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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