Adding upstream version 86.0.1.upstream/86.0.1upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 2300 insertions, 0 deletions

diff --git a/gfx/2d/Matrix.h b/gfx/2d/Matrix.h
new file mode 100644
index 0000000000..21f053da8b
--- /dev/null
+++ b/gfx/2d/Matrix.h
@@ -0,0 +1,2300 @@
+/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
+/* vim: set ts=8 sts=2 et sw=2 tw=80: */
+/* 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"
+#include "mozilla/Span.h"
+
+namespace mozilla {
+namespace gfx {
+
+static inline 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;
+}
+
+template <typename F>
+Span<Point4DTyped<UnknownUnits, F>> IntersectPolygon(
+    Span<Point4DTyped<UnknownUnits, F>> aPoints,
+    const Point4DTyped<UnknownUnits, F>& aPlaneNormal,
+    Span<Point4DTyped<UnknownUnits, F>> aDestBuffer);
+
+template <class T>
+class BaseMatrix {
+  // Alias that maps to either Point or PointDouble depending on whether T is a
+  // float or a double.
+  typedef PointTyped<UnknownUnits, T> MatrixPoint;
+  // Same for size and rect
+  typedef SizeTyped<UnknownUnits, T> MatrixSize;
+  typedef RectTyped<UnknownUnits, T> MatrixRect;
+
+ public:
+  BaseMatrix() : _11(1.0f), _12(0), _21(0), _22(1.0f), _31(0), _32(0) {}
+  BaseMatrix(T a11, T a12, T a21, T a22, T a31, T a32)
+      : _11(a11), _12(a12), _21(a21), _22(a22), _31(a31), _32(a32) {}
+  union {
+    struct {
+      T _11, _12;
+      T _21, _22;
+      T _31, _32;
+    };
+    T components[6];
+  };
+
+  template <class T2>
+  explicit BaseMatrix(const BaseMatrix<T2>& aOther)
+      : _11(aOther._11),
+        _12(aOther._12),
+        _21(aOther._21),
+        _22(aOther._22),
+        _31(aOther._31),
+        _32(aOther._32) {}
+
+  MOZ_ALWAYS_INLINE BaseMatrix Copy() const { return BaseMatrix<T>(*this); }
+
+  friend std::ostream& operator<<(std::ostream& aStream,
+                                  const BaseMatrix& aMatrix) {
+    if (aMatrix.IsIdentity()) {
+      return aStream << "[ I ]";
+    }
+    return aStream << "[ " << aMatrix._11 << " " << aMatrix._12 << "; "
+                   << aMatrix._21 << " " << aMatrix._22 << "; " << aMatrix._31
+                   << " " << aMatrix._32 << "; ]";
+  }
+
+  MatrixPoint TransformPoint(const MatrixPoint& aPoint) const {
+    MatrixPoint retPoint;
+
+    retPoint.x = aPoint.x * _11 + aPoint.y * _21 + _31;
+    retPoint.y = aPoint.x * _12 + aPoint.y * _22 + _32;
+
+    return retPoint;
+  }
+
+  MatrixSize TransformSize(const MatrixSize& aSize) const {
+    MatrixSize retSize;
+
+    retSize.width = aSize.width * _11 + aSize.height * _21;
+    retSize.height = aSize.width * _12 + aSize.height * _22;
+
+    return retSize;
+  }
+
+  /**
+   * In most cases you probably want to use TransformBounds. This function
+   * just transforms the top-left and size separately and constructs a rect
+   * from those results.
+   */
+  MatrixRect TransformRect(const MatrixRect& aRect) const {
+    return MatrixRect(TransformPoint(aRect.TopLeft()),
+                      TransformSize(aRect.Size()));
+  }
+
+  GFX2D_API MatrixRect TransformBounds(const MatrixRect& aRect) const {
+    int i;
+    MatrixPoint quad[4];
+    T min_x, max_x;
+    T 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 (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 MatrixRect(min_x, min_y, max_x - min_x, max_y - min_y);
+  }
+
+  static BaseMatrix<T> Translation(T aX, T aY) {
+    return BaseMatrix<T>(1.0f, 0.0f, 0.0f, 1.0f, aX, aY);
+  }
+
+  static BaseMatrix<T> Translation(MatrixPoint 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:
+   *
+   *   BaseMatrix<T>::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.)
+   */
+  BaseMatrix<T>& PreTranslate(T aX, T aY) {
+    _31 += _11 * aX + _21 * aY;
+    _32 += _12 * aX + _22 * aY;
+
+    return *this;
+  }
+
+  BaseMatrix<T>& PreTranslate(const MatrixPoint& 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.
+   */
+  BaseMatrix<T>& PostTranslate(T aX, T aY) {
+    _31 += aX;
+    _32 += aY;
+    return *this;
+  }
+
+  BaseMatrix<T>& PostTranslate(const MatrixPoint& aPoint) {
+    return PostTranslate(aPoint.x, aPoint.y);
+  }
+
+  static BaseMatrix<T> Scaling(T aScaleX, T aScaleY) {
+    return BaseMatrix<T>(aScaleX, 0.0f, 0.0f, aScaleY, 0.0f, 0.0f);
+  }
+
+  /**
+   * Similar to PreTranslate, but applies a scale instead of a translation.
+   */
+  BaseMatrix<T>& PreScale(T aX, T aY) {
+    _11 *= aX;
+    _12 *= aX;
+    _21 *= aY;
+    _22 *= aY;
+
+    return *this;
+  }
+
+  /**
+   * Similar to PostTranslate, but applies a scale instead of a translation.
+   */
+  BaseMatrix<T>& PostScale(T aScaleX, T aScaleY) {
+    _11 *= aScaleX;
+    _12 *= aScaleY;
+    _21 *= aScaleX;
+    _22 *= aScaleY;
+    _31 *= aScaleX;
+    _32 *= aScaleY;
+
+    return *this;
+  }
+
+  GFX2D_API static BaseMatrix<T> Rotation(T aAngle);
+
+  /**
+   * Similar to PreTranslate, but applies a rotation instead of a translation.
+   */
+  BaseMatrix<T>& PreRotate(T aAngle) {
+    return *this = BaseMatrix<T>::Rotation(aAngle) * *this;
+  }
+
+  bool Invert() {
+    // Compute co-factors.
+    T A = _22;
+    T B = -_21;
+    T C = _21 * _32 - _22 * _31;
+    T D = -_12;
+    T E = _11;
+    T F = _31 * _12 - _11 * _32;
+
+    T det = Determinant();
+
+    if (!det) {
+      return false;
+    }
+
+    T 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;
+  }
+
+  BaseMatrix<T> Inverse() const {
+    BaseMatrix<T> clone = *this;
+    DebugOnly<bool> inverted = clone.Invert();
+    MOZ_ASSERT(inverted,
+               "Attempted to get the inverse of a non-invertible matrix");
+    return clone;
+  }
+
+  T Determinant() const { return _11 * _22 - _12 * _21; }
+
+  BaseMatrix<T> operator*(const BaseMatrix<T>& aMatrix) const {
+    BaseMatrix<T> 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;
+  }
+
+  BaseMatrix<T>& operator*=(const BaseMatrix<T>& aMatrix) {
+    *this = *this * aMatrix;
+    return *this;
+  }
+
+  /**
+   * Multiplies *this with aMatrix and returns the result.
+   */
+  Matrix4x4 operator*(const Matrix4x4& aMatrix) const;
+
+  /**
+   * Multiplies in the opposite order to operator=*.
+   */
+  BaseMatrix<T>& PreMultiply(const BaseMatrix<T>& aMatrix) {
+    *this = aMatrix * *this;
+    return *this;
+  }
+
+  /**
+   * Please explicitly use either FuzzyEquals or ExactlyEquals.
+   */
+  bool operator==(const BaseMatrix<T>& other) const = delete;
+  bool operator!=(const BaseMatrix<T>& other) const = delete;
+
+  /* Returns true if the other matrix is fuzzy-equal to this matrix.
+   * Note that this isn't a cheap comparison!
+   */
+  bool FuzzyEquals(const BaseMatrix<T>& o) const {
+    return FuzzyEqual(_11, o._11) && FuzzyEqual(_12, o._12) &&
+           FuzzyEqual(_21, o._21) && FuzzyEqual(_22, o._22) &&
+           FuzzyEqual(_31, o._31) && FuzzyEqual(_32, o._32);
+  }
+
+  bool ExactlyEquals(const BaseMatrix<T>& 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 + 0.5f)) ||
+           !FuzzyEqual(_32, floor(_32 + 0.5f));
+  }
+
+  /**
+   * 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 {
+    T det = Determinant();
+    return !mozilla::IsFinite(det) || det == 0;
+  }
+
+  GFX2D_API BaseMatrix<T>& NudgeToIntegers() {
+    NudgeToInteger(&_11);
+    NudgeToInteger(&_12);
+    NudgeToInteger(&_21);
+    NudgeToInteger(&_22);
+    NudgeToInteger(&_31);
+    NudgeToInteger(&_32);
+    return *this;
+  }
+
+  bool IsTranslation() const {
+    return FuzzyEqual(_11, 1.0f) && FuzzyEqual(_12, 0.0f) &&
+           FuzzyEqual(_21, 0.0f) && FuzzyEqual(_22, 1.0f);
+  }
+
+  static bool FuzzyIsInteger(T 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);
+  }
+
+  MatrixPoint GetTranslation() const { return MatrixPoint(_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); }
+
+  /**
+   * Computes the scale factors of this matrix; that is,
+   * the amounts each basis vector is scaled by.
+   * The xMajor parameter indicates if the larger scale is
+   * to be assumed to be in the X direction or not.
+   */
+  MatrixSize ScaleFactors() const {
+    T det = Determinant();
+
+    if (det == 0.0) {
+      return MatrixSize(0.0, 0.0);
+    }
+
+    MatrixSize sz = MatrixSize(1.0, 0.0);
+    sz = TransformSize(sz);
+
+    T major = sqrt(sz.width * sz.width + sz.height * sz.height);
+    T minor = 0.0;
+
+    // ignore mirroring
+    if (det < 0.0) {
+      det = -det;
+    }
+
+    if (major) {
+      minor = det / major;
+    }
+
+    return MatrixSize(major, minor);
+  }
+};
+
+typedef BaseMatrix<Float> Matrix;
+typedef BaseMatrix<Double> MatrixDouble;
+
+// 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 <class SourceUnits, class TargetUnits, class T>
+class Matrix4x4Typed {
+ public:
+  typedef PointTyped<SourceUnits, T> SourcePoint;
+  typedef PointTyped<TargetUnits, T> TargetPoint;
+  typedef Point3DTyped<SourceUnits, T> SourcePoint3D;
+  typedef Point3DTyped<TargetUnits, T> TargetPoint3D;
+  typedef Point4DTyped<SourceUnits, T> SourcePoint4D;
+  typedef Point4DTyped<TargetUnits, T> TargetPoint4D;
+  typedef RectTyped<SourceUnits, T> SourceRect;
+  typedef RectTyped<TargetUnits, T> 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(T a11, T a12, T a13, T a14, T a21, T a22, T a23, T a24, T a31,
+                 T a32, T a33, T a34, T a41, T a42, T a43, T 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 T aArray[16]) {
+    memcpy(components, aArray, sizeof(components));
+  }
+
+  Matrix4x4Typed(const Matrix4x4Typed& aOther) {
+    memcpy(components, aOther.components, sizeof(components));
+  }
+
+  template <class T2>
+  explicit Matrix4x4Typed(
+      const Matrix4x4Typed<SourceUnits, TargetUnits, T2>& aOther)
+      : _11(aOther._11),
+        _12(aOther._12),
+        _13(aOther._13),
+        _14(aOther._14),
+        _21(aOther._21),
+        _22(aOther._22),
+        _23(aOther._23),
+        _24(aOther._24),
+        _31(aOther._31),
+        _32(aOther._32),
+        _33(aOther._33),
+        _34(aOther._34),
+        _41(aOther._41),
+        _42(aOther._42),
+        _43(aOther._43),
+        _44(aOther._44) {}
+
+  union {
+    struct {
+      T _11, _12, _13, _14;
+      T _21, _22, _23, _24;
+      T _31, _32, _33, _34;
+      T _41, _42, _43, _44;
+    };
+    T components[16];
+  };
+
+  friend std::ostream& operator<<(std::ostream& aStream,
+                                  const Matrix4x4Typed& aMatrix) {
+    if (aMatrix.Is2D()) {
+      BaseMatrix<T> matrix = aMatrix.As2D();
+      return aStream << matrix;
+    }
+    const T* f = &aMatrix._11;
+    aStream << "[ " << f[0] << ' ' << f[1] << ' ' << f[2] << ' ' << f[3] << ';';
+    f += 4;
+    aStream << ' ' << f[0] << ' ' << f[1] << ' ' << f[2] << ' ' << f[3] << ';';
+    f += 4;
+    aStream << ' ' << f[0] << ' ' << f[1] << ' ' << f[2] << ' ' << f[3] << ';';
+    f += 4;
+    aStream << ' ' << f[0] << ' ' << f[1] << ' ' << f[2] << ' ' << f[3]
+            << "; ]";
+    return aStream;
+  }
+
+  Point4DTyped<UnknownUnits, T>& operator[](int aIndex) {
+    MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
+    return *reinterpret_cast<Point4DTyped<UnknownUnits, T>*>((&_11) +
+                                                             4 * aIndex);
+  }
+  const Point4DTyped<UnknownUnits, T>& operator[](int aIndex) const {
+    MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
+    return *reinterpret_cast<const Point4DTyped<UnknownUnits, T>*>((&_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(BaseMatrix<T>* 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;
+  }
+
+  BaseMatrix<T> As2D() const {
+    MOZ_ASSERT(Is2D(), "Matrix is not a 2D affine transform");
+
+    return BaseMatrix<T>(_11, _12, _21, _22, _41, _42);
+  }
+
+  bool CanDraw2D(BaseMatrix<T>* 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) {
+      T 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 than 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 {
+    typedef Point4DTyped<UnknownUnits, F> P4D;
+
+    // The initial polygon is made up by the corners of aRect in homogenous
+    // space, mapped into the destination space of this transform.
+    P4D rectCorners[] = {
+        TransformPoint(P4D(aRect.X(), aRect.Y(), 0, 1)),
+        TransformPoint(P4D(aRect.XMost(), aRect.Y(), 0, 1)),
+        TransformPoint(P4D(aRect.XMost(), aRect.YMost(), 0, 1)),
+        TransformPoint(P4D(aRect.X(), aRect.YMost(), 0, 1)),
+    };
+
+    // Cut off pieces of the polygon that are outside of aClip (the "view
+    // frustrum"), by consecutively intersecting the polygon with the half space
+    // induced by the clipping plane for each side of aClip.
+    // View frustum clipping planes are described as normals originating from
+    // the 0,0,0,0 origin.
+    // Each pass can increase or decrease the number of points that make up the
+    // current clipped polygon. We double buffer the set of points, alternating
+    // between polygonBufA and polygonBufB. Duplicated points in the polygons
+    // are kept around until all clipping is done. The loop at the end filters
+    // out any consecutive duplicates.
+    P4D polygonBufA[kTransformAndClipRectMaxVerts];
+    P4D polygonBufB[kTransformAndClipRectMaxVerts];
+
+    Span<P4D> polygon(rectCorners);
+    polygon = IntersectPolygon<F>(polygon, P4D(1.0, 0.0, 0.0, -aClip.X()),
+                                  polygonBufA);
+    polygon = IntersectPolygon<F>(polygon, P4D(-1.0, 0.0, 0.0, aClip.XMost()),
+                                  polygonBufB);
+    polygon = IntersectPolygon<F>(polygon, P4D(0.0, 1.0, 0.0, -aClip.Y()),
+                                  polygonBufA);
+    polygon = IntersectPolygon<F>(polygon, P4D(0.0, -1.0, 0.0, aClip.YMost()),
+                                  polygonBufB);
+
+    size_t vertCount = 0;
+    for (const auto& srcPoint : polygon) {
+      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 (vertCount == 0 || p != aVerts[vertCount - 1]) {
+        aVerts[vertCount++] = p;
+      }
+    }
+
+    return vertCount;
+  }
+
+  static const int kTransformAndClipRectMaxVerts = 32;
+
+  static Matrix4x4Typed From2D(const BaseMatrix<T>& 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 {
+    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(T aX, T aY, T 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(T aX, T aY, T 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 Point3DTyped<UnknownUnits, T>& 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(T aX, T aY, T 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(T aScaleX, T aScaleY, T 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(T aX, T aY, T 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(T aScaleX, T aScaleY, T 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(T aSkew) { (*this)[1] += (*this)[0] * aSkew; }
+
+  void SkewXZ(T aSkew) { (*this)[2] += (*this)[0] * aSkew; }
+
+  void SkewYZ(T aSkew) { (*this)[2] += (*this)[1] * aSkew; }
+
+  Matrix4x4Typed& ChangeBasis(const Point3DTyped<UnknownUnits, T>& aOrigin) {
+    return ChangeBasis(aOrigin.x, aOrigin.y, aOrigin.z);
+  }
+
+  Matrix4x4Typed& ChangeBasis(T aX, T aY, T 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); }
+
+  Matrix4x4Typed& operator=(const Matrix4x4Typed& aOther) {
+    memcpy(components, aOther.components, sizeof(components));
+    return *this;
+  }
+
+  template <typename NewTargetUnits>
+  Matrix4x4Typed<SourceUnits, NewTargetUnits, T> operator*(
+      const Matrix4x4Typed<TargetUnits, NewTargetUnits, T>& aMatrix) const {
+    Matrix4x4Typed<SourceUnits, NewTargetUnits, T> 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, T>& 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; }
+
+  T 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() {
+    T det = Determinant();
+    if (!det) {
+      return false;
+    }
+
+    Matrix4x4Typed<SourceUnits, TargetUnits, T> 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, T> Inverse() const {
+    typedef Matrix4x4Typed<TargetUnits, SourceUnits, T> 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;
+  }
+
+  Maybe<Matrix4x4Typed<TargetUnits, SourceUnits, T>> MaybeInverse() const {
+    typedef Matrix4x4Typed<TargetUnits, SourceUnits, T> InvertedMatrix;
+    InvertedMatrix clone = InvertedMatrix::FromUnknownMatrix(ToUnknownMatrix());
+    if (clone.Invert()) {
+      return Some(clone);
+    }
+    return Nothing();
+  }
+
+  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;
+    T det = Determinant();
+    T __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 Point4DTyped<UnknownUnits, T>(*((&_11) + aIndex), *((&_21) + aIndex),
+                                         *((&_31) + aIndex),
+                                         *((&_41) + aIndex));
+  }
+
+  void SetTransposedVector(int aIndex, Point4DTyped<UnknownUnits, T>& 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;
+  }
+
+  bool Decompose(Point3DTyped<UnknownUnits, T>& translation,
+                 BaseQuaternion<T>& rotation,
+                 Point3DTyped<UnknownUnits, T>& scale) const {
+    // Ensure matrix can be normalized
+    if (gfx::FuzzyEqual(_44, 0.0f)) {
+      return false;
+    }
+    Matrix4x4Typed mat = *this;
+    mat.Normalize();
+    if (HasPerspectiveComponent()) {
+      // We do not support projection matrices
+      return false;
+    }
+
+    // Extract translation
+    translation.x = mat._41;
+    translation.y = mat._42;
+    translation.z = mat._43;
+
+    // Remove translation
+    mat._41 = 0.0f;
+    mat._42 = 0.0f;
+    mat._43 = 0.0f;
+
+    // Extract scale
+    scale.x = sqrtf(_11 * _11 + _21 * _21 + _31 * _31);
+    scale.y = sqrtf(_12 * _12 + _22 * _22 + _32 * _32);
+    scale.z = sqrtf(_13 * _13 + _23 * _23 + _33 * _33);
+
+    // Remove scale
+    if (gfx::FuzzyEqual(scale.x, 0.0f) || gfx::FuzzyEqual(scale.y, 0.0f) ||
+        gfx::FuzzyEqual(scale.z, 0.0f)) {
+      // We do not support matrices with a zero scale component
+      return false;
+    }
+
+    // Extract rotation
+    rotation.SetFromRotationMatrix(*this);
+    return true;
+  }
+
+  // Sets this matrix to a rotation matrix given by aQuat.
+  // This quaternion *MUST* be normalized!
+  // Implemented in Quaternion.cpp
+  void SetRotationFromQuaternion(const BaseQuaternion<T>& q) {
+    const T x2 = q.x + q.x, y2 = q.y + q.y, z2 = q.z + q.z;
+    const T xx = q.x * x2, xy = q.x * y2, xz = q.x * z2;
+    const T yy = q.y * y2, yz = q.y * z2, zz = q.z * z2;
+    const T 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<T>();
+    _21 = UnspecifiedNaN<T>();
+    _31 = UnspecifiedNaN<T>();
+    _41 = UnspecifiedNaN<T>();
+    _12 = UnspecifiedNaN<T>();
+    _22 = UnspecifiedNaN<T>();
+    _32 = UnspecifiedNaN<T>();
+    _42 = UnspecifiedNaN<T>();
+    _13 = UnspecifiedNaN<T>();
+    _23 = UnspecifiedNaN<T>();
+    _33 = UnspecifiedNaN<T>();
+    _43 = UnspecifiedNaN<T>();
+    _14 = UnspecifiedNaN<T>();
+    _24 = UnspecifiedNaN<T>();
+    _34 = UnspecifiedNaN<T>();
+    _44 = UnspecifiedNaN<T>();
+  }
+
+  void SkewXY(double aXSkew, double aYSkew) {
+    // XXX Is double precision really necessary here
+    T tanX = SafeTangent(aXSkew);
+    T tanY = SafeTangent(aYSkew);
+    T 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));
+
+    T 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));
+
+    T 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));
+
+    T 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://drafts.csswg.org/css-transforms-2/#Rotate3dDefined
+  void SetRotateAxisAngle(double aX, double aY, double aZ, double aTheta) {
+    Point3DTyped<UnknownUnits, T> vector(aX, aY, aZ);
+    if (!vector.Length()) {
+      return;
+    }
+    vector.RobustNormalize();
+
+    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(T 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.
+    Point3DTyped<UnknownUnits, T> a =
+        TransformPoint(Point3DTyped<UnknownUnits, T>(0, 0, 0));
+    Point3DTyped<UnknownUnits, T> b =
+        TransformPoint(Point3DTyped<UnknownUnits, T>(0, 1, 0));
+    Point3DTyped<UnknownUnits, T> c =
+        TransformPoint(Point3DTyped<UnknownUnits, T>(1, 0, 0));
+
+    // Convert to two vectors on the surface of the plane.
+    Point3DTyped<UnknownUnits, T> ab = b - a;
+    Point3DTyped<UnknownUnits, T> 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;
+  }
+
+  /* Returns true if the matrix is a rectilinear transformation (i.e.
+   * grid-aligned rectangles are transformed to grid-aligned rectangles).
+   * This should only be called on 2D matrices.
+   */
+  bool IsRectilinear() const {
+    MOZ_ASSERT(Is2D());
+    if (gfx::FuzzyEqual(_12, 0) && gfx::FuzzyEqual(_21, 0)) {
+      return true;
+    } else if (gfx::FuzzyEqual(_22, 0) && gfx::FuzzyEqual(_11, 0)) {
+      return true;
+    }
+    return false;
+  }
+
+  /**
+   * 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};
+  }
+  /**
+   * For convenience, overload FromUnknownMatrix() for Maybe<Matrix>.
+   */
+  static Maybe<Matrix4x4Typed> FromUnknownMatrix(
+      const Maybe<Matrix4x4>& aUnknown) {
+    if (aUnknown.isSome()) {
+      return Some(FromUnknownMatrix(*aUnknown));
+    }
+    return Nothing();
+  }
+};
+
+typedef Matrix4x4Typed<UnknownUnits, UnknownUnits> Matrix4x4;
+typedef Matrix4x4Typed<UnknownUnits, UnknownUnits, double> Matrix4x4Double;
+
+// This typedef is for IPDL, which can't reference a template-id directly.
+typedef Maybe<Matrix4x4> MaybeMatrix4x4;
+
+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;
+  }
+
+  friend std::ostream& operator<<(std::ostream& aStream,
+                                  const Matrix5x4& aMatrix) {
+    const Float* f = &aMatrix._11;
+    aStream << "[ " << f[0] << ' ' << f[1] << ' ' << f[2] << ' ' << f[3] << ';';
+    f += 4;
+    aStream << ' ' << f[0] << ' ' << f[1] << ' ' << f[2] << ' ' << f[3] << ';';
+    f += 4;
+    aStream << ' ' << f[0] << ' ' << f[1] << ' ' << f[2] << ' ' << f[3] << ';';
+    f += 4;
+    aStream << ' ' << f[0] << ' ' << f[1] << ' ' << f[2] << ' ' << f[3] << ';';
+    f += 4;
+    aStream << ' ' << f[0] << ' ' << f[1] << ' ' << f[2] << ' ' << f[3]
+            << "; ]";
+    return aStream;
+  }
+
+  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];
+  };
+};
+
+/* This Matrix class will carry one additional type field in order to
+ * track what type of 4x4 matrix we're dealing with, it can then execute
+ * simplified versions of certain operations when applicable.
+ * This does not allow access to the parent class directly, as a caller
+ * could then mutate the parent class without updating the type.
+ */
+template <typename SourceUnits, typename TargetUnits>
+class Matrix4x4TypedFlagged
+    : protected Matrix4x4Typed<SourceUnits, TargetUnits> {
+ public:
+  using Parent = Matrix4x4Typed<SourceUnits, TargetUnits>;
+  using TargetPoint = PointTyped<TargetUnits>;
+  using Parent::_11;
+  using Parent::_12;
+  using Parent::_13;
+  using Parent::_14;
+  using Parent::_21;
+  using Parent::_22;
+  using Parent::_23;
+  using Parent::_24;
+  using Parent::_31;
+  using Parent::_32;
+  using Parent::_33;
+  using Parent::_34;
+  using Parent::_41;
+  using Parent::_42;
+  using Parent::_43;
+  using Parent::_44;
+
+  Matrix4x4TypedFlagged() : mType(MatrixType::Identity) {}
+
+  Matrix4x4TypedFlagged(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)
+      : Parent(a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34, a41,
+               a42, a43, a44) {
+    Analyze();
+  }
+
+  MOZ_IMPLICIT Matrix4x4TypedFlagged(const Parent& aOther) : Parent(aOther) {
+    Analyze();
+  }
+
+  template <class F>
+  PointTyped<TargetUnits, F> TransformPoint(
+      const PointTyped<SourceUnits, F>& aPoint) const {
+    if (mType == MatrixType::Identity) {
+      return aPoint;
+    }
+
+    if (mType == MatrixType::Simple) {
+      return TransformPointSimple(aPoint);
+    }
+
+    return Parent::TransformPoint(aPoint);
+  }
+
+  template <class F>
+  RectTyped<TargetUnits, F> TransformAndClipBounds(
+      const RectTyped<SourceUnits, F>& aRect,
+      const RectTyped<TargetUnits, F>& aClip) const {
+    if (mType == MatrixType::Identity) {
+      const RectTyped<SourceUnits, F>& clipped = aRect.Intersect(aClip);
+      return RectTyped<TargetUnits, F>(clipped.X(), clipped.Y(),
+                                       clipped.Width(), clipped.Height());
+    }
+
+    if (mType == MatrixType::Simple) {
+      PointTyped<UnknownUnits, F> p1 = TransformPointSimple(aRect.TopLeft());
+      PointTyped<UnknownUnits, F> p2 = TransformPointSimple(aRect.TopRight());
+      PointTyped<UnknownUnits, F> p3 = TransformPointSimple(aRect.BottomLeft());
+      PointTyped<UnknownUnits, F> p4 =
+          TransformPointSimple(aRect.BottomRight());
+
+      F min_x = std::min(std::min(std::min(p1.x, p2.x), p3.x), p4.x);
+      F max_x = std::max(std::max(std::max(p1.x, p2.x), p3.x), p4.x);
+      F min_y = std::min(std::min(std::min(p1.y, p2.y), p3.y), p4.y);
+      F max_y = std::max(std::max(std::max(p1.y, p2.y), p3.y), p4.y);
+
+      TargetPoint topLeft(std::max(min_x, aClip.x), std::max(min_y, aClip.y));
+      F width = std::min(max_x, aClip.XMost()) - topLeft.x;
+      F height = std::min(max_y, aClip.YMost()) - topLeft.y;
+
+      return RectTyped<TargetUnits, F>(topLeft.x, topLeft.y, width, height);
+    }
+    return Parent::TransformAndClipBounds(aRect, aClip);
+  }
+
+  bool FuzzyEqual(const Parent& o) const { return Parent::FuzzyEqual(o); }
+
+  bool FuzzyEqual(const Matrix4x4TypedFlagged& o) const {
+    if (mType == MatrixType::Identity && o.mType == MatrixType::Identity) {
+      return true;
+    }
+    return Parent::FuzzyEqual(o);
+  }
+
+  Matrix4x4TypedFlagged& PreTranslate(Float aX, Float aY, Float aZ) {
+    if (mType == MatrixType::Identity) {
+      _41 = aX;
+      _42 = aY;
+      _43 = aZ;
+
+      if (!aZ) {
+        mType = MatrixType::Simple;
+        return *this;
+      }
+      mType = MatrixType::Full;
+      return *this;
+    }
+
+    Parent::PreTranslate(aX, aY, aZ);
+
+    if (aZ != 0) {
+      mType = MatrixType::Full;
+    }
+
+    return *this;
+  }
+
+  Matrix4x4TypedFlagged& PostTranslate(Float aX, Float aY, Float aZ) {
+    if (mType == MatrixType::Identity) {
+      _41 = aX;
+      _42 = aY;
+      _43 = aZ;
+
+      if (!aZ) {
+        mType = MatrixType::Simple;
+        return *this;
+      }
+      mType = MatrixType::Full;
+      return *this;
+    }
+
+    Parent::PostTranslate(aX, aY, aZ);
+
+    if (aZ != 0) {
+      mType = MatrixType::Full;
+    }
+
+    return *this;
+  }
+
+  Matrix4x4TypedFlagged& 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;
+  }
+
+  bool IsIdentity() const { return mType == MatrixType::Identity; }
+
+  template <class F>
+  Point4DTyped<TargetUnits, F> ProjectPoint(
+      const PointTyped<SourceUnits, F>& aPoint) const {
+    if (mType == MatrixType::Identity) {
+      return Point4DTyped<TargetUnits, F>(aPoint.x, aPoint.y, 0, 1);
+    }
+
+    if (mType == MatrixType::Simple) {
+      TargetPoint point = TransformPointSimple(aPoint);
+      return Point4DTyped<TargetUnits, F>(point.x, point.y, 0, 1);
+    }
+
+    return Parent::ProjectPoint(aPoint);
+  }
+
+  Matrix4x4TypedFlagged& ProjectTo2D() {
+    if (mType == MatrixType::Full) {
+      Parent::ProjectTo2D();
+    }
+    return *this;
+  }
+
+  bool IsSingular() const {
+    if (mType == MatrixType::Identity) {
+      return false;
+    }
+    return Parent::Determinant() == 0.0;
+  }
+
+  bool Invert() {
+    if (mType == MatrixType::Identity) {
+      return true;
+    }
+
+    return Parent::Invert();
+  }
+
+  Matrix4x4TypedFlagged<TargetUnits, SourceUnits> Inverse() const {
+    typedef Matrix4x4TypedFlagged<TargetUnits, SourceUnits> InvertedMatrix;
+    InvertedMatrix clone = InvertedMatrix::FromUnknownMatrix(ToUnknownMatrix());
+    if (mType == MatrixType::Identity) {
+      return clone;
+    }
+    DebugOnly<bool> inverted = clone.Invert();
+    MOZ_ASSERT(inverted,
+               "Attempted to get the inverse of a non-invertible matrix");
+
+    // Inverting a 2D Matrix should result in a 2D matrix, ergo mType doesn't
+    // change.
+    return clone;
+  }
+
+  template <typename NewTargetUnits>
+  bool operator==(
+      const Matrix4x4TypedFlagged<TargetUnits, NewTargetUnits>& aMatrix) const {
+    if (mType == MatrixType::Identity &&
+        aMatrix.mType == MatrixType::Identity) {
+      return true;
+    }
+    // Depending on the usage it may make sense to compare more flags.
+    return Parent::operator==(aMatrix);
+  }
+
+  template <typename NewTargetUnits>
+  bool operator!=(
+      const Matrix4x4TypedFlagged<TargetUnits, NewTargetUnits>& aMatrix) const {
+    if (mType == MatrixType::Identity &&
+        aMatrix.mType == MatrixType::Identity) {
+      return false;
+    }
+    // Depending on the usage it may make sense to compare more flags.
+    return Parent::operator!=(aMatrix);
+  }
+
+  template <typename NewTargetUnits>
+  Matrix4x4TypedFlagged<SourceUnits, NewTargetUnits> operator*(
+      const Matrix4x4Typed<TargetUnits, NewTargetUnits>& aMatrix) const {
+    if (mType == MatrixType::Identity) {
+      return aMatrix;
+    }
+
+    if (mType == MatrixType::Simple) {
+      Matrix4x4TypedFlagged<SourceUnits, NewTargetUnits> matrix;
+      matrix._11 = _11 * aMatrix._11 + _12 * aMatrix._21;
+      matrix._21 = _21 * aMatrix._11 + _22 * aMatrix._21;
+      matrix._31 = aMatrix._31;
+      matrix._41 = _41 * aMatrix._11 + _42 * aMatrix._21 + aMatrix._41;
+      matrix._12 = _11 * aMatrix._12 + _12 * aMatrix._22;
+      matrix._22 = _21 * aMatrix._12 + _22 * aMatrix._22;
+      matrix._32 = aMatrix._32;
+      matrix._42 = _41 * aMatrix._12 + _42 * aMatrix._22 + aMatrix._42;
+      matrix._13 = _11 * aMatrix._13 + _12 * aMatrix._23;
+      matrix._23 = _21 * aMatrix._13 + _22 * aMatrix._23;
+      matrix._33 = aMatrix._33;
+      matrix._43 = _41 * aMatrix._13 + _42 * aMatrix._23 + aMatrix._43;
+      matrix._14 = _11 * aMatrix._14 + _12 * aMatrix._24;
+      matrix._24 = _21 * aMatrix._14 + _22 * aMatrix._24;
+      matrix._34 = aMatrix._34;
+      matrix._44 = _41 * aMatrix._14 + _42 * aMatrix._24 + aMatrix._44;
+      matrix.Analyze();
+      return matrix;
+    }
+
+    return Parent::operator*(aMatrix);
+  }
+
+  template <typename NewTargetUnits>
+  Matrix4x4TypedFlagged<SourceUnits, NewTargetUnits> operator*(
+      const Matrix4x4TypedFlagged<TargetUnits, NewTargetUnits>& aMatrix) const {
+    if (mType == MatrixType::Identity) {
+      return aMatrix;
+    }
+
+    if (aMatrix.mType == MatrixType::Identity) {
+      return Matrix4x4TypedFlagged<SourceUnits, NewTargetUnits>::
+          FromUnknownMatrix(this->ToUnknownMatrix());
+    }
+
+    if (mType == MatrixType::Simple && aMatrix.mType == MatrixType::Simple) {
+      Matrix4x4TypedFlagged<SourceUnits, NewTargetUnits> matrix;
+      matrix._11 = _11 * aMatrix._11 + _12 * aMatrix._21;
+      matrix._21 = _21 * aMatrix._11 + _22 * aMatrix._21;
+      matrix._41 = _41 * aMatrix._11 + _42 * aMatrix._21 + aMatrix._41;
+      matrix._12 = _11 * aMatrix._12 + _12 * aMatrix._22;
+      matrix._22 = _21 * aMatrix._12 + _22 * aMatrix._22;
+      matrix._42 = _41 * aMatrix._12 + _42 * aMatrix._22 + aMatrix._42;
+      matrix.mType = MatrixType::Simple;
+      return matrix;
+    } else if (mType == MatrixType::Simple) {
+      Matrix4x4TypedFlagged<SourceUnits, NewTargetUnits> matrix;
+      matrix._11 = _11 * aMatrix._11 + _12 * aMatrix._21;
+      matrix._21 = _21 * aMatrix._11 + _22 * aMatrix._21;
+      matrix._31 = aMatrix._31;
+      matrix._41 = _41 * aMatrix._11 + _42 * aMatrix._21 + aMatrix._41;
+      matrix._12 = _11 * aMatrix._12 + _12 * aMatrix._22;
+      matrix._22 = _21 * aMatrix._12 + _22 * aMatrix._22;
+      matrix._32 = aMatrix._32;
+      matrix._42 = _41 * aMatrix._12 + _42 * aMatrix._22 + aMatrix._42;
+      matrix._13 = _11 * aMatrix._13 + _12 * aMatrix._23;
+      matrix._23 = _21 * aMatrix._13 + _22 * aMatrix._23;
+      matrix._33 = aMatrix._33;
+      matrix._43 = _41 * aMatrix._13 + _42 * aMatrix._23 + aMatrix._43;
+      matrix._14 = _11 * aMatrix._14 + _12 * aMatrix._24;
+      matrix._24 = _21 * aMatrix._14 + _22 * aMatrix._24;
+      matrix._34 = aMatrix._34;
+      matrix._44 = _41 * aMatrix._14 + _42 * aMatrix._24 + aMatrix._44;
+      matrix.mType = MatrixType::Full;
+      return matrix;
+    } else if (aMatrix.mType == MatrixType::Simple) {
+      Matrix4x4TypedFlagged<SourceUnits, NewTargetUnits> matrix;
+      matrix._11 = _11 * aMatrix._11 + _12 * aMatrix._21 + _14 * aMatrix._41;
+      matrix._21 = _21 * aMatrix._11 + _22 * aMatrix._21 + _24 * aMatrix._41;
+      matrix._31 = _31 * aMatrix._11 + _32 * aMatrix._21 + _34 * aMatrix._41;
+      matrix._41 = _41 * aMatrix._11 + _42 * aMatrix._21 + _44 * aMatrix._41;
+      matrix._12 = _11 * aMatrix._12 + _12 * aMatrix._22 + _14 * aMatrix._42;
+      matrix._22 = _21 * aMatrix._12 + _22 * aMatrix._22 + _24 * aMatrix._42;
+      matrix._32 = _31 * aMatrix._12 + _32 * aMatrix._22 + _34 * aMatrix._42;
+      matrix._42 = _41 * aMatrix._12 + _42 * aMatrix._22 + _44 * aMatrix._42;
+      matrix._13 = _13;
+      matrix._23 = _23;
+      matrix._33 = _33;
+      matrix._43 = _43;
+      matrix._14 = _14;
+      matrix._24 = _24;
+      matrix._34 = _34;
+      matrix._44 = _44;
+      matrix.mType = MatrixType::Full;
+      return matrix;
+    }
+
+    return Parent::operator*(aMatrix);
+  }
+
+  bool Is2D() const { return mType != MatrixType::Full; }
+
+  bool CanDraw2D(Matrix* aMatrix = nullptr) const {
+    if (mType != MatrixType::Full) {
+      if (aMatrix) {
+        aMatrix->_11 = _11;
+        aMatrix->_12 = _12;
+        aMatrix->_21 = _21;
+        aMatrix->_22 = _22;
+        aMatrix->_31 = _41;
+        aMatrix->_32 = _42;
+      }
+      return true;
+    }
+    return Parent::CanDraw2D(aMatrix);
+  }
+
+  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;
+  }
+
+  template <class F>
+  RectTyped<TargetUnits, F> ProjectRectBounds(
+      const RectTyped<SourceUnits, F>& aRect,
+      const RectTyped<TargetUnits, F>& aClip) const {
+    return Parent::ProjectRectBounds(aRect, aClip);
+  }
+
+  const Parent& GetMatrix() const { return *this; }
+
+ private:
+  enum class MatrixType : uint8_t {
+    Identity,
+    Simple,  // 2x3 Matrix
+    Full     // 4x4 Matrix
+  };
+
+  Matrix4x4TypedFlagged(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,
+                        typename Matrix4x4TypedFlagged::MatrixType aType)
+      : Parent(a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34, a41,
+               a42, a43, a44) {
+    mType = aType;
+  }
+  static Matrix4x4TypedFlagged FromUnknownMatrix(
+      const Matrix4x4Flagged& aUnknown) {
+    return Matrix4x4TypedFlagged{
+        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, aUnknown.mType};
+  }
+  Matrix4x4Flagged ToUnknownMatrix() const {
+    return Matrix4x4Flagged{_11, _12, _13, _14, _21, _22, _23, _24,  _31,
+                            _32, _33, _34, _41, _42, _43, _44, mType};
+  }
+
+  template <class F>
+  PointTyped<TargetUnits, F> TransformPointSimple(
+      const PointTyped<SourceUnits, F>& aPoint) const {
+    PointTyped<SourceUnits, F> temp;
+    temp.x = aPoint.x * _11 + aPoint.y * +_21 + _41;
+    temp.y = aPoint.x * _12 + aPoint.y * +_22 + _42;
+    return temp;
+  }
+
+  void Analyze() {
+    if (Parent::IsIdentity()) {
+      mType = MatrixType::Identity;
+      return;
+    }
+
+    if (Parent::Is2D()) {
+      mType = MatrixType::Simple;
+      return;
+    }
+
+    mType = MatrixType::Full;
+  }
+
+  MatrixType mType;
+};
+
+using Matrix4x4Flagged = Matrix4x4TypedFlagged<UnknownUnits, UnknownUnits>;
+
+}  // namespace gfx
+}  // namespace mozilla
+
+#endif /* MOZILLA_GFX_MATRIX_H_ */