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/****************************************************************************
**
** Copyright (C) 2019 The Qt Company Ltd.
** Copyright (C) 2018 Intel Corporation.
** Contact: https://www.qt.io/licensing/
**
** This file is part of the QtCore module of the Qt Toolkit.
**
** $QT_BEGIN_LICENSE:LGPL$
** Commercial License Usage
** Licensees holding valid commercial Qt licenses may use this file in
** accordance with the commercial license agreement provided with the
** Software or, alternatively, in accordance with the terms contained in
** a written agreement between you and The Qt Company. For licensing terms
** and conditions see https://www.qt.io/terms-conditions. For further
** information use the contact form at https://www.qt.io/contact-us.
**
** GNU Lesser General Public License Usage
** Alternatively, this file may be used under the terms of the GNU Lesser
** General Public License version 3 as published by the Free Software
** Foundation and appearing in the file LICENSE.LGPL3 included in the
** packaging of this file. Please review the following information to
** ensure the GNU Lesser General Public License version 3 requirements
** will be met: https://www.gnu.org/licenses/lgpl-3.0.html.
**
** GNU General Public License Usage
** Alternatively, this file may be used under the terms of the GNU
** General Public License version 2.0 or (at your option) the GNU General
** Public license version 3 or any later version approved by the KDE Free
** Qt Foundation. The licenses are as published by the Free Software
** Foundation and appearing in the file LICENSE.GPL2 and LICENSE.GPL3
** included in the packaging of this file. Please review the following
** information to ensure the GNU General Public License requirements will
** be met: https://www.gnu.org/licenses/gpl-2.0.html and
** https://www.gnu.org/licenses/gpl-3.0.html.
**
** $QT_END_LICENSE$
**
****************************************************************************/
#ifndef QNUMERIC_P_H
#define QNUMERIC_P_H
//
// W A R N I N G
// -------------
//
// This file is not part of the Qt API. It exists purely as an
// implementation detail. This header file may change from version to
// version without notice, or even be removed.
//
// We mean it.
//
#include "QtCore/private/qglobal_p.h"
#include <cmath>
#include <limits>
#if defined(Q_CC_MSVC)
# include <intrin.h>
# include <float.h>
# if defined(Q_PROCESSOR_X86_64) || defined(Q_PROCESSOR_ARM_64)
# define Q_INTRINSIC_MUL_OVERFLOW64
# define Q_UMULH(v1, v2) __umulh(v1, v2);
# define Q_SMULH(v1, v2) __mulh(v1, v2);
# pragma intrinsic(__umulh)
# pragma intrinsic(__mulh)
# endif
#endif
# if defined(Q_OS_INTEGRITY) && defined(Q_PROCESSOR_ARM_64)
#include <arm64_ghs.h>
# define Q_INTRINSIC_MUL_OVERFLOW64
# define Q_UMULH(v1, v2) __MULUH64(v1, v2);
# define Q_SMULH(v1, v2) __MULSH64(v1, v2);
#endif
#if !defined(Q_CC_MSVC) && (defined(Q_OS_QNX) || defined(Q_CC_INTEL))
# include <math.h>
# ifdef isnan
# define QT_MATH_H_DEFINES_MACROS
QT_BEGIN_NAMESPACE
namespace qnumeric_std_wrapper {
// the 'using namespace std' below is cases where the stdlib already put the math.h functions in the std namespace and undefined the macros.
Q_DECL_CONST_FUNCTION static inline bool math_h_isnan(double d) { using namespace std; return isnan(d); }
Q_DECL_CONST_FUNCTION static inline bool math_h_isinf(double d) { using namespace std; return isinf(d); }
Q_DECL_CONST_FUNCTION static inline bool math_h_isfinite(double d) { using namespace std; return isfinite(d); }
Q_DECL_CONST_FUNCTION static inline int math_h_fpclassify(double d) { using namespace std; return fpclassify(d); }
Q_DECL_CONST_FUNCTION static inline bool math_h_isnan(float f) { using namespace std; return isnan(f); }
Q_DECL_CONST_FUNCTION static inline bool math_h_isinf(float f) { using namespace std; return isinf(f); }
Q_DECL_CONST_FUNCTION static inline bool math_h_isfinite(float f) { using namespace std; return isfinite(f); }
Q_DECL_CONST_FUNCTION static inline int math_h_fpclassify(float f) { using namespace std; return fpclassify(f); }
}
QT_END_NAMESPACE
// These macros from math.h conflict with the real functions in the std namespace.
# undef signbit
# undef isnan
# undef isinf
# undef isfinite
# undef fpclassify
# endif // defined(isnan)
#endif
QT_BEGIN_NAMESPACE
namespace qnumeric_std_wrapper {
#if defined(QT_MATH_H_DEFINES_MACROS)
# undef QT_MATH_H_DEFINES_MACROS
Q_DECL_CONST_FUNCTION static inline bool isnan(double d) { return math_h_isnan(d); }
Q_DECL_CONST_FUNCTION static inline bool isinf(double d) { return math_h_isinf(d); }
Q_DECL_CONST_FUNCTION static inline bool isfinite(double d) { return math_h_isfinite(d); }
Q_DECL_CONST_FUNCTION static inline int fpclassify(double d) { return math_h_fpclassify(d); }
Q_DECL_CONST_FUNCTION static inline bool isnan(float f) { return math_h_isnan(f); }
Q_DECL_CONST_FUNCTION static inline bool isinf(float f) { return math_h_isinf(f); }
Q_DECL_CONST_FUNCTION static inline bool isfinite(float f) { return math_h_isfinite(f); }
Q_DECL_CONST_FUNCTION static inline int fpclassify(float f) { return math_h_fpclassify(f); }
#else
Q_DECL_CONST_FUNCTION static inline bool isnan(double d) { return std::isnan(d); }
Q_DECL_CONST_FUNCTION static inline bool isinf(double d) { return std::isinf(d); }
Q_DECL_CONST_FUNCTION static inline bool isfinite(double d) { return std::isfinite(d); }
Q_DECL_CONST_FUNCTION static inline int fpclassify(double d) { return std::fpclassify(d); }
Q_DECL_CONST_FUNCTION static inline bool isnan(float f) { return std::isnan(f); }
Q_DECL_CONST_FUNCTION static inline bool isinf(float f) { return std::isinf(f); }
Q_DECL_CONST_FUNCTION static inline bool isfinite(float f) { return std::isfinite(f); }
Q_DECL_CONST_FUNCTION static inline int fpclassify(float f) { return std::fpclassify(f); }
#endif
}
Q_DECL_CONSTEXPR Q_DECL_CONST_FUNCTION static inline double qt_inf() noexcept
{
Q_STATIC_ASSERT_X(std::numeric_limits<double>::has_infinity,
"platform has no definition for infinity for type double");
return std::numeric_limits<double>::infinity();
}
#if QT_CONFIG(signaling_nan)
Q_DECL_CONSTEXPR Q_DECL_CONST_FUNCTION static inline double qt_snan() noexcept
{
Q_STATIC_ASSERT_X(std::numeric_limits<double>::has_signaling_NaN,
"platform has no definition for signaling NaN for type double");
return std::numeric_limits<double>::signaling_NaN();
}
#endif
// Quiet NaN
Q_DECL_CONSTEXPR Q_DECL_CONST_FUNCTION static inline double qt_qnan() noexcept
{
Q_STATIC_ASSERT_X(std::numeric_limits<double>::has_quiet_NaN,
"platform has no definition for quiet NaN for type double");
return std::numeric_limits<double>::quiet_NaN();
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_inf(double d)
{
return qnumeric_std_wrapper::isinf(d);
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_nan(double d)
{
return qnumeric_std_wrapper::isnan(d);
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_finite(double d)
{
return qnumeric_std_wrapper::isfinite(d);
}
Q_DECL_CONST_FUNCTION static inline int qt_fpclassify(double d)
{
return qnumeric_std_wrapper::fpclassify(d);
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_inf(float f)
{
return qnumeric_std_wrapper::isinf(f);
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_nan(float f)
{
return qnumeric_std_wrapper::isnan(f);
}
Q_DECL_CONST_FUNCTION static inline bool qt_is_finite(float f)
{
return qnumeric_std_wrapper::isfinite(f);
}
Q_DECL_CONST_FUNCTION static inline int qt_fpclassify(float f)
{
return qnumeric_std_wrapper::fpclassify(f);
}
#ifndef Q_CLANG_QDOC
namespace {
/*!
Returns true if the double \a v can be converted to type \c T, false if
it's out of range. If the conversion is successful, the converted value is
stored in \a value; if it was not successful, \a value will contain the
minimum or maximum of T, depending on the sign of \a d. If \c T is
unsigned, then \a value contains the absolute value of \a v.
This function works for v containing infinities, but not NaN. It's the
caller's responsibility to exclude that possibility before calling it.
*/
template <typename T> static inline bool convertDoubleTo(double v, T *value)
{
Q_STATIC_ASSERT(std::numeric_limits<T>::is_integer);
// The [conv.fpint] (7.10 Floating-integral conversions) section of the C++
// standard says only exact conversions are guaranteed. Converting
// integrals to floating-point with loss of precision has implementation-
// defined behavior whether the next higher or next lower is returned;
// converting FP to integral is UB if it can't be represented.
//
// That means we can't write UINT64_MAX+1. Writing ldexp(1, 64) would be
// correct, but Clang, ICC and MSVC don't realize that it's a constant and
// the math call stays in the compiled code.
double supremum;
if (std::numeric_limits<T>::is_signed) {
supremum = -1.0 * std::numeric_limits<T>::min(); // -1 * (-2^63) = 2^63, exact (for T = qint64)
*value = std::numeric_limits<T>::min();
if (v < std::numeric_limits<T>::min())
return false;
} else {
using ST = typename std::make_signed<T>::type;
supremum = -2.0 * std::numeric_limits<ST>::min(); // -2 * (-2^63) = 2^64, exact (for T = quint64)
v = fabs(v);
}
*value = std::numeric_limits<T>::max();
if (v >= supremum)
return false;
// Now we can convert, these two conversions cannot be UB
*value = T(v);
QT_WARNING_PUSH
QT_WARNING_DISABLE_GCC("-Wfloat-equal")
QT_WARNING_DISABLE_CLANG("-Wfloat-equal")
return *value == v;
QT_WARNING_POP
}
// Overflow math.
// This provides efficient implementations for int, unsigned, qsizetype and
// size_t. Implementations for 8- and 16-bit types will work but may not be as
// efficient. Implementations for 64-bit may be missing on 32-bit platforms.
#if ((defined(Q_CC_INTEL) ? (Q_CC_INTEL >= 1800 && !defined(Q_OS_WIN)) : defined(Q_CC_GNU)) \
&& Q_CC_GNU >= 500) || __has_builtin(__builtin_add_overflow)
// GCC 5, ICC 18, and Clang 3.8 have builtins to detect overflows
template <typename T> inline
typename std::enable_if<std::is_unsigned<T>::value || std::is_signed<T>::value, bool>::type
add_overflow(T v1, T v2, T *r)
{ return __builtin_add_overflow(v1, v2, r); }
template <typename T> inline
typename std::enable_if<std::is_unsigned<T>::value || std::is_signed<T>::value, bool>::type
sub_overflow(T v1, T v2, T *r)
{ return __builtin_sub_overflow(v1, v2, r); }
template <typename T> inline
typename std::enable_if<std::is_unsigned<T>::value || std::is_signed<T>::value, bool>::type
mul_overflow(T v1, T v2, T *r)
{ return __builtin_mul_overflow(v1, v2, r); }
#else
// Generic implementations
template <typename T> inline typename std::enable_if<std::is_unsigned<T>::value, bool>::type
add_overflow(T v1, T v2, T *r)
{
// unsigned additions are well-defined
*r = v1 + v2;
return v1 > T(v1 + v2);
}
template <typename T> inline typename std::enable_if<std::is_signed<T>::value, bool>::type
add_overflow(T v1, T v2, T *r)
{
// Here's how we calculate the overflow:
// 1) unsigned addition is well-defined, so we can always execute it
// 2) conversion from unsigned back to signed is implementation-
// defined and in the implementations we use, it's a no-op.
// 3) signed integer overflow happens if the sign of the two input operands
// is the same but the sign of the result is different. In other words,
// the sign of the result must be the same as the sign of either
// operand.
using U = typename std::make_unsigned<T>::type;
*r = T(U(v1) + U(v2));
// If int is two's complement, assume all integer types are too.
if (std::is_same<int32_t, int>::value) {
// Two's complement equivalent (generates slightly shorter code):
// x ^ y is negative if x and y have different signs
// x & y is negative if x and y are negative
// (x ^ z) & (y ^ z) is negative if x and z have different signs
// AND y and z have different signs
return ((v1 ^ *r) & (v2 ^ *r)) < 0;
}
bool s1 = (v1 < 0);
bool s2 = (v2 < 0);
bool sr = (*r < 0);
return s1 != sr && s2 != sr;
// also: return s1 == s2 && s1 != sr;
}
template <typename T> inline typename std::enable_if<std::is_unsigned<T>::value, bool>::type
sub_overflow(T v1, T v2, T *r)
{
// unsigned subtractions are well-defined
*r = v1 - v2;
return v1 < v2;
}
template <typename T> inline typename std::enable_if<std::is_signed<T>::value, bool>::type
sub_overflow(T v1, T v2, T *r)
{
// See above for explanation. This is the same with some signs reversed.
// We can't use add_overflow(v1, -v2, r) because it would be UB if
// v2 == std::numeric_limits<T>::min().
using U = typename std::make_unsigned<T>::type;
*r = T(U(v1) - U(v2));
if (std::is_same<int32_t, int>::value)
return ((v1 ^ *r) & (~v2 ^ *r)) < 0;
bool s1 = (v1 < 0);
bool s2 = !(v2 < 0);
bool sr = (*r < 0);
return s1 != sr && s2 != sr;
// also: return s1 == s2 && s1 != sr;
}
template <typename T> inline
typename std::enable_if<std::is_unsigned<T>::value || std::is_signed<T>::value, bool>::type
mul_overflow(T v1, T v2, T *r)
{
// use the next biggest type
// Note: for 64-bit systems where __int128 isn't supported, this will cause an error.
using LargerInt = QIntegerForSize<sizeof(T) * 2>;
using Larger = typename std::conditional<std::is_signed<T>::value,
typename LargerInt::Signed, typename LargerInt::Unsigned>::type;
Larger lr = Larger(v1) * Larger(v2);
*r = T(lr);
return lr > std::numeric_limits<T>::max() || lr < std::numeric_limits<T>::min();
}
# if defined(Q_INTRINSIC_MUL_OVERFLOW64)
template <> inline bool mul_overflow(quint64 v1, quint64 v2, quint64 *r)
{
*r = v1 * v2;
return Q_UMULH(v1, v2);
}
template <> inline bool mul_overflow(qint64 v1, qint64 v2, qint64 *r)
{
// This is slightly more complex than the unsigned case above: the sign bit
// of 'low' must be replicated as the entire 'high', so the only valid
// values for 'high' are 0 and -1. Use unsigned multiply since it's the same
// as signed for the low bits and use a signed right shift to verify that
// 'high' is nothing but sign bits that match the sign of 'low'.
qint64 high = Q_SMULH(v1, v2);
*r = qint64(quint64(v1) * quint64(v2));
return (*r >> 63) != high;
}
# if defined(Q_OS_INTEGRITY) && defined(Q_PROCESSOR_ARM_64)
template <> inline bool mul_overflow(uint64_t v1, uint64_t v2, uint64_t *r)
{
return mul_overflow<quint64>(v1,v2,reinterpret_cast<quint64*>(r));
}
template <> inline bool mul_overflow(int64_t v1, int64_t v2, int64_t *r)
{
return mul_overflow<qint64>(v1,v2,reinterpret_cast<qint64*>(r));
}
# endif // OS_INTEGRITY ARM64
# endif // Q_INTRINSIC_MUL_OVERFLOW64
# if defined(Q_CC_MSVC) && defined(Q_PROCESSOR_X86)
// We can use intrinsics for the unsigned operations with MSVC
template <> inline bool add_overflow(unsigned v1, unsigned v2, unsigned *r)
{ return _addcarry_u32(0, v1, v2, r); }
// 32-bit mul_overflow is fine with the generic code above
template <> inline bool add_overflow(quint64 v1, quint64 v2, quint64 *r)
{
# if defined(Q_PROCESSOR_X86_64)
return _addcarry_u64(0, v1, v2, reinterpret_cast<unsigned __int64 *>(r));
# else
uint low, high;
uchar carry = _addcarry_u32(0, unsigned(v1), unsigned(v2), &low);
carry = _addcarry_u32(carry, v1 >> 32, v2 >> 32, &high);
*r = (quint64(high) << 32) | low;
return carry;
# endif // !x86-64
}
# endif // MSVC X86
#endif // !GCC
}
#endif // Q_CLANG_QDOC
QT_END_NAMESPACE
#endif // QNUMERIC_P_H
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