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++ // Copyright (C) 2019 The Qt Company Ltd.
++ // 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
++
++ #include "qnumeric.h"
++ #include "qnumeric_p.h"
++ #include <string.h>
++
++ #include <q20bit.h>
++
++ QT_BEGIN_NAMESPACE
++
++ /*!
++ \headerfile <QtNumeric>
++ \inmodule QtCore
++ \title Qt Numeric Functions
++
++ \brief The <QtNumeric> header file provides common numeric functions.
++
++ The <QtNumeric> header file contains various numeric functions
++ for comparing and adjusting a numeric value.
++ */
++
++ /*!
++ Returns \c true if the double \a {d} is equivalent to infinity.
++ \relates <QtNumeric>
++ \sa qInf()
++ */
++ Q_CORE_EXPORT bool qIsInf(double d) { return qt_is_inf(d); }
++
++ /*!
++ Returns \c true if the double \a {d} is not a number (NaN).
++ \relates <QtNumeric>
++ */
++ Q_CORE_EXPORT bool qIsNaN(double d) { return qt_is_nan(d); }
++
++ /*!
++ Returns \c true if the double \a {d} is a finite number.
++ \relates <QtNumeric>
++ */
++ Q_CORE_EXPORT bool qIsFinite(double d) { return qt_is_finite(d); }
++
++ /*!
++ Returns \c true if the float \a {f} is equivalent to infinity.
++ \relates <QtNumeric>
++ \sa qInf()
++ */
++ Q_CORE_EXPORT bool qIsInf(float f) { return qt_is_inf(f); }
++
++ /*!
++ Returns \c true if the float \a {f} is not a number (NaN).
++ \relates <QtNumeric>
++ */
++ Q_CORE_EXPORT bool qIsNaN(float f) { return qt_is_nan(f); }
++
++ /*!
++ Returns \c true if the float \a {f} is a finite number.
++ \relates <QtNumeric>
++ */
++ Q_CORE_EXPORT bool qIsFinite(float f) { return qt_is_finite(f); }
++
++ #if QT_CONFIG(signaling_nan)
++ /*!
++ Returns the bit pattern of a signalling NaN as a double.
++ \relates <QtNumeric>
++ */
++ Q_CORE_EXPORT double qSNaN() { return qt_snan(); }
++ #endif
++
++ /*!
++ Returns the bit pattern of a quiet NaN as a double.
++ \relates <QtNumeric>
++ \sa qIsNaN()
++ */
++ Q_CORE_EXPORT double qQNaN() { return qt_qnan(); }
++
++ /*!
++ Returns the bit pattern for an infinite number as a double.
++ \relates <QtNumeric>
++ \sa qIsInf()
++ */
++ Q_CORE_EXPORT double qInf() { return qt_inf(); }
++
++ /*!
++ \fn int qFpClassify(double val)
++ \fn int qFpClassify(float val)
++
++ \relates <QtNumeric>
++ Classifies a floating-point value.
++
++ The return values are defined in \c{<cmath>}: returns one of the following,
++ determined by the floating-point class of \a val:
++ \list
++ \li FP_NAN not a number
++ \li FP_INFINITE infinities (positive or negative)
++ \li FP_ZERO zero (positive or negative)
++ \li FP_NORMAL finite with a full mantissa
++ \li FP_SUBNORMAL finite with a reduced mantissa
++ \endlist
++ */
++ Q_CORE_EXPORT int qFpClassify(double val) { return qt_fpclassify(val); }
++ Q_CORE_EXPORT int qFpClassify(float val) { return qt_fpclassify(val); }
++
++
++ /*!
++ \internal
++ */
++ static inline quint32 f2i(float f)
++ {
++ quint32 i;
++ memcpy(&i, &f, sizeof(f));
++ return i;
++ }
++
++ /*!
++ Returns the number of representable floating-point numbers between \a a and \a b.
++
++ This function provides an alternative way of doing approximated comparisons of floating-point
++ numbers similar to qFuzzyCompare(). However, it returns the distance between two numbers, which
++ gives the caller a possibility to choose the accepted error. Errors are relative, so for
++ instance the distance between 1.0E-5 and 1.00001E-5 will give 110, while the distance between
++ 1.0E36 and 1.00001E36 will give 127.
++
++ This function is useful if a floating point comparison requires a certain precision.
++ Therefore, if \a a and \a b are equal it will return 0. The maximum value it will return for 32-bit
++ floating point numbers is 4,278,190,078. This is the distance between \c{-FLT_MAX} and
++ \c{+FLT_MAX}.
++
++ The function does not give meaningful results if any of the arguments are \c Infinite or \c NaN.
++ You can check for this by calling qIsFinite().
++
++ The return value can be considered as the "error", so if you for instance want to compare
++ two 32-bit floating point numbers and all you need is an approximated 24-bit precision, you can
++ use this function like this:
++
++ \snippet code/src_corelib_global_qnumeric.cpp 0
++
++ \sa qFuzzyCompare()
++ \since 5.2
++ \relates <QtNumeric>
++ */
++ Q_CORE_EXPORT quint32 qFloatDistance(float a, float b)
++ {
++ static const quint32 smallestPositiveFloatAsBits = 0x00000001; // denormalized, (SMALLEST), (1.4E-45)
++ /* Assumes:
++ * IEE754 format.
++ * Integers and floats have the same endian
++ */
++ static_assert(sizeof(quint32) == sizeof(float));
++ Q_ASSERT(qIsFinite(a) && qIsFinite(b));
++ if (a == b)
++ return 0;
++ if ((a < 0) != (b < 0)) {
++ // if they have different signs
++ if (a < 0)
++ a = -a;
++ else /*if (b < 0)*/
++ b = -b;
++ return qFloatDistance(0.0F, a) + qFloatDistance(0.0F, b);
++ }
++ if (a < 0) {
++ a = -a;
++ b = -b;
++ }
++ // at this point a and b should not be negative
++
++ // 0 is special
++ if (!a)
++ return f2i(b) - smallestPositiveFloatAsBits + 1;
++ if (!b)
++ return f2i(a) - smallestPositiveFloatAsBits + 1;
++
++ // finally do the common integer subtraction
++ return a > b ? f2i(a) - f2i(b) : f2i(b) - f2i(a);
++ }
++
++
++ /*!
++ \internal
++ */
++ static inline quint64 d2i(double d)
++ {
++ quint64 i;
++ memcpy(&i, &d, sizeof(d));
++ return i;
++ }
++
++ /*!
++ Returns the number of representable floating-point numbers between \a a and \a b.
++
++ This function serves the same purpose as \c{qFloatDistance(float, float)}, but
++ returns the distance between two \c double numbers. Since the range is larger
++ than for two \c float numbers (\c{[-DBL_MAX,DBL_MAX]}), the return type is quint64.
++
++
++ \sa qFuzzyCompare()
++ \since 5.2
++ \relates <QtNumeric>
++ */
++ Q_CORE_EXPORT quint64 qFloatDistance(double a, double b)
++ {
++ static const quint64 smallestPositiveFloatAsBits = 0x1; // denormalized, (SMALLEST)
++ /* Assumes:
++ * IEE754 format double precision
++ * Integers and floats have the same endian
++ */
++ static_assert(sizeof(quint64) == sizeof(double));
++ Q_ASSERT(qIsFinite(a) && qIsFinite(b));
++ if (a == b)
++ return 0;
++ if ((a < 0) != (b < 0)) {
++ // if they have different signs
++ if (a < 0)
++ a = -a;
++ else /*if (b < 0)*/
++ b = -b;
++ return qFloatDistance(0.0, a) + qFloatDistance(0.0, b);
++ }
++ if (a < 0) {
++ a = -a;
++ b = -b;
++ }
++ // at this point a and b should not be negative
++
++ // 0 is special
++ if (!a)
++ return d2i(b) - smallestPositiveFloatAsBits + 1;
++ if (!b)
++ return d2i(a) - smallestPositiveFloatAsBits + 1;
++
++ // finally do the common integer subtraction
++ return a > b ? d2i(a) - d2i(b) : d2i(b) - d2i(a);
++ }
++
++ /*!
++ \fn template<typename T> bool qAddOverflow(T v1, T v2, T *result)
++ \relates <QtNumeric>
++ \since 6.1
++
++ Adds two values \a v1 and \a v2, of a numeric type \c T and records the
++ value in \a result. If the addition overflows the valid range for type \c T,
++ returns \c true, otherwise returns \c false.
++
++ An implementation is guaranteed to be available for 8-, 16-, and 32-bit
++ integer types, as well as integer types of the size of a pointer. Overflow
++ math for other types, if available, is considered private API.
++ */
++
++ /*!
++ \fn template <typename T, T V2> bool qAddOverflow(T v1, std::integral_constant<T, V2>, T *r)
++ \since 6.1
++ \internal
++
++ Equivalent to qAddOverflow(v1, v2, r) with \a v1 as first argument, the
++ compile time constant \c V2 as second argument, and \a r as third argument.
++ */
++
++ /*!
++ \fn template <auto V2, typename T> bool qAddOverflow(T v1, T *r)
++ \since 6.1
++ \internal
++
++ Equivalent to qAddOverflow(v1, v2, r) with \a v1 as first argument, the
++ compile time constant \c V2 as second argument, and \a r as third argument.
++ */
++
++ /*!
++ \fn template<typename T> bool qSubOverflow(T v1, T v2, T *result)
++ \relates <QtNumeric>
++ \since 6.1
++
++ Subtracts \a v2 from \a v1 and records the resulting value in \a result. If
++ the subtraction overflows the valid range for type \c T, returns \c true,
++ otherwise returns \c false.
++
++ An implementation is guaranteed to be available for 8-, 16-, and 32-bit
++ integer types, as well as integer types of the size of a pointer. Overflow
++ math for other types, if available, is considered private API.
++ */
++
++ /*!
++ \fn template <typename T, T V2> bool qSubOverflow(T v1, std::integral_constant<T, V2>, T *r)
++ \since 6.1
++ \internal
++
++ Equivalent to qSubOverflow(v1, v2, r) with \a v1 as first argument, the
++ compile time constant \c V2 as second argument, and \a r as third argument.
++ */
++
++ /*!
++ \fn template <auto V2, typename T> bool qSubOverflow(T v1, T *r)
++ \since 6.1
++ \internal
++
++ Equivalent to qSubOverflow(v1, v2, r) with \a v1 as first argument, the
++ compile time constant \c V2 as second argument, and \a r as third argument.
++ */
++
++ /*!
++ \fn template<typename T> bool qMulOverflow(T v1, T v2, T *result)
++ \relates <QtNumeric>
++ \since 6.1
++
++ Multiplies \a v1 and \a v2, and records the resulting value in \a result. If
++ the multiplication overflows the valid range for type \c T, returns
++ \c true, otherwise returns \c false.
++
++ An implementation is guaranteed to be available for 8-, 16-, and 32-bit
++ integer types, as well as integer types of the size of a pointer. Overflow
++ math for other types, if available, is considered private API.
++ */
++
++ /*!
++ \fn template <typename T, T V2> bool qMulOverflow(T v1, std::integral_constant<T, V2>, T *r)
++ \since 6.1
++ \internal
++
++ Equivalent to qMulOverflow(v1, v2, r) with \a v1 as first argument, the
++ compile time constant \c V2 as second argument, and \a r as third argument.
++ This can be faster than calling the version with only variable arguments.
++ */
++
++ /*!
++ \fn template <auto V2, typename T> bool qMulOverflow(T v1, T *r)
++ \since 6.1
++ \internal
++
++ Equivalent to qMulOverflow(v1, v2, r) with \a v1 as first argument, the
++ compile time constant \c V2 as second argument, and \a r as third argument.
++ This can be faster than calling the version with only variable arguments.
++ */
++
++ /*! \fn template <typename T> T qAbs(const T &t)
++ \relates <QtNumeric>
++
++ Compares \a t to the 0 of type T and returns the absolute
++ value. Thus if T is \e {double}, then \a t is compared to
++ \e{(double) 0}.
++
++ Example:
++
++ \snippet code/src_corelib_global_qglobal.cpp 10
++
++ \note If \c {T} is a \e {signed integral} type, and \a t has the value
++ of \c {std::numeric_limits<T>::min()}, the behavior is undefined.
++ */
++
++ /*! \fn int qRound(double d)
++ \relates <QtNumeric>
++
++ Rounds \a d to the nearest integer.
++
++ Rounds half away from zero (e.g. 0.5 -> 1, -0.5 -> -1).
++
++ \note This function does not guarantee correctness for high precisions.
++
++ Example:
++
++ \snippet code/src_corelib_global_qglobal.cpp 11A
++
++ \note If the value \a d is outside the range of \c int,
++ the behavior is undefined.
++ */
++
++ /*! \fn int qRound(float d)
++ \relates <QtNumeric>
++
++ Rounds \a d to the nearest integer.
++
++ Rounds half away from zero (e.g. 0.5f -> 1, -0.5f -> -1).
++
++ \note This function does not guarantee correctness for high precisions.
++
++ Example:
++
++ \snippet code/src_corelib_global_qglobal.cpp 11B
++
++ \note If the value \a d is outside the range of \c int,
++ the behavior is undefined.
++ */
++
++ /*! \fn qint64 qRound64(double d)
++ \relates <QtNumeric>
++
++ Rounds \a d to the nearest 64-bit integer.
++
++ Rounds half away from zero (e.g. 0.5 -> 1, -0.5 -> -1).
++
++ \note This function does not guarantee correctness for high precisions.
++
++ Example:
++
++ \snippet code/src_corelib_global_qglobal.cpp 12A
++
++ \note If the value \a d is outside the range of \c qint64,
++ the behavior is undefined.
++ */
++
++ /*! \fn qint64 qRound64(float d)
++ \relates <QtNumeric>
++
++ Rounds \a d to the nearest 64-bit integer.
++
++ Rounds half away from zero (e.g. 0.5f -> 1, -0.5f -> -1).
++
++ \note This function does not guarantee correctness for high precisions.
++
++ Example:
++
++ \snippet code/src_corelib_global_qglobal.cpp 12B
++
++ \note If the value \a d is outside the range of \c qint64,
++ the behavior is undefined.
++ */
++
++ /*!
++ \fn bool qFuzzyCompare(double p1, double p2)
++ \relates <QtNumeric>
++ \since 4.4
++ \threadsafe
++
++ Compares the floating point value \a p1 and \a p2 and
++ returns \c true if they are considered equal, otherwise \c false.
++
++ Note that comparing values where either \a p1 or \a p2 is 0.0 will not work,
++ nor does comparing values where one of the values is NaN or infinity.
++ If one of the values is always 0.0, use qFuzzyIsNull instead. If one of the
++ values is likely to be 0.0, one solution is to add 1.0 to both values.
++
++ \snippet code/src_corelib_global_qglobal.cpp 46
++
++ The two numbers are compared in a relative way, where the
++ exactness is stronger the smaller the numbers are.
++ */
++
++ /*!
++ \fn bool qFuzzyCompare(float p1, float p2)
++ \relates <QtNumeric>
++ \since 4.4
++ \threadsafe
++
++ Compares the floating point value \a p1 and \a p2 and
++ returns \c true if they are considered equal, otherwise \c false.
++
++ The two numbers are compared in a relative way, where the
++ exactness is stronger the smaller the numbers are.
++ */
++
++ /*!
++ \fn bool qFuzzyIsNull(double d)
++ \relates <QtNumeric>
++ \since 4.4
++ \threadsafe
++
++ Returns true if the absolute value of \a d is within 0.000000000001 of 0.0.
++ */
++
++ /*!
++ \fn bool qFuzzyIsNull(float f)
++ \relates <QtNumeric>
++ \since 4.4
++ \threadsafe
++
++ Returns true if the absolute value of \a f is within 0.00001f of 0.0.
++ */
++
++ namespace q20 {
++ static_assert(rotl(1U, 1) == 2);
++ static_assert(rotl(0x8000'0000U, 1) == 1);
++ static_assert(rotl(0x8000'0001U, 1) == 3);
++ static_assert(rotl(1U, -1) == 0x8000'0000U);
++ static_assert(rotl(0x8000'0000U, -1) == 0x4000'0000U);
++ static_assert(rotl(0x8000'0001U, -1) == 0xc000'0000U);
++
++ static_assert(rotr(1U, 1) == 0x8000'0000U);
++ static_assert(rotr(0x8000'0000U, 1) == 0x4000'0000U);
++ static_assert(rotr(0x8000'0001U, 1) == 0xc000'0000U);
++ static_assert(rotr(1U, -1) == 2);
++ static_assert(rotr(0x8000'0000U, -1) == 1);
++ static_assert(rotr(0x8000'0001U, -1) == 3);
++ }
++
++ QT_END_NAMESPACE