Add m-esr52 at 52.6.0

1 files changed, 1676 insertions, 0 deletions

diff --git a/gfx/2d/Matrix.h b/gfx/2d/Matrix.h
new file mode 100644
index 0000000000..22a01ca103
--- /dev/null
+++ b/gfx/2d/Matrix.h
@@ -0,0 +1,1676 @@
+/* -*- Mode: C++; tab-width: 20; indent-tabs-mode: nil; c-basic-offset: 2 -*-
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
+
+#ifndef MOZILLA_GFX_MATRIX_H_
+#define MOZILLA_GFX_MATRIX_H_
+
+#include "Types.h"
+#include "Triangle.h"
+#include "Rect.h"
+#include "Point.h"
+#include "Quaternion.h"
+#include <iosfwd>
+#include <math.h>
+#include "mozilla/Attributes.h"
+#include "mozilla/DebugOnly.h"
+#include "mozilla/FloatingPoint.h"
+
+namespace mozilla {
+namespace gfx {
+
+static bool FuzzyEqual(Float aV1, Float aV2) {
+  // XXX - Check if fabs does the smart thing and just negates the sign bit.
+  return fabs(aV2 - aV1) < 1e-6;
+}
+
+class Matrix
+{
+public:
+  Matrix()
+    : _11(1.0f), _12(0)
+    , _21(0), _22(1.0f)
+    , _31(0), _32(0)
+  {}
+  Matrix(Float a11, Float a12, Float a21, Float a22, Float a31, Float a32)
+    : _11(a11), _12(a12)
+    , _21(a21), _22(a22)
+    , _31(a31), _32(a32)
+  {}
+  union {
+    struct {
+      Float _11, _12;
+      Float _21, _22;
+      Float _31, _32;
+    };
+    Float components[6];
+  };
+
+  MOZ_ALWAYS_INLINE Matrix Copy() const
+  {
+    return Matrix(*this);
+  }
+
+  friend std::ostream& operator<<(std::ostream& aStream, const Matrix& aMatrix);
+
+  Point TransformPoint(const Point &aPoint) const
+  {
+    Point retPoint;
+
+    retPoint.x = aPoint.x * _11 + aPoint.y * _21 + _31;
+    retPoint.y = aPoint.x * _12 + aPoint.y * _22 + _32;
+
+    return retPoint;
+  }
+
+  Size TransformSize(const Size &aSize) const
+  {
+    Size retSize;
+
+    retSize.width = aSize.width * _11 + aSize.height * _21;
+    retSize.height = aSize.width * _12 + aSize.height * _22;
+
+    return retSize;
+  }
+
+  GFX2D_API Rect TransformBounds(const Rect& rect) const;
+
+  static Matrix Translation(Float aX, Float aY)
+  {
+    return Matrix(1.0f, 0.0f, 0.0f, 1.0f, aX, aY);
+  }
+
+  static Matrix Translation(Point aPoint)
+  {
+    return Translation(aPoint.x, aPoint.y);
+  }
+
+  /**
+   * Apply a translation to this matrix.
+   *
+   * The "Pre" in this method's name means that the translation is applied
+   * -before- this matrix's existing transformation. That is, any vector that
+   * is multiplied by the resulting matrix will first be translated, then be
+   * transformed by the original transform.
+   *
+   * Calling this method will result in this matrix having the same value as
+   * the result of:
+   *
+   *   Matrix::Translation(x, y) * this
+   *
+   * (Note that in performance critical code multiplying by the result of a
+   * Translation()/Scaling() call is not recommended since that results in a
+   * full matrix multiply involving 12 floating-point multiplications. Calling
+   * this method would be preferred since it only involves four floating-point
+   * multiplications.)
+   */
+  Matrix &PreTranslate(Float aX, Float aY)
+  {
+    _31 += _11 * aX + _21 * aY;
+    _32 += _12 * aX + _22 * aY;
+
+    return *this;
+  }
+
+  Matrix &PreTranslate(const Point &aPoint)
+  {
+    return PreTranslate(aPoint.x, aPoint.y);
+  }
+
+  /**
+   * Similar to PreTranslate, but the translation is applied -after- this
+   * matrix's existing transformation instead of before it.
+   *
+   * This method is generally less used than PreTranslate since typically code
+   * want to adjust an existing user space to device space matrix to create a
+   * transform to device space from a -new- user space (translated from the
+   * previous user space). In that case consumers will need to use the Pre*
+   * variants of the matrix methods rather than using the Post* methods, since
+   * the Post* methods add a transform to the device space end of the
+   * transformation.
+   */
+  Matrix &PostTranslate(Float aX, Float aY)
+  {
+    _31 += aX;
+    _32 += aY;
+    return *this;
+  }
+
+  Matrix &PostTranslate(const Point &aPoint)
+  {
+    return PostTranslate(aPoint.x, aPoint.y);
+  }
+
+  static Matrix Scaling(Float aScaleX, Float aScaleY)
+  {
+    return Matrix(aScaleX, 0.0f, 0.0f, aScaleY, 0.0f, 0.0f);
+  }
+  
+  /**
+   * Similar to PreTranslate, but applies a scale instead of a translation.
+   */
+  Matrix &PreScale(Float aX, Float aY)
+  {
+    _11 *= aX;
+    _12 *= aX;
+    _21 *= aY;
+    _22 *= aY;
+
+    return *this;
+  }
+
+  /**
+   * Similar to PostTranslate, but applies a scale instead of a translation.
+   */
+  Matrix &PostScale(Float aScaleX, Float aScaleY)
+  {
+    _11 *= aScaleX;
+    _12 *= aScaleY;
+    _21 *= aScaleX;
+    _22 *= aScaleY;
+    _31 *= aScaleX;
+    _32 *= aScaleY;
+
+    return *this;
+  }
+
+  GFX2D_API static Matrix Rotation(Float aAngle);
+
+  /**
+   * Similar to PreTranslate, but applies a rotation instead of a translation.
+   */
+  Matrix &PreRotate(Float aAngle)
+  {
+    return *this = Matrix::Rotation(aAngle) * *this;
+  }
+
+  bool Invert()
+  {
+    // Compute co-factors.
+    Float A = _22;
+    Float B = -_21;
+    Float C = _21 * _32 - _22 * _31;
+    Float D = -_12;
+    Float E = _11;
+    Float F = _31 * _12 - _11 * _32;
+
+    Float det = Determinant();
+
+    if (!det) {
+      return false;
+    }
+
+    Float inv_det = 1 / det;
+
+    _11 = inv_det * A;
+    _12 = inv_det * D;
+    _21 = inv_det * B;
+    _22 = inv_det * E;
+    _31 = inv_det * C;
+    _32 = inv_det * F;
+
+    return true;
+  }
+
+  Matrix Inverse() const
+  {
+    Matrix clone = *this;
+    DebugOnly<bool> inverted = clone.Invert();
+    MOZ_ASSERT(inverted, "Attempted to get the inverse of a non-invertible matrix");
+    return clone;
+  }
+
+  Float Determinant() const
+  {
+    return _11 * _22 - _12 * _21;
+  }
+
+  Matrix operator*(const Matrix &aMatrix) const
+  {
+    Matrix resultMatrix;
+
+    resultMatrix._11 = this->_11 * aMatrix._11 + this->_12 * aMatrix._21;
+    resultMatrix._12 = this->_11 * aMatrix._12 + this->_12 * aMatrix._22;
+    resultMatrix._21 = this->_21 * aMatrix._11 + this->_22 * aMatrix._21;
+    resultMatrix._22 = this->_21 * aMatrix._12 + this->_22 * aMatrix._22;
+    resultMatrix._31 = this->_31 * aMatrix._11 + this->_32 * aMatrix._21 + aMatrix._31;
+    resultMatrix._32 = this->_31 * aMatrix._12 + this->_32 * aMatrix._22 + aMatrix._32;
+
+    return resultMatrix;
+  }
+
+  Matrix& operator*=(const Matrix &aMatrix)
+  {
+    *this = *this * aMatrix;
+    return *this;
+  }
+
+  /**
+   * Multiplies in the opposite order to operator=*.
+   */
+  Matrix &PreMultiply(const Matrix &aMatrix)
+  {
+    *this = aMatrix * *this;
+    return *this;
+  }
+
+  /* Returns true if the other matrix is fuzzy-equal to this matrix.
+   * Note that this isn't a cheap comparison!
+   */
+  bool operator==(const Matrix& other) const
+  {
+    return FuzzyEqual(_11, other._11) && FuzzyEqual(_12, other._12) &&
+           FuzzyEqual(_21, other._21) && FuzzyEqual(_22, other._22) &&
+           FuzzyEqual(_31, other._31) && FuzzyEqual(_32, other._32);
+  }
+
+  bool operator!=(const Matrix& other) const
+  {
+    return !(*this == other);
+  }
+
+  bool ExactlyEquals(const Matrix& o) const
+  {
+    return _11 == o._11 && _12 == o._12 &&
+           _21 == o._21 && _22 == o._22 &&
+           _31 == o._31 && _32 == o._32;
+  }
+
+  /* Verifies that the matrix contains no Infs or NaNs. */
+  bool IsFinite() const
+  {
+    return mozilla::IsFinite(_11) && mozilla::IsFinite(_12) &&
+           mozilla::IsFinite(_21) && mozilla::IsFinite(_22) &&
+           mozilla::IsFinite(_31) && mozilla::IsFinite(_32);
+  }
+
+  /* Returns true if the matrix is a rectilinear transformation (i.e.
+   * grid-aligned rectangles are transformed to grid-aligned rectangles)
+   */
+  bool IsRectilinear() const {
+    if (FuzzyEqual(_12, 0) && FuzzyEqual(_21, 0)) {
+      return true;
+    } else if (FuzzyEqual(_22, 0) && FuzzyEqual(_11, 0)) {
+      return true;
+    }
+
+    return false;
+  }
+
+  /**
+   * Returns true if the matrix is anything other than a straight
+   * translation by integers.
+  */
+  bool HasNonIntegerTranslation() const {
+    return HasNonTranslation() ||
+      !FuzzyEqual(_31, floor(_31 + Float(0.5))) ||
+      !FuzzyEqual(_32, floor(_32 + Float(0.5)));
+  }
+
+  /**
+   * Returns true if the matrix only has an integer translation.
+   */
+  bool HasOnlyIntegerTranslation() const {
+    return !HasNonIntegerTranslation();
+  }
+
+  /**
+   * Returns true if the matrix has any transform other
+   * than a straight translation.
+   */
+  bool HasNonTranslation() const {
+    return !FuzzyEqual(_11, 1.0) || !FuzzyEqual(_22, 1.0) ||
+           !FuzzyEqual(_12, 0.0) || !FuzzyEqual(_21, 0.0);
+  }
+
+  /**
+   * Returns true if the matrix has any transform other
+   * than a translation or a -1 y scale (y axis flip)
+   */
+  bool HasNonTranslationOrFlip() const {
+      return !FuzzyEqual(_11, 1.0) ||
+             (!FuzzyEqual(_22, 1.0) && !FuzzyEqual(_22, -1.0)) ||
+             !FuzzyEqual(_21, 0.0) || !FuzzyEqual(_12, 0.0);
+  }
+
+  /* Returns true if the matrix is an identity matrix.
+   */
+  bool IsIdentity() const
+  {
+    return _11 == 1.0f && _12 == 0.0f &&
+           _21 == 0.0f && _22 == 1.0f &&
+           _31 == 0.0f && _32 == 0.0f;
+  }
+
+  /* Returns true if the matrix is singular.
+   */
+  bool IsSingular() const
+  {
+    Float det = Determinant();
+    return !mozilla::IsFinite(det) || det == 0;
+  }
+
+  GFX2D_API Matrix &NudgeToIntegers();
+
+  bool IsTranslation() const
+  {
+    return FuzzyEqual(_11, 1.0f) && FuzzyEqual(_12, 0.0f) &&
+           FuzzyEqual(_21, 0.0f) && FuzzyEqual(_22, 1.0f);
+  }
+
+  static bool FuzzyIsInteger(Float aValue)
+  {
+    return FuzzyEqual(aValue, floorf(aValue + 0.5f));
+  }
+
+  bool IsIntegerTranslation() const
+  {
+    return IsTranslation() && FuzzyIsInteger(_31) && FuzzyIsInteger(_32);
+  }
+
+  bool IsAllIntegers() const
+  {
+    return FuzzyIsInteger(_11) && FuzzyIsInteger(_12) &&
+           FuzzyIsInteger(_21) && FuzzyIsInteger(_22) &&
+           FuzzyIsInteger(_31) && FuzzyIsInteger(_32);
+  }
+
+  Point GetTranslation() const {
+    return Point(_31, _32);
+  }
+
+  /**
+   * Returns true if matrix is multiple of 90 degrees rotation with flipping,
+   * scaling and translation.
+   */
+  bool PreservesAxisAlignedRectangles() const {
+      return ((FuzzyEqual(_11, 0.0) && FuzzyEqual(_22, 0.0))
+          || (FuzzyEqual(_12, 0.0) && FuzzyEqual(_21, 0.0)));
+  }
+
+  /**
+   * Returns true if the matrix has any transform other
+   * than a translation or scale; this is, if there is
+   * rotation.
+   */
+  bool HasNonAxisAlignedTransform() const {
+      return !FuzzyEqual(_21, 0.0) || !FuzzyEqual(_12, 0.0);
+  }
+
+  /**
+   * Returns true if the matrix has negative scaling (i.e. flip).
+   */
+  bool HasNegativeScaling() const {
+      return (_11 < 0.0) || (_22 < 0.0);
+  }
+};
+
+// Helper functions used by Matrix4x4Typed defined in Matrix.cpp
+double
+SafeTangent(double aTheta);
+double
+FlushToZero(double aVal);
+
+template<class Units, class F>
+Point4DTyped<Units, F>
+ComputePerspectivePlaneIntercept(const Point4DTyped<Units, F>& aFirst,
+                                 const Point4DTyped<Units, F>& aSecond)
+{
+  // This function will always return a point with a w value of 0.
+  // The X, Y, and Z components will point towards an infinite vanishing
+  // point.
+
+  // We want to interpolate aFirst and aSecond to find the point intersecting
+  // with the w=0 plane.
+
+  // Since we know what we want the w component to be, we can rearrange the
+  // interpolation equation and solve for t.
+  float t = -aFirst.w / (aSecond.w - aFirst.w);
+
+  // Use t to find the remainder of the components
+  return aFirst + (aSecond - aFirst) * t;
+}
+
+
+template <typename SourceUnits, typename TargetUnits>
+class Matrix4x4Typed
+{
+public:
+  typedef PointTyped<SourceUnits> SourcePoint;
+  typedef PointTyped<TargetUnits> TargetPoint;
+  typedef Point3DTyped<SourceUnits> SourcePoint3D;
+  typedef Point3DTyped<TargetUnits> TargetPoint3D;
+  typedef Point4DTyped<SourceUnits> SourcePoint4D;
+  typedef Point4DTyped<TargetUnits> TargetPoint4D;
+  typedef RectTyped<SourceUnits> SourceRect;
+  typedef RectTyped<TargetUnits> TargetRect;
+
+  Matrix4x4Typed()
+    : _11(1.0f), _12(0.0f), _13(0.0f), _14(0.0f)
+    , _21(0.0f), _22(1.0f), _23(0.0f), _24(0.0f)
+    , _31(0.0f), _32(0.0f), _33(1.0f), _34(0.0f)
+    , _41(0.0f), _42(0.0f), _43(0.0f), _44(1.0f)
+  {}
+
+  Matrix4x4Typed(Float a11, Float a12, Float a13, Float a14,
+                 Float a21, Float a22, Float a23, Float a24,
+                 Float a31, Float a32, Float a33, Float a34,
+                 Float a41, Float a42, Float a43, Float a44)
+    : _11(a11), _12(a12), _13(a13), _14(a14)
+    , _21(a21), _22(a22), _23(a23), _24(a24)
+    , _31(a31), _32(a32), _33(a33), _34(a34)
+    , _41(a41), _42(a42), _43(a43), _44(a44)
+  {}
+
+  explicit Matrix4x4Typed(const Float aArray[16])
+  {
+    memcpy(components, aArray, sizeof(components));
+  }
+
+  Matrix4x4Typed(const Matrix4x4Typed& aOther)
+  {
+    memcpy(this, &aOther, sizeof(*this));
+  }
+
+  union {
+    struct {
+      Float _11, _12, _13, _14;
+      Float _21, _22, _23, _24;
+      Float _31, _32, _33, _34;
+      Float _41, _42, _43, _44;
+    };
+    Float components[16];
+  };
+
+  friend std::ostream& operator<<(std::ostream& aStream, const Matrix4x4Typed& aMatrix)
+  {
+    const Float *f = &aMatrix._11;
+    aStream << "[ " << f[0] << " "  << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4;
+    aStream << "  " << f[0] << " "  << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4;
+    aStream << "  " << f[0] << " "  << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4;
+    aStream << "  " << f[0] << " "  << f[1] << " " << f[2] << " " << f[3] << " ]" << std::endl;
+    return aStream;
+  }
+
+  Point4D& operator[](int aIndex)
+  {
+      MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
+      return *reinterpret_cast<Point4D*>((&_11)+4*aIndex);
+  }
+  const Point4D& operator[](int aIndex) const
+  {
+      MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
+      return *reinterpret_cast<const Point4D*>((&_11)+4*aIndex);
+  }
+
+  /**
+   * Returns true if the matrix is isomorphic to a 2D affine transformation.
+   */
+  bool Is2D() const
+  {
+    if (_13 != 0.0f || _14 != 0.0f ||
+        _23 != 0.0f || _24 != 0.0f ||
+        _31 != 0.0f || _32 != 0.0f || _33 != 1.0f || _34 != 0.0f ||
+        _43 != 0.0f || _44 != 1.0f) {
+      return false;
+    }
+    return true;
+  }
+
+  bool Is2D(Matrix* aMatrix) const {
+    if (!Is2D()) {
+      return false;
+    }
+    if (aMatrix) {
+      aMatrix->_11 = _11;
+      aMatrix->_12 = _12;
+      aMatrix->_21 = _21;
+      aMatrix->_22 = _22;
+      aMatrix->_31 = _41;
+      aMatrix->_32 = _42;
+    }
+    return true;
+  }
+
+  Matrix As2D() const
+  {
+    MOZ_ASSERT(Is2D(), "Matrix is not a 2D affine transform");
+
+    return Matrix(_11, _12, _21, _22, _41, _42);
+  }
+
+  bool CanDraw2D(Matrix* aMatrix = nullptr) const {
+    if (_14 != 0.0f ||
+        _24 != 0.0f ||
+        _44 != 1.0f) {
+      return false;
+    }
+    if (aMatrix) {
+      aMatrix->_11 = _11;
+      aMatrix->_12 = _12;
+      aMatrix->_21 = _21;
+      aMatrix->_22 = _22;
+      aMatrix->_31 = _41;
+      aMatrix->_32 = _42;
+    }
+    return true;
+  }
+
+  Matrix4x4Typed& ProjectTo2D() {
+    _31 = 0.0f;
+    _32 = 0.0f;
+    _13 = 0.0f;
+    _23 = 0.0f;
+    _33 = 1.0f;
+    _43 = 0.0f;
+    _34 = 0.0f;
+    // Some matrices, such as those derived from perspective transforms,
+    // can modify _44 from 1, while leaving the rest of the fourth column
+    // (_14, _24) at 0. In this case, after resetting the third row and
+    // third column above, the value of _44 functions only to scale the
+    // coordinate transform divide by W. The matrix can be converted to
+    // a true 2D matrix by normalizing out the scaling effect of _44 on
+    // the remaining components ahead of time.
+    if (_14 == 0.0f && _24 == 0.0f &&
+        _44 != 1.0f && _44 != 0.0f) {
+      Float scale = 1.0f / _44;
+      _11 *= scale;
+      _12 *= scale;
+      _21 *= scale;
+      _22 *= scale;
+      _41 *= scale;
+      _42 *= scale;
+      _44 = 1.0f;
+    }
+    return *this;
+  }
+
+  template<class F>
+  Point4DTyped<TargetUnits, F>
+  ProjectPoint(const PointTyped<SourceUnits, F>& aPoint) const {
+    // Find a value for z that will transform to 0.
+
+    // The transformed value of z is computed as:
+    // z' = aPoint.x * _13 + aPoint.y * _23 + z * _33 + _43;
+
+    // Solving for z when z' = 0 gives us:
+    F z = -(aPoint.x * _13 + aPoint.y * _23 + _43) / _33;
+
+    // Compute the transformed point
+    return this->TransformPoint(Point4DTyped<SourceUnits, F>(aPoint.x, aPoint.y, z, 1));
+  }
+
+  template<class F>
+  RectTyped<TargetUnits, F>
+  ProjectRectBounds(const RectTyped<SourceUnits, F>& aRect, const RectTyped<TargetUnits, F>& aClip) const
+  {
+    // This function must never return std::numeric_limits<Float>::max() or any
+    // other arbitrary large value in place of inifinity.  This often occurs when
+    // aRect is an inversed projection matrix or when aRect is transformed to be
+    // partly behind and in front of the camera (w=0 plane in homogenous
+    // coordinates) - See Bug 1035611
+
+    // Some call-sites will call RoundGfxRectToAppRect which clips both the
+    // extents and dimensions of the rect to be bounded by nscoord_MAX.
+    // If we return a Rect that, when converted to nscoords, has a width or height
+    // greater than nscoord_MAX, RoundGfxRectToAppRect will clip the overflow
+    // off both the min and max end of the rect after clipping the extents of the
+    // rect, resulting in a translation of the rect towards the infinite end.
+
+    // The bounds returned by ProjectRectBounds are expected to be clipped only on
+    // the edges beyond the bounds of the coordinate system; otherwise, the
+    // clipped bounding box would be smaller than the correct one and result
+    // bugs such as incorrect culling (eg. Bug 1073056)
+
+    // To address this without requiring all code to work in homogenous
+    // coordinates or interpret infinite values correctly, a specialized
+    // clipping function is integrated into ProjectRectBounds.
+
+    // Callers should pass an aClip value that represents the extents to clip
+    // the result to, in the same coordinate system as aRect.
+    Point4DTyped<TargetUnits, F> points[4];
+
+    points[0] = ProjectPoint(aRect.TopLeft());
+    points[1] = ProjectPoint(aRect.TopRight());
+    points[2] = ProjectPoint(aRect.BottomRight());
+    points[3] = ProjectPoint(aRect.BottomLeft());
+
+    F min_x = std::numeric_limits<F>::max();
+    F min_y = std::numeric_limits<F>::max();
+    F max_x = -std::numeric_limits<F>::max();
+    F max_y = -std::numeric_limits<F>::max();
+
+    for (int i=0; i<4; i++) {
+      // Only use points that exist above the w=0 plane
+      if (points[i].HasPositiveWCoord()) {
+        PointTyped<TargetUnits, F> point2d = aClip.ClampPoint(points[i].As2DPoint());
+        min_x = std::min<F>(point2d.x, min_x);
+        max_x = std::max<F>(point2d.x, max_x);
+        min_y = std::min<F>(point2d.y, min_y);
+        max_y = std::max<F>(point2d.y, max_y);
+      }
+
+      int next = (i == 3) ? 0 : i + 1;
+      if (points[i].HasPositiveWCoord() != points[next].HasPositiveWCoord()) {
+        // If the line between two points crosses the w=0 plane, then interpolate
+        // to find the point of intersection with the w=0 plane and use that
+        // instead.
+        Point4DTyped<TargetUnits, F> intercept =
+          ComputePerspectivePlaneIntercept(points[i], points[next]);
+        // Since intercept.w will always be 0 here, we interpret x,y,z as a
+        // direction towards an infinite vanishing point.
+        if (intercept.x < 0.0f) {
+          min_x = aClip.x;
+        } else if (intercept.x > 0.0f) {
+          max_x = aClip.XMost();
+        }
+        if (intercept.y < 0.0f) {
+          min_y = aClip.y;
+        } else if (intercept.y > 0.0f) {
+          max_y = aClip.YMost();
+        }
+      }
+    }
+
+    if (max_x < min_x || max_y < min_y) {
+      return RectTyped<TargetUnits, F>(0, 0, 0, 0);
+    }
+
+    return RectTyped<TargetUnits, F>(min_x, min_y, max_x - min_x, max_y - min_y);
+  }
+
+  /**
+   * TransformAndClipBounds transforms aRect as a bounding box, while clipping
+   * the transformed bounds to the extents of aClip.
+   */
+  template<class F>
+  RectTyped<TargetUnits, F> TransformAndClipBounds(const RectTyped<SourceUnits, F>& aRect,
+                                                   const RectTyped<TargetUnits, F>& aClip) const
+  {
+    PointTyped<UnknownUnits, F> verts[kTransformAndClipRectMaxVerts];
+    size_t vertCount = TransformAndClipRect(aRect, aClip, verts);
+
+    F min_x = std::numeric_limits<F>::max();
+    F min_y = std::numeric_limits<F>::max();
+    F max_x = -std::numeric_limits<F>::max();
+    F max_y = -std::numeric_limits<F>::max();
+    for (size_t i=0; i < vertCount; i++) {
+      min_x = std::min(min_x, verts[i].x);
+      max_x = std::max(max_x, verts[i].x);
+      min_y = std::min(min_y, verts[i].y);
+      max_y = std::max(max_y, verts[i].y);
+    }
+
+    if (max_x < min_x || max_y < min_y) {
+      return RectTyped<TargetUnits, F>(0, 0, 0, 0);
+    }
+
+    return RectTyped<TargetUnits, F>(min_x, min_y, max_x - min_x, max_y - min_y);
+  }
+
+  template<class F>
+  RectTyped<TargetUnits, F> TransformAndClipBounds(const TriangleTyped<SourceUnits, F>& aTriangle,
+                                                   const RectTyped<TargetUnits, F>& aClip) const
+  {
+    return TransformAndClipBounds(aTriangle.BoundingBox(), aClip);
+  }
+
+  /**
+   * TransformAndClipRect projects a rectangle and clips against view frustum
+   * clipping planes in homogenous space so that its projected vertices are
+   * constrained within the 2d rectangle passed in aClip.
+   * The resulting vertices are populated in aVerts.  aVerts must be
+   * pre-allocated to hold at least kTransformAndClipRectMaxVerts Points.
+   * The vertex count is returned by TransformAndClipRect.  It is possible to
+   * emit fewer that 3 vertices, indicating that aRect will not be visible
+   * within aClip.
+   */
+  template<class F>
+  size_t TransformAndClipRect(const RectTyped<SourceUnits, F>& aRect,
+                              const RectTyped<TargetUnits, F>& aClip,
+                              PointTyped<TargetUnits, F>* aVerts) const
+  {
+    // Initialize a double-buffered array of points in homogenous space with
+    // the input rectangle, aRect.
+    Point4DTyped<UnknownUnits, F> points[2][kTransformAndClipRectMaxVerts];
+    Point4DTyped<UnknownUnits, F>* dstPoint = points[0];
+
+    *dstPoint++ = TransformPoint(Point4DTyped<UnknownUnits, F>(aRect.x, aRect.y, 0, 1));
+    *dstPoint++ = TransformPoint(Point4DTyped<UnknownUnits, F>(aRect.XMost(), aRect.y, 0, 1));
+    *dstPoint++ = TransformPoint(Point4DTyped<UnknownUnits, F>(aRect.XMost(), aRect.YMost(), 0, 1));
+    *dstPoint++ = TransformPoint(Point4DTyped<UnknownUnits, F>(aRect.x, aRect.YMost(), 0, 1));
+
+    // View frustum clipping planes are described as normals originating from
+    // the 0,0,0,0 origin.
+    Point4DTyped<UnknownUnits, F> planeNormals[4];
+    planeNormals[0] = Point4DTyped<UnknownUnits, F>(1.0, 0.0, 0.0, -aClip.x);
+    planeNormals[1] = Point4DTyped<UnknownUnits, F>(-1.0, 0.0, 0.0, aClip.XMost());
+    planeNormals[2] = Point4DTyped<UnknownUnits, F>(0.0, 1.0, 0.0, -aClip.y);
+    planeNormals[3] = Point4DTyped<UnknownUnits, F>(0.0, -1.0, 0.0, aClip.YMost());
+
+    // Iterate through each clipping plane and clip the polygon.
+    // In each pass, we double buffer, alternating between points[0] and
+    // points[1].
+    for (int plane=0; plane < 4; plane++) {
+      planeNormals[plane].Normalize();
+      Point4DTyped<UnknownUnits, F>* srcPoint = points[plane & 1];
+      Point4DTyped<UnknownUnits, F>* srcPointEnd = dstPoint;
+
+      dstPoint = points[~plane & 1];
+      Point4DTyped<UnknownUnits, F>* dstPointStart = dstPoint;
+
+      Point4DTyped<UnknownUnits, F>* prevPoint = srcPointEnd - 1;
+      F prevDot = planeNormals[plane].DotProduct(*prevPoint);
+      while (srcPoint < srcPointEnd && ((dstPoint - dstPointStart) < kTransformAndClipRectMaxVerts)) {
+        F nextDot = planeNormals[plane].DotProduct(*srcPoint);
+
+        if ((nextDot >= 0.0) != (prevDot >= 0.0)) {
+          // An intersection with the clipping plane has been detected.
+          // Interpolate to find the intersecting point and emit it.
+          F t = -prevDot / (nextDot - prevDot);
+          *dstPoint++ = *srcPoint * t + *prevPoint * (1.0 - t);
+        }
+
+        if (nextDot >= 0.0) {
+          // Emit any source points that are on the positive side of the
+          // clipping plane.
+          *dstPoint++ = *srcPoint;
+        }
+
+        prevPoint = srcPoint++;
+        prevDot = nextDot;
+      }
+
+      if (dstPoint == dstPointStart) {
+        break;
+      }
+    }
+
+    size_t dstPointCount = 0;
+    size_t srcPointCount = dstPoint - points[0];
+    for (Point4DTyped<UnknownUnits, F>* srcPoint = points[0]; srcPoint < points[0] + srcPointCount; srcPoint++) {
+
+      PointTyped<TargetUnits, F> p;
+      if (srcPoint->w == 0.0) {
+        // If a point lies on the intersection of the clipping planes at
+        // (0,0,0,0), we must avoid a division by zero w component.
+        p = PointTyped<TargetUnits, F>(0.0, 0.0);
+      } else {
+        p = srcPoint->As2DPoint();
+      }
+      // Emit only unique points
+      if (dstPointCount == 0 || p != aVerts[dstPointCount - 1]) {
+        aVerts[dstPointCount++] = p;
+      }
+    }
+
+    return dstPointCount;
+  }
+
+  static const int kTransformAndClipRectMaxVerts = 32;
+
+  static Matrix4x4Typed From2D(const Matrix &aMatrix) {
+    Matrix4x4Typed matrix;
+    matrix._11 = aMatrix._11;
+    matrix._12 = aMatrix._12;
+    matrix._21 = aMatrix._21;
+    matrix._22 = aMatrix._22;
+    matrix._41 = aMatrix._31;
+    matrix._42 = aMatrix._32;
+    return matrix;
+  }
+
+  bool Is2DIntegerTranslation() const
+  {
+    return Is2D() && As2D().IsIntegerTranslation();
+  }
+
+  TargetPoint4D TransposeTransform4D(const SourcePoint4D& aPoint) const
+  {
+      Float x = aPoint.x * _11 + aPoint.y * _12 + aPoint.z * _13 + aPoint.w * _14;
+      Float y = aPoint.x * _21 + aPoint.y * _22 + aPoint.z * _23 + aPoint.w * _24;
+      Float z = aPoint.x * _31 + aPoint.y * _32 + aPoint.z * _33 + aPoint.w * _34;
+      Float w = aPoint.x * _41 + aPoint.y * _42 + aPoint.z * _43 + aPoint.w * _44;
+
+      return TargetPoint4D(x, y, z, w);
+  }
+
+  template<class F>
+  Point4DTyped<TargetUnits, F> TransformPoint(const Point4DTyped<SourceUnits, F>& aPoint) const
+  {
+    Point4DTyped<TargetUnits, F> retPoint;
+
+    retPoint.x = aPoint.x * _11 + aPoint.y * _21 + aPoint.z * _31 + aPoint.w * _41;
+    retPoint.y = aPoint.x * _12 + aPoint.y * _22 + aPoint.z * _32 + aPoint.w * _42;
+    retPoint.z = aPoint.x * _13 + aPoint.y * _23 + aPoint.z * _33 + aPoint.w * _43;
+    retPoint.w = aPoint.x * _14 + aPoint.y * _24 + aPoint.z * _34 + aPoint.w * _44;
+
+    return retPoint;
+  }
+
+  template<class F>
+  Point3DTyped<TargetUnits, F> TransformPoint(const Point3DTyped<SourceUnits, F>& aPoint) const
+  {
+    Point3DTyped<TargetUnits, F> result;
+    result.x = aPoint.x * _11 + aPoint.y * _21 + aPoint.z * _31 + _41;
+    result.y = aPoint.x * _12 + aPoint.y * _22 + aPoint.z * _32 + _42;
+    result.z = aPoint.x * _13 + aPoint.y * _23 + aPoint.z * _33 + _43;
+
+    result /= (aPoint.x * _14 + aPoint.y * _24 + aPoint.z * _34 + _44);
+
+    return result;
+  }
+
+  template<class F>
+  PointTyped<TargetUnits, F> TransformPoint(const PointTyped<SourceUnits, F> &aPoint) const
+  {
+    Point4DTyped<SourceUnits, F> temp(aPoint.x, aPoint.y, 0, 1);
+    return TransformPoint(temp).As2DPoint();
+  }
+
+  template<class F>
+  GFX2D_API RectTyped<TargetUnits, F> TransformBounds(const RectTyped<SourceUnits, F>& aRect) const
+  {
+    Point4DTyped<TargetUnits, F> verts[4];
+    verts[0] = TransformPoint(Point4DTyped<SourceUnits, F>(aRect.x, aRect.y, 0.0, 1.0));
+    verts[1] = TransformPoint(Point4DTyped<SourceUnits, F>(aRect.XMost(), aRect.y, 0.0, 1.0));
+    verts[2] = TransformPoint(Point4DTyped<SourceUnits, F>(aRect.XMost(), aRect.YMost(), 0.0, 1.0));
+    verts[3] = TransformPoint(Point4DTyped<SourceUnits, F>(aRect.x, aRect.YMost(), 0.0, 1.0));
+
+    PointTyped<TargetUnits, F> quad[4];
+    F min_x, max_x;
+    F min_y, max_y;
+
+    quad[0] = TransformPoint(aRect.TopLeft());
+    quad[1] = TransformPoint(aRect.TopRight());
+    quad[2] = TransformPoint(aRect.BottomLeft());
+    quad[3] = TransformPoint(aRect.BottomRight());
+
+    min_x = max_x = quad[0].x;
+    min_y = max_y = quad[0].y;
+
+    for (int i = 1; i < 4; i++) {
+      if (quad[i].x < min_x) {
+        min_x = quad[i].x;
+      }
+      if (quad[i].x > max_x) {
+        max_x = quad[i].x;
+      }
+
+      if (quad[i].y < min_y) {
+        min_y = quad[i].y;
+      }
+      if (quad[i].y > max_y) {
+        max_y = quad[i].y;
+      }
+    }
+
+    return RectTyped<TargetUnits, F>(min_x, min_y, max_x - min_x, max_y - min_y);
+  }
+
+  static Matrix4x4Typed Translation(Float aX, Float aY, Float aZ)
+  {
+    return Matrix4x4Typed(1.0f, 0.0f, 0.0f, 0.0f,
+                          0.0f, 1.0f, 0.0f, 0.0f,
+                          0.0f, 0.0f, 1.0f, 0.0f,
+                          aX,   aY,   aZ, 1.0f);
+  }
+
+  static Matrix4x4Typed Translation(const TargetPoint3D& aP)
+  {
+    return Translation(aP.x, aP.y, aP.z);
+  }
+
+  static Matrix4x4Typed Translation(const TargetPoint& aP)
+  {
+    return Translation(aP.x, aP.y, 0);
+  }
+
+  /**
+   * Apply a translation to this matrix.
+   *
+   * The "Pre" in this method's name means that the translation is applied
+   * -before- this matrix's existing transformation. That is, any vector that
+   * is multiplied by the resulting matrix will first be translated, then be
+   * transformed by the original transform.
+   *
+   * Calling this method will result in this matrix having the same value as
+   * the result of:
+   *
+   *   Matrix4x4::Translation(x, y) * this
+   *
+   * (Note that in performance critical code multiplying by the result of a
+   * Translation()/Scaling() call is not recommended since that results in a
+   * full matrix multiply involving 64 floating-point multiplications. Calling
+   * this method would be preferred since it only involves 12 floating-point
+   * multiplications.)
+   */
+  Matrix4x4Typed &PreTranslate(Float aX, Float aY, Float aZ)
+  {
+    _41 += aX * _11 + aY * _21 + aZ * _31;
+    _42 += aX * _12 + aY * _22 + aZ * _32;
+    _43 += aX * _13 + aY * _23 + aZ * _33;
+    _44 += aX * _14 + aY * _24 + aZ * _34;
+
+    return *this;
+  }
+
+  Matrix4x4Typed &PreTranslate(const Point3D& aPoint) {
+    return PreTranslate(aPoint.x, aPoint.y, aPoint.z);
+  }
+
+  /**
+   * Similar to PreTranslate, but the translation is applied -after- this
+   * matrix's existing transformation instead of before it.
+   *
+   * This method is generally less used than PreTranslate since typically code
+   * wants to adjust an existing user space to device space matrix to create a
+   * transform to device space from a -new- user space (translated from the
+   * previous user space). In that case consumers will need to use the Pre*
+   * variants of the matrix methods rather than using the Post* methods, since
+   * the Post* methods add a transform to the device space end of the
+   * transformation.
+   */
+  Matrix4x4Typed &PostTranslate(Float aX, Float aY, Float aZ)
+  {
+    _11 += _14 * aX;
+    _21 += _24 * aX;
+    _31 += _34 * aX;
+    _41 += _44 * aX;
+    _12 += _14 * aY;
+    _22 += _24 * aY;
+    _32 += _34 * aY;
+    _42 += _44 * aY;
+    _13 += _14 * aZ;
+    _23 += _24 * aZ;
+    _33 += _34 * aZ;
+    _43 += _44 * aZ;
+
+    return *this;
+  }
+
+  Matrix4x4Typed &PostTranslate(const TargetPoint3D& aPoint) {
+    return PostTranslate(aPoint.x, aPoint.y, aPoint.z);
+  }
+
+  Matrix4x4Typed &PostTranslate(const TargetPoint& aPoint) {
+    return PostTranslate(aPoint.x, aPoint.y, 0);
+  }
+
+  static Matrix4x4Typed Scaling(Float aScaleX, Float aScaleY, float aScaleZ)
+  {
+    return Matrix4x4Typed(aScaleX, 0.0f, 0.0f, 0.0f,
+                          0.0f, aScaleY, 0.0f, 0.0f,
+                          0.0f, 0.0f, aScaleZ, 0.0f,
+                          0.0f, 0.0f, 0.0f, 1.0f);
+  }
+
+  /**
+   * Similar to PreTranslate, but applies a scale instead of a translation.
+   */
+  Matrix4x4Typed &PreScale(Float aX, Float aY, Float aZ)
+  {
+    _11 *= aX;
+    _12 *= aX;
+    _13 *= aX;
+    _14 *= aX;
+    _21 *= aY;
+    _22 *= aY;
+    _23 *= aY;
+    _24 *= aY;
+    _31 *= aZ;
+    _32 *= aZ;
+    _33 *= aZ;
+    _34 *= aZ;
+
+    return *this;
+  }
+
+  /**
+   * Similar to PostTranslate, but applies a scale instead of a translation.
+   */
+  Matrix4x4Typed &PostScale(Float aScaleX, Float aScaleY, Float aScaleZ)
+  {
+    _11 *= aScaleX;
+    _21 *= aScaleX;
+    _31 *= aScaleX;
+    _41 *= aScaleX;
+    _12 *= aScaleY;
+    _22 *= aScaleY;
+    _32 *= aScaleY;
+    _42 *= aScaleY;
+    _13 *= aScaleZ;
+    _23 *= aScaleZ;
+    _33 *= aScaleZ;
+    _43 *= aScaleZ;
+
+    return *this;
+  }
+
+  void SkewXY(Float aSkew)
+  {
+    (*this)[1] += (*this)[0] * aSkew;
+  }
+
+  void SkewXZ(Float aSkew)
+  {
+      (*this)[2] += (*this)[0] * aSkew;
+  }
+
+  void SkewYZ(Float aSkew)
+  {
+      (*this)[2] += (*this)[1] * aSkew;
+  }
+
+  Matrix4x4Typed &ChangeBasis(const Point3D& aOrigin)
+  {
+    return ChangeBasis(aOrigin.x, aOrigin.y, aOrigin.z);
+  }
+
+  Matrix4x4Typed &ChangeBasis(Float aX, Float aY, Float aZ)
+  {
+    // Translate to the origin before applying this matrix
+    PreTranslate(-aX, -aY, -aZ);
+
+    // Translate back into position after applying this matrix
+    PostTranslate(aX, aY, aZ);
+
+    return *this;
+  }
+
+  Matrix4x4Typed& Transpose() {
+    std::swap(_12, _21);
+    std::swap(_13, _31);
+    std::swap(_14, _41);
+
+    std::swap(_23, _32);
+    std::swap(_24, _42);
+
+    std::swap(_34, _43);
+
+    return *this;
+  }
+
+  bool operator==(const Matrix4x4Typed& o) const
+  {
+    // XXX would be nice to memcmp here, but that breaks IEEE 754 semantics
+    return _11 == o._11 && _12 == o._12 && _13 == o._13 && _14 == o._14 &&
+           _21 == o._21 && _22 == o._22 && _23 == o._23 && _24 == o._24 &&
+           _31 == o._31 && _32 == o._32 && _33 == o._33 && _34 == o._34 &&
+           _41 == o._41 && _42 == o._42 && _43 == o._43 && _44 == o._44;
+  }
+
+  bool operator!=(const Matrix4x4Typed& o) const
+  {
+    return !((*this) == o);
+  }
+
+  template <typename NewTargetUnits>
+  Matrix4x4Typed<SourceUnits, NewTargetUnits> operator*(const Matrix4x4Typed<TargetUnits, NewTargetUnits> &aMatrix) const
+  {
+    Matrix4x4Typed<SourceUnits, NewTargetUnits> matrix;
+
+    matrix._11 = _11 * aMatrix._11 + _12 * aMatrix._21 + _13 * aMatrix._31 + _14 * aMatrix._41;
+    matrix._21 = _21 * aMatrix._11 + _22 * aMatrix._21 + _23 * aMatrix._31 + _24 * aMatrix._41;
+    matrix._31 = _31 * aMatrix._11 + _32 * aMatrix._21 + _33 * aMatrix._31 + _34 * aMatrix._41;
+    matrix._41 = _41 * aMatrix._11 + _42 * aMatrix._21 + _43 * aMatrix._31 + _44 * aMatrix._41;
+    matrix._12 = _11 * aMatrix._12 + _12 * aMatrix._22 + _13 * aMatrix._32 + _14 * aMatrix._42;
+    matrix._22 = _21 * aMatrix._12 + _22 * aMatrix._22 + _23 * aMatrix._32 + _24 * aMatrix._42;
+    matrix._32 = _31 * aMatrix._12 + _32 * aMatrix._22 + _33 * aMatrix._32 + _34 * aMatrix._42;
+    matrix._42 = _41 * aMatrix._12 + _42 * aMatrix._22 + _43 * aMatrix._32 + _44 * aMatrix._42;
+    matrix._13 = _11 * aMatrix._13 + _12 * aMatrix._23 + _13 * aMatrix._33 + _14 * aMatrix._43;
+    matrix._23 = _21 * aMatrix._13 + _22 * aMatrix._23 + _23 * aMatrix._33 + _24 * aMatrix._43;
+    matrix._33 = _31 * aMatrix._13 + _32 * aMatrix._23 + _33 * aMatrix._33 + _34 * aMatrix._43;
+    matrix._43 = _41 * aMatrix._13 + _42 * aMatrix._23 + _43 * aMatrix._33 + _44 * aMatrix._43;
+    matrix._14 = _11 * aMatrix._14 + _12 * aMatrix._24 + _13 * aMatrix._34 + _14 * aMatrix._44;
+    matrix._24 = _21 * aMatrix._14 + _22 * aMatrix._24 + _23 * aMatrix._34 + _24 * aMatrix._44;
+    matrix._34 = _31 * aMatrix._14 + _32 * aMatrix._24 + _33 * aMatrix._34 + _34 * aMatrix._44;
+    matrix._44 = _41 * aMatrix._14 + _42 * aMatrix._24 + _43 * aMatrix._34 + _44 * aMatrix._44;
+
+    return matrix;
+  }
+
+  Matrix4x4Typed& operator*=(const Matrix4x4Typed<TargetUnits, TargetUnits> &aMatrix)
+  {
+    *this = *this * aMatrix;
+    return *this;
+  }
+
+  /* Returns true if the matrix is an identity matrix.
+   */
+  bool IsIdentity() const
+  {
+    return _11 == 1.0f && _12 == 0.0f && _13 == 0.0f && _14 == 0.0f &&
+           _21 == 0.0f && _22 == 1.0f && _23 == 0.0f && _24 == 0.0f &&
+           _31 == 0.0f && _32 == 0.0f && _33 == 1.0f && _34 == 0.0f &&
+           _41 == 0.0f && _42 == 0.0f && _43 == 0.0f && _44 == 1.0f;
+  }
+
+  bool IsSingular() const
+  {
+    return Determinant() == 0.0;
+  }
+
+  Float Determinant() const
+  {
+    return _14 * _23 * _32 * _41
+         - _13 * _24 * _32 * _41
+         - _14 * _22 * _33 * _41
+         + _12 * _24 * _33 * _41
+         + _13 * _22 * _34 * _41
+         - _12 * _23 * _34 * _41
+         - _14 * _23 * _31 * _42
+         + _13 * _24 * _31 * _42
+         + _14 * _21 * _33 * _42
+         - _11 * _24 * _33 * _42
+         - _13 * _21 * _34 * _42
+         + _11 * _23 * _34 * _42
+         + _14 * _22 * _31 * _43
+         - _12 * _24 * _31 * _43
+         - _14 * _21 * _32 * _43
+         + _11 * _24 * _32 * _43
+         + _12 * _21 * _34 * _43
+         - _11 * _22 * _34 * _43
+         - _13 * _22 * _31 * _44
+         + _12 * _23 * _31 * _44
+         + _13 * _21 * _32 * _44
+         - _11 * _23 * _32 * _44
+         - _12 * _21 * _33 * _44
+         + _11 * _22 * _33 * _44;
+  }
+
+  // Invert() is not unit-correct. Prefer Inverse() where possible.
+  bool Invert()
+  {
+    Float det = Determinant();
+    if (!det) {
+      return false;
+    }
+
+    Matrix4x4Typed<SourceUnits, TargetUnits> result;
+    result._11 = _23 * _34 * _42 - _24 * _33 * _42 + _24 * _32 * _43 - _22 * _34 * _43 - _23 * _32 * _44 + _22 * _33 * _44;
+    result._12 = _14 * _33 * _42 - _13 * _34 * _42 - _14 * _32 * _43 + _12 * _34 * _43 + _13 * _32 * _44 - _12 * _33 * _44;
+    result._13 = _13 * _24 * _42 - _14 * _23 * _42 + _14 * _22 * _43 - _12 * _24 * _43 - _13 * _22 * _44 + _12 * _23 * _44;
+    result._14 = _14 * _23 * _32 - _13 * _24 * _32 - _14 * _22 * _33 + _12 * _24 * _33 + _13 * _22 * _34 - _12 * _23 * _34;
+    result._21 = _24 * _33 * _41 - _23 * _34 * _41 - _24 * _31 * _43 + _21 * _34 * _43 + _23 * _31 * _44 - _21 * _33 * _44;
+    result._22 = _13 * _34 * _41 - _14 * _33 * _41 + _14 * _31 * _43 - _11 * _34 * _43 - _13 * _31 * _44 + _11 * _33 * _44;
+    result._23 = _14 * _23 * _41 - _13 * _24 * _41 - _14 * _21 * _43 + _11 * _24 * _43 + _13 * _21 * _44 - _11 * _23 * _44;
+    result._24 = _13 * _24 * _31 - _14 * _23 * _31 + _14 * _21 * _33 - _11 * _24 * _33 - _13 * _21 * _34 + _11 * _23 * _34;
+    result._31 = _22 * _34 * _41 - _24 * _32 * _41 + _24 * _31 * _42 - _21 * _34 * _42 - _22 * _31 * _44 + _21 * _32 * _44;
+    result._32 = _14 * _32 * _41 - _12 * _34 * _41 - _14 * _31 * _42 + _11 * _34 * _42 + _12 * _31 * _44 - _11 * _32 * _44;
+    result._33 = _12 * _24 * _41 - _14 * _22 * _41 + _14 * _21 * _42 - _11 * _24 * _42 - _12 * _21 * _44 + _11 * _22 * _44;
+    result._34 = _14 * _22 * _31 - _12 * _24 * _31 - _14 * _21 * _32 + _11 * _24 * _32 + _12 * _21 * _34 - _11 * _22 * _34;
+    result._41 = _23 * _32 * _41 - _22 * _33 * _41 - _23 * _31 * _42 + _21 * _33 * _42 + _22 * _31 * _43 - _21 * _32 * _43;
+    result._42 = _12 * _33 * _41 - _13 * _32 * _41 + _13 * _31 * _42 - _11 * _33 * _42 - _12 * _31 * _43 + _11 * _32 * _43;
+    result._43 = _13 * _22 * _41 - _12 * _23 * _41 - _13 * _21 * _42 + _11 * _23 * _42 + _12 * _21 * _43 - _11 * _22 * _43;
+    result._44 = _12 * _23 * _31 - _13 * _22 * _31 + _13 * _21 * _32 - _11 * _23 * _32 - _12 * _21 * _33 + _11 * _22 * _33;
+
+    result._11 /= det;
+    result._12 /= det;
+    result._13 /= det;
+    result._14 /= det;
+    result._21 /= det;
+    result._22 /= det;
+    result._23 /= det;
+    result._24 /= det;
+    result._31 /= det;
+    result._32 /= det;
+    result._33 /= det;
+    result._34 /= det;
+    result._41 /= det;
+    result._42 /= det;
+    result._43 /= det;
+    result._44 /= det;
+    *this = result;
+
+    return true;
+  }
+
+  Matrix4x4Typed<TargetUnits, SourceUnits> Inverse() const
+  {
+    typedef Matrix4x4Typed<TargetUnits, SourceUnits> InvertedMatrix;
+    InvertedMatrix clone = InvertedMatrix::FromUnknownMatrix(ToUnknownMatrix());
+    DebugOnly<bool> inverted = clone.Invert();
+    MOZ_ASSERT(inverted, "Attempted to get the inverse of a non-invertible matrix");
+    return clone;
+  }
+
+  void Normalize()
+  {
+      for (int i = 0; i < 4; i++) {
+          for (int j = 0; j < 4; j++) {
+              (*this)[i][j] /= (*this)[3][3];
+         }
+      }
+  }
+
+  bool FuzzyEqual(const Matrix4x4Typed& o) const
+  {
+    return gfx::FuzzyEqual(_11, o._11) && gfx::FuzzyEqual(_12, o._12) &&
+           gfx::FuzzyEqual(_13, o._13) && gfx::FuzzyEqual(_14, o._14) &&
+           gfx::FuzzyEqual(_21, o._21) && gfx::FuzzyEqual(_22, o._22) &&
+           gfx::FuzzyEqual(_23, o._23) && gfx::FuzzyEqual(_24, o._24) &&
+           gfx::FuzzyEqual(_31, o._31) && gfx::FuzzyEqual(_32, o._32) &&
+           gfx::FuzzyEqual(_33, o._33) && gfx::FuzzyEqual(_34, o._34) &&
+           gfx::FuzzyEqual(_41, o._41) && gfx::FuzzyEqual(_42, o._42) &&
+           gfx::FuzzyEqual(_43, o._43) && gfx::FuzzyEqual(_44, o._44);
+  }
+
+  bool FuzzyEqualsMultiplicative(const Matrix4x4Typed& o) const
+  {
+    return ::mozilla::FuzzyEqualsMultiplicative(_11, o._11) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_12, o._12) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_13, o._13) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_14, o._14) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_21, o._21) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_22, o._22) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_23, o._23) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_24, o._24) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_31, o._31) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_32, o._32) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_33, o._33) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_34, o._34) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_41, o._41) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_42, o._42) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_43, o._43) &&
+           ::mozilla::FuzzyEqualsMultiplicative(_44, o._44);
+  }
+
+  bool IsBackfaceVisible() const
+  {
+    // Inverse()._33 < 0;
+    Float det = Determinant();
+    Float __33 = _12*_24*_41 - _14*_22*_41 +
+                _14*_21*_42 - _11*_24*_42 -
+                _12*_21*_44 + _11*_22*_44;
+    return (__33 * det) < 0;
+  }
+
+  Matrix4x4Typed &NudgeToIntegersFixedEpsilon()
+  {
+    NudgeToInteger(&_11);
+    NudgeToInteger(&_12);
+    NudgeToInteger(&_13);
+    NudgeToInteger(&_14);
+    NudgeToInteger(&_21);
+    NudgeToInteger(&_22);
+    NudgeToInteger(&_23);
+    NudgeToInteger(&_24);
+    NudgeToInteger(&_31);
+    NudgeToInteger(&_32);
+    NudgeToInteger(&_33);
+    NudgeToInteger(&_34);
+    static const float error = 1e-5f;
+    NudgeToInteger(&_41, error);
+    NudgeToInteger(&_42, error);
+    NudgeToInteger(&_43, error);
+    NudgeToInteger(&_44, error);
+    return *this;
+  }
+
+  Point4D TransposedVector(int aIndex) const
+  {
+      MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
+      return Point4D(*((&_11)+aIndex), *((&_21)+aIndex), *((&_31)+aIndex), *((&_41)+aIndex));
+  }
+
+  void SetTransposedVector(int aIndex, Point4D &aVector)
+  {
+      MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
+      *((&_11)+aIndex) = aVector.x;
+      *((&_21)+aIndex) = aVector.y;
+      *((&_31)+aIndex) = aVector.z;
+      *((&_41)+aIndex) = aVector.w;
+  }
+
+  // Sets this matrix to a rotation matrix given by aQuat.
+  // This quaternion *MUST* be normalized!
+  // Implemented in Quaternion.cpp
+  void SetRotationFromQuaternion(const Quaternion& q)
+  {
+    const Float x2 = q.x + q.x, y2 = q.y + q.y, z2 = q.z + q.z;
+    const Float xx = q.x * x2, xy = q.x * y2, xz = q.x * z2;
+    const Float yy = q.y * y2, yz = q.y * z2, zz = q.z * z2;
+    const Float wx = q.w * x2, wy = q.w * y2, wz = q.w * z2;
+
+    _11 = 1.0f - (yy + zz);
+    _21 = xy + wz;
+    _31 = xz - wy;
+    _41 = 0.0f;
+
+    _12 = xy - wz;
+    _22 = 1.0f - (xx + zz);
+    _32 = yz + wx;
+    _42 = 0.0f;
+
+    _13 = xz + wy;
+    _23 = yz - wx;
+    _33 = 1.0f - (xx + yy);
+    _43 = 0.0f;
+
+    _14 = _42 = _43 = 0.0f;
+    _44 = 1.0f;
+  }
+
+  // Set all the members of the matrix to NaN
+  void SetNAN()
+  {
+    _11 = UnspecifiedNaN<Float>();
+    _21 = UnspecifiedNaN<Float>();
+    _31 = UnspecifiedNaN<Float>();
+    _41 = UnspecifiedNaN<Float>();
+    _12 = UnspecifiedNaN<Float>();
+    _22 = UnspecifiedNaN<Float>();
+    _32 = UnspecifiedNaN<Float>();
+    _42 = UnspecifiedNaN<Float>();
+    _13 = UnspecifiedNaN<Float>();
+    _23 = UnspecifiedNaN<Float>();
+    _33 = UnspecifiedNaN<Float>();
+    _43 = UnspecifiedNaN<Float>();
+    _14 = UnspecifiedNaN<Float>();
+    _24 = UnspecifiedNaN<Float>();
+    _34 = UnspecifiedNaN<Float>();
+    _44 = UnspecifiedNaN<Float>();
+  }
+
+  void SkewXY(double aXSkew, double aYSkew)
+  {
+    // XXX Is double precision really necessary here
+    float tanX = SafeTangent(aXSkew);
+    float tanY = SafeTangent(aYSkew);
+    float temp;
+
+    temp = _11;
+    _11 += tanY * _21;
+    _21 += tanX * temp;
+
+    temp = _12;
+    _12 += tanY * _22;
+    _22 += tanX * temp;
+
+    temp = _13;
+    _13 += tanY * _23;
+    _23 += tanX * temp;
+
+    temp = _14;
+    _14 += tanY * _24;
+    _24 += tanX * temp;
+  }
+
+  void RotateX(double aTheta)
+  {
+    // XXX Is double precision really necessary here
+    double cosTheta = FlushToZero(cos(aTheta));
+    double sinTheta = FlushToZero(sin(aTheta));
+
+    float temp;
+
+    temp = _21;
+    _21 = cosTheta * _21 + sinTheta * _31;
+    _31 = -sinTheta * temp + cosTheta * _31;
+
+    temp = _22;
+    _22 = cosTheta * _22 + sinTheta * _32;
+    _32 = -sinTheta * temp + cosTheta * _32;
+
+    temp = _23;
+    _23 = cosTheta * _23 + sinTheta * _33;
+    _33 = -sinTheta * temp + cosTheta * _33;
+
+    temp = _24;
+    _24 = cosTheta * _24 + sinTheta * _34;
+    _34 = -sinTheta * temp + cosTheta * _34;
+  }
+
+  void RotateY(double aTheta)
+  {
+    // XXX Is double precision really necessary here
+    double cosTheta = FlushToZero(cos(aTheta));
+    double sinTheta = FlushToZero(sin(aTheta));
+
+    float temp;
+
+    temp = _11;
+    _11 = cosTheta * _11 + -sinTheta * _31;
+    _31 = sinTheta * temp + cosTheta * _31;
+
+    temp = _12;
+    _12 = cosTheta * _12 + -sinTheta * _32;
+    _32 = sinTheta * temp + cosTheta * _32;
+
+    temp = _13;
+    _13 = cosTheta * _13 + -sinTheta * _33;
+    _33 = sinTheta * temp + cosTheta * _33;
+
+    temp = _14;
+    _14 = cosTheta * _14 + -sinTheta * _34;
+    _34 = sinTheta * temp + cosTheta * _34;
+  }
+
+  void RotateZ(double aTheta)
+  {
+    // XXX Is double precision really necessary here
+    double cosTheta = FlushToZero(cos(aTheta));
+    double sinTheta = FlushToZero(sin(aTheta));
+
+    float temp;
+
+    temp = _11;
+    _11 = cosTheta * _11 + sinTheta * _21;
+    _21 = -sinTheta * temp + cosTheta * _21;
+
+    temp = _12;
+    _12 = cosTheta * _12 + sinTheta * _22;
+    _22 = -sinTheta * temp + cosTheta * _22;
+
+    temp = _13;
+    _13 = cosTheta * _13 + sinTheta * _23;
+    _23 = -sinTheta * temp + cosTheta * _23;
+
+    temp = _14;
+    _14 = cosTheta * _14 + sinTheta * _24;
+    _24 = -sinTheta * temp + cosTheta * _24;
+  }
+
+  // Sets this matrix to a rotation matrix about a
+  // vector [x,y,z] by angle theta. The vector is normalized
+  // to a unit vector.
+  // https://www.w3.org/TR/css3-3d-transforms/#Rotate3dDefined
+  void SetRotateAxisAngle(double aX, double aY, double aZ, double aTheta)
+  {
+    Point3D vector(aX, aY, aZ);
+    if (!vector.Length()) {
+      return;
+    }
+    vector.Normalize();
+
+    double x = vector.x;
+    double y = vector.y;
+    double z = vector.z;
+
+    double cosTheta = FlushToZero(cos(aTheta));
+    double sinTheta = FlushToZero(sin(aTheta));
+
+    // sin(aTheta / 2) * cos(aTheta / 2)
+    double sc = sinTheta / 2;
+    // pow(sin(aTheta / 2), 2)
+    double sq = (1 - cosTheta) / 2;
+
+    _11 = 1 - 2 * (y * y + z * z) * sq;
+    _12 = 2 * (x * y * sq + z * sc);
+    _13 = 2 * (x * z * sq - y * sc);
+    _14 = 0.0f;
+    _21 = 2 * (x * y * sq - z * sc);
+    _22 = 1 - 2 * (x * x + z * z) * sq;
+    _23 = 2 * (y * z * sq + x * sc);
+    _24 = 0.0f;
+    _31 = 2 * (x * z * sq + y * sc);
+    _32 = 2 * (y * z * sq - x * sc);
+    _33 = 1 - 2 * (x * x + y * y) * sq;
+    _34 = 0.0f;
+    _41 = 0.0f;
+    _42 = 0.0f;
+    _43 = 0.0f;
+    _44 = 1.0f;
+  }
+
+  void Perspective(float aDepth)
+  {
+    MOZ_ASSERT(aDepth > 0.0f, "Perspective must be positive!");
+    _31 += -1.0/aDepth * _41;
+    _32 += -1.0/aDepth * _42;
+    _33 += -1.0/aDepth * _43;
+    _34 += -1.0/aDepth * _44;
+  }
+
+  Point3D GetNormalVector() const
+  {
+    // Define a plane in transformed space as the transformations
+    // of 3 points on the z=0 screen plane.
+    Point3D a = TransformPoint(Point3D(0, 0, 0));
+    Point3D b = TransformPoint(Point3D(0, 1, 0));
+    Point3D c = TransformPoint(Point3D(1, 0, 0));
+
+    // Convert to two vectors on the surface of the plane.
+    Point3D ab = b - a;
+    Point3D ac = c - a;
+
+    return ac.CrossProduct(ab);
+  }
+
+  /**
+   * Returns true if the matrix has any transform other
+   * than a straight translation.
+   */
+  bool HasNonTranslation() const {
+    return !gfx::FuzzyEqual(_11, 1.0) || !gfx::FuzzyEqual(_22, 1.0) ||
+           !gfx::FuzzyEqual(_12, 0.0) || !gfx::FuzzyEqual(_21, 0.0) ||
+           !gfx::FuzzyEqual(_13, 0.0) || !gfx::FuzzyEqual(_23, 0.0) ||
+           !gfx::FuzzyEqual(_31, 0.0) || !gfx::FuzzyEqual(_32, 0.0) ||
+           !gfx::FuzzyEqual(_33, 1.0);
+  }
+
+  /**
+   * Returns true if the matrix is anything other than a straight
+   * translation by integers.
+  */
+  bool HasNonIntegerTranslation() const {
+    return HasNonTranslation() ||
+      !gfx::FuzzyEqual(_41, floor(_41 + 0.5)) ||
+      !gfx::FuzzyEqual(_42, floor(_42 + 0.5)) ||
+      !gfx::FuzzyEqual(_43, floor(_43 + 0.5));
+  }
+
+  /**
+   * Return true if the matrix is with perspective (w).
+   */
+  bool HasPerspectiveComponent() const {
+    return _14 != 0 || _24 != 0 || _34 != 0 || _44 != 1;
+  }
+
+  /**
+   * Convert between typed and untyped matrices.
+   */
+  Matrix4x4 ToUnknownMatrix() const {
+    return Matrix4x4{_11, _12, _13, _14,
+                     _21, _22, _23, _24,
+                     _31, _32, _33, _34,
+                     _41, _42, _43, _44};
+  }
+  static Matrix4x4Typed FromUnknownMatrix(const Matrix4x4& aUnknown) {
+    return Matrix4x4Typed{aUnknown._11, aUnknown._12, aUnknown._13, aUnknown._14,
+                          aUnknown._21, aUnknown._22, aUnknown._23, aUnknown._24,
+                          aUnknown._31, aUnknown._32, aUnknown._33, aUnknown._34,
+                          aUnknown._41, aUnknown._42, aUnknown._43, aUnknown._44};
+  }
+};
+
+typedef Matrix4x4Typed<UnknownUnits, UnknownUnits> Matrix4x4;
+
+class Matrix5x4
+{
+public:
+  Matrix5x4()
+    : _11(1.0f), _12(0), _13(0), _14(0)
+    , _21(0), _22(1.0f), _23(0), _24(0)
+    , _31(0), _32(0), _33(1.0f), _34(0)
+    , _41(0), _42(0), _43(0), _44(1.0f)
+    , _51(0), _52(0), _53(0), _54(0)
+  {}
+  Matrix5x4(Float a11, Float a12, Float a13, Float a14,
+         Float a21, Float a22, Float a23, Float a24,
+         Float a31, Float a32, Float a33, Float a34,
+         Float a41, Float a42, Float a43, Float a44,
+         Float a51, Float a52, Float a53, Float a54)
+    : _11(a11), _12(a12), _13(a13), _14(a14)
+    , _21(a21), _22(a22), _23(a23), _24(a24)
+    , _31(a31), _32(a32), _33(a33), _34(a34)
+    , _41(a41), _42(a42), _43(a43), _44(a44)
+    , _51(a51), _52(a52), _53(a53), _54(a54)
+  {}
+
+  bool operator==(const Matrix5x4 &o) const
+  {
+    return _11 == o._11 && _12 == o._12 && _13 == o._13 && _14 == o._14 &&
+           _21 == o._21 && _22 == o._22 && _23 == o._23 && _24 == o._24 &&
+           _31 == o._31 && _32 == o._32 && _33 == o._33 && _34 == o._34 &&
+           _41 == o._41 && _42 == o._42 && _43 == o._43 && _44 == o._44 &&
+           _51 == o._51 && _52 == o._52 && _53 == o._53 && _54 == o._54;
+  }
+
+  bool operator!=(const Matrix5x4 &aMatrix) const
+  {
+    return !(*this == aMatrix);
+  }
+
+  Matrix5x4 operator*(const Matrix5x4 &aMatrix) const
+  {
+    Matrix5x4 resultMatrix;
+
+    resultMatrix._11 = this->_11 * aMatrix._11 + this->_12 * aMatrix._21 + this->_13 * aMatrix._31 + this->_14 * aMatrix._41;
+    resultMatrix._12 = this->_11 * aMatrix._12 + this->_12 * aMatrix._22 + this->_13 * aMatrix._32 + this->_14 * aMatrix._42;
+    resultMatrix._13 = this->_11 * aMatrix._13 + this->_12 * aMatrix._23 + this->_13 * aMatrix._33 + this->_14 * aMatrix._43;
+    resultMatrix._14 = this->_11 * aMatrix._14 + this->_12 * aMatrix._24 + this->_13 * aMatrix._34 + this->_14 * aMatrix._44;
+    resultMatrix._21 = this->_21 * aMatrix._11 + this->_22 * aMatrix._21 + this->_23 * aMatrix._31 + this->_24 * aMatrix._41;
+    resultMatrix._22 = this->_21 * aMatrix._12 + this->_22 * aMatrix._22 + this->_23 * aMatrix._32 + this->_24 * aMatrix._42;
+    resultMatrix._23 = this->_21 * aMatrix._13 + this->_22 * aMatrix._23 + this->_23 * aMatrix._33 + this->_24 * aMatrix._43;
+    resultMatrix._24 = this->_21 * aMatrix._14 + this->_22 * aMatrix._24 + this->_23 * aMatrix._34 + this->_24 * aMatrix._44;
+    resultMatrix._31 = this->_31 * aMatrix._11 + this->_32 * aMatrix._21 + this->_33 * aMatrix._31 + this->_34 * aMatrix._41;
+    resultMatrix._32 = this->_31 * aMatrix._12 + this->_32 * aMatrix._22 + this->_33 * aMatrix._32 + this->_34 * aMatrix._42;
+    resultMatrix._33 = this->_31 * aMatrix._13 + this->_32 * aMatrix._23 + this->_33 * aMatrix._33 + this->_34 * aMatrix._43;
+    resultMatrix._34 = this->_31 * aMatrix._14 + this->_32 * aMatrix._24 + this->_33 * aMatrix._34 + this->_34 * aMatrix._44;
+    resultMatrix._41 = this->_41 * aMatrix._11 + this->_42 * aMatrix._21 + this->_43 * aMatrix._31 + this->_44 * aMatrix._41;
+    resultMatrix._42 = this->_41 * aMatrix._12 + this->_42 * aMatrix._22 + this->_43 * aMatrix._32 + this->_44 * aMatrix._42;
+    resultMatrix._43 = this->_41 * aMatrix._13 + this->_42 * aMatrix._23 + this->_43 * aMatrix._33 + this->_44 * aMatrix._43;
+    resultMatrix._44 = this->_41 * aMatrix._14 + this->_42 * aMatrix._24 + this->_43 * aMatrix._34 + this->_44 * aMatrix._44;
+    resultMatrix._51 = this->_51 * aMatrix._11 + this->_52 * aMatrix._21 + this->_53 * aMatrix._31 + this->_54 * aMatrix._41 + aMatrix._51;
+    resultMatrix._52 = this->_51 * aMatrix._12 + this->_52 * aMatrix._22 + this->_53 * aMatrix._32 + this->_54 * aMatrix._42 + aMatrix._52;
+    resultMatrix._53 = this->_51 * aMatrix._13 + this->_52 * aMatrix._23 + this->_53 * aMatrix._33 + this->_54 * aMatrix._43 + aMatrix._53;
+    resultMatrix._54 = this->_51 * aMatrix._14 + this->_52 * aMatrix._24 + this->_53 * aMatrix._34 + this->_54 * aMatrix._44 + aMatrix._54;
+
+    return resultMatrix;
+  }
+
+  Matrix5x4& operator*=(const Matrix5x4 &aMatrix)
+  {
+    *this = *this * aMatrix;
+    return *this;
+  }
+
+  union {
+    struct {
+      Float _11, _12, _13, _14;
+      Float _21, _22, _23, _24;
+      Float _31, _32, _33, _34;
+      Float _41, _42, _43, _44;
+      Float _51, _52, _53, _54;
+    };
+    Float components[20];
+  };
+};
+
+} // namespace gfx
+} // namespace mozilla
+
+#endif /* MOZILLA_GFX_MATRIX_H_ */