Optimise QMatrix and QTransform

Add some private inline constructors and do inlining
other places.
All test still pass.

4 files changed, 220 insertions, 89 deletions

diff --git a/src/gui/painting/qmatrix.cpp b/src/gui/painting/qmatrix.cpp
index 4439d52..31abcad 100644
--- a/src/gui/painting/qmatrix.cpp
+++ b/src/gui/painting/qmatrix.cpp
@@ -208,9 +208,13 @@ QT_BEGIN_NAMESPACE
 */
 
 QMatrix::QMatrix()
+    : _m11(1.)
+    , _m12(0.)
+    , _m21(0.)
+    , _m22(1.)
+    , _dx(0.)
+    , _dy(0.)
 {
-    _m11 = _m22 = 1.0;
-    _m12 = _m21 = _dx = _dy = 0.0;
 }
 
 /*!
@@ -220,12 +224,14 @@ QMatrix::QMatrix()
     \sa setMatrix()
 */
 
-QMatrix::QMatrix(qreal m11, qreal m12, qreal m21, qreal m22,
-                    qreal dx, qreal dy)
+QMatrix::QMatrix(qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
+    : _m11(m11)
+    , _m12(m12)
+    , _m21(m21)
+    , _m22(m22)
+    , _dx(dx)
+    , _dy(dy)
 {
-    _m11 = m11;         _m12 = m12;
-    _m21 = m21;         _m22 = m22;
-    _dx         = dx;         _dy  = dy;
 }
 
 
@@ -233,8 +239,13 @@ QMatrix::QMatrix(qreal m11, qreal m12, qreal m21, qreal m22,
      Constructs a matrix that is a copy of the given \a matrix.
  */
 QMatrix::QMatrix(const QMatrix &matrix)
+    : _m11(matrix._m11)
+    , _m12(matrix._m12)
+    , _m21(matrix._m21)
+    , _m22(matrix._m22)
+    , _dx(matrix._dx)
+    , _dy(matrix._dy)
 {
-    *this = matrix;
 }
 
 /*!
@@ -249,12 +260,14 @@ QMatrix::QMatrix(const QMatrix &matrix)
     \sa QMatrix()
 */
 
-void QMatrix::setMatrix(qreal m11, qreal m12, qreal m21, qreal m22,
-                          qreal dx, qreal dy)
+void QMatrix::setMatrix(qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
 {
-    _m11 = m11;         _m12 = m12;
-    _m21 = m21;         _m22 = m22;
-    _dx         = dx;         _dy  = dy;
+    _m11 = m11;
+    _m12 = m12;
+    _m21 = m21;
+    _m22 = m22;
+    _dx  = dx;
+    _dy  = dy;
 }
 
 
@@ -968,18 +981,17 @@ QMatrix QMatrix::inverted(bool *invertible) const
     if (determinant == 0.0) {
         if (invertible)
             *invertible = false;                // singular matrix
-        QMatrix defaultMatrix;
-        return defaultMatrix;
+        return QMatrix(true);
     }
     else {                                        // invertible matrix
         if (invertible)
             *invertible = true;
         qreal dinv = 1.0/determinant;
-        QMatrix imatrix((_m22*dinv),        (-_m12*dinv),
-                          (-_m21*dinv), (_m11*dinv),
-                          ((_m21*_dy - _m22*_dx)*dinv),
-                          ((_m12*_dx - _m11*_dy)*dinv));
-        return imatrix;
+        return QMatrix((_m22*dinv),        (-_m12*dinv),
+                       (-_m21*dinv), (_m11*dinv),
+                       ((_m21*_dy - _m22*_dx)*dinv),
+                       ((_m12*_dx - _m11*_dy)*dinv),
+                       true);
     }
 }
 
@@ -1054,9 +1066,14 @@ QMatrix &QMatrix::operator *=(const QMatrix &m)
 
 QMatrix QMatrix::operator *(const QMatrix &m) const
 {
-    QMatrix result = *this;
-    result *= m;
-    return result;
+    qreal tm11 = _m11*m._m11 + _m12*m._m21;
+    qreal tm12 = _m11*m._m12 + _m12*m._m22;
+    qreal tm21 = _m21*m._m11 + _m22*m._m21;
+    qreal tm22 = _m21*m._m12 + _m22*m._m22;
+
+    qreal tdx  = _dx*m._m11  + _dy*m._m21 + m._dx;
+    qreal tdy =  _dx*m._m12  + _dy*m._m22 + m._dy;
+    return QMatrix(tm11, tm12, tm21, tm22, tdx, tdy, true);
 }
 
 /*!
diff --git a/src/gui/painting/qmatrix.h b/src/gui/painting/qmatrix.h
index bf53c32..1b6bd6d 100644
--- a/src/gui/painting/qmatrix.h
+++ b/src/gui/painting/qmatrix.h
@@ -121,6 +121,20 @@ public:
 #endif
 
 private:
+    inline QMatrix(bool)
+            : _m11(1.)
+            , _m12(0.)
+            , _m21(0.)
+            , _m22(1.)
+            , _dx(0.)
+            , _dy(0.) {}
+    inline QMatrix(qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy, bool)
+            : _m11(m11)
+            , _m12(m12)
+            , _m21(m21)
+            , _m22(m22)
+            , _dx(dx)
+            , _dy(dy) {}
     friend class QTransform;
     qreal _m11, _m12;
     qreal _m21, _m22;
@@ -147,8 +161,8 @@ Q_GUI_EXPORT QPainterPath operator *(const QPainterPath &p, const QMatrix &m);
 
 inline bool QMatrix::isIdentity() const
 {
-    return qFuzzyCompare(_m11, 1) && qFuzzyCompare(_m22, 1) && qFuzzyCompare(_m12 + 1, 1)
-           && qFuzzyCompare(_m21 + 1, 1) && qFuzzyCompare(_dx + 1, 1) && qFuzzyCompare(_dy + 1, 1);
+    return qIsFuzzyNull(_m11 - 1) && qIsFuzzyNull(_m22 - 1) && qIsFuzzyNull(_m12)
+           && qIsFuzzyNull(_m21) && qIsFuzzyNull(_dx) && qIsFuzzyNull(_dy);
 }
 
 /*****************************************************************************
diff --git a/src/gui/painting/qtransform.cpp b/src/gui/painting/qtransform.cpp
index b25146d..6c37ab6 100644
--- a/src/gui/painting/qtransform.cpp
+++ b/src/gui/painting/qtransform.cpp
@@ -238,11 +238,11 @@ QT_BEGIN_NAMESPACE
     \sa reset()
 */
 QTransform::QTransform()
-    : m_13(0), m_23(0), m_33(1)
+    : affine(true)
+    , m_13(0), m_23(0), m_33(1)
     , m_type(TxNone)
     , m_dirty(TxNone)
 {
-
 }
 
 /*!
@@ -256,12 +256,11 @@ QTransform::QTransform()
 QTransform::QTransform(qreal h11, qreal h12, qreal h13,
                        qreal h21, qreal h22, qreal h23,
                        qreal h31, qreal h32, qreal h33)
-    : affine(h11, h12, h21, h22, h31, h32),
-      m_13(h13), m_23(h23), m_33(h33)
+    : affine(h11, h12, h21, h22, h31, h32, true)
+    , m_13(h13), m_23(h23), m_33(h33)
     , m_type(TxNone)
     , m_dirty(TxProject)
 {
-
 }
 
 /*!
@@ -273,12 +272,11 @@ QTransform::QTransform(qreal h11, qreal h12, qreal h13,
 */
 QTransform::QTransform(qreal h11, qreal h12, qreal h21,
                        qreal h22, qreal dx, qreal dy)
-    : affine(h11, h12, h21, h22, dx, dy),
-      m_13(0), m_23(0), m_33(1)
+    : affine(h11, h12, h21, h22, dx, dy, true)
+    , m_13(0), m_23(0), m_33(1)
     , m_type(TxNone)
     , m_dirty(TxShear)
 {
-
 }
 
 /*!
@@ -289,12 +287,11 @@ QTransform::QTransform(qreal h11, qreal h12, qreal h21,
     and 1 respectively.
  */
 QTransform::QTransform(const QMatrix &mtx)
-    : affine(mtx),
+    : affine(mtx._m11, mtx._m12, mtx._m21, mtx._m22, mtx._dx, mtx._dy, true),
       m_13(0), m_23(0), m_33(1)
     , m_type(TxNone)
     , m_dirty(TxShear)
 {
-
 }
 
 /*!
@@ -317,7 +314,7 @@ QTransform QTransform::adjoint() const
 
     return QTransform(h11, h12, h13,
                       h21, h22, h23,
-                      h31, h32, h33);
+                      h31, h32, h33, true);
 }
 
 /*!
@@ -327,7 +324,7 @@ QTransform QTransform::transposed() const
 {
     QTransform t(affine._m11, affine._m21, affine._dx,
                  affine._m12, affine._m22, affine._dy,
-                 m_13, m_23, m_33);
+                 m_13, m_23, m_33, true);
     t.m_type = m_type;
     t.m_dirty = m_dirty;
     return t;
@@ -345,11 +342,10 @@ QTransform QTransform::transposed() const
 */
 QTransform QTransform::inverted(bool *invertible) const
 {
-    QTransform invert;
+    QTransform invert(true);
     bool inv = true;
-    qreal det;
 
-    switch(type()) {
+    switch(inline_type()) {
     case TxNone:
         break;
     case TxTranslate:
@@ -357,11 +353,11 @@ QTransform QTransform::inverted(bool *invertible) const
         invert.affine._dy = -affine._dy;
         break;
     case TxScale:
-        inv = !qFuzzyCompare(affine._m11 + 1, 1);
-        inv &= !qFuzzyCompare(affine._m22 + 1, 1);
+        inv = !qIsFuzzyNull(affine._m11);
+        inv &= !qIsFuzzyNull(affine._m22);
         if (inv) {
-            invert.affine._m11 = 1 / affine._m11;
-            invert.affine._m22 = 1 / affine._m22;
+            invert.affine._m11 = 1. / affine._m11;
+            invert.affine._m22 = 1. / affine._m22;
             invert.affine._dx = -affine._dx * invert.affine._m11;
             invert.affine._dy = -affine._dy * invert.affine._m22;
         }
@@ -372,8 +368,8 @@ QTransform QTransform::inverted(bool *invertible) const
         break;
     default:
         // general case
-        det = determinant();
-        inv = !qFuzzyCompare(det + 1, 1);
+        qreal det = determinant();
+        inv = !qIsFuzzyNull(det);
         if (inv)
             invert = adjoint() / det;
         break;
@@ -397,12 +393,12 @@ QTransform QTransform::inverted(bool *invertible) const
 
     \sa setMatrix()
 */
-QTransform & QTransform::translate(qreal dx, qreal dy)
+QTransform &QTransform::translate(qreal dx, qreal dy)
 {
     if (dx == 0 && dy == 0)
         return *this;
 
-    switch(type()) {
+    switch(inline_type()) {
     case TxNone:
         affine._dx = dx;
         affine._dy = dy;
@@ -437,7 +433,7 @@ QTransform & QTransform::translate(qreal dx, qreal dy)
 */
 QTransform QTransform::fromTranslate(qreal dx, qreal dy)
 {
-    QTransform transform(1, 0, 0, 1, dx, dy);
+    QTransform transform(1, 0, 0, 0, 1, 0, dx, dy, 1, true);
     if (dx == 0 && dy == 0)
         transform.m_dirty = TxNone;
     else
@@ -456,7 +452,7 @@ QTransform & QTransform::scale(qreal sx, qreal sy)
     if (sx == 1 && sy == 1)
         return *this;
 
-    switch(type()) {
+    switch(inline_type()) {
     case TxNone:
     case TxTranslate:
         affine._m11 = sx;
@@ -489,8 +485,8 @@ QTransform & QTransform::scale(qreal sx, qreal sy)
 */
 QTransform QTransform::fromScale(qreal sx, qreal sy)
 {
-    QTransform transform(sx, 0, 0, sy, 0, 0);
-    if (sx == 1 && sy == 1)
+    QTransform transform(sx, 0, 0, 0, sy, 0, 0, 0, 1, true);
+    if (sx == 1. && sy == 1.)
         transform.m_dirty = TxNone;
     else
         transform.m_dirty = TxScale;
@@ -505,7 +501,7 @@ QTransform QTransform::fromScale(qreal sx, qreal sy)
 */
 QTransform & QTransform::shear(qreal sh, qreal sv)
 {
-    switch(type()) {
+    switch(inline_type()) {
     case TxNone:
     case TxTranslate:
         affine._m12 = sv;
@@ -574,7 +570,7 @@ QTransform & QTransform::rotate(qreal a, Qt::Axis axis)
     }
 
     if (axis == Qt::ZAxis) {
-        switch(type()) {
+        switch(inline_type()) {
         case TxNone:
         case TxTranslate:
             affine._m11 = cosa;
@@ -646,7 +642,7 @@ QTransform & QTransform::rotateRadians(qreal a, Qt::Axis axis)
     qreal cosa = qCos(a);
 
     if (axis == Qt::ZAxis) {
-        switch(type()) {
+        switch(inline_type()) {
         case TxNone:
         case TxTranslate:
             affine._m11 = cosa;
@@ -730,11 +726,11 @@ bool QTransform::operator!=(const QTransform &o) const
 */
 QTransform & QTransform::operator*=(const QTransform &o)
 {
-    const TransformationType otherType = o.type();
+    const TransformationType otherType = o.inline_type();
     if (otherType == TxNone)
         return *this;
 
-    const TransformationType thisType = type();
+    const TransformationType thisType = inline_type();
     if (thisType == TxNone)
         return operator=(o);
 
@@ -812,9 +808,77 @@ QTransform & QTransform::operator*=(const QTransform &o)
 */
 QTransform QTransform::operator*(const QTransform &m) const
 {
-    QTransform result = *this;
-    result *= m;
-    return result;
+    const TransformationType otherType = m.inline_type();
+    if (otherType == TxNone)
+        return *this;
+
+    const TransformationType thisType = inline_type();
+    if (thisType == TxNone)
+        return m;
+
+    QTransform t(true);
+    TransformationType type = qMax(thisType, otherType);
+    switch(type) {
+    case TxNone:
+        break;
+    case TxTranslate:
+        t.affine._dx = affine._dx + m.affine._dx;
+        t.affine._dy += affine._dy + m.affine._dy;
+        break;
+    case TxScale:
+    {
+        qreal m11 = affine._m11*m.affine._m11;
+        qreal m22 = affine._m22*m.affine._m22;
+
+        qreal m31 = affine._dx*m.affine._m11 + m.affine._dx;
+        qreal m32 = affine._dy*m.affine._m22 + m.affine._dy;
+
+        t.affine._m11 = m11;
+        t.affine._m22 = m22;
+        t.affine._dx = m31; t.affine._dy = m32;
+        break;
+    }
+    case TxRotate:
+    case TxShear:
+    {
+        qreal m11 = affine._m11*m.affine._m11 + affine._m12*m.affine._m21;
+        qreal m12 = affine._m11*m.affine._m12 + affine._m12*m.affine._m22;
+
+        qreal m21 = affine._m21*m.affine._m11 + affine._m22*m.affine._m21;
+        qreal m22 = affine._m21*m.affine._m12 + affine._m22*m.affine._m22;
+
+        qreal m31 = affine._dx*m.affine._m11 + affine._dy*m.affine._m21 + m.affine._dx;
+        qreal m32 = affine._dx*m.affine._m12 + affine._dy*m.affine._m22 + m.affine._dy;
+
+        t.affine._m11 = m11; t.affine._m12 = m12;
+        t.affine._m21 = m21; t.affine._m22 = m22;
+        t.affine._dx = m31; t.affine._dy = m32;
+        break;
+    }
+    case TxProject:
+    {
+        qreal m11 = affine._m11*m.affine._m11 + affine._m12*m.affine._m21 + m_13*m.affine._dx;
+        qreal m12 = affine._m11*m.affine._m12 + affine._m12*m.affine._m22 + m_13*m.affine._dy;
+        qreal m13 = affine._m11*m.m_13 + affine._m12*m.m_23 + m_13*m.m_33;
+
+        qreal m21 = affine._m21*m.affine._m11 + affine._m22*m.affine._m21 + m_23*m.affine._dx;
+        qreal m22 = affine._m21*m.affine._m12 + affine._m22*m.affine._m22 + m_23*m.affine._dy;
+        qreal m23 = affine._m21*m.m_13 + affine._m22*m.m_23 + m_23*m.m_33;
+
+        qreal m31 = affine._dx*m.affine._m11 + affine._dy*m.affine._m21 + m_33*m.affine._dx;
+        qreal m32 = affine._dx*m.affine._m12 + affine._dy*m.affine._m22 + m_33*m.affine._dy;
+        qreal m33 = affine._dx*m.m_13 + affine._dy*m.m_23 + m_33*m.m_33;
+
+        t.affine._m11 = m11; t.affine._m12 = m12; t.m_13 = m13;
+        t.affine._m21 = m21; t.affine._m22 = m22; t.m_23 = m23;
+        t.affine._dx = m31; t.affine._dy = m32; t.m_33 = m33;
+    }
+    }
+
+    t.m_dirty = type;
+    t.m_type = type;
+
+    return t;
 }
 
 /*!
@@ -976,7 +1040,7 @@ QPoint QTransform::map(const QPoint &p) const
 
     qreal x = 0, y = 0;
 
-    TransformationType t = type();
+    TransformationType t = inline_type();
     switch(t) {
     case TxNone:
         x = fx;
@@ -1027,7 +1091,7 @@ QPointF QTransform::map(const QPointF &p) const
 
     qreal x = 0, y = 0;
 
-    TransformationType t = type();
+    TransformationType t = inline_type();
     switch(t) {
     case TxNone:
         x = fx;
@@ -1098,7 +1162,7 @@ QLine QTransform::map(const QLine &l) const
 
     qreal x1 = 0, y1 = 0, x2 = 0, y2 = 0;
 
-    TransformationType t = type();
+    TransformationType t = inline_type();
     switch(t) {
     case TxNone:
         x1 = fx1;
@@ -1157,7 +1221,7 @@ QLineF QTransform::map(const QLineF &l) const
 
     qreal x1 = 0, y1 = 0, x2 = 0, y2 = 0;
 
-    TransformationType t = type();
+    TransformationType t = inline_type();
     switch(t) {
     case TxNone:
         x1 = fx1;
@@ -1245,7 +1309,7 @@ static QPolygonF mapProjective(const QTransform &transform, const QPolygonF &pol
 */
 QPolygonF QTransform::map(const QPolygonF &a) const
 {
-    TransformationType t = type();
+    TransformationType t = inline_type();
     if (t <= TxTranslate)
         return a.translated(affine._dx, affine._dy);
 
@@ -1275,7 +1339,7 @@ QPolygonF QTransform::map(const QPolygonF &a) const
 */
 QPolygon QTransform::map(const QPolygon &a) const
 {
-    TransformationType t = type();
+    TransformationType t = inline_type();
     if (t <= TxTranslate)
         return a.translated(qRound(affine._dx), qRound(affine._dy));
 
@@ -1320,7 +1384,7 @@ extern QPainterPath qt_regionToPath(const QRegion &region);
 */
 QRegion QTransform::map(const QRegion &r) const
 {
-    TransformationType t = type();
+    TransformationType t = inline_type();
     if (t == TxNone)
         return r;
     if (t == TxTranslate) {
@@ -1343,7 +1407,7 @@ struct QHomogeneousCoordinate
     QHomogeneousCoordinate(qreal x_, qreal y_, qreal w_) : x(x_), y(y_), w(w_) {}
 
     const QPointF toPoint() const {
-        qreal iw = 1 / w;
+        qreal iw = 1. / w;
         return QPointF(x * iw, y * iw);
     }
 };
@@ -1481,7 +1545,7 @@ static QPainterPath mapProjective(const QTransform &transform, const QPainterPat
 */
 QPainterPath QTransform::map(const QPainterPath &path) const
 {
-    TransformationType t = type();
+    TransformationType t = inline_type();
     if (t == TxNone || path.isEmpty())
         return path;
 
@@ -1526,7 +1590,7 @@ QPainterPath QTransform::map(const QPainterPath &path) const
 */
 QPolygon QTransform::mapToPolygon(const QRect &rect) const
 {
-    TransformationType t = type();
+    TransformationType t = inline_type();
 
     QPolygon a(4);
     qreal x[4] = { 0, 0, 0, 0 }, y[4] = { 0, 0, 0, 0 };
@@ -1700,7 +1764,7 @@ void QTransform::setMatrix(qreal m11, qreal m12, qreal m13,
 
 QRect QTransform::mapRect(const QRect &rect) const
 {
-    TransformationType t = type();
+    TransformationType t = inline_type();
     if (t <= TxTranslate)
         return rect.translated(qRound(affine._dx), qRound(affine._dy));
 
@@ -1771,7 +1835,7 @@ QRect QTransform::mapRect(const QRect &rect) const
 */
 QRectF QTransform::mapRect(const QRectF &rect) const
 {
-    TransformationType t = type();
+    TransformationType t = inline_type();
     if (t <= TxTranslate)
         return rect.translated(affine._dx, affine._dy);
 
@@ -1846,7 +1910,7 @@ QRectF QTransform::mapRect(const QRectF &rect) const
 */
 void QTransform::map(qreal x, qreal y, qreal *tx, qreal *ty) const
 {
-    TransformationType t = type();
+    TransformationType t = inline_type();
     MAP(x, y, *tx, *ty);
 }
 
@@ -1860,7 +1924,7 @@ void QTransform::map(qreal x, qreal y, qreal *tx, qreal *ty) const
 */
 void QTransform::map(int x, int y, int *tx, int *ty) const
 {
-    TransformationType t = type();
+    TransformationType t = inline_type();
     qreal fx = 0, fy = 0;
     MAP(x, y, fx, fy);
     *tx = qRound(fx);
@@ -1889,25 +1953,41 @@ const QMatrix &QTransform::toAffine() const
   */
 QTransform::TransformationType QTransform::type() const
 {
-    if (m_dirty >= m_type) {
-        if (m_dirty > TxShear && (!qFuzzyCompare(m_13 + 1, 1) || !qFuzzyCompare(m_23 + 1, 1)))
+    if(m_dirty == TxNone || m_dirty < m_type)
+        return static_cast<TransformationType>(m_type);
+
+    switch (static_cast<TransformationType>(m_dirty)) {
+    case TxProject:
+        if (!qIsFuzzyNull(m_13) || !qIsFuzzyNull(m_23) || !qIsFuzzyNull(m_33 - 1)) {
              m_type = TxProject;
-        else if (m_dirty > TxScale && (!qFuzzyCompare(affine._m12 + 1, 1) || !qFuzzyCompare(affine._m21 + 1, 1))) {
+             break;
+         }
+    case TxShear:
+    case TxRotate:
+        if (!qIsFuzzyNull(affine._m12) || !qIsFuzzyNull(affine._m21)) {
             const qreal dot = affine._m11 * affine._m12 + affine._m21 * affine._m22;
-            if (qFuzzyCompare(dot + 1, 1))
+            if (qIsFuzzyNull(dot))
                 m_type = TxRotate;
             else
                 m_type = TxShear;
-        } else if (m_dirty > TxTranslate && (!qFuzzyCompare(affine._m11, 1) || !qFuzzyCompare(affine._m22, 1) || !qFuzzyCompare(m_33, 1)))
+            break;
+        }
+    case TxScale:
+        if (!qIsFuzzyNull(affine._m11 - 1) || !qIsFuzzyNull(affine._m22 - 1)) {
             m_type = TxScale;
-        else if (m_dirty > TxNone && (!qFuzzyCompare(affine._dx + 1, 1) || !qFuzzyCompare(affine._dy + 1, 1)))
+            break;
+        }
+    case TxTranslate:
+        if (!qIsFuzzyNull(affine._dx) || !qIsFuzzyNull(affine._dy)) {
             m_type = TxTranslate;
-        else
-            m_type = TxNone;
-
-        m_dirty = TxNone;
+            break;
+        }
+    case TxNone:
+        m_type = TxNone;
+        break;
     }
 
+    m_dirty = TxNone;
     return static_cast<TransformationType>(m_type);
 }
 
diff --git a/src/gui/painting/qtransform.h b/src/gui/painting/qtransform.h
index c76409b..2d6c889 100644
--- a/src/gui/painting/qtransform.h
+++ b/src/gui/painting/qtransform.h
@@ -159,6 +159,19 @@ public:
     static QTransform fromScale(qreal dx, qreal dy);
 
 private:
+    inline QTransform(qreal h11, qreal h12, qreal h13,
+                      qreal h21, qreal h22, qreal h23,
+                      qreal h31, qreal h32, qreal h33, bool)
+        : affine(h11, h12, h21, h22, h31, h32, true)
+        , m_13(h13), m_23(h23), m_33(h33)
+        , m_type(TxNone)
+        , m_dirty(TxProject) {}
+    inline QTransform(bool)
+        : affine(true)
+        , m_13(0), m_23(0), m_33(1)
+        , m_type(TxNone)
+        , m_dirty(TxNone) {}
+    inline TransformationType inline_type() const;
     QMatrix affine;
     qreal   m_13;
     qreal   m_23;
@@ -173,18 +186,25 @@ private:
 Q_DECLARE_TYPEINFO(QTransform, Q_MOVABLE_TYPE);
 
 /******* inlines *****/
+inline QTransform::TransformationType QTransform::inline_type() const
+{
+    if (m_dirty == TxNone)
+        return static_cast<TransformationType>(m_type);
+    return type();
+}
+
 inline bool QTransform::isAffine() const
 {
-    return type() < TxProject;
+    return inline_type() < TxProject;
 }
 inline bool QTransform::isIdentity() const
 {
-    return type() == TxNone;
+    return inline_type() == TxNone;
 }
 
 inline bool QTransform::isInvertible() const
 {
-    return !qFuzzyCompare(determinant() + 1, 1);
+    return !qIsFuzzyNull(determinant());
 }
 
 inline bool QTransform::isScaling() const
@@ -193,12 +213,12 @@ inline bool QTransform::isScaling() const
 }
 inline bool QTransform::isRotating() const
 {
-    return type() >= TxRotate;
+    return inline_type() >= TxRotate;
 }
 
 inline bool QTransform::isTranslating() const
 {
-    return type() >= TxTranslate;
+    return inline_type() >= TxTranslate;
 }
 
 inline qreal QTransform::determinant() const