include <limits.h>
#include <stdint.h>
#include <limits>
#include "base/template_util.h"
namespace base {
namespace internal {
// The std library doesn't provide a binary max_exponent for integers, however
// we can compute one by adding one to the number of non-sign bits. This allows
// for accurate range comparisons between floating point and integer types.
template <typename NumericType>
struct MaxExponent {
static const int value = std::numeric_limits<NumericType>::is_iec559
? std::numeric_limits<NumericType>::max_exponent
: (sizeof(NumericType) * 8 + 1 -
std::numeric_limits<NumericType>::is_signed);
};
enum IntegerRepresentation {
INTEGER_REPRESENTATION_UNSIGNED,
INTEGER_REPRESENTATION_SIGNED
};
// A range for a given nunmeric Src type is contained for a given numeric Dst
// type if both numeric_limits<Src>::max() <= numeric_limits<Dst>::max() and
// numeric_limits<Src>::min() >= numeric_limits<Dst>::min() are true.
// We implement this as template specializations rather than simple static
// comparisons to ensure type correctness in our comparisons.
enum NumericRangeRepresentation {
NUMERIC_RANGE_NOT_CONTAINED,
NUMERIC_RANGE_CONTAINED
};
// Helper templates to statically determine if our destination type can contain
// maximum and minimum values represented by the source type.
template <
typename Dst,
typename Src,
IntegerRepresentation DstSign = std::numeric_limits<Dst>::is_signed
? INTEGER_REPRESENTATION_SIGNED
: INTEGER_REPRESENTATION_UNSIGNED,
IntegerRepresentation SrcSign =
std::numeric_limits<Src>::is_signed
? INTEGER_REPRESENTATION_SIGNED
: INTEGER_REPRESENTATION_UNSIGNED >
struct StaticDstRangeRelationToSrcRange;
// Same sign: Dst is guaranteed to contain Src only if its range is equal or
// larger.
template <typename Dst, typename Src, IntegerRepresentation Sign>
struct StaticDstRangeRelationToSrcRange<Dst, Src, Sign, Sign> {
static const NumericRangeRepresentation value =
MaxExponent<Dst>::value >= MaxExponent<Src>::value
? NUMERIC_RANGE_CONTAINED
: NUMERIC_RANGE_NOT_CONTAINED;
};
// Unsigned to signed: Dst is guaranteed to contain source only if its range is
// larger.
template <typename Dst, typename Src>
struct StaticDstRangeRelationToSrcRange<Dst,
Src,
INTEGER_REPRESENTATION_SIGNED,
INTEGER_REPRESENTATION_UNSIGNED> {
static const NumericRangeRepresentation value =
MaxExponent<Dst>::value > MaxExponent<Src>::value
? NUMERIC_RANGE_CONTAINED
: NUMERIC_RANGE_NOT_CONTAINED;
};
// Signed to unsigned: Dst cannot be statically determined to contain Src.
template <typename Dst, typename Src>
struct StaticDstRangeRelationToSrcRange<Dst,
Src,
INTEGER_REPRESENTATION_UNSIGNED,
INTEGER_REPRESENTATION_SIGNED> {
static const NumericRangeRepresentation value = NUMERIC_RANGE_NOT_CONTAINED;
};
enum RangeConstraint {
RANGE_VALID = 0x0, // Value can be represented by the destination type.
RANGE_UNDERFLOW = 0x1, // Value would overflow.
RANGE_OVERFLOW = 0x2, // Value would underflow.
RANGE_INVALID = RANGE_UNDERFLOW | RANGE_OVERFLOW // Invalid (i.e. NaN).
};
// Helper function for coercing an int back to a RangeContraint.
inline RangeConstraint GetRangeConstraint(int integer_range_constraint) {
DCHECK(integer_range_constraint >= RANGE_VALID &&
integer_range_constraint <= RANGE_INVALID);
return static_cast<RangeConstraint>(integer_range_constraint);
}
// This function creates a RangeConstraint from an upper and lower bound
// check by taking advantage of the fact that only NaN can be out of range in
// both directions at once.
inline RangeConstraint GetRangeConstraint(bool is_in_upper_bound,
bool is_in_lower_bound) {
return GetRangeConstraint((is_in_upper_bound ? 0 : RANGE_OVERFLOW) |
(is_in_lower_bound ? 0 : RANGE_UNDERFLOW));
}
// The following helper template addresses a corner case in range checks for
// conversion from a floating-point type to an integral type of smaller range
// but larger precision (e.g. float -> unsigned). The problem is as follows:
// 1. Integral maximum is always one less than a power of two, so it must be
// truncated to fit the mantissa of the floating point. The direction of
// rounding is implementation defined, but by default it's always IEEE
// floats, which round to nearest and thus result in a value of larger
// magnitude than the integral value.
// Example: float f = UINT_MAX; // f is 4294967296f but UINT_MAX
// // is 4294967295u.
// 2. If the floating point value is equal to the promoted integral maximum
// value, a range check will erroneously pass.
// Example: (4294967296f <= 4294967295u) // This is true due to a precision
// // loss in rounding up to float.
// 3. When the floating point value is then converted to an integral, the
// resulting value is out of range for the target integral type and
// thus is implementation defined.
// Example: unsigned u = (float)INT_MAX; // u will typically overflow to 0.
// To fix this bug we manually truncate the maximum value when the destination
// type is an integral of larger precision than the source floating-point type,
// such that the resulting maximum is represented exactly as a floating point.
template <typename Dst, typename Src>
struct NarrowingRange {
typedef typename std::numeric_limits<Src> SrcLimits;
typedef typename std::numeric_limits<Dst> DstLimits;
static Dst max() {
// The following logic avoids warnings where the max function is
// instantiated with invalid values for a bit shift (even though
// such a function can never be called).
static const int shift =
(MaxExponent<Src>::value > MaxExponent<Dst>::value &&
SrcLimits::digits < DstLimits::digits && SrcLimits::is_iec559 &&
DstLimits::is_integer)
? (DstLimits::digits - SrcLimits::digits)
: 0;
// We use UINTMAX_C below to avoid compiler warnings about shifting floating
// points. Since it's a compile time calculation, it shouldn't have any
// performance impact.
return DstLimits::max() - static_cast<Dst>((UINTMAX_C(1) << shift) - 1);
}
static Dst min() {
return std::numeric_limits<Dst>::is_iec559 ? -DstLimits::max()
: DstLimits::min();
}
};
template <
typename Dst,
typename Src,
IntegerRepresentation DstSign = std::numeric_limits<Dst>::is_signed
? INTEGER_REPRESENTATION_SIGNED
: INTEGER_REPRESENTATION_UNSIGNED,
IntegerRepresentation SrcSign = std::numeric_limits<Src>::is_signed
? INTEGER_REPRESENTATION_SIGNED
: INTEGER_REPRESENTATION_UNSIGNED,
NumericRangeRepresentation DstRange =
StaticDstRangeRelationToSrcRange<Dst, Src>::value >
struct DstRangeRelationToSrcRangeImpl;
// The following templates are for ranges that must be verified at runtime. We
// split it into checks based on signedness to avoid confusing casts and
// compiler warnings on signed an unsigned comparisons.
// Dst range is statically determined to contain Src: Nothing to check.
template <typename Dst,
typename Src,
IntegerRepresentation DstSign,
IntegerRepresentation SrcSign>
struct DstRangeRelationToSrcRangeImpl<Dst,
Src,
DstSign,
SrcSign,
NUMERIC_RANGE_CONTAINED> {
static RangeConstraint Check(Src /* value */) { return RANGE_VALID; }
};
// Signed to signed narrowing: Both the upper and lower boundaries may be
// exceeded.
template <typename Dst, typename Src>
struct DstRangeRelationToSrcRangeImpl<Dst,
Src,
INTEGER_REPRESENTATION_SIGNED,
INTEGER_REPRESENTATION_SIGNED,
NUMERIC_RANGE_NOT_CONTAINED> {
static RangeConstraint Check(Src value) {
return GetRangeConstraint((value <= NarrowingRange<Dst, Src>::max()),
(value >= NarrowingRange<Dst, Src>::min()));
}
};
// Unsigned to unsigned narrowing: Only the upper boundary can be exceeded.
template <typename Dst, typename Src>
struct DstRangeRelationToSrcRangeImpl<Dst,
Src,
INTEGER_REPRESENTATION_UNSIGNED,
INTEGER_REPRESENTATION_UNSIGNED,
NUMERIC_RANGE_NOT_CONTAINED> {
static RangeConstraint Check(Src value) {
return GetRangeConstraint(value <= NarrowingRange<Dst, Src>::max(), true);
}
};
// Unsigned to signed: The upper boundary may be exceeded.
template <typename Dst, typename Src>
struct DstRangeRelationToSrcRangeImpl<Dst,
Src,
INTEGER_REPRESENTATION_SIGNED,
INTEGER_REPRESENTATION_UNSIGNED,
NUMERIC_RANGE_NOT_CONTAINED> {
static RangeConstraint Check(Src value) {
return sizeof(Dst) > sizeof(Src)
? RANGE_VALID
: GetRangeConstraint(
value <= static_cast<Src>(NarrowingRange<Dst, Src>::max()),
true);
}
};
// Signed to unsigned: The upper boundary may be exceeded for a narrower Dst,
// and any negative value exceeds the lower boundary.
template <typename Dst, typename Src>
struct DstRangeRelationToSrcRangeImpl<Dst,
Src,
INTEGER_REPRESENTATION_UNSIGNED,
INTEGER_REPRESENTATION_SIGNED,
NUMERIC_RANGE_NOT_CONTAINED> {
static RangeConstraint Check(Src value) {
return (MaxExponent<Dst>::value >= MaxExponent<Src>::value)
? GetRangeConstraint(true, value >= static_cast<Src>(0))
: GetRangeConstraint(
value <= static_cast<Src>(NarrowingRange<Dst, Src>::max()),
value >= static_cast<Src>(0));
}
};
template <typename Dst, typename Src>
inline RangeConstraint DstRangeRelationToSrcRange(Src value) {
static_assert(std::numeric_limits<Src>::is_specialized,
"Argument must be numeric.");
static_assert(std::numeric_limits<Dst>::is_specialized,
"Result must be numeric.");
return DstRangeRelationToSrcRangeImpl<Dst, Src>::Check(value);
}
} // namespace internal
} // namespace base
#endif // BASE_NUMERICS_SAFE_CONVERSIONS_IMPL_H_