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 // Copyright (C) 2021 The Qt Company Ltd.
 // Copyright (C) 2025 Klarälvdalens Datakonsult AB, a KDAB Group company, info@kdab.com, author Giuseppe D'Angelo <giuseppe.dangelo@kdab.com>
 // SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
 // Qt-Security score:critical reason:data-parser
 
 #ifndef QNUMERIC_H
 #define QNUMERIC_H
 
 #if 0
 #pragma qt_class(QtNumeric)
 #endif
 
 #include <QtCore/qassert.h>
 #include <QtCore/qminmax.h>
 #include <QtCore/qtconfigmacros.h>
 #include <QtCore/qtcoreexports.h>
 #include <QtCore/qtypes.h>
 
 #include <cmath>
 #include <limits>
 #include <QtCore/q20type_traits.h>
 
 // min() and max() may be #defined by windows.h if that is included before, but we need them
 // for std::numeric_limits below. You should not use the min() and max() macros, so we just #undef.
 #ifdef min
 #  undef min
 #  undef max
 #endif
 
 //
 // SIMDe (SIMD Everywhere) can't be used if intrin.h has been included as many definitions
 // conflict.   Defining Q_NUMERIC_NO_INTRINSICS allows SIMDe users to use Qt, at the cost of
 // falling back to the prior implementations of qMulOverflow and qAddOverflow.
 //
 #if defined(Q_CC_MSVC) && !defined(Q_NUMERIC_NO_INTRINSICS)
 #  include <intrin.h>
 #  include <float.h>
 #  if defined(Q_PROCESSOR_X86) || defined(Q_PROCESSOR_X86_64)
 #    define Q_HAVE_ADDCARRY
 #  endif
 #  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
 
 QT_BEGIN_NAMESPACE
 
 // To match std::is{inf,nan,finite} functions:
 template <typename T>
 constexpr typename std::enable_if<std::is_integral<T>::value, bool>::type
 qIsInf(T) { return false; }
 template <typename T>
 constexpr typename std::enable_if<std::is_integral<T>::value, bool>::type
 qIsNaN(T) { return false; }
 template <typename T>
 constexpr typename std::enable_if<std::is_integral<T>::value, bool>::type
 qIsFinite(T) { return true; }
 
 // Floating-point types (see qfloat16.h for its overloads).
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION bool qIsInf(double d);
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION bool qIsNaN(double d);
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION bool qIsFinite(double d);
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION int qFpClassify(double val);
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION bool qIsInf(float f);
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION bool qIsNaN(float f);
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION bool qIsFinite(float f);
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION int qFpClassify(float val);
 
 #if QT_CONFIG(signaling_nan)
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION double qSNaN();
 #endif
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION double qQNaN();
 Q_CORE_EXPORT Q_DECL_CONST_FUNCTION double qInf();
 
 Q_CORE_EXPORT quint32 qFloatDistance(float a, float b);
 Q_CORE_EXPORT quint64 qFloatDistance(double a, double b);
 
 #define Q_INFINITY (QT_PREPEND_NAMESPACE(qInf)())
 #if QT_CONFIG(signaling_nan)
 #  define Q_SNAN (QT_PREPEND_NAMESPACE(qSNaN)())
 #endif
 #define Q_QNAN (QT_PREPEND_NAMESPACE(qQNaN)())
 
 // 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.
 
 // All the GCC and Clang versions we support have constexpr
 // builtins for overflowing arithmetic.
 #if defined(Q_CC_GNU_ONLY) \
     || defined(Q_CC_CLANG_ONLY) \
     || __has_builtin(__builtin_add_overflow)
 # define Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS
 // On 32-bit, Clang < 14 will fail to link if multiplying 64-bit
 // quantities (emits an unresolved call to __mulodi4), so we can't use
 // the builtin in that case.
 # if !(QT_POINTER_SIZE == 4 && defined(Q_CC_CLANG_ONLY) && Q_CC_CLANG_ONLY < 1400)
 #  define Q_INTRINSIC_MUL_OVERFLOW64
 # endif
 #endif
 
 namespace QtPrivate {
 // Generic versions of (some) overflowing math functions, private API.
 template <typename T>
 constexpr inline
 typename std::enable_if_t<std::is_unsigned_v<T>, bool>
 qAddOverflowGeneric(T v1, T v2, T *r)
 {
     // unsigned additions are well-defined
     *r = v1 + v2;
     return v1 > T(v1 + v2);
 }
 
 // Wide multiplication.
 // It has been isolated in its own function so that it can be tested.
 // Note that this implementation requires a T that doesn't undergo
 // promotions.
 template <typename T>
 constexpr inline
 typename std::enable_if_t<std::is_same_v<T, decltype(+T{})>, bool>
 qMulOverflowWideMultiplication(T v1, T v2, T *r)
 {
     // This is a glorified long/school-grade multiplication,
     // that considers each input of N bits as two halves of N/2 bits:
     //
     // v1 = 2^(N/2) * v1_hi + v1_lo
     // v2 = 2^(N/2) * v2_hi + v2_lo
     //
     // Therefore, v1*v2 = 2^N     * v1_hi * v2_hi +
     //                    2^(N/2) * v1_hi * v2_lo +
     //                    2^(N/2) * v1_lo * v2_hi +
     //                            * v1_lo * v2_lo
     //
     // Using the N bits of precision we have we can perform the hi*lo
     // multiplications safely; that is never going to overflow.
     //
     // Then we can sum together these partial results:
     //
     //                 [ v1_hi | v1_lo ] *
     //                 [ v2_hi | v2_lo ] =
     //                 -------------------
     //                 [ v1_lo * v2_lo ] +
     //         [ v1_hi * v2_lo ]         +  // shifted because it's * 2^(N/2)
     //         [ v2_hi * v1_lo ]         +  // shifted because it's * 2^(N/2)
     // [ v1_hi * v2_hi ]                 =  // shifted because it's * 2^N
     // -------------------------------
     // [     high     ][     low       ]    // exact result (in 2^(2N) bits)
     //
     // ... except that this way we'll need to bring some carries, so
     // we'll do a slightly smarter sum.
     //
     // We need high for detecting overflows, even if we are not returning it.
 
     // Get multiplication by zero out of the way
     if (v1 == 0 || v2 == 0) {
         *r = T(0);
         return false;
     }
 
     // Extract the absolute values as unsigned
     // (will fix the sign later)
     using U = std::make_unsigned_t<T>;
     const U v1_abs = (v1 >= 0) ? U(v1) : (U(0) - U(v1));
     const U v2_abs = (v2 >= 0) ? U(v2) : (U(0) - U(v2));
 
     // Masks for N/2 bits
     constexpr std::size_t half_width = (sizeof(U) * 8) / 2;
     const U half_mask = ~U(0) >> half_width;
 
     // Split in low and half quantities
     const U v1_lo = v1_abs & half_mask;
     const U v1_hi = v1_abs >> half_width;
     const U v2_lo = v2_abs & half_mask;
     const U v2_hi = v2_abs >> half_width;
 
     // Cross-product; this will never overflow
     const U lo_lo = v1_lo * v2_lo;
     const U lo_hi = v1_lo * v2_hi;
     const U hi_lo = v1_hi * v2_lo;
     const U hi_hi = v1_hi * v2_hi;
 
     // We could sum directly the cross-products, but then we'd have to
     // keep track of carries. This avoids it.
     const U tmp = (lo_lo >> half_width) + (hi_lo & half_mask) + lo_hi;
     U result_hi = (hi_lo >> half_width) + (tmp >> half_width) + hi_hi;
     U result_lo = (tmp << half_width) | (lo_lo & half_mask);
 
     if constexpr (std::is_unsigned_v<T>) {
         // If the source was unsigned, we're done; a non-zero high
         // signals overflow.
         *r = result_lo;
         return result_hi != U(0);
     } else {
         // We need to set the correct sign back, and check for overflow.
         const bool isNegative = (v1 < T(0)) != (v2 < T(0));
         if (isNegative) {
             // Result is negative; calculate two's complement of the
             // [high, low] pair, by inverting the bits and adding 1,
             // which is equivalent to negating it in unsigned
             // arithmetic.
             // This operation should be done on the pair as a whole,
             // but we have the individual components, so start by
             // calculating two's complement of low:
             result_lo = U(0) - result_lo;
 
             // If result_lo is 0, it means that the addition of 1 into
             // it has overflown, so now we have a carry to add into the
             // inverted high:
             result_hi = ~result_hi;
             if (result_lo == 0)
                 result_hi += U(1);
         }
 
         *r = result_lo;
         // Overflow has happened if result_hi is not a sign extension
         // of the sign bit of result_lo. Note the usage of T, not U.
         return result_hi != U(*r >> std::numeric_limits<T>::digits);
     }
 }
 
 template <typename T, typename Enable = void>
 constexpr inline bool HasLargerInt = false;
 template <typename T>
 constexpr inline bool HasLargerInt<T, std::void_t<typename QIntegerForSize<sizeof(T) * 2>::Unsigned>> = true;
 
 template <typename T>
 constexpr inline
 typename std::enable_if_t<(std::is_unsigned_v<T> || std::is_signed_v<T>), bool>
 qMulOverflowGeneric(T v1, T v2, T *r)
 {
     // This function is a generic fallback for qMulOverflow,
     // called either by constant or non-constant evaluation,
     // if the compiler does not have builtins or intrinsics itself.
     //
     // (For instance, this is never going to be called on GCC or recent
     // Clang, as their builtins will be used in all cases.)
     //
     // If a compiler does have builtins, please amend qMulOverflow
     // directly.
 
     if constexpr (HasLargerInt<T>) {
         // Use the next biggest type if available
         using LargerInt = QIntegerForSize<sizeof(T) * 2>;
         using Larger = typename std::conditional_t<std::is_signed_v<T>,
                 typename LargerInt::Signed, typename LargerInt::Unsigned>;
         Larger lr = Larger(v1) * Larger(v2);
         *r = T(lr);
         return lr > (std::numeric_limits<T>::max)() || lr < (std::numeric_limits<T>::min)();
     } else {
         // Otherwise fall back to a wide multiplication
         return qMulOverflowWideMultiplication(v1, v2, r);
     }
 }
 } // namespace QtPrivate
 
 template <typename T>
 constexpr inline
 typename std::enable_if_t<std::is_unsigned_v<T>, bool>
 qAddOverflow(T v1, T v2, T *r)
 {
     static_assert(!std::is_same_v<T, char>, "Template must be an integral other than plain 'char'");
 #if defined(Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS)
     return __builtin_add_overflow(v1, v2, r);
 #else
     if (q20::is_constant_evaluated())
         return QtPrivate::qAddOverflowGeneric(v1, v2, r);
 # if defined(Q_HAVE_ADDCARRY)
     // We can use intrinsics for the unsigned operations with MSVC
     if constexpr (std::is_same_v<T, unsigned>) {
         return _addcarry_u32(0, v1, v2, r);
     } else if constexpr (std::is_same_v<T, quint64>) {
 #    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 // defined(Q_PROCESSOR_X86_64)
     }
 # endif // defined(Q_HAVE_ADDCARRY)
     return QtPrivate::qAddOverflowGeneric(v1, v2, r);
 #endif // defined(Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS)
 }
 
 template <typename T>
 constexpr inline
 typename std::enable_if_t<std::is_signed_v<T>, bool>
 qAddOverflow(T v1, T v2, T *r)
 {
     static_assert(!std::is_same_v<T, char>, "Template must be an integral other than plain 'char'");
 #if defined(Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS)
     return __builtin_add_overflow(v1, v2, r);
 #else
     // 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<T>;
     *r = T(U(v1) + U(v2));
 
     // 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;
 #endif // defined(Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS)
 }
 
 template <typename T>
 constexpr inline
 typename std::enable_if_t<std::is_unsigned_v<T>, bool>
 qSubOverflow(T v1, T v2, T *r)
 {
     static_assert(!std::is_same_v<T, char>, "Template must be an integral other than plain 'char'");
 #if defined(Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS)
     return __builtin_sub_overflow(v1, v2, r);
 #else
     // unsigned subtractions are well-defined
     *r = v1 - v2;
     return v1 < v2;
 #endif
 }
 
 template <typename T>
 constexpr inline
 typename std::enable_if_t<std::is_signed_v<T>, bool>
 qSubOverflow(T v1, T v2, T *r)
 {
     static_assert(!std::is_same_v<T, char>, "Template must be an integral other than plain 'char'");
 #if defined(Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS)
     return __builtin_sub_overflow(v1, v2, r);
 #else
     // See above for explanation. This is the same with some signs reversed.
     // We can't use qAddOverflow(v1, -v2, r) because it would be UB if
     // v2 == std::numeric_limits<T>::min().
 
     using U = typename std::make_unsigned_t<T>;
     *r = T(U(v1) - U(v2));
 
     return ((v1 ^ *r) & (~v2 ^ *r)) < 0;
 #endif // defined(Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS)
 }
 
 template <typename T>
 constexpr inline
 typename std::enable_if_t<std::is_unsigned_v<T> || std::is_signed_v<T>, bool>
 qMulOverflow(T v1, T v2, T *r)
 {
     static_assert(!std::is_same_v<T, char>, "Template must be an integral other than plain 'char'");
 #if defined(Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS)
 # if defined(Q_INTRINSIC_MUL_OVERFLOW64)
     return __builtin_mul_overflow(v1, v2, r);
 # else
     if constexpr (sizeof(T) <= 4)
         return __builtin_mul_overflow(v1, v2, r);
     else
         return QtPrivate::qMulOverflowGeneric(v1, v2, r);
 # endif
 #else
     if (q20::is_constant_evaluated())
         return QtPrivate::qMulOverflowGeneric(v1, v2, r);
 
 # if defined(Q_INTRINSIC_MUL_OVERFLOW64)
     if constexpr (std::is_unsigned_v<T> && (sizeof(T) == sizeof(quint64))) {
         // T is 64 bit; either unsigned long long,
         // or unsigned long on LP64 platforms.
         *r = v1 * v2;
         return T(Q_UMULH(v1, v2));
     } else if constexpr (std::is_signed_v<T> && (sizeof(T) == sizeof(qint64))) {
         // 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;
     }
 # endif // defined(Q_INTRINSIC_MUL_OVERFLOW64)
 
     return QtPrivate::qMulOverflowGeneric(v1, v2, r);
 #endif // defined(Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS)
 }
 
 #undef Q_HAVE_ADDCARRY
 #undef Q_NUMERIC_USE_GCC_OVERFLOW_BUILTINS
 
 // Implementations for addition, subtraction or multiplication by a
 // compile-time constant. For addition and subtraction, we simply call the code
 // that detects overflow at runtime. For multiplication, we compare to the
 // maximum possible values before multiplying to ensure no overflow happens.
 
 template <typename T, T V2> constexpr bool qAddOverflow(T v1, std::integral_constant<T, V2>, T *r)
 {
     return qAddOverflow(v1, V2, r);
 }
 
 template <auto V2, typename T> constexpr bool qAddOverflow(T v1, T *r)
 {
     return qAddOverflow(v1, std::integral_constant<T, V2>{}, r);
 }
 
 template <typename T, T V2> constexpr bool qSubOverflow(T v1, std::integral_constant<T, V2>, T *r)
 {
     return qSubOverflow(v1, V2, r);
 }
 
 template <auto V2, typename T> constexpr bool qSubOverflow(T v1, T *r)
 {
     return qSubOverflow(v1, std::integral_constant<T, V2>{}, r);
 }
 
 template <typename T, T V2> constexpr bool qMulOverflow(T v1, std::integral_constant<T, V2>, T *r)
 {
     static_assert(!std::is_same_v<T, char>, "Template must be an integral other than plain 'char'");
 
     // Runtime detection for anything smaller than or equal to a register
     // width, as most architectures' multiplication instructions actually
     // produce a result twice as wide as the input registers, allowing us to
     // efficiently detect the overflow.
     if constexpr (sizeof(T) <= sizeof(qregisteruint)) {
         return qMulOverflow(v1, V2, r);
 
 #ifdef Q_INTRINSIC_MUL_OVERFLOW64
     } else if constexpr (sizeof(T) <= sizeof(quint64)) {
         // If we have intrinsics detecting overflow of 64-bit multiplications,
         // then detect overflows through them up to 64 bits.
         return qMulOverflow(v1, V2, r);
 #endif
 
     } else if constexpr (V2 == 0 || V2 == 1) {
         // trivial cases (and simplify logic below due to division by zero)
         *r = v1 * V2;
         return false;
     } else if constexpr (V2 == -1) {
         // multiplication by -1 is valid *except* for signed minimum values
         // (necessary to avoid diving min() by -1, which is an overflow)
         if (v1 < 0 && v1 == (std::numeric_limits<T>::min)())
             return true;
         *r = -v1;
         return false;
     } else {
         // For 64-bit multiplications on 32-bit platforms, let's instead compare v1
         // against the bounds that would overflow.
         constexpr T Highest = (std::numeric_limits<T>::max)() / V2;
         constexpr T Lowest = (std::numeric_limits<T>::min)() / V2;
         if constexpr (Highest > Lowest) {
             if (v1 > Highest || v1 < Lowest)
                 return true;
         } else {
             // this can only happen if V2 < 0
             static_assert(V2 < 0);
             if (v1 > Lowest || v1 < Highest)
                 return true;
         }
 
         *r = v1 * V2;
         return false;
     }
 }
 
 template <auto V2, typename T> constexpr bool qMulOverflow(T v1, T *r)
 {
     if constexpr (V2 == 2)
         return qAddOverflow(v1, v1, r);
     return qMulOverflow(v1, std::integral_constant<T, V2>{}, r);
 }
 
 template <typename T>
 constexpr inline T qAbs(const T &t)
 {
     if constexpr (std::is_integral_v<T> && std::is_signed_v<T>)
         Q_ASSERT(t != std::numeric_limits<T>::min());
     return t >= 0 ? t : -t;
 }
 
 namespace QtPrivate {
 template <typename T,
           typename std::enable_if_t<std::is_integral_v<T>, bool> = true>
 constexpr inline auto qUnsignedAbs(T t)
 {
     using U = std::make_unsigned_t<T>;
     return (t >= 0) ? U(t) : U(~U(t) + U(1));
 }
 
 template <typename Result,
           typename FP,
           typename std::enable_if_t<std::is_integral_v<Result>, bool> = true,
           typename std::enable_if_t<std::is_floating_point_v<FP>, bool> = true>
 constexpr inline Result qCheckedFPConversionToInteger(FP value)
 {
 #ifdef QT_SUPPORTS_IS_CONSTANT_EVALUATED
     if (!q20::is_constant_evaluated())
         Q_ASSERT(!std::isnan(value));
 #endif
 
     constexpr Result minimal = (std::numeric_limits<Result>::min)();
     constexpr Result maximal = (std::numeric_limits<Result>::max)();
 
     // We want to check that `value > minimal-1`. `minimal` is
     // precisely representable as FP (it's -2^N), but `minimal-1`
     // may not be. Just rearrange the terms:
     Q_ASSERT(value - FP(minimal) > FP(-1));
 
     // Symmetrically, `maximal` may not have a precise
     // representation, but `maximal+1` has, so calculate that:
     constexpr FP maximalPlusOne = FP(2) * (maximal / 2 + 1);
     // And check that we're below that:
     Q_ASSERT(value < maximalPlusOne);
 
     // If both checks passed, the result of truncation is representable
     // as `Result`:
     return Result(value);
 }
 
 namespace QRoundImpl {
 // gcc < 10 doesn't have __has_builtin
 #if defined(Q_PROCESSOR_ARM_64) && (__has_builtin(__builtin_round) || defined(Q_CC_GNU)) && !defined(Q_CC_CLANG)
 // ARM64 has a single instruction that can do C++ rounding with conversion to integer.
 // Note current clang versions have non-constexpr __builtin_round, ### allow clang this path when they fix it.
 constexpr inline double qRound(double d)
 { return __builtin_round(d); }
 constexpr inline float qRound(float f)
 { return __builtin_roundf(f); }
 #elif defined(__SSE2__) && (__has_builtin(__builtin_copysign) || defined(Q_CC_GNU))
 // SSE has binary operations directly on floating point making copysign fast
 constexpr inline double qRound(double d)
 { return d + __builtin_copysign(0.5, d); }
 constexpr inline float qRound(float f)
 { return f + __builtin_copysignf(0.5f, f); }
 #else
 constexpr inline double qRound(double d)
 { return d >= 0.0 ? d + 0.5 : d - 0.5; }
 constexpr inline float qRound(float d)
 { return d >= 0.0f ? d + 0.5f : d - 0.5f; }
 #endif
 } // namespace QRoundImpl
 
 // Like qRound, but have well-defined saturating behavior.
 // NaN is not handled.
 template <typename FP,
           typename std::enable_if_t<std::is_floating_point_v<FP>, bool> = true>
 constexpr inline int qSaturateRound(FP value)
 {
 #ifdef QT_SUPPORTS_IS_CONSTANT_EVALUATED
     if (!q20::is_constant_evaluated())
         Q_ASSERT(!qIsNaN(value));
 #endif
     constexpr FP MinBound = FP((std::numeric_limits<int>::min)());
     constexpr FP MaxBound = FP((std::numeric_limits<int>::max)());
     const FP beforeTruncation = QRoundImpl::qRound(value);
     return int(qBound(MinBound, beforeTruncation, MaxBound));
 }
 } // namespace QtPrivate
 
 constexpr inline int qRound(double d)
 {
     return QtPrivate::qCheckedFPConversionToInteger<int>(QtPrivate::QRoundImpl::qRound(d));
 }
 
 constexpr inline int qRound(float f)
 {
     return QtPrivate::qCheckedFPConversionToInteger<int>(QtPrivate::QRoundImpl::qRound(f));
 }
 
 constexpr inline qint64 qRound64(double d)
 {
     return QtPrivate::qCheckedFPConversionToInteger<qint64>(QtPrivate::QRoundImpl::qRound(d));
 }
 
 constexpr inline qint64 qRound64(float f)
 {
     return QtPrivate::qCheckedFPConversionToInteger<qint64>(QtPrivate::QRoundImpl::qRound(f));
 }
 
 namespace QtPrivate {
 template <typename T>
 constexpr inline const T &min(const T &a, const T &b) { return (a < b) ? a : b; }
 }
 
 [[nodiscard]] constexpr bool qFuzzyCompare(double p1, double p2) noexcept
 {
     return (qAbs(p1 - p2) * 1000000000000. <= QtPrivate::min(qAbs(p1), qAbs(p2)));
 }
 
 [[nodiscard]] constexpr bool qFuzzyCompare(float p1, float p2) noexcept
 {
     return (qAbs(p1 - p2) * 100000.f <= QtPrivate::min(qAbs(p1), qAbs(p2)));
 }
 
 [[nodiscard]] constexpr bool qFuzzyIsNull(double d) noexcept
 {
     return qAbs(d) <= 0.000000000001;
 }
 
 [[nodiscard]] constexpr bool qFuzzyIsNull(float f) noexcept
 {
     return qAbs(f) <= 0.00001f;
 }
 
 QT_WARNING_PUSH
 QT_WARNING_DISABLE_FLOAT_COMPARE
 
 [[nodiscard]] constexpr bool qIsNull(double d) noexcept
 {
     return d == 0.0;
 }
 
 [[nodiscard]] constexpr bool qIsNull(float f) noexcept
 {
     return f == 0.0f;
 }
 
 QT_WARNING_POP
 
 namespace QtPrivate {
 /*
     A version of qFuzzyCompare that works for all values (qFuzzyCompare()
     requires that neither argument is numerically 0).
 
     It's private because we need a fix for the many qFuzzyCompare() uses that
     ignore the precondition, even for older branches.
 
     See QTBUG-142020 for discussion of a longer-term solution.
 */
 template <typename T, typename S>
 [[nodiscard]] constexpr bool fuzzyCompare(const T &lhs, const S &rhs) noexcept
 {
     static_assert(noexcept(qIsNull(lhs) && qIsNull(rhs) && qFuzzyIsNull(lhs - rhs) && qFuzzyCompare(lhs, rhs)),
                   "The operations qIsNull(), qFuzzyIsNull() and qFuzzyCompare() must be noexcept "
                   "for both argument types!");
     return qIsNull(lhs) || qIsNull(rhs) ? qFuzzyIsNull(lhs - rhs) : qFuzzyCompare(lhs, rhs);
 }
 } // namespace QtPrivate
 
 
 inline int qIntCast(double f) { return int(f); }
 inline int qIntCast(float f) { return int(f); }
 
 QT_END_NAMESPACE
 
 #endif // QNUMERIC_H

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