/*!
    Align and divide an interval

   \param maxNumSteps Max. number of steps
   \param x1 First limit of the interval (In/Out)
   \param x2 Second limit of the interval (In/Out)
   \param stepSize Step size (Out)

   \sa QwtScaleEngine::setAttribute()
*/
void QwtLog10ScaleEngine::autoScale(int maxNumSteps, 
    double &x1, double &x2, double &stepSize) const
{
    if ( x1 > x2 )
        qSwap(x1, x2);

    QwtDoubleInterval interval(x1 / pow(10.0, lowerMargin()), 
        x2 * pow(10.0, upperMargin()) );

    if (interval.maxValue() / interval.minValue() < 10.0)
    {
        // scale width is less than one decade -> build linear scale

        QwtLinearScaleEngine linearScaler;
        linearScaler.setAttributes(attributes());
        linearScaler.setReference(reference());
        linearScaler.setMargins(lowerMargin(), upperMargin());

        linearScaler.autoScale(maxNumSteps, x1, x2, stepSize);
        stepSize = ::log10(stepSize);

        return;
    }

    double logRef = 1.0;
    if (reference() > LOG_MIN / 2)
        logRef = qwtMin(reference(), LOG_MAX / 2);

    if (testAttribute(QwtScaleEngine::Symmetric))
    {
        const double delta = qwtMax(interval.maxValue() / logRef,  
            logRef / interval.minValue());
        interval.setInterval(logRef / delta, logRef * delta);
    }

    if (testAttribute(QwtScaleEngine::IncludeReference))
        interval = interval.extend(logRef);

    interval = interval.limited(LOG_MIN, LOG_MAX);

    if (interval.width() == 0.0)
        interval = buildInterval(interval.minValue());

    stepSize = divideInterval(log10(interval).width(), qwtMax(maxNumSteps, 1));
    if ( stepSize < 1.0 )
        stepSize = 1.0;

    if (!testAttribute(QwtScaleEngine::Floating))
        interval = align(interval, stepSize);

    x1 = interval.minValue();
    x2 = interval.maxValue();

    if (testAttribute(QwtScaleEngine::Inverted))
    {
        qSwap(x1, x2);
        stepSize = -stepSize;
    }
}
/*!
    Align and divide an interval

   \param maxNumSteps Max. number of steps
   \param x1 First limit of the interval (In/Out)
   \param x2 Second limit of the interval (In/Out)
   \param stepSize Step size (Out)

   \sa QwtScaleEngine::setAttribute()
*/
void QwtLogScaleEngine::autoScale( int maxNumSteps,
    double &x1, double &x2, double &stepSize ) const
{
    if ( x1 > x2 )
        qSwap( x1, x2 );

    const double logBase = base();

    QwtInterval interval( x1 / qPow( logBase, lowerMargin() ),
        x2 * qPow( logBase, upperMargin() ) );

    if ( interval.maxValue() / interval.minValue() < logBase )
    {
        // scale width is less than one step -> try to build a linear scale

        QwtLinearScaleEngine linearScaler;
        linearScaler.setAttributes( attributes() );
        linearScaler.setReference( reference() );
        linearScaler.setMargins( lowerMargin(), upperMargin() );

        linearScaler.autoScale( maxNumSteps, x1, x2, stepSize );

        QwtInterval linearInterval = QwtInterval( x1, x2 ).normalized();
        linearInterval = linearInterval.limited( LOG_MIN, LOG_MAX );

        if ( linearInterval.maxValue() / linearInterval.minValue() < logBase )
        {
            // the aligned scale is still less than one step
            if ( stepSize < 0.0 )
                stepSize = -qwtLog( logBase, qAbs( stepSize ) );
            else
                stepSize = qwtLog( logBase, stepSize );

            return;
        }
    }

    double logRef = 1.0;
    if ( reference() > LOG_MIN / 2 )
        logRef = qMin( reference(), LOG_MAX / 2 );

    if ( testAttribute( QwtScaleEngine::Symmetric ) )
    {
        const double delta = qMax( interval.maxValue() / logRef,
            logRef / interval.minValue() );
        interval.setInterval( logRef / delta, logRef * delta );
    }

    if ( testAttribute( QwtScaleEngine::IncludeReference ) )
        interval = interval.extend( logRef );

    interval = interval.limited( LOG_MIN, LOG_MAX );

    if ( interval.width() == 0.0 )
        interval = buildInterval( interval.minValue() );

    stepSize = divideInterval( qwtLogInterval( logBase, interval ).width(), 
        qMax( maxNumSteps, 1 ) );
    if ( stepSize < 1.0 )
        stepSize = 1.0;

    if ( !testAttribute( QwtScaleEngine::Floating ) )
        interval = align( interval, stepSize );

    x1 = interval.minValue();
    x2 = interval.maxValue();

    if ( testAttribute( QwtScaleEngine::Inverted ) )
    {
        qSwap( x1, x2 );
        stepSize = -stepSize;
    }
}