233 lines
7.0 KiB
C++
233 lines
7.0 KiB
C++
/****************************************************************************
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**
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** Copyright (C) 2015 The Qt Company Ltd.
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** Contact: http://www.qt.io/licensing/
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**
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** This file is part of the QtCore module of the Qt Toolkit.
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**
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** $QT_BEGIN_LICENSE:LGPL21$
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** Commercial License Usage
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** Licensees holding valid commercial Qt licenses may use this file in
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** accordance with the commercial license agreement provided with the
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** Software or, alternatively, in accordance with the terms contained in
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** a written agreement between you and The Qt Company. For licensing terms
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** and conditions see http://www.qt.io/terms-conditions. For further
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** information use the contact form at http://www.qt.io/contact-us.
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**
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** GNU Lesser General Public License Usage
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** Alternatively, this file may be used under the terms of the GNU Lesser
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** General Public License version 2.1 or version 3 as published by the Free
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** Software Foundation and appearing in the file LICENSE.LGPLv21 and
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** LICENSE.LGPLv3 included in the packaging of this file. Please review the
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** following information to ensure the GNU Lesser General Public License
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** requirements will be met: https://www.gnu.org/licenses/lgpl.html and
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** http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
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**
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** As a special exception, The Qt Company gives you certain additional
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** rights. These rights are described in The Qt Company LGPL Exception
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** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
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**
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** $QT_END_LICENSE$
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**
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****************************************************************************/
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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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Returns \c true if the double \a {d} is equivalent to infinity.
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\relates <QtGlobal>
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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 <QtGlobal>
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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 <QtGlobal>
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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 <QtGlobal>
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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 <QtGlobal>
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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 <QtGlobal>
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*/
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Q_CORE_EXPORT bool qIsFinite(float f) { return qt_is_finite(f); }
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/*!
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Returns the bit pattern of a signalling NaN as a double.
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\relates <QtGlobal>
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*/
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Q_CORE_EXPORT double qSNaN() { return qt_snan(); }
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/*!
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Returns the bit pattern of a quiet NaN as a double.
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\relates <QtGlobal>
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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 <QtGlobal>
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*/
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Q_CORE_EXPORT double qInf() { return qt_inf(); }
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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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\code
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if (qFloatDistance(a, b) < (1 << 7)) { // The last 7 bits are not
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// significant
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// precise enough
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}
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\endcode
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\sa qFuzzyCompare()
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\since 5.2
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\relates <QtGlobal>
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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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Q_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 <QtGlobal>
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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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Q_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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QT_END_NAMESPACE
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