qeasingcurve.cpp

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// Copyright (C) 2016 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:significant reason:default
 
/*
 
| *property* | *Used for type* |
| period     | QEasingCurve::{In,Out,InOut,OutIn}Elastic |
| amplitude  | QEasingCurve::{In,Out,InOut,OutIn}Bounce, QEasingCurve::{In,Out,InOut,OutIn}Elastic |
| overshoot  | QEasingCurve::{In,Out,InOut,OutIn}Back   |
 
*/
 
 
 
 
/*!
    \class QEasingCurve
    \inmodule QtCore
    \since 4.6
    \ingroup animation
    \brief The QEasingCurve class provides easing curves for controlling animation.
 
    Easing curves describe a function that controls how the speed of the interpolation
    between 0 and 1 should be. Easing curves allow transitions from
    one value to another to appear more natural than a simple constant speed would allow.
    The QEasingCurve class is usually used in conjunction with the QVariantAnimation and
    QPropertyAnimation classes but can be used on its own. It is usually used to accelerate
    the interpolation from zero velocity (ease in) or decelerate to zero velocity (ease out).
    Ease in and ease out can also be combined in the same easing curve.
 
    To calculate the speed of the interpolation, the easing curve provides the function
    valueForProgress(), where the \a progress argument specifies the progress of the
    interpolation: 0 is the start value of the interpolation, 1 is the end value of the
    interpolation. The returned value is the effective progress of the interpolation.
    If the returned value is the same as the input value for all input values the easing
    curve is a linear curve. This is the default behaviour.
 
    For example,
 
    \snippet code/src_corelib_tools_qeasingcurve.cpp 0
 
    will print the effective progress of the interpolation between 0 and 1.
 
    When using a QPropertyAnimation, the associated easing curve will be used to control the
    progress of the interpolation between startValue and endValue:
 
    \snippet code/src_corelib_tools_qeasingcurve.cpp 1
 
    The ability to set an amplitude, overshoot, or period depends on
    the QEasingCurve type. Amplitude access is available to curves
    that behave as springs such as elastic and bounce curves. Changing
    the amplitude changes the height of the curve. Period access is
    only available to elastic curves and setting a higher period slows
    the rate of bounce. Only curves that have "boomerang" behaviors
    such as the InBack, OutBack, InOutBack, and OutInBack have
    overshoot settings. These curves will interpolate beyond the end
    points and return to the end point, acting similar to a boomerang.
 
    The \l{Easing Curves Example} contains samples of QEasingCurve
    types and lets you change the curve settings.
 
 */
 
/*!
    \enum QEasingCurve::Type
 
    The type of easing curve.
 
    \value Linear       \image qeasingcurve-linear.png {Graph of a
                               linear function.}
                        \caption Easing curve for a linear (t) function:
                        velocity is constant.
    \value InQuad       \image qeasingcurve-inquad.png {Graph of a
                               InQuadratic function.}
                        \caption Easing curve for a quadratic (t^2) function:
                        accelerating from zero velocity.
    \value OutQuad      \image qeasingcurve-outquad.png {Graph of a
                               OutQuadratic function}
                        \caption Easing curve for a quadratic (t^2) function:
                        decelerating to zero velocity.
    \value InOutQuad    \image qeasingcurve-inoutquad.png {Graph of a
                               InOutquad quadratic function}
                        \caption Easing curve for a quadratic (t^2) function:
                        acceleration until halfway, then deceleration.
    \value OutInQuad    \image qeasingcurve-outinquad.png {Graph of a
                               OutInquad quadratic function}
                        \caption Easing curve for a quadratic (t^2) function:
                        deceleration until halfway, then acceleration.
    \value InCubic      \image qeasingcurve-incubic.png {Graph of a
                               InCubic function}
                        \caption Easing curve for a cubic (t^3) function:
                        accelerating from zero velocity.
    \value OutCubic     \image qeasingcurve-outcubic.png {Graph of a
                               OutCubic function}
                        \caption Easing curve for a cubic (t^3) function:
                        decelerating to zero velocity.
    \value InOutCubic   \image qeasingcurve-inoutcubic.png {Graph of a
                               InOutCubic function.}
                        \caption Easing curve for a cubic (t^3) function:
                        acceleration until halfway, then deceleration.
    \value OutInCubic   \image qeasingcurve-outincubic.png {Graph of a
                               OutInCubic function.}
                        \caption Easing curve for a cubic (t^3) function:
                        deceleration until halfway, then acceleration.
    \value InQuart      \image qeasingcurve-inquart.png {Graph of a
                               InQuartic function.}
                        \caption Easing curve for a quartic (t^4) function:
                        accelerating from zero velocity.
    \value OutQuart     \image qeasingcurve-outquart.png {Graph of a
                               OutQuartic function.}
                        \caption
                        Easing curve for a quartic (t^4) function:
                        decelerating to zero velocity.
    \value InOutQuart   \image qeasingcurve-inoutquart.png {Graph of a
                               InOutQuartic function.}
                        \caption
                        Easing curve for a quartic (t^4) function:
                        acceleration until halfway, then deceleration.
    \value OutInQuart   \image qeasingcurve-outinquart.png {Graph of a
                               OutInQuartic function.}
                        \caption
                        Easing curve for a quartic (t^4) function:
                        deceleration until halfway, then acceleration.
    \value InQuint      \image qeasingcurve-inquint.png {Graph of a
                               InQuintic function}
                        \caption
                        Easing curve for a quintic (t^5) easing
                        in: accelerating from zero velocity.
    \value OutQuint     \image qeasingcurve-outquint.png {Graph of a
                               OutQuintic function}
                        \caption
                        Easing curve for a quintic (t^5) function:
                        decelerating to zero velocity.
    \value InOutQuint   \image qeasingcurve-inoutquint.png {Graph of a
                               InOutQuintic function}
                        \caption
                        Easing curve for a quintic (t^5) function:
                        acceleration until halfway, then deceleration.
    \value OutInQuint   \image qeasingcurve-outinquint.png {Graph of a
                               OutInQuintic function}
                        \caption
                        Easing curve for a quintic (t^5) function:
                        deceleration until halfway, then acceleration.
    \value InSine       \image qeasingcurve-insine.png {Graph of a
                               InSinusoidal function}
                        \caption
                        Easing curve for a sinusoidal (sin(t)) function:
                        accelerating from zero velocity.
    \value OutSine      \image qeasingcurve-outsine.png {Graph of a
                               OutSinusoidal function}
                        \caption
                        Easing curve for a sinusoidal (sin(t)) function:
                        decelerating to zero velocity.
    \value InOutSine    \image qeasingcurve-inoutsine.png {Graph of a
                               InOutSinusoidal function}
                        \caption
                        Easing curve for a sinusoidal (sin(t)) function:
                        acceleration until halfway, then deceleration.
    \value OutInSine    \image qeasingcurve-outinsine.png {Graph of a
                               OutInSinusoidal function}
                        \caption
                        Easing curve for a sinusoidal (sin(t)) function:
                        deceleration until halfway, then acceleration.
    \value InExpo       \image qeasingcurve-inexpo.png {Graph of a
                               InExponential function}
                        \caption
                        Easing curve for an exponential (2^t) function:
                        accelerating from zero velocity.
    \value OutExpo      \image qeasingcurve-outexpo.png {Graph of a
                               OutExponential function}
                        \caption
                        Easing curve for an exponential (2^t) function:
                        decelerating to zero velocity.
    \value InOutExpo    \image qeasingcurve-inoutexpo.png {Graph of a
                               InOutExponential function}
                        \caption
                        Easing curve for an exponential (2^t) function:
                        acceleration until halfway, then deceleration.
    \value OutInExpo    \image qeasingcurve-outinexpo.png {Graph of a
                               OutInExponential function}
                        \caption
                        Easing curve for an exponential (2^t) function:
                        deceleration until halfway, then acceleration.
    \value InCirc       \image qeasingcurve-incirc.png {Graph of a
                               InCircular function}
                        \caption
                        Easing curve for a circular (sqrt(1-t^2)) function:
                        accelerating from zero velocity.
    \value OutCirc      \image qeasingcurve-outcirc.png {Graph of a
                               OutCircular function}
                        \caption
                        Easing curve for a circular (sqrt(1-t^2)) function:
                        decelerating to zero velocity.
    \value InOutCirc    \image qeasingcurve-inoutcirc.png {Graph of a
                               InOutCircular function}
                        \caption
                        Easing curve for a circular (sqrt(1-t^2)) function:
                        acceleration until halfway, then deceleration.
    \value OutInCirc    \image qeasingcurve-outincirc.png {Graph of a
                               OutInCircular function}
                        \caption
                        Easing curve for a circular (sqrt(1-t^2)) function:
                        deceleration until halfway, then acceleration.
    \value InElastic    \image qeasingcurve-inelastic.png {Graph of a
                               InElastic function}
                        \caption
                        Easing curve for an elastic
                        (exponentially decaying sine wave) function:
                        accelerating from zero velocity.  The peak amplitude
                        can be set with the \e amplitude parameter, and the
                        period of decay by the \e period parameter.
    \value OutElastic   \image qeasingcurve-outelastic.png {Graph of a
                               OutElastic function}
                        \caption
                        Easing curve for an elastic
                        (exponentially decaying sine wave) function:
                        decelerating to zero velocity.  The peak amplitude
                        can be set with the \e amplitude parameter, and the
                        period of decay by the \e period parameter.
    \value InOutElastic \image qeasingcurve-inoutelastic.png {Graph of a
                               InOutElastic function}
                        \caption
                        Easing curve for an elastic
                        (exponentially decaying sine wave) function:
                        acceleration until halfway, then deceleration.
    \value OutInElastic \image qeasingcurve-outinelastic.png {Graph of a
                               OutInElastic function}
                        \caption
                        Easing curve for an elastic
                        (exponentially decaying sine wave) function:
                        deceleration until halfway, then acceleration.
    \value InBack       \image qeasingcurve-inback.png {Graph of a
                               InBack function}
                        \caption
                        Easing curve for a back (overshooting
                        cubic function: (s+1)*t^3 - s*t^2) easing in:
                        accelerating from zero velocity.
    \value OutBack      \image qeasingcurve-outback.png {Graph of a
                               OutBack function}
                        \caption
                        Easing curve for a back (overshooting
                        cubic function: (s+1)*t^3 - s*t^2) easing out:
                        decelerating to zero velocity.
    \value InOutBack    \image qeasingcurve-inoutback.png Graph of a
                               InOutBack function}
                        \caption
                        Easing curve for a back (overshooting
                        cubic function: (s+1)*t^3 - s*t^2) easing in/out:
                        acceleration until halfway, then deceleration.
    \value OutInBack    \image qeasingcurve-outinback.png {Graph of a
                               OutInBack function}
                        \caption
                        Easing curve for a back (overshooting
                        cubic easing: (s+1)*t^3 - s*t^2) easing out/in:
                        deceleration until halfway, then acceleration.
    \value InBounce     \image qeasingcurve-inbounce.png {Graph of a
                               InBounce function}
                        \caption
                        Easing curve for a bounce (exponentially
                        decaying parabolic bounce) function: accelerating
                        from zero velocity.
    \value OutBounce    \image qeasingcurve-outbounce.png {Graph of a
                               OutBounce function}
                        \caption
                        Easing curve for a bounce (exponentially
                        decaying parabolic bounce) function: decelerating
                        from zero velocity.
    \value InOutBounce  \image qeasingcurve-inoutbounce.png {Graph of a
                               InOutBounce function}
                        \caption
                        Easing curve for a bounce (exponentially
                        decaying parabolic bounce) function easing in/out:
                        acceleration until halfway, then deceleration.
    \value OutInBounce  \image qeasingcurve-outinbounce.png {Graph of a
                               OutInBounce function}
                        \caption
                        Easing curve for a bounce (exponentially
                        decaying parabolic bounce) function easing out/in:
                        deceleration until halfway, then acceleration.
    \omitvalue InCurve
    \omitvalue OutCurve
    \omitvalue SineCurve
    \omitvalue CosineCurve
    \value BezierSpline Allows defining a custom easing curve using a cubic bezier spline
                        \sa addCubicBezierSegment()
    \value TCBSpline    Allows defining a custom easing curve using a TCB spline
                        \sa addTCBSegment()
    \value Custom       This is returned if the user specified a custom curve type with
                        setCustomType(). Note that you cannot call setType() with this value,
                        but type() can return it.
    \omitvalue NCurveTypes
*/
 
/*!
    \typedef QEasingCurve::EasingFunction
 
    This is a typedef for a pointer to a function with the following
    signature:
 
    \snippet code/src_corelib_tools_qeasingcurve.cpp typedef
*/
 
#include "qeasingcurve.h"
#include <cmath>
 
#ifndef QT_NO_DEBUG_STREAM
#include <QtCore/qdebug.h>
#include <QtCore/qstring.h>
#endif
 
#ifndef QT_NO_DATASTREAM
#include <QtCore/qdatastream.h>
#endif
 
#include <QtCore/qpoint.h>
#include <QtCore/qlist.h>
 
QT_BEGIN_NAMESPACE
 
static constexpr bool isConfigFunction(QEasingCurve::Type type)
{
    return (type >= QEasingCurve::InElastic
            && type <= QEasingCurve::OutInBounce) ||
            type == QEasingCurve::BezierSpline ||
            type == QEasingCurve::TCBSpline;
}
 
struct TCBPoint
{
    QPointF _point;
    qreal _t;
    qreal _c;
    qreal _b;
 
 
    friend bool operator==(const TCBPoint &lhs, const TCBPoint &rhs) noexcept
    {
        return qFuzzyCompare(lhs._point, rhs._point)
            && QtPrivate::fuzzyCompare(lhs._t, rhs._t)
            && QtPrivate::fuzzyCompare(lhs._c, rhs._c)
            && QtPrivate::fuzzyCompare(lhs._b, rhs._b);
    }
};
Q_DECLARE_TYPEINFO(TCBPoint, Q_PRIMITIVE_TYPE);
 
QDataStream &operator<<(QDataStream &stream, const TCBPoint &point)
{
    stream << point._point
           << point._t
           << point._c
           << point._b;
    return stream;
}
 
QDataStream &operator>>(QDataStream &stream, TCBPoint &point)
{
    stream >> point._point
           >> point._t
           >> point._c
           >> point._b;
    return stream;
}
 
typedef QList<TCBPoint> TCBPoints;
 
class QEasingCurveFunction
{
    QEasingCurveFunction &operator=(const QEasingCurveFunction &) = delete;
    QEasingCurveFunction &operator=(QEasingCurveFunction &&) = delete;
    QEasingCurveFunction(QEasingCurveFunction &&) = delete;
protected:
    QEasingCurveFunction(const QEasingCurveFunction &) = default; // used by clone()
public:
    QEasingCurveFunction(QEasingCurve::Type type, qreal period = 0.3, qreal amplitude = 1.0,
        qreal overshoot = 1.70158)
        : _t(type), _p(period), _a(amplitude), _o(overshoot)
    { }
    virtual ~QEasingCurveFunction() {}
    virtual qreal value(qreal t);
    virtual QEasingCurveFunction *clone() const { return new QEasingCurveFunction{*this}; }
    // ### virtual? (cf. QTBUG-142709)
    bool fuzzyCompare(const QEasingCurveFunction &other) const noexcept;
 
    QEasingCurve::Type _t;
    qreal _p;
    qreal _a;
    qreal _o;
    QList<QPointF> _bezierCurves;
    TCBPoints _tcbPoints;
 
};
 
QDataStream &operator<<(QDataStream &stream, QEasingCurveFunction *func)
{
    if (func) {
        stream << func->_p;
        stream << func->_a;
        stream << func->_o;
        if (stream.version() > QDataStream::Qt_5_12) {
            stream << func->_bezierCurves;
            stream << func->_tcbPoints;
        }
    }
    return stream;
}
 
QDataStream &operator>>(QDataStream &stream, QEasingCurveFunction *func)
{
    if (func) {
        stream >> func->_p;
        stream >> func->_a;
        stream >> func->_o;
        if (stream.version() > QDataStream::Qt_5_12) {
            stream >> func->_bezierCurves;
            stream >> func->_tcbPoints;
        }
    }
    return stream;
}
 
static QEasingCurve::EasingFunction curveToFunc(QEasingCurve::Type curve);
 
qreal QEasingCurveFunction::value(qreal t)
{
    QEasingCurve::EasingFunction func = curveToFunc(_t);
    return func(t);
}
 
bool QEasingCurveFunction::fuzzyCompare(const QEasingCurveFunction &other) const noexcept
{
    return _t == other._t
        && QtPrivate::fuzzyCompare(_p, other._p)
        && QtPrivate::fuzzyCompare(_a, other._a)
        && QtPrivate::fuzzyCompare(_o, other._o)
        && _bezierCurves == other._bezierCurves
        && _tcbPoints == other._tcbPoints;
}
 
QT_BEGIN_INCLUDE_NAMESPACE
#include "../../3rdparty/easing/easing.cpp"
QT_END_INCLUDE_NAMESPACE
 
class QEasingCurvePrivate
{
public:
    QEasingCurvePrivate()
        : type(QEasingCurve::Linear),
          config(nullptr),
          func(&easeNone)
    { }
    QEasingCurvePrivate(const QEasingCurvePrivate &other)
        : type(other.type),
          config(other.config ? other.config->clone() : nullptr),
          func(other.func)
    { }
    ~QEasingCurvePrivate() { delete config; }
    void setType_helper(QEasingCurve::Type);
 
    QEasingCurve::Type type;
    QEasingCurveFunction *config;
    QEasingCurve::EasingFunction func;
};
 
struct BezierEase : public QEasingCurveFunction
{
    struct SingleCubicBezier {
        qreal p0x, p0y;
        qreal p1x, p1y;
        qreal p2x, p2y;
        qreal p3x, p3y;
    };
 
    QList<SingleCubicBezier> _curves;
    QList<qreal> _intervals;
    int _curveCount;
    bool _init;
    bool _valid;
 
    BezierEase(QEasingCurve::Type type = QEasingCurve::BezierSpline)
        : QEasingCurveFunction(type), _curves(10), _intervals(10), _init(false), _valid(false)
    { }
 
    void init()
    {
        if (_bezierCurves.constLast() == QPointF(1.0, 1.0)) {
            _init = true;
            _curveCount = _bezierCurves.size() / 3;
 
            for (int i=0; i < _curveCount; i++) {
                _intervals[i] = _bezierCurves.at(i * 3 + 2).x();
 
                if (i == 0) {
                    _curves[0].p0x = 0.0;
                    _curves[0].p0y = 0.0;
 
                    _curves[0].p1x = _bezierCurves.at(0).x();
                    _curves[0].p1y = _bezierCurves.at(0).y();
 
                    _curves[0].p2x = _bezierCurves.at(1).x();
                    _curves[0].p2y = _bezierCurves.at(1).y();
 
                    _curves[0].p3x = _bezierCurves.at(2).x();
                    _curves[0].p3y = _bezierCurves.at(2).y();
 
                } else if (i == (_curveCount - 1)) {
                    _curves[i].p0x = _bezierCurves.at(_bezierCurves.size() - 4).x();
                    _curves[i].p0y = _bezierCurves.at(_bezierCurves.size() - 4).y();
 
                    _curves[i].p1x = _bezierCurves.at(_bezierCurves.size() - 3).x();
                    _curves[i].p1y = _bezierCurves.at(_bezierCurves.size() - 3).y();
 
                    _curves[i].p2x = _bezierCurves.at(_bezierCurves.size() - 2).x();
                    _curves[i].p2y = _bezierCurves.at(_bezierCurves.size() - 2).y();
 
                    _curves[i].p3x = _bezierCurves.at(_bezierCurves.size() - 1).x();
                    _curves[i].p3y = _bezierCurves.at(_bezierCurves.size() - 1).y();
                } else {
                    _curves[i].p0x = _bezierCurves.at(i * 3 - 1).x();
                    _curves[i].p0y = _bezierCurves.at(i * 3 - 1).y();
 
                    _curves[i].p1x = _bezierCurves.at(i * 3).x();
                    _curves[i].p1y = _bezierCurves.at(i * 3).y();
 
                    _curves[i].p2x = _bezierCurves.at(i * 3 + 1).x();
                    _curves[i].p2y = _bezierCurves.at(i * 3 + 1).y();
 
                    _curves[i].p3x = _bezierCurves.at(i * 3 + 2).x();
                    _curves[i].p3y = _bezierCurves.at(i * 3 + 2).y();
                }
            }
            _valid = true;
        } else {
            _valid = false;
        }
    }
 
    BezierEase *clone() const override { return new BezierEase{*this}; }
 
    void getBezierSegment(SingleCubicBezier * &singleCubicBezier, qreal x)
    {
 
        int currentSegment = 0;
 
        while (currentSegment < _curveCount) {
            if (x <= _intervals.data()[currentSegment])
                break;
            currentSegment++;
        }
 
        singleCubicBezier = &_curves.data()[currentSegment];
    }
 
 
    qreal static inline newtonIteration(const SingleCubicBezier &singleCubicBezier, qreal t, qreal x)
    {
        qreal currentXValue = evaluateForX(singleCubicBezier, t);
 
        const qreal newT = t - (currentXValue - x) / evaluateDerivateForX(singleCubicBezier, t);
 
        return newT;
    }
 
    qreal value(qreal x) override
    {
        Q_ASSERT(_bezierCurves.size() % 3 == 0);
 
        if (_bezierCurves.isEmpty()) {
            return x;
        }
 
        if (!_init)
            init();
 
        if (!_valid) {
            qWarning("QEasingCurve: Invalid bezier curve");
            return x;
        }
 
        // The bezier computation is not always precise on the endpoints, so handle explicitly
        if (!(x > 0))
            return 0;
        if (!(x < 1))
            return 1;
 
        SingleCubicBezier *singleCubicBezier = nullptr;
        getBezierSegment(singleCubicBezier, x);
 
        return evaluateSegmentForY(*singleCubicBezier, findTForX(*singleCubicBezier, x));
    }
 
    qreal static inline evaluateSegmentForY(const SingleCubicBezier &singleCubicBezier, qreal t)
    {
        const qreal p0 = singleCubicBezier.p0y;
        const qreal p1 = singleCubicBezier.p1y;
        const qreal p2 = singleCubicBezier.p2y;
        const qreal p3 = singleCubicBezier.p3y;
 
        const qreal s = 1 - t;
 
        const qreal s_squared = s * s;
        const qreal t_squared = t * t;
 
        const qreal s_cubic = s_squared * s;
        const qreal t_cubic = t_squared * t;
 
        return s_cubic * p0 + 3 * s_squared * t * p1 + 3 * s * t_squared * p2 + t_cubic * p3;
    }
 
    qreal static inline evaluateForX(const SingleCubicBezier &singleCubicBezier, qreal t)
    {
        const qreal p0 = singleCubicBezier.p0x;
        const qreal p1 = singleCubicBezier.p1x;
        const qreal p2 = singleCubicBezier.p2x;
        const qreal p3 = singleCubicBezier.p3x;
 
        const qreal s = 1 - t;
 
        const qreal s_squared = s * s;
        const qreal t_squared = t * t;
 
        const qreal s_cubic = s_squared * s;
        const qreal t_cubic = t_squared * t;
 
        return s_cubic * p0 + 3 * s_squared * t * p1 + 3 * s * t_squared * p2 + t_cubic * p3;
    }
 
    qreal static inline evaluateDerivateForX(const SingleCubicBezier &singleCubicBezier, qreal t)
    {
        const qreal p0 = singleCubicBezier.p0x;
        const qreal p1 = singleCubicBezier.p1x;
        const qreal p2 = singleCubicBezier.p2x;
        const qreal p3 = singleCubicBezier.p3x;
 
        const qreal t_squared = t * t;
 
        return -3*p0 + 3*p1 + 6*p0*t - 12*p1*t + 6*p2*t + 3*p3*t_squared - 3*p0*t_squared + 9*p1*t_squared - 9*p2*t_squared;
    }
 
    qreal static inline _cbrt(qreal d)
    {
        qreal sign = 1;
        if (d < 0)
            sign = -1;
        d = d * sign;
 
        qreal t = _fast_cbrt(d);
 
        //one step of Halley's Method to get a better approximation
        const qreal t_cubic = t * t * t;
        const qreal f = t_cubic + t_cubic + d;
        if (f != qreal(0.0))
            t = t * (t_cubic + d + d) / f;
 
        //another step
        /*qreal t_i = t;
         t_i_cubic = pow(t_i, 3);
         t = t_i * (t_i_cubic + d + d) / (t_i_cubic + t_i_cubic + d);*/
 
        return t * sign;
    }
 
    float static inline _fast_cbrt(float x)
    {
        union {
            float f;
            quint32 i;
        } ux;
 
        const unsigned int B1 = 709921077;
 
        ux.f = x;
        ux.i = (ux.i / 3 + B1);
 
        return ux.f;
    }
 
    double static inline _fast_cbrt(double d)
    {
        union {
            double d;
            quint32 pt[2];
        } ut, ux;
 
        const unsigned int B1 = 715094163;
 
#if Q_BYTE_ORDER == Q_LITTLE_ENDIAN
        const int h0 = 1;
#else
        const int h0 = 0;
#endif
        ut.d = 0.0;
        ux.d = d;
 
        quint32 hx = ux.pt[h0]; //high word of d
        ut.pt[h0] = hx / 3 + B1;
 
        return ut.d;
    }
 
    qreal static inline _acos(qreal x)
    {
        return std::sqrt(1-x)*(1.5707963267948966192313216916398f + x*(-0.213300989f + x*(0.077980478f + x*-0.02164095f)));
    }
 
    qreal static inline _cos(qreal x) //super fast _cos
    {
        const qreal pi_times2 = 2 * M_PI;
        const qreal pi_neg = -1 * M_PI;
        const qreal pi_by2 = M_PI / 2.0;
 
        x += pi_by2; //the polynom is for sin
 
        if (x < pi_neg)
            x += pi_times2;
        else if (x > M_PI)
            x -= pi_times2;
 
        const qreal a = 0.405284735;
        const qreal b = 1.27323954;
 
        const qreal x_squared = x * x;
 
        if (x < 0) {
            qreal cos = b * x + a * x_squared;
 
            if (cos < 0)
                return 0.225 * (cos * -1 * cos - cos) + cos;
            return 0.225 * (cos * cos - cos) + cos;
        } //else
 
        qreal cos = b * x - a * x_squared;
 
        if (cos < 0)
            return 0.225 * (cos * 1 * -cos - cos) + cos;
        return 0.225 * (cos * cos - cos) + cos;
    }
 
    bool static inline inRange(qreal f)
    {
        return (f >= -0.01 && f <= 1.01);
    }
 
    void static inline cosacos(qreal x, qreal &s1, qreal &s2, qreal &s3 )
    {
        //This function has no proper algebraic representation in real numbers.
        //We use approximations instead
 
        const qreal x_squared = x * x;
        const qreal x_plus_one_sqrt = qSqrt(1.0 + x);
        const qreal one_minus_x_sqrt = qSqrt(1.0 - x);
 
        //cos(acos(x) / 3)
        //s1 = _cos(_acos(x) / 3);
        s1 = 0.463614 - 0.0347815 * x + 0.00218245 * x_squared +  0.402421 * x_plus_one_sqrt;
 
        //cos(acos((x) -  M_PI) / 3)
        //s3 = _cos((_acos(x) - M_PI) / 3);
        s3 = 0.463614 + 0.402421 * one_minus_x_sqrt + 0.0347815 * x + 0.00218245 * x_squared;
 
        //cos((acos(x) +  M_PI) / 3)
        //s2 = _cos((_acos(x) + M_PI) / 3);
        s2 = -0.401644 * one_minus_x_sqrt - 0.0686804  * x + 0.401644 * x_plus_one_sqrt;
    }
 
    qreal static inline singleRealSolutionForCubic(qreal a, qreal b, qreal c)
    {
        //returns the real solutiuon in [0..1]
        //We use the Cardano formula
 
        //substituiton: x = z - a/3
        // z^3+pz+q=0
 
        if (c < 0.000001 && c > -0.000001)
            return 0;
 
        const qreal a_by3 = a / 3.0;
 
        const qreal a_cubic = a * a * a;
 
        const qreal p = b - a * a_by3;
        const qreal q = 2.0 * a_cubic / 27.0 - a * b / 3.0 + c;
 
        const qreal q_squared = q * q;
        const qreal p_cubic = p * p * p;
        const qreal D = 0.25 * q_squared + p_cubic / 27.0;
 
        if (D >= 0) {
            const qreal D_sqrt = qSqrt(D);
            qreal u = _cbrt(-q * 0.5 + D_sqrt);
            qreal v = _cbrt(-q * 0.5 - D_sqrt);
            qreal z1 = u + v;
 
            qreal t1 = z1 - a_by3;
 
            if (inRange(t1))
                return t1;
            qreal z2 = -1 * u;
            qreal t2 = z2 - a_by3;
            return t2;
        }
 
        //casus irreducibilis
        const qreal p_minus_sqrt = qSqrt(-p);
 
        //const qreal f = sqrt(4.0 / 3.0 * -p);
        const qreal f = qSqrt(4.0 / 3.0) * p_minus_sqrt;
 
        //const qreal sqrtP = sqrt(27.0 / -p_cubic);
        const qreal sqrtP = -3.0*qSqrt(3.0) / (p_minus_sqrt * p);
 
 
        const qreal g = -q * 0.5 * sqrtP;
 
        qreal s1;
        qreal s2;
        qreal s3;
 
        cosacos(g, s1, s2, s3);
 
        qreal z1 = -1 * f * s2;
        qreal t1 = z1 - a_by3;
        if (inRange(t1))
            return t1;
 
        qreal z2 = f * s1;
        qreal t2 = z2 - a_by3;
        if (inRange(t2))
            return t2;
 
        qreal z3 = -1 * f * s3;
        qreal t3 = z3 - a_by3;
        return t3;
    }
 
    bool static inline almostZero(qreal value)
    {
        // 1e-3 might seem excessively fuzzy, but any smaller value will make the
        // factors a, b, and c large enough to knock out the cubic solver.
        return value > -1e-3 && value < 1e-3;
    }
 
    qreal static inline findTForX(const SingleCubicBezier &singleCubicBezier, qreal x)
    {
        const qreal p0 = singleCubicBezier.p0x;
        const qreal p1 = singleCubicBezier.p1x;
        const qreal p2 = singleCubicBezier.p2x;
        const qreal p3 = singleCubicBezier.p3x;
 
        const qreal factorT3 = p3 - p0 + 3 * p1 - 3 * p2;
        const qreal factorT2 = 3 * p0 - 6 * p1 + 3 * p2;
        const qreal factorT1 = -3 * p0 + 3 * p1;
        const qreal factorT0 = p0 - x;
 
        // Cases for quadratic, linear and invalid equations
        if (almostZero(factorT3)) {
            if (almostZero(factorT2)) {
                if (almostZero(factorT1))
                    return 0.0;
 
                return -factorT0 / factorT1;
            }
            const qreal discriminant = factorT1 * factorT1 - 4.0 * factorT2 * factorT0;
            if (discriminant < 0.0)
                return 0.0;
 
            if (discriminant == 0.0)
                return -factorT1 / (2.0 * factorT2);
 
            const qreal solution1 = (-factorT1 + std::sqrt(discriminant)) / (2.0 * factorT2);
            if (solution1 >= 0.0 && solution1 <= 1.0)
                return solution1;
 
            const qreal solution2 = (-factorT1 - std::sqrt(discriminant)) / (2.0 * factorT2);
            if (solution2 >= 0.0 && solution2 <= 1.0)
                return solution2;
 
            return 0.0;
        }
 
        const qreal a = factorT2 / factorT3;
        const qreal b = factorT1 / factorT3;
        const qreal c = factorT0 / factorT3;
 
        return singleRealSolutionForCubic(a, b, c);
 
        //one new iteration to increase numeric stability
        //return newtonIteration(singleCubicBezier, t, x);
    }
};
 
struct TCBEase : public BezierEase
{
    TCBEase()
        : BezierEase(QEasingCurve::TCBSpline)
    { }
 
    qreal value(qreal x) override
    {
        Q_ASSERT(_bezierCurves.size() % 3 == 0);
 
        if (_bezierCurves.isEmpty()) {
            qWarning("QEasingCurve: Invalid tcb curve");
            return x;
        }
 
        return BezierEase::value(x);
    }
 
    TCBEase *clone() const override
    {
        return new TCBEase{*this};
    }
};
 
struct ElasticEase : public QEasingCurveFunction
{
    ElasticEase(QEasingCurve::Type type)
        : QEasingCurveFunction(type, qreal(0.3), qreal(1.0))
    { }
 
    ElasticEase *clone() const override { return new ElasticEase{*this}; }
 
    qreal value(qreal t) override
    {
        qreal p = (_p < 0) ? qreal(0.3) : _p;
        qreal a = (_a < 0) ? qreal(1.0) : _a;
        switch (_t) {
        case QEasingCurve::InElastic:
            return easeInElastic(t, a, p);
        case QEasingCurve::OutElastic:
            return easeOutElastic(t, a, p);
        case QEasingCurve::InOutElastic:
            return easeInOutElastic(t, a, p);
        case QEasingCurve::OutInElastic:
            return easeOutInElastic(t, a, p);
        default:
            return t;
        }
    }
};
 
struct BounceEase : public QEasingCurveFunction
{
    BounceEase(QEasingCurve::Type type)
        : QEasingCurveFunction(type, qreal(0.3), qreal(1.0))
    { }
 
    BounceEase *clone() const override { return new BounceEase{*this}; }
 
    qreal value(qreal t) override
    {
        qreal a = (_a < 0) ? qreal(1.0) : _a;
        switch (_t) {
        case QEasingCurve::InBounce:
            return easeInBounce(t, a);
        case QEasingCurve::OutBounce:
            return easeOutBounce(t, a);
        case QEasingCurve::InOutBounce:
            return easeInOutBounce(t, a);
        case QEasingCurve::OutInBounce:
            return easeOutInBounce(t, a);
        default:
            return t;
        }
    }
};
 
struct BackEase : public QEasingCurveFunction
{
    BackEase(QEasingCurve::Type type)
        : QEasingCurveFunction(type, qreal(0.3), qreal(1.0), qreal(1.70158))
    { }
 
    BackEase *clone() const override { return new BackEase{*this}; }
 
    qreal value(qreal t) override
    {
        // The *Back() functions are not always precise on the endpoints, so handle explicitly
        if (!(t > 0))
            return 0;
        if (!(t < 1))
            return 1;
        qreal o = (_o < 0) ? qreal(1.70158) : _o;
        switch (_t) {
        case QEasingCurve::InBack:
            return easeInBack(t, o);
        case QEasingCurve::OutBack:
            return easeOutBack(t, o);
        case QEasingCurve::InOutBack:
            return easeInOutBack(t, o);
        case QEasingCurve::OutInBack:
            return easeOutInBack(t, o);
        default:
            return t;
        }
    }
};
 
static QEasingCurve::EasingFunction curveToFunc(QEasingCurve::Type curve)
{
    switch (curve) {
    case QEasingCurve::Linear:
        return &easeNone;
    case QEasingCurve::InQuad:
        return &easeInQuad;
    case QEasingCurve::OutQuad:
        return &easeOutQuad;
    case QEasingCurve::InOutQuad:
        return &easeInOutQuad;
    case QEasingCurve::OutInQuad:
        return &easeOutInQuad;
    case QEasingCurve::InCubic:
        return &easeInCubic;
    case QEasingCurve::OutCubic:
        return &easeOutCubic;
    case QEasingCurve::InOutCubic:
        return &easeInOutCubic;
    case QEasingCurve::OutInCubic:
        return &easeOutInCubic;
    case QEasingCurve::InQuart:
        return &easeInQuart;
    case QEasingCurve::OutQuart:
        return &easeOutQuart;
    case QEasingCurve::InOutQuart:
        return &easeInOutQuart;
    case QEasingCurve::OutInQuart:
        return &easeOutInQuart;
    case QEasingCurve::InQuint:
        return &easeInQuint;
    case QEasingCurve::OutQuint:
        return &easeOutQuint;
    case QEasingCurve::InOutQuint:
        return &easeInOutQuint;
    case QEasingCurve::OutInQuint:
        return &easeOutInQuint;
    case QEasingCurve::InSine:
        return &easeInSine;
    case QEasingCurve::OutSine:
        return &easeOutSine;
    case QEasingCurve::InOutSine:
        return &easeInOutSine;
    case QEasingCurve::OutInSine:
        return &easeOutInSine;
    case QEasingCurve::InExpo:
        return &easeInExpo;
    case QEasingCurve::OutExpo:
        return &easeOutExpo;
    case QEasingCurve::InOutExpo:
        return &easeInOutExpo;
    case QEasingCurve::OutInExpo:
        return &easeOutInExpo;
    case QEasingCurve::InCirc:
        return &easeInCirc;
    case QEasingCurve::OutCirc:
        return &easeOutCirc;
    case QEasingCurve::InOutCirc:
        return &easeInOutCirc;
    case QEasingCurve::OutInCirc:
        return &easeOutInCirc;
    // Internal - needed for QTimeLine backward-compatibility:
    case QEasingCurve::InCurve:
        return &easeInCurve;
    case QEasingCurve::OutCurve:
        return &easeOutCurve;
    case QEasingCurve::SineCurve:
        return &easeSineCurve;
    case QEasingCurve::CosineCurve:
        return &easeCosineCurve;
    default:
        return nullptr;
    };
}
 
static QEasingCurveFunction *curveToFunctionObject(QEasingCurve::Type type)
{
    switch (type) {
    case QEasingCurve::InElastic:
    case QEasingCurve::OutElastic:
    case QEasingCurve::InOutElastic:
    case QEasingCurve::OutInElastic:
        return new ElasticEase(type);
    case QEasingCurve::OutBounce:
    case QEasingCurve::InBounce:
    case QEasingCurve::OutInBounce:
    case QEasingCurve::InOutBounce:
        return new BounceEase(type);
    case QEasingCurve::InBack:
    case QEasingCurve::OutBack:
    case QEasingCurve::InOutBack:
    case QEasingCurve::OutInBack:
        return new BackEase(type);
    case QEasingCurve::BezierSpline:
        return new BezierEase;
    case QEasingCurve::TCBSpline:
        return new TCBEase;
    default:
        return new QEasingCurveFunction(type, qreal(0.3), qreal(1.0), qreal(1.70158));
    }
 
    return nullptr;
}
 
/*!
    \fn QEasingCurve::QEasingCurve(QEasingCurve &&other)
 
    Move-constructs a QEasingCurve instance, making it point at the same
    object that \a other was pointing to.
 
    \since 5.2
*/
 
/*!
    Constructs an easing curve of the given \a type.
 */
QEasingCurve::QEasingCurve(Type type)
    : d_ptr(new QEasingCurvePrivate)
{
    setType(type);
}
 
/*!
    Construct a copy of \a other.
 */
QEasingCurve::QEasingCurve(const QEasingCurve &other)
    : d_ptr(new QEasingCurvePrivate(*other.d_ptr))
{
    // ### non-atomic, requires malloc on shallow copy
}
 
/*!
    Destructor.
 */
 
QEasingCurve::~QEasingCurve()
{
    delete d_ptr;
}
 
/*!
    \fn QEasingCurve &QEasingCurve::operator=(const QEasingCurve &other)
    Copy \a other.
 */
 
/*!
    \fn QEasingCurve &QEasingCurve::operator=(QEasingCurve &&other)
 
    Move-assigns \a other to this QEasingCurve instance.
 
    \since 5.2
*/
 
/*!
    \fn void QEasingCurve::swap(QEasingCurve &other)
    \since 5.0
    \memberswap{curve}
*/
 
/*!
    \fn bool QEasingCurve::operator==(const QEasingCurve &lhs, const QEasingCurve &rhs)
 
    Compares easing curve \a lhs with \a rhs and returns \c true if they are
    equal; otherwise returns \c false.
    It will also compare the properties of the curves.
 */
bool comparesEqual(const QEasingCurve &lhs, const QEasingCurve &rhs)
{
    bool res = lhs.d_ptr->func == rhs.d_ptr->func
            && lhs.d_ptr->type == rhs.d_ptr->type;
    if (res) {
        if (lhs.d_ptr->config && rhs.d_ptr->config) {
            // catch the config content
            res = lhs.d_ptr->config->fuzzyCompare(*rhs.d_ptr->config);
        } else if (lhs.d_ptr->config || rhs.d_ptr->config) {
            // one one has a config object, which could contain default values
            res = QtPrivate::fuzzyCompare(lhs.amplitude(), rhs.amplitude())
               && QtPrivate::fuzzyCompare(lhs.period(), rhs.period())
               && QtPrivate::fuzzyCompare(lhs.overshoot(), rhs.overshoot());
        }
    }
    return res;
}
 
/*!
    \fn bool QEasingCurve::operator!=(const QEasingCurve &lhs, const QEasingCurve &rhs)
 
    Compares easing curve \a lhs with \a rhs and returns \c true if they are
    not equal; otherwise returns \c false.
    It will also compare the properties of the curves.
 
    \sa operator==()
*/
 
/*!
    Returns the amplitude. This is not applicable for all curve types.
    It is only applicable for bounce and elastic curves (curves of type()
    QEasingCurve::InBounce, QEasingCurve::OutBounce, QEasingCurve::InOutBounce,
    QEasingCurve::OutInBounce, QEasingCurve::InElastic, QEasingCurve::OutElastic,
    QEasingCurve::InOutElastic or QEasingCurve::OutInElastic).
 */
qreal QEasingCurve::amplitude() const
{
    return d_ptr->config ? d_ptr->config->_a : qreal(1.0);
}
 
/*!
    Sets the amplitude to \a amplitude.
 
    This will set the amplitude of the bounce or the amplitude of the
    elastic "spring" effect. The higher the number, the higher the amplitude.
    \sa amplitude()
*/
void QEasingCurve::setAmplitude(qreal amplitude)
{
    if (!d_ptr->config)
        d_ptr->config = curveToFunctionObject(d_ptr->type);
    d_ptr->config->_a = amplitude;
}
 
/*!
    Returns the period. This is not applicable for all curve types.
    It is only applicable if type() is QEasingCurve::InElastic, QEasingCurve::OutElastic,
    QEasingCurve::InOutElastic or QEasingCurve::OutInElastic.
 */
qreal QEasingCurve::period() const
{
    return d_ptr->config ? d_ptr->config->_p : qreal(0.3);
}
 
/*!
    Sets the period to \a period.
    Setting a small period value will give a high frequency of the curve. A
    large period will give it a small frequency.
 
    \sa period()
*/
void QEasingCurve::setPeriod(qreal period)
{
    if (!d_ptr->config)
        d_ptr->config = curveToFunctionObject(d_ptr->type);
    d_ptr->config->_p = period;
}
 
/*!
    Returns the overshoot. This is not applicable for all curve types.
    It is only applicable if type() is QEasingCurve::InBack, QEasingCurve::OutBack,
    QEasingCurve::InOutBack or QEasingCurve::OutInBack.
 */
qreal QEasingCurve::overshoot() const
{
    return d_ptr->config ? d_ptr->config->_o : qreal(1.70158);
}
 
/*!
    Sets the overshoot to \a overshoot.
 
    0 produces no overshoot, and the default value of 1.70158 produces an overshoot of 10 percent.
 
    \sa overshoot()
*/
void QEasingCurve::setOvershoot(qreal overshoot)
{
    if (!d_ptr->config)
        d_ptr->config = curveToFunctionObject(d_ptr->type);
    d_ptr->config->_o = overshoot;
}
 
/*!
    Adds a segment of a cubic bezier spline to define a custom easing curve.
    It is only applicable if type() is QEasingCurve::BezierSpline.
    Note that the spline implicitly starts at (0.0, 0.0) and has to end at (1.0, 1.0) to
    be a valid easing curve.
    \a c1 and \a c2 are the control points used for drawing the curve.
    \a endPoint is the endpoint of the curve.
 */
void QEasingCurve::addCubicBezierSegment(const QPointF & c1, const QPointF & c2, const QPointF & endPoint)
{
    if (!d_ptr->config)
        d_ptr->config = curveToFunctionObject(d_ptr->type);
    d_ptr->config->_bezierCurves << c1 << c2 << endPoint;
}
 
QList<QPointF> static inline tcbToBezier(const TCBPoints &tcbPoints)
{
    const int count = tcbPoints.size();
    QList<QPointF> bezierPoints;
    bezierPoints.reserve(3 * (count - 1));
 
    for (int i = 1; i < count; i++) {
        const qreal t_0 = tcbPoints.at(i - 1)._t;
        const qreal c_0 = tcbPoints.at(i - 1)._c;
        qreal b_0 = -1;
 
        qreal const t_1 = tcbPoints.at(i)._t;
        qreal const c_1 = tcbPoints.at(i)._c;
        qreal b_1 = 1;
 
        QPointF c_minusOne;                                   //P1 last segment - not available for the first point
        const QPointF c0(tcbPoints.at(i - 1)._point);         //P0 Hermite/TBC
        const QPointF c3(tcbPoints.at(i)._point);             //P1 Hermite/TBC
        QPointF c4;                                           //P0 next segment - not available for the last point
 
        if (i > 1) { //first point no left tangent
            c_minusOne = tcbPoints.at(i - 2)._point;
            b_0 = tcbPoints.at(i - 1)._b;
        }
 
        if (i < (count - 1)) { //last point no right tangent
            c4 = tcbPoints.at(i + 1)._point;
            b_1 = tcbPoints.at(i)._b;
        }
 
        const qreal dx_0 = 0.5 * (1-t_0) *  ((1 + b_0) * (1 + c_0) * (c0.x() - c_minusOne.x()) + (1- b_0) * (1 - c_0) * (c3.x() - c0.x()));
        const qreal dy_0 = 0.5 * (1-t_0) *  ((1 + b_0) * (1 + c_0) * (c0.y() - c_minusOne.y()) + (1- b_0) * (1 - c_0) * (c3.y() - c0.y()));
 
        const qreal dx_1 =  0.5 * (1-t_1) * ((1 + b_1) * (1 - c_1) * (c3.x() - c0.x()) + (1 - b_1) * (1 + c_1) * (c4.x() - c3.x()));
        const qreal dy_1 =  0.5 * (1-t_1) * ((1 + b_1) * (1 - c_1) * (c3.y() - c0.y()) + (1 - b_1) * (1 + c_1) * (c4.y() - c3.y()));
 
        const QPointF d_0 = QPointF(dx_0, dy_0);
        const QPointF d_1 = QPointF(dx_1, dy_1);
 
        QPointF c1 = (3 * c0 + d_0) / 3;
        QPointF c2 = (3 * c3 - d_1) / 3;
        bezierPoints << c1 << c2 << c3;
    }
    return bezierPoints;
}
 
/*!
    Adds a segment of a TCB bezier spline to define a custom easing curve.
    It is only applicable if type() is QEasingCurve::TCBSpline.
    The spline has to start explicitly at (0.0, 0.0) and has to end at (1.0, 1.0) to
    be a valid easing curve.
    The tension \a t changes the length of the tangent vector.
    The continuity \a c changes the sharpness in change between the tangents.
    The bias \a b changes the direction of the tangent vector.
    \a nextPoint is the sample position.
    All three parameters are valid between -1 and 1 and define the
    tangent of the control point.
    If all three parameters are 0 the resulting spline is a Catmull-Rom spline.
    The begin and endpoint always have a bias of -1 and 1, since the outer tangent is not defined.
 */
void QEasingCurve::addTCBSegment(const QPointF &nextPoint, qreal t, qreal c, qreal b)
{
    if (!d_ptr->config)
        d_ptr->config = curveToFunctionObject(d_ptr->type);
 
    d_ptr->config->_tcbPoints.append(TCBPoint{nextPoint, t, c, b});
 
    if (nextPoint == QPointF(1.0, 1.0)) {
        d_ptr->config->_bezierCurves = tcbToBezier(d_ptr->config->_tcbPoints);
        d_ptr->config->_tcbPoints.clear();
    }
 
}
 
/*!
    \since 5.0
 
    Returns the cubicBezierSpline that defines a custom easing curve.
    If the easing curve does not have a custom bezier easing curve the list
    is empty.
*/
QList<QPointF> QEasingCurve::toCubicSpline() const
{
    return d_ptr->config ? d_ptr->config->_bezierCurves : QList<QPointF>();
}
 
/*!
    Returns the type of the easing curve.
*/
QEasingCurve::Type QEasingCurve::type() const
{
    return d_ptr->type;
}
 
void QEasingCurvePrivate::setType_helper(QEasingCurve::Type newType)
{
    qreal amp = -1.0;
    qreal period = -1.0;
    qreal overshoot = -1.0;
    QList<QPointF> bezierCurves;
    QList<TCBPoint> tcbPoints;
 
    if (config) {
        amp = config->_a;
        period = config->_p;
        overshoot = config->_o;
        bezierCurves = std::move(config->_bezierCurves);
        tcbPoints = std::move(config->_tcbPoints);
 
        delete config;
        config = nullptr;
    }
 
    if (isConfigFunction(newType) || (amp != -1.0) || (period != -1.0) || (overshoot != -1.0) ||
        !bezierCurves.isEmpty()) {
        config = curveToFunctionObject(newType);
        if (amp != -1.0)
            config->_a = amp;
        if (period != -1.0)
            config->_p = period;
        if (overshoot != -1.0)
            config->_o = overshoot;
        config->_bezierCurves = std::move(bezierCurves);
        config->_tcbPoints = std::move(tcbPoints);
        func = nullptr;
    } else if (newType != QEasingCurve::Custom) {
        func = curveToFunc(newType);
    }
    Q_ASSERT((func == nullptr) == (config != nullptr));
    type = newType;
}
 
/*!
    Sets the type of the easing curve to \a type.
*/
void QEasingCurve::setType(Type type)
{
    if (d_ptr->type == type)
        return;
    if (type < Linear || type >= NCurveTypes - 1) {
        qWarning("QEasingCurve: Invalid curve type %d", type);
        return;
    }
 
    d_ptr->setType_helper(type);
}
 
/*!
    Sets a custom easing curve that is defined by the user in the function \a func.
    The signature of the function is qreal myEasingFunction(qreal progress),
    where \e progress and the return value are considered to be normalized between 0 and 1.
    (In some cases the return value can be outside that range)
    After calling this function type() will return QEasingCurve::Custom.
    \a func cannot be \nullptr.
 
    \sa customType()
    \sa valueForProgress()
*/
void QEasingCurve::setCustomType(EasingFunction func)
{
    if (!func) {
        qWarning("Function pointer must not be null");
        return;
    }
    d_ptr->func = func;
    d_ptr->setType_helper(Custom);
}
 
/*!
    Returns the function pointer to the custom easing curve.
    If type() does not return QEasingCurve::Custom, this function
    will return 0.
*/
QEasingCurve::EasingFunction QEasingCurve::customType() const
{
    return d_ptr->type == Custom ? d_ptr->func : nullptr;
}
 
/*!
    Return the effective progress for the easing curve at \a progress.
    Whereas \a progress must be between 0 and 1, the returned effective progress
    can be outside those bounds. For example, QEasingCurve::InBack will
    return negative values in the beginning of the function.
 */
qreal QEasingCurve::valueForProgress(qreal progress) const
{
    progress = qBound<qreal>(0, progress, 1);
    if (d_ptr->func)
        return d_ptr->func(progress);
    else if (d_ptr->config)
        return d_ptr->config->value(progress);
    else
        return progress;
}
 
#ifndef QT_NO_DEBUG_STREAM
QDebug operator<<(QDebug debug, const QEasingCurve &item)
{
    QDebugStateSaver saver(debug);
    debug << "type:" << item.d_ptr->type
          << "func:" << reinterpret_cast<const void *>(item.d_ptr->func);
    if (item.d_ptr->config) {
        debug << QString::fromLatin1("period:%1").arg(item.d_ptr->config->_p, 0, 'f', 20)
              << QString::fromLatin1("amp:%1").arg(item.d_ptr->config->_a, 0, 'f', 20)
              << QString::fromLatin1("overshoot:%1").arg(item.d_ptr->config->_o, 0, 'f', 20);
    }
    return debug;
}
#endif // QT_NO_DEBUG_STREAM
 
#ifndef QT_NO_DATASTREAM
/*!
    \fn QDataStream &operator<<(QDataStream &stream, const QEasingCurve &easing)
    \relates QEasingCurve
 
    Writes the given \a easing curve to the given \a stream and returns a
    reference to the stream.
 
    \warning Writing easing curves of QEasingCurve::Custom type
    (that is, curves with a custom easing function) is not supported.
 
    \sa {Serializing Qt Data Types}
*/
 
QDataStream &operator<<(QDataStream &stream, const QEasingCurve &easing)
{
    if (easing.d_ptr->type == QEasingCurve::Custom) {
        qWarning("QEasingCurve: Cannot serialize an easing curve with a custom easing function");
 
        // Backwards compatibility: stream _something_ out.
        // Deliberately choose a curve that uses a config and not a
        // easing function. If this curve is deserialized from old
        // code, it will ignore the function pointer (cf.
        // QTBUG-132575).
        static_assert(isConfigFunction(QEasingCurve::InElastic));
        stream << QEasingCurve(QEasingCurve::InElastic);
        return stream;
    }
 
    stream << quint8(easing.d_ptr->type);
    // Unused; for backwards compatibility
    stream << quint64(0);
 
    bool hasConfig = easing.d_ptr->config;
    stream << hasConfig;
    if (hasConfig) {
        stream << easing.d_ptr->config;
    }
    return stream;
}
 
/*!
    \fn QDataStream &operator>>(QDataStream &stream, QEasingCurve &easing)
    \relates QEasingCurve
 
    Reads an easing curve from the given \a stream into the given \a
    easing curve and returns a reference to the stream.
 
    \sa {Serializing Qt Data Types}
*/
 
QDataStream &operator>>(QDataStream &stream, QEasingCurve &easing)
{
    QEasingCurve::Type type;
    quint8 int_type;
    stream >> int_type;
    type = static_cast<QEasingCurve::Type>(int_type);
    if (type == QEasingCurve::Custom) {
        qWarning("QEasingCurve: Cannot deserialize an easing curve with a custom easing function");
        stream.setStatus(QDataStream::ReadCorruptData);
        type = QEasingCurve::Linear;
    }
    easing.setType(type);
 
    // Unused; for backwards compatibility
    [[maybe_unused]] quint64 ptr_func;
    stream >> ptr_func;
 
    bool hasConfig;
    stream >> hasConfig;
    delete easing.d_ptr->config;
    easing.d_ptr->config = nullptr;
    if (hasConfig) {
        QEasingCurveFunction *config = curveToFunctionObject(type);
        stream >> config;
        easing.d_ptr->config = config;
    }
    return stream;
}
#endif // QT_NO_DATASTREAM
 
QT_END_NAMESPACE
 
#include "moc_qeasingcurve.cpp"