diff -r 000000000000 -r 6474c204b198 gfx/skia/trunk/src/core/SkMatrix.cpp
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/gfx/skia/trunk/src/core/SkMatrix.cpp	Wed Dec 31 06:09:35 2014 +0100
@@ -0,0 +1,1763 @@
+/*
+ * Copyright 2006 The Android Open Source Project
+ *
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+
+#include "SkMatrix.h"
+#include "SkFloatBits.h"
+#include "SkOnce.h"
+#include "SkString.h"
+
+// In a few places, we performed the following
+//      a * b + c * d + e
+// as
+//      a * b + (c * d + e)
+//
+// sdot and scross are indended to capture these compound operations into a
+// function, with an eye toward considering upscaling the intermediates to
+// doubles for more precision (as we do in concat and invert).
+//
+// However, these few lines that performed the last add before the "dot", cause
+// tiny image differences, so we guard that change until we see the impact on
+// chrome's layouttests.
+//
+#define SK_LEGACY_MATRIX_MATH_ORDER
+
+static inline float SkDoubleToFloat(double x) {
+    return static_cast<float>(x);
+}
+
+/*      [scale-x    skew-x      trans-x]   [X]   [X']
+        [skew-y     scale-y     trans-y] * [Y] = [Y']
+        [persp-0    persp-1     persp-2]   [1]   [1 ]
+*/
+
+void SkMatrix::reset() {
+    fMat[kMScaleX] = fMat[kMScaleY] = fMat[kMPersp2] = 1;
+    fMat[kMSkewX]  = fMat[kMSkewY] =
+    fMat[kMTransX] = fMat[kMTransY] =
+    fMat[kMPersp0] = fMat[kMPersp1] = 0;
+
+    this->setTypeMask(kIdentity_Mask | kRectStaysRect_Mask);
+}
+
+// this guy aligns with the masks, so we can compute a mask from a varaible 0/1
+enum {
+    kTranslate_Shift,
+    kScale_Shift,
+    kAffine_Shift,
+    kPerspective_Shift,
+    kRectStaysRect_Shift
+};
+
+static const int32_t kScalar1Int = 0x3f800000;
+
+uint8_t SkMatrix::computePerspectiveTypeMask() const {
+    // Benchmarking suggests that replacing this set of SkScalarAs2sCompliment
+    // is a win, but replacing those below is not. We don't yet understand
+    // that result.
+    if (fMat[kMPersp0] != 0 || fMat[kMPersp1] != 0 || fMat[kMPersp2] != 1) {
+        // If this is a perspective transform, we return true for all other
+        // transform flags - this does not disable any optimizations, respects
+        // the rule that the type mask must be conservative, and speeds up
+        // type mask computation.
+        return SkToU8(kORableMasks);
+    }
+
+    return SkToU8(kOnlyPerspectiveValid_Mask | kUnknown_Mask);
+}
+
+uint8_t SkMatrix::computeTypeMask() const {
+    unsigned mask = 0;
+
+    if (fMat[kMPersp0] != 0 || fMat[kMPersp1] != 0 || fMat[kMPersp2] != 1) {
+        // Once it is determined that that this is a perspective transform,
+        // all other flags are moot as far as optimizations are concerned.
+        return SkToU8(kORableMasks);
+    }
+
+    if (fMat[kMTransX] != 0 || fMat[kMTransY] != 0) {
+        mask |= kTranslate_Mask;
+    }
+
+    int m00 = SkScalarAs2sCompliment(fMat[SkMatrix::kMScaleX]);
+    int m01 = SkScalarAs2sCompliment(fMat[SkMatrix::kMSkewX]);
+    int m10 = SkScalarAs2sCompliment(fMat[SkMatrix::kMSkewY]);
+    int m11 = SkScalarAs2sCompliment(fMat[SkMatrix::kMScaleY]);
+
+    if (m01 | m10) {
+        // The skew components may be scale-inducing, unless we are dealing
+        // with a pure rotation.  Testing for a pure rotation is expensive,
+        // so we opt for being conservative by always setting the scale bit.
+        // along with affine.
+        // By doing this, we are also ensuring that matrices have the same
+        // type masks as their inverses.
+        mask |= kAffine_Mask | kScale_Mask;
+
+        // For rectStaysRect, in the affine case, we only need check that
+        // the primary diagonal is all zeros and that the secondary diagonal
+        // is all non-zero.
+
+        // map non-zero to 1
+        m01 = m01 != 0;
+        m10 = m10 != 0;
+
+        int dp0 = 0 == (m00 | m11) ;  // true if both are 0
+        int ds1 = m01 & m10;        // true if both are 1
+
+        mask |= (dp0 & ds1) << kRectStaysRect_Shift;
+    } else {
+        // Only test for scale explicitly if not affine, since affine sets the
+        // scale bit.
+        if ((m00 - kScalar1Int) | (m11 - kScalar1Int)) {
+            mask |= kScale_Mask;
+        }
+
+        // Not affine, therefore we already know secondary diagonal is
+        // all zeros, so we just need to check that primary diagonal is
+        // all non-zero.
+
+        // map non-zero to 1
+        m00 = m00 != 0;
+        m11 = m11 != 0;
+
+        // record if the (p)rimary diagonal is all non-zero
+        mask |= (m00 & m11) << kRectStaysRect_Shift;
+    }
+
+    return SkToU8(mask);
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+bool operator==(const SkMatrix& a, const SkMatrix& b) {
+    const SkScalar* SK_RESTRICT ma = a.fMat;
+    const SkScalar* SK_RESTRICT mb = b.fMat;
+
+    return  ma[0] == mb[0] && ma[1] == mb[1] && ma[2] == mb[2] &&
+            ma[3] == mb[3] && ma[4] == mb[4] && ma[5] == mb[5] &&
+            ma[6] == mb[6] && ma[7] == mb[7] && ma[8] == mb[8];
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+// helper function to determine if upper-left 2x2 of matrix is degenerate
+static inline bool is_degenerate_2x2(SkScalar scaleX, SkScalar skewX,
+                                     SkScalar skewY,  SkScalar scaleY) {
+    SkScalar perp_dot = scaleX*scaleY - skewX*skewY;
+    return SkScalarNearlyZero(perp_dot, SK_ScalarNearlyZero*SK_ScalarNearlyZero);
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+bool SkMatrix::isSimilarity(SkScalar tol) const {
+    // if identity or translate matrix
+    TypeMask mask = this->getType();
+    if (mask <= kTranslate_Mask) {
+        return true;
+    }
+    if (mask & kPerspective_Mask) {
+        return false;
+    }
+
+    SkScalar mx = fMat[kMScaleX];
+    SkScalar my = fMat[kMScaleY];
+    // if no skew, can just compare scale factors
+    if (!(mask & kAffine_Mask)) {
+        return !SkScalarNearlyZero(mx) && SkScalarNearlyEqual(SkScalarAbs(mx), SkScalarAbs(my));
+    }
+    SkScalar sx = fMat[kMSkewX];
+    SkScalar sy = fMat[kMSkewY];
+
+    if (is_degenerate_2x2(mx, sx, sy, my)) {
+        return false;
+    }
+
+    // it has scales and skews, but it could also be rotation, check it out.
+    SkVector vec[2];
+    vec[0].set(mx, sx);
+    vec[1].set(sy, my);
+
+    return SkScalarNearlyZero(vec[0].dot(vec[1]), SkScalarSquare(tol)) &&
+           SkScalarNearlyEqual(vec[0].lengthSqd(), vec[1].lengthSqd(),
+                               SkScalarSquare(tol));
+}
+
+bool SkMatrix::preservesRightAngles(SkScalar tol) const {
+    TypeMask mask = this->getType();
+
+    if (mask <= (SkMatrix::kTranslate_Mask | SkMatrix::kScale_Mask)) {
+        // identity, translate and/or scale
+        return true;
+    }
+    if (mask & kPerspective_Mask) {
+        return false;
+    }
+
+    SkASSERT(mask & kAffine_Mask);
+
+    SkScalar mx = fMat[kMScaleX];
+    SkScalar my = fMat[kMScaleY];
+    SkScalar sx = fMat[kMSkewX];
+    SkScalar sy = fMat[kMSkewY];
+
+    if (is_degenerate_2x2(mx, sx, sy, my)) {
+        return false;
+    }
+
+    // it has scales and skews, but it could also be rotation, check it out.
+    SkVector vec[2];
+    vec[0].set(mx, sx);
+    vec[1].set(sy, my);
+
+    return SkScalarNearlyZero(vec[0].dot(vec[1]), SkScalarSquare(tol)) &&
+           SkScalarNearlyEqual(vec[0].lengthSqd(), vec[1].lengthSqd(),
+                               SkScalarSquare(tol));
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+static inline SkScalar sdot(SkScalar a, SkScalar b, SkScalar c, SkScalar d) {
+    return a * b + c * d;
+}
+
+static inline SkScalar sdot(SkScalar a, SkScalar b, SkScalar c, SkScalar d,
+                             SkScalar e, SkScalar f) {
+    return a * b + c * d + e * f;
+}
+
+static inline SkScalar scross(SkScalar a, SkScalar b, SkScalar c, SkScalar d) {
+    return a * b - c * d;
+}
+
+void SkMatrix::setTranslate(SkScalar dx, SkScalar dy) {
+    if (dx || dy) {
+        fMat[kMTransX] = dx;
+        fMat[kMTransY] = dy;
+
+        fMat[kMScaleX] = fMat[kMScaleY] = fMat[kMPersp2] = 1;
+        fMat[kMSkewX]  = fMat[kMSkewY] =
+        fMat[kMPersp0] = fMat[kMPersp1] = 0;
+
+        this->setTypeMask(kTranslate_Mask | kRectStaysRect_Mask);
+    } else {
+        this->reset();
+    }
+}
+
+bool SkMatrix::preTranslate(SkScalar dx, SkScalar dy) {
+    if (this->hasPerspective()) {
+        SkMatrix    m;
+        m.setTranslate(dx, dy);
+        return this->preConcat(m);
+    }
+
+    if (dx || dy) {
+        fMat[kMTransX] += sdot(fMat[kMScaleX], dx, fMat[kMSkewX], dy);
+        fMat[kMTransY] += sdot(fMat[kMSkewY], dx, fMat[kMScaleY], dy);
+
+        this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask);
+    }
+    return true;
+}
+
+bool SkMatrix::postTranslate(SkScalar dx, SkScalar dy) {
+    if (this->hasPerspective()) {
+        SkMatrix    m;
+        m.setTranslate(dx, dy);
+        return this->postConcat(m);
+    }
+
+    if (dx || dy) {
+        fMat[kMTransX] += dx;
+        fMat[kMTransY] += dy;
+        this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask);
+    }
+    return true;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+void SkMatrix::setScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) {
+    if (1 == sx && 1 == sy) {
+        this->reset();
+    } else {
+        fMat[kMScaleX] = sx;
+        fMat[kMScaleY] = sy;
+        fMat[kMTransX] = px - sx * px;
+        fMat[kMTransY] = py - sy * py;
+        fMat[kMPersp2] = 1;
+
+        fMat[kMSkewX]  = fMat[kMSkewY] =
+        fMat[kMPersp0] = fMat[kMPersp1] = 0;
+
+        this->setTypeMask(kScale_Mask | kTranslate_Mask | kRectStaysRect_Mask);
+    }
+}
+
+void SkMatrix::setScale(SkScalar sx, SkScalar sy) {
+    if (1 == sx && 1 == sy) {
+        this->reset();
+    } else {
+        fMat[kMScaleX] = sx;
+        fMat[kMScaleY] = sy;
+        fMat[kMPersp2] = 1;
+
+        fMat[kMTransX] = fMat[kMTransY] =
+        fMat[kMSkewX]  = fMat[kMSkewY] =
+        fMat[kMPersp0] = fMat[kMPersp1] = 0;
+
+        this->setTypeMask(kScale_Mask | kRectStaysRect_Mask);
+    }
+}
+
+bool SkMatrix::setIDiv(int divx, int divy) {
+    if (!divx || !divy) {
+        return false;
+    }
+    this->setScale(SkScalarInvert(divx), SkScalarInvert(divy));
+    return true;
+}
+
+bool SkMatrix::preScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) {
+    SkMatrix    m;
+    m.setScale(sx, sy, px, py);
+    return this->preConcat(m);
+}
+
+bool SkMatrix::preScale(SkScalar sx, SkScalar sy) {
+    if (1 == sx && 1 == sy) {
+        return true;
+    }
+
+    // the assumption is that these multiplies are very cheap, and that
+    // a full concat and/or just computing the matrix type is more expensive.
+    // Also, the fixed-point case checks for overflow, but the float doesn't,
+    // so we can get away with these blind multiplies.
+
+    fMat[kMScaleX] *= sx;
+    fMat[kMSkewY]  *= sx;
+    fMat[kMPersp0] *= sx;
+
+    fMat[kMSkewX]  *= sy;
+    fMat[kMScaleY] *= sy;
+    fMat[kMPersp1] *= sy;
+
+    this->orTypeMask(kScale_Mask);
+    return true;
+}
+
+bool SkMatrix::postScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) {
+    if (1 == sx && 1 == sy) {
+        return true;
+    }
+    SkMatrix    m;
+    m.setScale(sx, sy, px, py);
+    return this->postConcat(m);
+}
+
+bool SkMatrix::postScale(SkScalar sx, SkScalar sy) {
+    if (1 == sx && 1 == sy) {
+        return true;
+    }
+    SkMatrix    m;
+    m.setScale(sx, sy);
+    return this->postConcat(m);
+}
+
+// this guy perhaps can go away, if we have a fract/high-precision way to
+// scale matrices
+bool SkMatrix::postIDiv(int divx, int divy) {
+    if (divx == 0 || divy == 0) {
+        return false;
+    }
+
+    const float invX = 1.f / divx;
+    const float invY = 1.f / divy;
+
+    fMat[kMScaleX] *= invX;
+    fMat[kMSkewX]  *= invX;
+    fMat[kMTransX] *= invX;
+
+    fMat[kMScaleY] *= invY;
+    fMat[kMSkewY]  *= invY;
+    fMat[kMTransY] *= invY;
+
+    this->setTypeMask(kUnknown_Mask);
+    return true;
+}
+
+////////////////////////////////////////////////////////////////////////////////////
+
+void SkMatrix::setSinCos(SkScalar sinV, SkScalar cosV,
+                         SkScalar px, SkScalar py) {
+    const SkScalar oneMinusCosV = 1 - cosV;
+
+    fMat[kMScaleX]  = cosV;
+    fMat[kMSkewX]   = -sinV;
+    fMat[kMTransX]  = sdot(sinV, py, oneMinusCosV, px);
+
+    fMat[kMSkewY]   = sinV;
+    fMat[kMScaleY]  = cosV;
+    fMat[kMTransY]  = sdot(-sinV, px, oneMinusCosV, py);
+
+    fMat[kMPersp0] = fMat[kMPersp1] = 0;
+    fMat[kMPersp2] = 1;
+
+    this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask);
+}
+
+void SkMatrix::setSinCos(SkScalar sinV, SkScalar cosV) {
+    fMat[kMScaleX]  = cosV;
+    fMat[kMSkewX]   = -sinV;
+    fMat[kMTransX]  = 0;
+
+    fMat[kMSkewY]   = sinV;
+    fMat[kMScaleY]  = cosV;
+    fMat[kMTransY]  = 0;
+
+    fMat[kMPersp0] = fMat[kMPersp1] = 0;
+    fMat[kMPersp2] = 1;
+
+    this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask);
+}
+
+void SkMatrix::setRotate(SkScalar degrees, SkScalar px, SkScalar py) {
+    SkScalar sinV, cosV;
+    sinV = SkScalarSinCos(SkDegreesToRadians(degrees), &cosV);
+    this->setSinCos(sinV, cosV, px, py);
+}
+
+void SkMatrix::setRotate(SkScalar degrees) {
+    SkScalar sinV, cosV;
+    sinV = SkScalarSinCos(SkDegreesToRadians(degrees), &cosV);
+    this->setSinCos(sinV, cosV);
+}
+
+bool SkMatrix::preRotate(SkScalar degrees, SkScalar px, SkScalar py) {
+    SkMatrix    m;
+    m.setRotate(degrees, px, py);
+    return this->preConcat(m);
+}
+
+bool SkMatrix::preRotate(SkScalar degrees) {
+    SkMatrix    m;
+    m.setRotate(degrees);
+    return this->preConcat(m);
+}
+
+bool SkMatrix::postRotate(SkScalar degrees, SkScalar px, SkScalar py) {
+    SkMatrix    m;
+    m.setRotate(degrees, px, py);
+    return this->postConcat(m);
+}
+
+bool SkMatrix::postRotate(SkScalar degrees) {
+    SkMatrix    m;
+    m.setRotate(degrees);
+    return this->postConcat(m);
+}
+
+////////////////////////////////////////////////////////////////////////////////////
+
+void SkMatrix::setSkew(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) {
+    fMat[kMScaleX]  = 1;
+    fMat[kMSkewX]   = sx;
+    fMat[kMTransX]  = -sx * py;
+
+    fMat[kMSkewY]   = sy;
+    fMat[kMScaleY]  = 1;
+    fMat[kMTransY]  = -sy * px;
+
+    fMat[kMPersp0] = fMat[kMPersp1] = 0;
+    fMat[kMPersp2] = 1;
+
+    this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask);
+}
+
+void SkMatrix::setSkew(SkScalar sx, SkScalar sy) {
+    fMat[kMScaleX]  = 1;
+    fMat[kMSkewX]   = sx;
+    fMat[kMTransX]  = 0;
+
+    fMat[kMSkewY]   = sy;
+    fMat[kMScaleY]  = 1;
+    fMat[kMTransY]  = 0;
+
+    fMat[kMPersp0] = fMat[kMPersp1] = 0;
+    fMat[kMPersp2] = 1;
+
+    this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask);
+}
+
+bool SkMatrix::preSkew(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) {
+    SkMatrix    m;
+    m.setSkew(sx, sy, px, py);
+    return this->preConcat(m);
+}
+
+bool SkMatrix::preSkew(SkScalar sx, SkScalar sy) {
+    SkMatrix    m;
+    m.setSkew(sx, sy);
+    return this->preConcat(m);
+}
+
+bool SkMatrix::postSkew(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) {
+    SkMatrix    m;
+    m.setSkew(sx, sy, px, py);
+    return this->postConcat(m);
+}
+
+bool SkMatrix::postSkew(SkScalar sx, SkScalar sy) {
+    SkMatrix    m;
+    m.setSkew(sx, sy);
+    return this->postConcat(m);
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+bool SkMatrix::setRectToRect(const SkRect& src, const SkRect& dst,
+                             ScaleToFit align)
+{
+    if (src.isEmpty()) {
+        this->reset();
+        return false;
+    }
+
+    if (dst.isEmpty()) {
+        sk_bzero(fMat, 8 * sizeof(SkScalar));
+        this->setTypeMask(kScale_Mask | kRectStaysRect_Mask);
+    } else {
+        SkScalar    tx, sx = dst.width() / src.width();
+        SkScalar    ty, sy = dst.height() / src.height();
+        bool        xLarger = false;
+
+        if (align != kFill_ScaleToFit) {
+            if (sx > sy) {
+                xLarger = true;
+                sx = sy;
+            } else {
+                sy = sx;
+            }
+        }
+
+        tx = dst.fLeft - src.fLeft * sx;
+        ty = dst.fTop - src.fTop * sy;
+        if (align == kCenter_ScaleToFit || align == kEnd_ScaleToFit) {
+            SkScalar diff;
+
+            if (xLarger) {
+                diff = dst.width() - src.width() * sy;
+            } else {
+                diff = dst.height() - src.height() * sy;
+            }
+
+            if (align == kCenter_ScaleToFit) {
+                diff = SkScalarHalf(diff);
+            }
+
+            if (xLarger) {
+                tx += diff;
+            } else {
+                ty += diff;
+            }
+        }
+
+        fMat[kMScaleX] = sx;
+        fMat[kMScaleY] = sy;
+        fMat[kMTransX] = tx;
+        fMat[kMTransY] = ty;
+        fMat[kMSkewX]  = fMat[kMSkewY] =
+        fMat[kMPersp0] = fMat[kMPersp1] = 0;
+
+        unsigned mask = kRectStaysRect_Mask;
+        if (sx != 1 || sy != 1) {
+            mask |= kScale_Mask;
+        }
+        if (tx || ty) {
+            mask |= kTranslate_Mask;
+        }
+        this->setTypeMask(mask);
+    }
+    // shared cleanup
+    fMat[kMPersp2] = 1;
+    return true;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+static inline int fixmuladdmul(float a, float b, float c, float d,
+                               float* result) {
+    *result = SkDoubleToFloat((double)a * b + (double)c * d);
+    return true;
+}
+
+static inline bool rowcol3(const float row[], const float col[],
+                           float* result) {
+    *result = row[0] * col[0] + row[1] * col[3] + row[2] * col[6];
+    return true;
+}
+
+static inline int negifaddoverflows(float& result, float a, float b) {
+    result = a + b;
+    return 0;
+}
+
+static void normalize_perspective(SkScalar mat[9]) {
+    if (SkScalarAbs(mat[SkMatrix::kMPersp2]) > 1) {
+        for (int i = 0; i < 9; i++)
+            mat[i] = SkScalarHalf(mat[i]);
+    }
+}
+
+bool SkMatrix::setConcat(const SkMatrix& a, const SkMatrix& b) {
+    TypeMask aType = a.getPerspectiveTypeMaskOnly();
+    TypeMask bType = b.getPerspectiveTypeMaskOnly();
+
+    if (a.isTriviallyIdentity()) {
+        *this = b;
+    } else if (b.isTriviallyIdentity()) {
+        *this = a;
+    } else {
+        SkMatrix tmp;
+
+        if ((aType | bType) & kPerspective_Mask) {
+            if (!rowcol3(&a.fMat[0], &b.fMat[0], &tmp.fMat[kMScaleX])) {
+                return false;
+            }
+            if (!rowcol3(&a.fMat[0], &b.fMat[1], &tmp.fMat[kMSkewX])) {
+                return false;
+            }
+            if (!rowcol3(&a.fMat[0], &b.fMat[2], &tmp.fMat[kMTransX])) {
+                return false;
+            }
+
+            if (!rowcol3(&a.fMat[3], &b.fMat[0], &tmp.fMat[kMSkewY])) {
+                return false;
+            }
+            if (!rowcol3(&a.fMat[3], &b.fMat[1], &tmp.fMat[kMScaleY])) {
+                return false;
+            }
+            if (!rowcol3(&a.fMat[3], &b.fMat[2], &tmp.fMat[kMTransY])) {
+                return false;
+            }
+
+            if (!rowcol3(&a.fMat[6], &b.fMat[0], &tmp.fMat[kMPersp0])) {
+                return false;
+            }
+            if (!rowcol3(&a.fMat[6], &b.fMat[1], &tmp.fMat[kMPersp1])) {
+                return false;
+            }
+            if (!rowcol3(&a.fMat[6], &b.fMat[2], &tmp.fMat[kMPersp2])) {
+                return false;
+            }
+
+            normalize_perspective(tmp.fMat);
+            tmp.setTypeMask(kUnknown_Mask);
+        } else {    // not perspective
+            if (!fixmuladdmul(a.fMat[kMScaleX], b.fMat[kMScaleX],
+                    a.fMat[kMSkewX], b.fMat[kMSkewY], &tmp.fMat[kMScaleX])) {
+                return false;
+            }
+            if (!fixmuladdmul(a.fMat[kMScaleX], b.fMat[kMSkewX],
+                      a.fMat[kMSkewX], b.fMat[kMScaleY], &tmp.fMat[kMSkewX])) {
+                return false;
+            }
+            if (!fixmuladdmul(a.fMat[kMScaleX], b.fMat[kMTransX],
+                      a.fMat[kMSkewX], b.fMat[kMTransY], &tmp.fMat[kMTransX])) {
+                return false;
+            }
+            if (negifaddoverflows(tmp.fMat[kMTransX], tmp.fMat[kMTransX],
+                                  a.fMat[kMTransX]) < 0) {
+                return false;
+            }
+
+            if (!fixmuladdmul(a.fMat[kMSkewY], b.fMat[kMScaleX],
+                      a.fMat[kMScaleY], b.fMat[kMSkewY], &tmp.fMat[kMSkewY])) {
+                return false;
+            }
+            if (!fixmuladdmul(a.fMat[kMSkewY], b.fMat[kMSkewX],
+                    a.fMat[kMScaleY], b.fMat[kMScaleY], &tmp.fMat[kMScaleY])) {
+                return false;
+            }
+            if (!fixmuladdmul(a.fMat[kMSkewY], b.fMat[kMTransX],
+                     a.fMat[kMScaleY], b.fMat[kMTransY], &tmp.fMat[kMTransY])) {
+                return false;
+            }
+            if (negifaddoverflows(tmp.fMat[kMTransY], tmp.fMat[kMTransY],
+                                  a.fMat[kMTransY]) < 0) {
+                return false;
+            }
+
+            tmp.fMat[kMPersp0] = tmp.fMat[kMPersp1] = 0;
+            tmp.fMat[kMPersp2] = 1;
+            //SkDebugf("Concat mat non-persp type: %d\n", tmp.getType());
+            //SkASSERT(!(tmp.getType() & kPerspective_Mask));
+            tmp.setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask);
+        }
+        *this = tmp;
+    }
+    return true;
+}
+
+bool SkMatrix::preConcat(const SkMatrix& mat) {
+    // check for identity first, so we don't do a needless copy of ourselves
+    // to ourselves inside setConcat()
+    return mat.isIdentity() || this->setConcat(*this, mat);
+}
+
+bool SkMatrix::postConcat(const SkMatrix& mat) {
+    // check for identity first, so we don't do a needless copy of ourselves
+    // to ourselves inside setConcat()
+    return mat.isIdentity() || this->setConcat(mat, *this);
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+/*  Matrix inversion is very expensive, but also the place where keeping
+    precision may be most important (here and matrix concat). Hence to avoid
+    bitmap blitting artifacts when walking the inverse, we use doubles for
+    the intermediate math, even though we know that is more expensive.
+ */
+
+static inline SkScalar scross_dscale(SkScalar a, SkScalar b,
+                                     SkScalar c, SkScalar d, double scale) {
+    return SkDoubleToScalar(scross(a, b, c, d) * scale);
+}
+
+static inline double dcross(double a, double b, double c, double d) {
+    return a * b - c * d;
+}
+
+static inline SkScalar dcross_dscale(double a, double b,
+                                     double c, double d, double scale) {
+    return SkDoubleToScalar(dcross(a, b, c, d) * scale);
+}
+
+static double sk_inv_determinant(const float mat[9], int isPerspective) {
+    double det;
+
+    if (isPerspective) {
+        det = mat[SkMatrix::kMScaleX] *
+              dcross(mat[SkMatrix::kMScaleY], mat[SkMatrix::kMPersp2],
+                     mat[SkMatrix::kMTransY], mat[SkMatrix::kMPersp1])
+              +
+              mat[SkMatrix::kMSkewX]  *
+              dcross(mat[SkMatrix::kMTransY], mat[SkMatrix::kMPersp0],
+                     mat[SkMatrix::kMSkewY],  mat[SkMatrix::kMPersp2])
+              +
+              mat[SkMatrix::kMTransX] *
+              dcross(mat[SkMatrix::kMSkewY],  mat[SkMatrix::kMPersp1],
+                     mat[SkMatrix::kMScaleY], mat[SkMatrix::kMPersp0]);
+    } else {
+        det = dcross(mat[SkMatrix::kMScaleX], mat[SkMatrix::kMScaleY],
+                     mat[SkMatrix::kMSkewX], mat[SkMatrix::kMSkewY]);
+    }
+
+    // Since the determinant is on the order of the cube of the matrix members,
+    // compare to the cube of the default nearly-zero constant (although an
+    // estimate of the condition number would be better if it wasn't so expensive).
+    if (SkScalarNearlyZero((float)det, SK_ScalarNearlyZero * SK_ScalarNearlyZero * SK_ScalarNearlyZero)) {
+        return 0;
+    }
+    return 1.0 / det;
+}
+
+void SkMatrix::SetAffineIdentity(SkScalar affine[6]) {
+    affine[kAScaleX] = 1;
+    affine[kASkewY] = 0;
+    affine[kASkewX] = 0;
+    affine[kAScaleY] = 1;
+    affine[kATransX] = 0;
+    affine[kATransY] = 0;
+}
+
+bool SkMatrix::asAffine(SkScalar affine[6]) const {
+    if (this->hasPerspective()) {
+        return false;
+    }
+    if (affine) {
+        affine[kAScaleX] = this->fMat[kMScaleX];
+        affine[kASkewY] = this->fMat[kMSkewY];
+        affine[kASkewX] = this->fMat[kMSkewX];
+        affine[kAScaleY] = this->fMat[kMScaleY];
+        affine[kATransX] = this->fMat[kMTransX];
+        affine[kATransY] = this->fMat[kMTransY];
+    }
+    return true;
+}
+
+bool SkMatrix::invertNonIdentity(SkMatrix* inv) const {
+    SkASSERT(!this->isIdentity());
+
+    TypeMask mask = this->getType();
+
+    if (0 == (mask & ~(kScale_Mask | kTranslate_Mask))) {
+        bool invertible = true;
+        if (inv) {
+            if (mask & kScale_Mask) {
+                SkScalar invX = fMat[kMScaleX];
+                SkScalar invY = fMat[kMScaleY];
+                if (0 == invX || 0 == invY) {
+                    return false;
+                }
+                invX = SkScalarInvert(invX);
+                invY = SkScalarInvert(invY);
+
+                // Must be careful when writing to inv, since it may be the
+                // same memory as this.
+
+                inv->fMat[kMSkewX] = inv->fMat[kMSkewY] =
+                inv->fMat[kMPersp0] = inv->fMat[kMPersp1] = 0;
+
+                inv->fMat[kMScaleX] = invX;
+                inv->fMat[kMScaleY] = invY;
+                inv->fMat[kMPersp2] = 1;
+                inv->fMat[kMTransX] = -fMat[kMTransX] * invX;
+                inv->fMat[kMTransY] = -fMat[kMTransY] * invY;
+
+                inv->setTypeMask(mask | kRectStaysRect_Mask);
+            } else {
+                // translate only
+                inv->setTranslate(-fMat[kMTransX], -fMat[kMTransY]);
+            }
+        } else {    // inv is NULL, just check if we're invertible
+            if (!fMat[kMScaleX] || !fMat[kMScaleY]) {
+                invertible = false;
+            }
+        }
+        return invertible;
+    }
+
+    int    isPersp = mask & kPerspective_Mask;
+    double scale = sk_inv_determinant(fMat, isPersp);
+
+    if (scale == 0) { // underflow
+        return false;
+    }
+
+    if (inv) {
+        SkMatrix tmp;
+        if (inv == this) {
+            inv = &tmp;
+        }
+
+        if (isPersp) {
+            inv->fMat[kMScaleX] = scross_dscale(fMat[kMScaleY], fMat[kMPersp2], fMat[kMTransY], fMat[kMPersp1], scale);
+            inv->fMat[kMSkewX]  = scross_dscale(fMat[kMTransX], fMat[kMPersp1], fMat[kMSkewX],  fMat[kMPersp2], scale);
+            inv->fMat[kMTransX] = scross_dscale(fMat[kMSkewX],  fMat[kMTransY], fMat[kMTransX], fMat[kMScaleY], scale);
+
+            inv->fMat[kMSkewY]  = scross_dscale(fMat[kMTransY], fMat[kMPersp0], fMat[kMSkewY],  fMat[kMPersp2], scale);
+            inv->fMat[kMScaleY] = scross_dscale(fMat[kMScaleX], fMat[kMPersp2], fMat[kMTransX], fMat[kMPersp0], scale);
+            inv->fMat[kMTransY] = scross_dscale(fMat[kMTransX], fMat[kMSkewY],  fMat[kMScaleX], fMat[kMTransY], scale);
+
+            inv->fMat[kMPersp0] = scross_dscale(fMat[kMSkewY],  fMat[kMPersp1], fMat[kMScaleY], fMat[kMPersp0], scale);
+            inv->fMat[kMPersp1] = scross_dscale(fMat[kMSkewX],  fMat[kMPersp0], fMat[kMScaleX], fMat[kMPersp1], scale);
+            inv->fMat[kMPersp2] = scross_dscale(fMat[kMScaleX], fMat[kMScaleY], fMat[kMSkewX],  fMat[kMSkewY],  scale);
+        } else {   // not perspective
+            inv->fMat[kMScaleX] = SkDoubleToScalar(fMat[kMScaleY] * scale);
+            inv->fMat[kMSkewX]  = SkDoubleToScalar(-fMat[kMSkewX] * scale);
+            inv->fMat[kMTransX] = dcross_dscale(fMat[kMSkewX], fMat[kMTransY], fMat[kMScaleY], fMat[kMTransX], scale);
+
+            inv->fMat[kMSkewY]  = SkDoubleToScalar(-fMat[kMSkewY] * scale);
+            inv->fMat[kMScaleY] = SkDoubleToScalar(fMat[kMScaleX] * scale);
+            inv->fMat[kMTransY] = dcross_dscale(fMat[kMSkewY], fMat[kMTransX], fMat[kMScaleX], fMat[kMTransY], scale);
+
+            inv->fMat[kMPersp0] = 0;
+            inv->fMat[kMPersp1] = 0;
+            inv->fMat[kMPersp2] = 1;
+        }
+
+        inv->setTypeMask(fTypeMask);
+
+        if (inv == &tmp) {
+            *(SkMatrix*)this = tmp;
+        }
+    }
+    return true;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+void SkMatrix::Identity_pts(const SkMatrix& m, SkPoint dst[],
+                            const SkPoint src[], int count) {
+    SkASSERT(m.getType() == 0);
+
+    if (dst != src && count > 0)
+        memcpy(dst, src, count * sizeof(SkPoint));
+}
+
+void SkMatrix::Trans_pts(const SkMatrix& m, SkPoint dst[],
+                         const SkPoint src[], int count) {
+    SkASSERT(m.getType() == kTranslate_Mask);
+
+    if (count > 0) {
+        SkScalar tx = m.fMat[kMTransX];
+        SkScalar ty = m.fMat[kMTransY];
+        do {
+            dst->fY = src->fY + ty;
+            dst->fX = src->fX + tx;
+            src += 1;
+            dst += 1;
+        } while (--count);
+    }
+}
+
+void SkMatrix::Scale_pts(const SkMatrix& m, SkPoint dst[],
+                         const SkPoint src[], int count) {
+    SkASSERT(m.getType() == kScale_Mask);
+
+    if (count > 0) {
+        SkScalar mx = m.fMat[kMScaleX];
+        SkScalar my = m.fMat[kMScaleY];
+        do {
+            dst->fY = src->fY * my;
+            dst->fX = src->fX * mx;
+            src += 1;
+            dst += 1;
+        } while (--count);
+    }
+}
+
+void SkMatrix::ScaleTrans_pts(const SkMatrix& m, SkPoint dst[],
+                              const SkPoint src[], int count) {
+    SkASSERT(m.getType() == (kScale_Mask | kTranslate_Mask));
+
+    if (count > 0) {
+        SkScalar mx = m.fMat[kMScaleX];
+        SkScalar my = m.fMat[kMScaleY];
+        SkScalar tx = m.fMat[kMTransX];
+        SkScalar ty = m.fMat[kMTransY];
+        do {
+            dst->fY = src->fY * my + ty;
+            dst->fX = src->fX * mx + tx;
+            src += 1;
+            dst += 1;
+        } while (--count);
+    }
+}
+
+void SkMatrix::Rot_pts(const SkMatrix& m, SkPoint dst[],
+                       const SkPoint src[], int count) {
+    SkASSERT((m.getType() & (kPerspective_Mask | kTranslate_Mask)) == 0);
+
+    if (count > 0) {
+        SkScalar mx = m.fMat[kMScaleX];
+        SkScalar my = m.fMat[kMScaleY];
+        SkScalar kx = m.fMat[kMSkewX];
+        SkScalar ky = m.fMat[kMSkewY];
+        do {
+            SkScalar sy = src->fY;
+            SkScalar sx = src->fX;
+            src += 1;
+            dst->fY = sdot(sx, ky, sy, my);
+            dst->fX = sdot(sx, mx, sy, kx);
+            dst += 1;
+        } while (--count);
+    }
+}
+
+void SkMatrix::RotTrans_pts(const SkMatrix& m, SkPoint dst[],
+                            const SkPoint src[], int count) {
+    SkASSERT(!m.hasPerspective());
+
+    if (count > 0) {
+        SkScalar mx = m.fMat[kMScaleX];
+        SkScalar my = m.fMat[kMScaleY];
+        SkScalar kx = m.fMat[kMSkewX];
+        SkScalar ky = m.fMat[kMSkewY];
+        SkScalar tx = m.fMat[kMTransX];
+        SkScalar ty = m.fMat[kMTransY];
+        do {
+            SkScalar sy = src->fY;
+            SkScalar sx = src->fX;
+            src += 1;
+#ifdef SK_LEGACY_MATRIX_MATH_ORDER
+            dst->fY = sx * ky + (sy * my + ty);
+            dst->fX = sx * mx + (sy * kx + tx);
+#else
+            dst->fY = sdot(sx, ky, sy, my) + ty;
+            dst->fX = sdot(sx, mx, sy, kx) + tx;
+#endif
+            dst += 1;
+        } while (--count);
+    }
+}
+
+void SkMatrix::Persp_pts(const SkMatrix& m, SkPoint dst[],
+                         const SkPoint src[], int count) {
+    SkASSERT(m.hasPerspective());
+
+    if (count > 0) {
+        do {
+            SkScalar sy = src->fY;
+            SkScalar sx = src->fX;
+            src += 1;
+
+            SkScalar x = sdot(sx, m.fMat[kMScaleX], sy, m.fMat[kMSkewX])  + m.fMat[kMTransX];
+            SkScalar y = sdot(sx, m.fMat[kMSkewY],  sy, m.fMat[kMScaleY]) + m.fMat[kMTransY];
+#ifdef SK_LEGACY_MATRIX_MATH_ORDER
+            SkScalar z = sx * m.fMat[kMPersp0] + (sy * m.fMat[kMPersp1] + m.fMat[kMPersp2]);
+#else
+            SkScalar z = sdot(sx, m.fMat[kMPersp0], sy, m.fMat[kMPersp1]) + m.fMat[kMPersp2];
+#endif
+            if (z) {
+                z = SkScalarFastInvert(z);
+            }
+
+            dst->fY = y * z;
+            dst->fX = x * z;
+            dst += 1;
+        } while (--count);
+    }
+}
+
+const SkMatrix::MapPtsProc SkMatrix::gMapPtsProcs[] = {
+    SkMatrix::Identity_pts, SkMatrix::Trans_pts,
+    SkMatrix::Scale_pts,    SkMatrix::ScaleTrans_pts,
+    SkMatrix::Rot_pts,      SkMatrix::RotTrans_pts,
+    SkMatrix::Rot_pts,      SkMatrix::RotTrans_pts,
+    // repeat the persp proc 8 times
+    SkMatrix::Persp_pts,    SkMatrix::Persp_pts,
+    SkMatrix::Persp_pts,    SkMatrix::Persp_pts,
+    SkMatrix::Persp_pts,    SkMatrix::Persp_pts,
+    SkMatrix::Persp_pts,    SkMatrix::Persp_pts
+};
+
+void SkMatrix::mapPoints(SkPoint dst[], const SkPoint src[], int count) const {
+    SkASSERT((dst && src && count > 0) || 0 == count);
+    // no partial overlap
+    SkASSERT(src == dst || &dst[count] <= &src[0] || &src[count] <= &dst[0]);
+
+    this->getMapPtsProc()(*this, dst, src, count);
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+void SkMatrix::mapHomogeneousPoints(SkScalar dst[], const SkScalar src[], int count) const {
+    SkASSERT((dst && src && count > 0) || 0 == count);
+    // no partial overlap
+    SkASSERT(src == dst || SkAbs32((int32_t)(src - dst)) >= 3*count);
+
+    if (count > 0) {
+        if (this->isIdentity()) {
+            memcpy(dst, src, 3*count*sizeof(SkScalar));
+            return;
+        }
+        do {
+            SkScalar sx = src[0];
+            SkScalar sy = src[1];
+            SkScalar sw = src[2];
+            src += 3;
+
+            SkScalar x = sdot(sx, fMat[kMScaleX], sy, fMat[kMSkewX],  sw, fMat[kMTransX]);
+            SkScalar y = sdot(sx, fMat[kMSkewY],  sy, fMat[kMScaleY], sw, fMat[kMTransY]);
+            SkScalar w = sdot(sx, fMat[kMPersp0], sy, fMat[kMPersp1], sw, fMat[kMPersp2]);
+
+            dst[0] = x;
+            dst[1] = y;
+            dst[2] = w;
+            dst += 3;
+        } while (--count);
+    }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+void SkMatrix::mapVectors(SkPoint dst[], const SkPoint src[], int count) const {
+    if (this->hasPerspective()) {
+        SkPoint origin;
+
+        MapXYProc proc = this->getMapXYProc();
+        proc(*this, 0, 0, &origin);
+
+        for (int i = count - 1; i >= 0; --i) {
+            SkPoint tmp;
+
+            proc(*this, src[i].fX, src[i].fY, &tmp);
+            dst[i].set(tmp.fX - origin.fX, tmp.fY - origin.fY);
+        }
+    } else {
+        SkMatrix tmp = *this;
+
+        tmp.fMat[kMTransX] = tmp.fMat[kMTransY] = 0;
+        tmp.clearTypeMask(kTranslate_Mask);
+        tmp.mapPoints(dst, src, count);
+    }
+}
+
+bool SkMatrix::mapRect(SkRect* dst, const SkRect& src) const {
+    SkASSERT(dst && &src);
+
+    if (this->rectStaysRect()) {
+        this->mapPoints((SkPoint*)dst, (const SkPoint*)&src, 2);
+        dst->sort();
+        return true;
+    } else {
+        SkPoint quad[4];
+
+        src.toQuad(quad);
+        this->mapPoints(quad, quad, 4);
+        dst->set(quad, 4);
+        return false;
+    }
+}
+
+SkScalar SkMatrix::mapRadius(SkScalar radius) const {
+    SkVector    vec[2];
+
+    vec[0].set(radius, 0);
+    vec[1].set(0, radius);
+    this->mapVectors(vec, 2);
+
+    SkScalar d0 = vec[0].length();
+    SkScalar d1 = vec[1].length();
+
+    // return geometric mean
+    return SkScalarSqrt(d0 * d1);
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+void SkMatrix::Persp_xy(const SkMatrix& m, SkScalar sx, SkScalar sy,
+                        SkPoint* pt) {
+    SkASSERT(m.hasPerspective());
+
+    SkScalar x = sdot(sx, m.fMat[kMScaleX], sy, m.fMat[kMSkewX])  + m.fMat[kMTransX];
+    SkScalar y = sdot(sx, m.fMat[kMSkewY],  sy, m.fMat[kMScaleY]) + m.fMat[kMTransY];
+    SkScalar z = sdot(sx, m.fMat[kMPersp0], sy, m.fMat[kMPersp1]) + m.fMat[kMPersp2];
+    if (z) {
+        z = SkScalarFastInvert(z);
+    }
+    pt->fX = x * z;
+    pt->fY = y * z;
+}
+
+void SkMatrix::RotTrans_xy(const SkMatrix& m, SkScalar sx, SkScalar sy,
+                           SkPoint* pt) {
+    SkASSERT((m.getType() & (kAffine_Mask | kPerspective_Mask)) == kAffine_Mask);
+
+#ifdef SK_LEGACY_MATRIX_MATH_ORDER
+    pt->fX = sx * m.fMat[kMScaleX] + (sy * m.fMat[kMSkewX]  +  m.fMat[kMTransX]);
+    pt->fY = sx * m.fMat[kMSkewY]  + (sy * m.fMat[kMScaleY] + m.fMat[kMTransY]);
+#else
+    pt->fX = sdot(sx, m.fMat[kMScaleX], sy, m.fMat[kMSkewX])  + m.fMat[kMTransX];
+    pt->fY = sdot(sx, m.fMat[kMSkewY],  sy, m.fMat[kMScaleY]) + m.fMat[kMTransY];
+#endif
+}
+
+void SkMatrix::Rot_xy(const SkMatrix& m, SkScalar sx, SkScalar sy,
+                      SkPoint* pt) {
+    SkASSERT((m.getType() & (kAffine_Mask | kPerspective_Mask))== kAffine_Mask);
+    SkASSERT(0 == m.fMat[kMTransX]);
+    SkASSERT(0 == m.fMat[kMTransY]);
+
+#ifdef SK_LEGACY_MATRIX_MATH_ORDER
+    pt->fX = sx * m.fMat[kMScaleX] + (sy * m.fMat[kMSkewX]  + m.fMat[kMTransX]);
+    pt->fY = sx * m.fMat[kMSkewY]  + (sy * m.fMat[kMScaleY] + m.fMat[kMTransY]);
+#else
+    pt->fX = sdot(sx, m.fMat[kMScaleX], sy, m.fMat[kMSkewX])  + m.fMat[kMTransX];
+    pt->fY = sdot(sx, m.fMat[kMSkewY],  sy, m.fMat[kMScaleY]) + m.fMat[kMTransY];
+#endif
+}
+
+void SkMatrix::ScaleTrans_xy(const SkMatrix& m, SkScalar sx, SkScalar sy,
+                             SkPoint* pt) {
+    SkASSERT((m.getType() & (kScale_Mask | kAffine_Mask | kPerspective_Mask))
+             == kScale_Mask);
+
+    pt->fX = sx * m.fMat[kMScaleX] + m.fMat[kMTransX];
+    pt->fY = sy * m.fMat[kMScaleY] + m.fMat[kMTransY];
+}
+
+void SkMatrix::Scale_xy(const SkMatrix& m, SkScalar sx, SkScalar sy,
+                        SkPoint* pt) {
+    SkASSERT((m.getType() & (kScale_Mask | kAffine_Mask | kPerspective_Mask))
+             == kScale_Mask);
+    SkASSERT(0 == m.fMat[kMTransX]);
+    SkASSERT(0 == m.fMat[kMTransY]);
+
+    pt->fX = sx * m.fMat[kMScaleX];
+    pt->fY = sy * m.fMat[kMScaleY];
+}
+
+void SkMatrix::Trans_xy(const SkMatrix& m, SkScalar sx, SkScalar sy,
+                        SkPoint* pt) {
+    SkASSERT(m.getType() == kTranslate_Mask);
+
+    pt->fX = sx + m.fMat[kMTransX];
+    pt->fY = sy + m.fMat[kMTransY];
+}
+
+void SkMatrix::Identity_xy(const SkMatrix& m, SkScalar sx, SkScalar sy,
+                           SkPoint* pt) {
+    SkASSERT(0 == m.getType());
+
+    pt->fX = sx;
+    pt->fY = sy;
+}
+
+const SkMatrix::MapXYProc SkMatrix::gMapXYProcs[] = {
+    SkMatrix::Identity_xy, SkMatrix::Trans_xy,
+    SkMatrix::Scale_xy,    SkMatrix::ScaleTrans_xy,
+    SkMatrix::Rot_xy,      SkMatrix::RotTrans_xy,
+    SkMatrix::Rot_xy,      SkMatrix::RotTrans_xy,
+    // repeat the persp proc 8 times
+    SkMatrix::Persp_xy,    SkMatrix::Persp_xy,
+    SkMatrix::Persp_xy,    SkMatrix::Persp_xy,
+    SkMatrix::Persp_xy,    SkMatrix::Persp_xy,
+    SkMatrix::Persp_xy,    SkMatrix::Persp_xy
+};
+
+///////////////////////////////////////////////////////////////////////////////
+
+// if its nearly zero (just made up 26, perhaps it should be bigger or smaller)
+#define PerspNearlyZero(x)  SkScalarNearlyZero(x, (1.0f / (1 << 26)))
+
+bool SkMatrix::fixedStepInX(SkScalar y, SkFixed* stepX, SkFixed* stepY) const {
+    if (PerspNearlyZero(fMat[kMPersp0])) {
+        if (stepX || stepY) {
+            if (PerspNearlyZero(fMat[kMPersp1]) &&
+                    PerspNearlyZero(fMat[kMPersp2] - 1)) {
+                if (stepX) {
+                    *stepX = SkScalarToFixed(fMat[kMScaleX]);
+                }
+                if (stepY) {
+                    *stepY = SkScalarToFixed(fMat[kMSkewY]);
+                }
+            } else {
+                SkScalar z = y * fMat[kMPersp1] + fMat[kMPersp2];
+                if (stepX) {
+                    *stepX = SkScalarToFixed(fMat[kMScaleX] / z);
+                }
+                if (stepY) {
+                    *stepY = SkScalarToFixed(fMat[kMSkewY] / z);
+                }
+            }
+        }
+        return true;
+    }
+    return false;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+#include "SkPerspIter.h"
+
+SkPerspIter::SkPerspIter(const SkMatrix& m, SkScalar x0, SkScalar y0, int count)
+        : fMatrix(m), fSX(x0), fSY(y0), fCount(count) {
+    SkPoint pt;
+
+    SkMatrix::Persp_xy(m, x0, y0, &pt);
+    fX = SkScalarToFixed(pt.fX);
+    fY = SkScalarToFixed(pt.fY);
+}
+
+int SkPerspIter::next() {
+    int n = fCount;
+
+    if (0 == n) {
+        return 0;
+    }
+    SkPoint pt;
+    SkFixed x = fX;
+    SkFixed y = fY;
+    SkFixed dx, dy;
+
+    if (n >= kCount) {
+        n = kCount;
+        fSX += SkIntToScalar(kCount);
+        SkMatrix::Persp_xy(fMatrix, fSX, fSY, &pt);
+        fX = SkScalarToFixed(pt.fX);
+        fY = SkScalarToFixed(pt.fY);
+        dx = (fX - x) >> kShift;
+        dy = (fY - y) >> kShift;
+    } else {
+        fSX += SkIntToScalar(n);
+        SkMatrix::Persp_xy(fMatrix, fSX, fSY, &pt);
+        fX = SkScalarToFixed(pt.fX);
+        fY = SkScalarToFixed(pt.fY);
+        dx = (fX - x) / n;
+        dy = (fY - y) / n;
+    }
+
+    SkFixed* p = fStorage;
+    for (int i = 0; i < n; i++) {
+        *p++ = x; x += dx;
+        *p++ = y; y += dy;
+    }
+
+    fCount -= n;
+    return n;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+static inline bool checkForZero(float x) {
+    return x*x == 0;
+}
+
+static inline bool poly_to_point(SkPoint* pt, const SkPoint poly[], int count) {
+    float   x = 1, y = 1;
+    SkPoint pt1, pt2;
+
+    if (count > 1) {
+        pt1.fX = poly[1].fX - poly[0].fX;
+        pt1.fY = poly[1].fY - poly[0].fY;
+        y = SkPoint::Length(pt1.fX, pt1.fY);
+        if (checkForZero(y)) {
+            return false;
+        }
+        switch (count) {
+            case 2:
+                break;
+            case 3:
+                pt2.fX = poly[0].fY - poly[2].fY;
+                pt2.fY = poly[2].fX - poly[0].fX;
+                goto CALC_X;
+            default:
+                pt2.fX = poly[0].fY - poly[3].fY;
+                pt2.fY = poly[3].fX - poly[0].fX;
+            CALC_X:
+                x = sdot(pt1.fX, pt2.fX, pt1.fY, pt2.fY) / y;
+                break;
+        }
+    }
+    pt->set(x, y);
+    return true;
+}
+
+bool SkMatrix::Poly2Proc(const SkPoint srcPt[], SkMatrix* dst,
+                         const SkPoint& scale) {
+    float invScale = 1 / scale.fY;
+
+    dst->fMat[kMScaleX] = (srcPt[1].fY - srcPt[0].fY) * invScale;
+    dst->fMat[kMSkewY] = (srcPt[0].fX - srcPt[1].fX) * invScale;
+    dst->fMat[kMPersp0] = 0;
+    dst->fMat[kMSkewX] = (srcPt[1].fX - srcPt[0].fX) * invScale;
+    dst->fMat[kMScaleY] = (srcPt[1].fY - srcPt[0].fY) * invScale;
+    dst->fMat[kMPersp1] = 0;
+    dst->fMat[kMTransX] = srcPt[0].fX;
+    dst->fMat[kMTransY] = srcPt[0].fY;
+    dst->fMat[kMPersp2] = 1;
+    dst->setTypeMask(kUnknown_Mask);
+    return true;
+}
+
+bool SkMatrix::Poly3Proc(const SkPoint srcPt[], SkMatrix* dst,
+                         const SkPoint& scale) {
+    float invScale = 1 / scale.fX;
+    dst->fMat[kMScaleX] = (srcPt[2].fX - srcPt[0].fX) * invScale;
+    dst->fMat[kMSkewY] = (srcPt[2].fY - srcPt[0].fY) * invScale;
+    dst->fMat[kMPersp0] = 0;
+
+    invScale = 1 / scale.fY;
+    dst->fMat[kMSkewX] = (srcPt[1].fX - srcPt[0].fX) * invScale;
+    dst->fMat[kMScaleY] = (srcPt[1].fY - srcPt[0].fY) * invScale;
+    dst->fMat[kMPersp1] = 0;
+
+    dst->fMat[kMTransX] = srcPt[0].fX;
+    dst->fMat[kMTransY] = srcPt[0].fY;
+    dst->fMat[kMPersp2] = 1;
+    dst->setTypeMask(kUnknown_Mask);
+    return true;
+}
+
+bool SkMatrix::Poly4Proc(const SkPoint srcPt[], SkMatrix* dst,
+                         const SkPoint& scale) {
+    float   a1, a2;
+    float   x0, y0, x1, y1, x2, y2;
+
+    x0 = srcPt[2].fX - srcPt[0].fX;
+    y0 = srcPt[2].fY - srcPt[0].fY;
+    x1 = srcPt[2].fX - srcPt[1].fX;
+    y1 = srcPt[2].fY - srcPt[1].fY;
+    x2 = srcPt[2].fX - srcPt[3].fX;
+    y2 = srcPt[2].fY - srcPt[3].fY;
+
+    /* check if abs(x2) > abs(y2) */
+    if ( x2 > 0 ? y2 > 0 ? x2 > y2 : x2 > -y2 : y2 > 0 ? -x2 > y2 : x2 < y2) {
+        float denom = SkScalarMulDiv(x1, y2, x2) - y1;
+        if (checkForZero(denom)) {
+            return false;
+        }
+        a1 = (SkScalarMulDiv(x0 - x1, y2, x2) - y0 + y1) / denom;
+    } else {
+        float denom = x1 - SkScalarMulDiv(y1, x2, y2);
+        if (checkForZero(denom)) {
+            return false;
+        }
+        a1 = (x0 - x1 - SkScalarMulDiv(y0 - y1, x2, y2)) / denom;
+    }
+
+    /* check if abs(x1) > abs(y1) */
+    if ( x1 > 0 ? y1 > 0 ? x1 > y1 : x1 > -y1 : y1 > 0 ? -x1 > y1 : x1 < y1) {
+        float denom = y2 - SkScalarMulDiv(x2, y1, x1);
+        if (checkForZero(denom)) {
+            return false;
+        }
+        a2 = (y0 - y2 - SkScalarMulDiv(x0 - x2, y1, x1)) / denom;
+    } else {
+        float denom = SkScalarMulDiv(y2, x1, y1) - x2;
+        if (checkForZero(denom)) {
+            return false;
+        }
+        a2 = (SkScalarMulDiv(y0 - y2, x1, y1) - x0 + x2) / denom;
+    }
+
+    float invScale = SkScalarInvert(scale.fX);
+    dst->fMat[kMScaleX] = (a2 * srcPt[3].fX + srcPt[3].fX - srcPt[0].fX) * invScale;
+    dst->fMat[kMSkewY]  = (a2 * srcPt[3].fY + srcPt[3].fY - srcPt[0].fY) * invScale;
+    dst->fMat[kMPersp0] = a2 * invScale;
+
+    invScale = SkScalarInvert(scale.fY);
+    dst->fMat[kMSkewX]  = (a1 * srcPt[1].fX + srcPt[1].fX - srcPt[0].fX) * invScale;
+    dst->fMat[kMScaleY] = (a1 * srcPt[1].fY + srcPt[1].fY - srcPt[0].fY) * invScale;
+    dst->fMat[kMPersp1] = a1 * invScale;
+
+    dst->fMat[kMTransX] = srcPt[0].fX;
+    dst->fMat[kMTransY] = srcPt[0].fY;
+    dst->fMat[kMPersp2] = 1;
+    dst->setTypeMask(kUnknown_Mask);
+    return true;
+}
+
+typedef bool (*PolyMapProc)(const SkPoint[], SkMatrix*, const SkPoint&);
+
+/*  Taken from Rob Johnson's original sample code in QuickDraw GX
+*/
+bool SkMatrix::setPolyToPoly(const SkPoint src[], const SkPoint dst[],
+                             int count) {
+    if ((unsigned)count > 4) {
+        SkDebugf("--- SkMatrix::setPolyToPoly count out of range %d\n", count);
+        return false;
+    }
+
+    if (0 == count) {
+        this->reset();
+        return true;
+    }
+    if (1 == count) {
+        this->setTranslate(dst[0].fX - src[0].fX, dst[0].fY - src[0].fY);
+        return true;
+    }
+
+    SkPoint scale;
+    if (!poly_to_point(&scale, src, count) ||
+            SkScalarNearlyZero(scale.fX) ||
+            SkScalarNearlyZero(scale.fY)) {
+        return false;
+    }
+
+    static const PolyMapProc gPolyMapProcs[] = {
+        SkMatrix::Poly2Proc, SkMatrix::Poly3Proc, SkMatrix::Poly4Proc
+    };
+    PolyMapProc proc = gPolyMapProcs[count - 2];
+
+    SkMatrix tempMap, result;
+    tempMap.setTypeMask(kUnknown_Mask);
+
+    if (!proc(src, &tempMap, scale)) {
+        return false;
+    }
+    if (!tempMap.invert(&result)) {
+        return false;
+    }
+    if (!proc(dst, &tempMap, scale)) {
+        return false;
+    }
+    if (!result.setConcat(tempMap, result)) {
+        return false;
+    }
+    *this = result;
+    return true;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+enum MinOrMax {
+    kMin_MinOrMax,
+    kMax_MinOrMax
+};
+
+template <MinOrMax MIN_OR_MAX> SkScalar get_stretch_factor(SkMatrix::TypeMask typeMask,
+                                                           const SkScalar m[9]) {
+    if (typeMask & SkMatrix::kPerspective_Mask) {
+        return -1;
+    }
+    if (SkMatrix::kIdentity_Mask == typeMask) {
+        return 1;
+    }
+    if (!(typeMask & SkMatrix::kAffine_Mask)) {
+        if (kMin_MinOrMax == MIN_OR_MAX) {
+             return SkMinScalar(SkScalarAbs(m[SkMatrix::kMScaleX]),
+                                SkScalarAbs(m[SkMatrix::kMScaleY]));
+        } else {
+             return SkMaxScalar(SkScalarAbs(m[SkMatrix::kMScaleX]),
+                                SkScalarAbs(m[SkMatrix::kMScaleY]));
+        }
+    }
+    // ignore the translation part of the matrix, just look at 2x2 portion.
+    // compute singular values, take largest or smallest abs value.
+    // [a b; b c] = A^T*A
+    SkScalar a = sdot(m[SkMatrix::kMScaleX], m[SkMatrix::kMScaleX],
+                      m[SkMatrix::kMSkewY],  m[SkMatrix::kMSkewY]);
+    SkScalar b = sdot(m[SkMatrix::kMScaleX], m[SkMatrix::kMSkewX],
+                      m[SkMatrix::kMScaleY], m[SkMatrix::kMSkewY]);
+    SkScalar c = sdot(m[SkMatrix::kMSkewX],  m[SkMatrix::kMSkewX],
+                      m[SkMatrix::kMScaleY], m[SkMatrix::kMScaleY]);
+    // eigenvalues of A^T*A are the squared singular values of A.
+    // characteristic equation is det((A^T*A) - l*I) = 0
+    // l^2 - (a + c)l + (ac-b^2)
+    // solve using quadratic equation (divisor is non-zero since l^2 has 1 coeff
+    // and roots are guaranteed to be pos and real).
+    SkScalar chosenRoot;
+    SkScalar bSqd = b * b;
+    // if upper left 2x2 is orthogonal save some math
+    if (bSqd <= SK_ScalarNearlyZero*SK_ScalarNearlyZero) {
+        if (kMin_MinOrMax == MIN_OR_MAX) {
+            chosenRoot = SkMinScalar(a, c);
+        } else {
+            chosenRoot = SkMaxScalar(a, c);
+        }
+    } else {
+        SkScalar aminusc = a - c;
+        SkScalar apluscdiv2 = SkScalarHalf(a + c);
+        SkScalar x = SkScalarHalf(SkScalarSqrt(aminusc * aminusc + 4 * bSqd));
+        if (kMin_MinOrMax == MIN_OR_MAX) {
+            chosenRoot = apluscdiv2 - x;
+        } else {
+            chosenRoot = apluscdiv2 + x;
+        }
+    }
+    SkASSERT(chosenRoot >= 0);
+    return SkScalarSqrt(chosenRoot);
+}
+
+SkScalar SkMatrix::getMinStretch() const {
+    return get_stretch_factor<kMin_MinOrMax>(this->getType(), fMat);
+}
+
+SkScalar SkMatrix::getMaxStretch() const {
+    return get_stretch_factor<kMax_MinOrMax>(this->getType(), fMat);
+}
+
+static void reset_identity_matrix(SkMatrix* identity) {
+    identity->reset();
+}
+
+const SkMatrix& SkMatrix::I() {
+    // If you can use C++11 now, you might consider replacing this with a constexpr constructor.
+    static SkMatrix gIdentity;
+    SK_DECLARE_STATIC_ONCE(once);
+    SkOnce(&once, reset_identity_matrix, &gIdentity);
+    return gIdentity;
+}
+
+const SkMatrix& SkMatrix::InvalidMatrix() {
+    static SkMatrix gInvalid;
+    static bool gOnce;
+    if (!gOnce) {
+        gInvalid.setAll(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax,
+                        SK_ScalarMax, SK_ScalarMax, SK_ScalarMax,
+                        SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
+        gInvalid.getType(); // force the type to be computed
+        gOnce = true;
+    }
+    return gInvalid;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+size_t SkMatrix::writeToMemory(void* buffer) const {
+    // TODO write less for simple matrices
+    static const size_t sizeInMemory = 9 * sizeof(SkScalar);
+    if (buffer) {
+        memcpy(buffer, fMat, sizeInMemory);
+    }
+    return sizeInMemory;
+}
+
+size_t SkMatrix::readFromMemory(const void* buffer, size_t length) {
+    static const size_t sizeInMemory = 9 * sizeof(SkScalar);
+    if (length < sizeInMemory) {
+        return 0;
+    }
+    if (buffer) {
+        memcpy(fMat, buffer, sizeInMemory);
+        this->setTypeMask(kUnknown_Mask);
+    }
+    return sizeInMemory;
+}
+
+#ifdef SK_DEVELOPER
+void SkMatrix::dump() const {
+    SkString str;
+    this->toString(&str);
+    SkDebugf("%s\n", str.c_str());
+}
+#endif
+
+#ifndef SK_IGNORE_TO_STRING
+void SkMatrix::toString(SkString* str) const {
+    str->appendf("[%8.4f %8.4f %8.4f][%8.4f %8.4f %8.4f][%8.4f %8.4f %8.4f]",
+             fMat[0], fMat[1], fMat[2], fMat[3], fMat[4], fMat[5],
+             fMat[6], fMat[7], fMat[8]);
+}
+#endif
+
+///////////////////////////////////////////////////////////////////////////////
+
+#include "SkMatrixUtils.h"
+
+bool SkTreatAsSprite(const SkMatrix& mat, int width, int height,
+                     unsigned subpixelBits) {
+    // quick reject on affine or perspective
+    if (mat.getType() & ~(SkMatrix::kScale_Mask | SkMatrix::kTranslate_Mask)) {
+        return false;
+    }
+
+    // quick success check
+    if (!subpixelBits && !(mat.getType() & ~SkMatrix::kTranslate_Mask)) {
+        return true;
+    }
+
+    // mapRect supports negative scales, so we eliminate those first
+    if (mat.getScaleX() < 0 || mat.getScaleY() < 0) {
+        return false;
+    }
+
+    SkRect dst;
+    SkIRect isrc = { 0, 0, width, height };
+
+    {
+        SkRect src;
+        src.set(isrc);
+        mat.mapRect(&dst, src);
+    }
+
+    // just apply the translate to isrc
+    isrc.offset(SkScalarRoundToInt(mat.getTranslateX()),
+                SkScalarRoundToInt(mat.getTranslateY()));
+
+    if (subpixelBits) {
+        isrc.fLeft <<= subpixelBits;
+        isrc.fTop <<= subpixelBits;
+        isrc.fRight <<= subpixelBits;
+        isrc.fBottom <<= subpixelBits;
+
+        const float scale = 1 << subpixelBits;
+        dst.fLeft *= scale;
+        dst.fTop *= scale;
+        dst.fRight *= scale;
+        dst.fBottom *= scale;
+    }
+
+    SkIRect idst;
+    dst.round(&idst);
+    return isrc == idst;
+}
+
+// A square matrix M can be decomposed (via polar decomposition) into two matrices --
+// an orthogonal matrix Q and a symmetric matrix S. In turn we can decompose S into U*W*U^T,
+// where U is another orthogonal matrix and W is a scale matrix. These can be recombined
+// to give M = (Q*U)*W*U^T, i.e., the product of two orthogonal matrices and a scale matrix.
+//
+// The one wrinkle is that traditionally Q may contain a reflection -- the
+// calculation has been rejiggered to put that reflection into W.
+bool SkDecomposeUpper2x2(const SkMatrix& matrix,
+                         SkPoint* rotation1,
+                         SkPoint* scale,
+                         SkPoint* rotation2) {
+
+    SkScalar A = matrix[SkMatrix::kMScaleX];
+    SkScalar B = matrix[SkMatrix::kMSkewX];
+    SkScalar C = matrix[SkMatrix::kMSkewY];
+    SkScalar D = matrix[SkMatrix::kMScaleY];
+
+    if (is_degenerate_2x2(A, B, C, D)) {
+        return false;
+    }
+
+    double w1, w2;
+    SkScalar cos1, sin1;
+    SkScalar cos2, sin2;
+
+    // do polar decomposition (M = Q*S)
+    SkScalar cosQ, sinQ;
+    double Sa, Sb, Sd;
+    // if M is already symmetric (i.e., M = I*S)
+    if (SkScalarNearlyEqual(B, C)) {
+        cosQ = 1;
+        sinQ = 0;
+
+        Sa = A;
+        Sb = B;
+        Sd = D;
+    } else {
+        cosQ = A + D;
+        sinQ = C - B;
+        SkScalar reciplen = SkScalarInvert(SkScalarSqrt(cosQ*cosQ + sinQ*sinQ));
+        cosQ *= reciplen;
+        sinQ *= reciplen;
+
+        // S = Q^-1*M
+        // we don't calc Sc since it's symmetric
+        Sa = A*cosQ + C*sinQ;
+        Sb = B*cosQ + D*sinQ;
+        Sd = -B*sinQ + D*cosQ;
+    }
+
+    // Now we need to compute eigenvalues of S (our scale factors)
+    // and eigenvectors (bases for our rotation)
+    // From this, should be able to reconstruct S as U*W*U^T
+    if (SkScalarNearlyZero(SkDoubleToScalar(Sb))) {
+        // already diagonalized
+        cos1 = 1;
+        sin1 = 0;
+        w1 = Sa;
+        w2 = Sd;
+        cos2 = cosQ;
+        sin2 = sinQ;
+    } else {
+        double diff = Sa - Sd;
+        double discriminant = sqrt(diff*diff + 4.0*Sb*Sb);
+        double trace = Sa + Sd;
+        if (diff > 0) {
+            w1 = 0.5*(trace + discriminant);
+            w2 = 0.5*(trace - discriminant);
+        } else {
+            w1 = 0.5*(trace - discriminant);
+            w2 = 0.5*(trace + discriminant);
+        }
+
+        cos1 = SkDoubleToScalar(Sb); sin1 = SkDoubleToScalar(w1 - Sa);
+        SkScalar reciplen = SkScalarInvert(SkScalarSqrt(cos1*cos1 + sin1*sin1));
+        cos1 *= reciplen;
+        sin1 *= reciplen;
+
+        // rotation 2 is composition of Q and U
+        cos2 = cos1*cosQ - sin1*sinQ;
+        sin2 = sin1*cosQ + cos1*sinQ;
+
+        // rotation 1 is U^T
+        sin1 = -sin1;
+    }
+
+    if (NULL != scale) {
+        scale->fX = SkDoubleToScalar(w1);
+        scale->fY = SkDoubleToScalar(w2);
+    }
+    if (NULL != rotation1) {
+        rotation1->fX = cos1;
+        rotation1->fY = sin1;
+    }
+    if (NULL != rotation2) {
+        rotation2->fX = cos2;
+        rotation2->fY = sin2;
+    }
+
+    return true;
+}