462 lines
13 KiB
C++
462 lines
13 KiB
C++
// Copyright (C) 2019 The Qt Company Ltd.
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// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
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#include "qnumeric.h"
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#include "qnumeric_p.h"
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#include <string.h>
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QT_BEGIN_NAMESPACE
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/*!
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\headerfile <QtNumeric>
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\inmodule QtCore
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\title Qt Numeric Functions
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\brief The <QtNumeric> header file provides common numeric functions.
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The <QtNumeric> header file contains various numeric functions
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for comparing and adjusting a numeric value.
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*/
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/*!
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Returns \c true if the double \a {d} is equivalent to infinity.
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\relates <QtNumeric>
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\sa qInf()
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*/
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Q_CORE_EXPORT bool qIsInf(double d) { return qt_is_inf(d); }
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/*!
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Returns \c true if the double \a {d} is not a number (NaN).
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\relates <QtNumeric>
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*/
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Q_CORE_EXPORT bool qIsNaN(double d) { return qt_is_nan(d); }
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/*!
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Returns \c true if the double \a {d} is a finite number.
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\relates <QtNumeric>
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*/
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Q_CORE_EXPORT bool qIsFinite(double d) { return qt_is_finite(d); }
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/*!
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Returns \c true if the float \a {f} is equivalent to infinity.
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\relates <QtNumeric>
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\sa qInf()
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*/
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Q_CORE_EXPORT bool qIsInf(float f) { return qt_is_inf(f); }
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/*!
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Returns \c true if the float \a {f} is not a number (NaN).
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\relates <QtNumeric>
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*/
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Q_CORE_EXPORT bool qIsNaN(float f) { return qt_is_nan(f); }
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/*!
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Returns \c true if the float \a {f} is a finite number.
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\relates <QtNumeric>
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*/
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Q_CORE_EXPORT bool qIsFinite(float f) { return qt_is_finite(f); }
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#if QT_CONFIG(signaling_nan)
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/*!
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Returns the bit pattern of a signalling NaN as a double.
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\relates <QtNumeric>
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*/
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Q_CORE_EXPORT double qSNaN() { return qt_snan(); }
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#endif
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/*!
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Returns the bit pattern of a quiet NaN as a double.
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\relates <QtNumeric>
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\sa qIsNaN()
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*/
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Q_CORE_EXPORT double qQNaN() { return qt_qnan(); }
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/*!
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Returns the bit pattern for an infinite number as a double.
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\relates <QtNumeric>
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\sa qIsInf()
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*/
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Q_CORE_EXPORT double qInf() { return qt_inf(); }
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/*!
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\fn int qFpClassify(double val)
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\fn int qFpClassify(float val)
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\relates <QtNumeric>
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Classifies a floating-point value.
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The return values are defined in \c{<cmath>}: returns one of the following,
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determined by the floating-point class of \a val:
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\list
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\li FP_NAN not a number
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\li FP_INFINITE infinities (positive or negative)
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\li FP_ZERO zero (positive or negative)
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\li FP_NORMAL finite with a full mantissa
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\li FP_SUBNORMAL finite with a reduced mantissa
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\endlist
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*/
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Q_CORE_EXPORT int qFpClassify(double val) { return qt_fpclassify(val); }
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Q_CORE_EXPORT int qFpClassify(float val) { return qt_fpclassify(val); }
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/*!
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\internal
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*/
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static inline quint32 f2i(float f)
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{
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quint32 i;
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memcpy(&i, &f, sizeof(f));
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return i;
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}
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/*!
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Returns the number of representable floating-point numbers between \a a and \a b.
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This function provides an alternative way of doing approximated comparisons of floating-point
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numbers similar to qFuzzyCompare(). However, it returns the distance between two numbers, which
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gives the caller a possibility to choose the accepted error. Errors are relative, so for
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instance the distance between 1.0E-5 and 1.00001E-5 will give 110, while the distance between
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1.0E36 and 1.00001E36 will give 127.
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This function is useful if a floating point comparison requires a certain precision.
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Therefore, if \a a and \a b are equal it will return 0. The maximum value it will return for 32-bit
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floating point numbers is 4,278,190,078. This is the distance between \c{-FLT_MAX} and
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\c{+FLT_MAX}.
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The function does not give meaningful results if any of the arguments are \c Infinite or \c NaN.
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You can check for this by calling qIsFinite().
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The return value can be considered as the "error", so if you for instance want to compare
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two 32-bit floating point numbers and all you need is an approximated 24-bit precision, you can
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use this function like this:
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\snippet code/src_corelib_global_qnumeric.cpp 0
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\sa qFuzzyCompare()
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\since 5.2
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\relates <QtNumeric>
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*/
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Q_CORE_EXPORT quint32 qFloatDistance(float a, float b)
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{
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static const quint32 smallestPositiveFloatAsBits = 0x00000001; // denormalized, (SMALLEST), (1.4E-45)
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/* Assumes:
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* IEE754 format.
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* Integers and floats have the same endian
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*/
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static_assert(sizeof(quint32) == sizeof(float));
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Q_ASSERT(qIsFinite(a) && qIsFinite(b));
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if (a == b)
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return 0;
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if ((a < 0) != (b < 0)) {
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// if they have different signs
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if (a < 0)
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a = -a;
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else /*if (b < 0)*/
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b = -b;
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return qFloatDistance(0.0F, a) + qFloatDistance(0.0F, b);
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}
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if (a < 0) {
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a = -a;
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b = -b;
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}
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// at this point a and b should not be negative
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// 0 is special
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if (!a)
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return f2i(b) - smallestPositiveFloatAsBits + 1;
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if (!b)
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return f2i(a) - smallestPositiveFloatAsBits + 1;
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// finally do the common integer subtraction
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return a > b ? f2i(a) - f2i(b) : f2i(b) - f2i(a);
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}
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/*!
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\internal
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*/
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static inline quint64 d2i(double d)
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{
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quint64 i;
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memcpy(&i, &d, sizeof(d));
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return i;
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}
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/*!
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Returns the number of representable floating-point numbers between \a a and \a b.
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This function serves the same purpose as \c{qFloatDistance(float, float)}, but
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returns the distance between two \c double numbers. Since the range is larger
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than for two \c float numbers (\c{[-DBL_MAX,DBL_MAX]}), the return type is quint64.
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\sa qFuzzyCompare()
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\since 5.2
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\relates <QtNumeric>
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*/
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Q_CORE_EXPORT quint64 qFloatDistance(double a, double b)
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{
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static const quint64 smallestPositiveFloatAsBits = 0x1; // denormalized, (SMALLEST)
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/* Assumes:
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* IEE754 format double precision
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* Integers and floats have the same endian
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*/
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static_assert(sizeof(quint64) == sizeof(double));
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Q_ASSERT(qIsFinite(a) && qIsFinite(b));
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if (a == b)
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return 0;
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if ((a < 0) != (b < 0)) {
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// if they have different signs
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if (a < 0)
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a = -a;
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else /*if (b < 0)*/
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b = -b;
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return qFloatDistance(0.0, a) + qFloatDistance(0.0, b);
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}
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if (a < 0) {
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a = -a;
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b = -b;
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}
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// at this point a and b should not be negative
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// 0 is special
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if (!a)
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return d2i(b) - smallestPositiveFloatAsBits + 1;
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if (!b)
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return d2i(a) - smallestPositiveFloatAsBits + 1;
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// finally do the common integer subtraction
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return a > b ? d2i(a) - d2i(b) : d2i(b) - d2i(a);
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}
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/*!
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\fn template<typename T> bool qAddOverflow(T v1, T v2, T *result)
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\relates <QtNumeric>
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\since 6.1
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Adds two values \a v1 and \a v2, of a numeric type \c T and records the
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value in \a result. If the addition overflows the valid range for type \c T,
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returns \c true, otherwise returns \c false.
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An implementation is guaranteed to be available for 8-, 16-, and 32-bit
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integer types, as well as integer types of the size of a pointer. Overflow
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math for other types, if available, is considered private API.
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*/
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/*!
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\fn template <typename T, T V2> bool qAddOverflow(T v1, std::integral_constant<T, V2>, T *r)
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\since 6.1
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\internal
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Equivalent to qAddOverflow(v1, v2, r) with \a v1 as first argument, the
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compile time constant \c V2 as second argument, and \a r as third argument.
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*/
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/*!
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\fn template <auto V2, typename T> bool qAddOverflow(T v1, T *r)
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\since 6.1
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\internal
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Equivalent to qAddOverflow(v1, v2, r) with \a v1 as first argument, the
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compile time constant \c V2 as second argument, and \a r as third argument.
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*/
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/*!
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\fn template<typename T> bool qSubOverflow(T v1, T v2, T *result)
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\relates <QtNumeric>
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\since 6.1
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Subtracts \a v2 from \a v1 and records the resulting value in \a result. If
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the subtraction overflows the valid range for type \c T, returns \c true,
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otherwise returns \c false.
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An implementation is guaranteed to be available for 8-, 16-, and 32-bit
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integer types, as well as integer types of the size of a pointer. Overflow
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math for other types, if available, is considered private API.
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*/
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/*!
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\fn template <typename T, T V2> bool qSubOverflow(T v1, std::integral_constant<T, V2>, T *r)
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\since 6.1
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\internal
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Equivalent to qSubOverflow(v1, v2, r) with \a v1 as first argument, the
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compile time constant \c V2 as second argument, and \a r as third argument.
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*/
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/*!
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\fn template <auto V2, typename T> bool qSubOverflow(T v1, T *r)
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\since 6.1
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\internal
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Equivalent to qSubOverflow(v1, v2, r) with \a v1 as first argument, the
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compile time constant \c V2 as second argument, and \a r as third argument.
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*/
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/*!
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\fn template<typename T> bool qMulOverflow(T v1, T v2, T *result)
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\relates <QtNumeric>
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\since 6.1
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Multiplies \a v1 and \a v2, and records the resulting value in \a result. If
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the multiplication overflows the valid range for type \c T, returns
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\c true, otherwise returns \c false.
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An implementation is guaranteed to be available for 8-, 16-, and 32-bit
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integer types, as well as integer types of the size of a pointer. Overflow
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math for other types, if available, is considered private API.
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*/
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/*!
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\fn template <typename T, T V2> bool qMulOverflow(T v1, std::integral_constant<T, V2>, T *r)
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\since 6.1
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\internal
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Equivalent to qMulOverflow(v1, v2, r) with \a v1 as first argument, the
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compile time constant \c V2 as second argument, and \a r as third argument.
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This can be faster than calling the version with only variable arguments.
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*/
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/*!
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\fn template <auto V2, typename T> bool qMulOverflow(T v1, T *r)
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\since 6.1
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\internal
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Equivalent to qMulOverflow(v1, v2, r) with \a v1 as first argument, the
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compile time constant \c V2 as second argument, and \a r as third argument.
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This can be faster than calling the version with only variable arguments.
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*/
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/*! \fn template <typename T> T qAbs(const T &t)
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\relates <QtNumeric>
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Compares \a t to the 0 of type T and returns the absolute
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value. Thus if T is \e {double}, then \a t is compared to
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\e{(double) 0}.
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Example:
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\snippet code/src_corelib_global_qglobal.cpp 10
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*/
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/*! \fn int qRound(double d)
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\relates <QtNumeric>
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Rounds \a d to the nearest integer.
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Rounds half away from zero (e.g. 0.5 -> 1, -0.5 -> -1).
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\note This function does not guarantee correctness for high precisions.
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Example:
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\snippet code/src_corelib_global_qglobal.cpp 11A
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\note If the value \a d is outside the range of \c int,
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the behavior is undefined.
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*/
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/*! \fn int qRound(float d)
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\relates <QtNumeric>
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Rounds \a d to the nearest integer.
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Rounds half away from zero (e.g. 0.5f -> 1, -0.5f -> -1).
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\note This function does not guarantee correctness for high precisions.
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Example:
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\snippet code/src_corelib_global_qglobal.cpp 11B
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\note If the value \a d is outside the range of \c int,
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the behavior is undefined.
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*/
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/*! \fn qint64 qRound64(double d)
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\relates <QtNumeric>
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Rounds \a d to the nearest 64-bit integer.
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Rounds half away from zero (e.g. 0.5 -> 1, -0.5 -> -1).
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\note This function does not guarantee correctness for high precisions.
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Example:
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\snippet code/src_corelib_global_qglobal.cpp 12A
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\note If the value \a d is outside the range of \c qint64,
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the behavior is undefined.
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*/
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/*! \fn qint64 qRound64(float d)
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\relates <QtNumeric>
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Rounds \a d to the nearest 64-bit integer.
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Rounds half away from zero (e.g. 0.5f -> 1, -0.5f -> -1).
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\note This function does not guarantee correctness for high precisions.
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Example:
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\snippet code/src_corelib_global_qglobal.cpp 12B
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\note If the value \a d is outside the range of \c qint64,
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the behavior is undefined.
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*/
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/*!
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\fn bool qFuzzyCompare(double p1, double p2)
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\relates <QtNumeric>
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\since 4.4
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\threadsafe
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Compares the floating point value \a p1 and \a p2 and
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returns \c true if they are considered equal, otherwise \c false.
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Note that comparing values where either \a p1 or \a p2 is 0.0 will not work,
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nor does comparing values where one of the values is NaN or infinity.
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If one of the values is always 0.0, use qFuzzyIsNull instead. If one of the
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values is likely to be 0.0, one solution is to add 1.0 to both values.
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\snippet code/src_corelib_global_qglobal.cpp 46
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The two numbers are compared in a relative way, where the
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exactness is stronger the smaller the numbers are.
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*/
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/*!
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\fn bool qFuzzyCompare(float p1, float p2)
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\relates <QtNumeric>
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\since 4.4
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\threadsafe
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Compares the floating point value \a p1 and \a p2 and
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returns \c true if they are considered equal, otherwise \c false.
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The two numbers are compared in a relative way, where the
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exactness is stronger the smaller the numbers are.
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*/
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/*!
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\fn bool qFuzzyIsNull(double d)
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\relates <QtNumeric>
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\since 4.4
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\threadsafe
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Returns true if the absolute value of \a d is within 0.000000000001 of 0.0.
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*/
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/*!
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\fn bool qFuzzyIsNull(float f)
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\relates <QtNumeric>
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\since 4.4
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\threadsafe
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Returns true if the absolute value of \a f is within 0.00001f of 0.0.
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*/
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QT_END_NAMESPACE
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