Simplify matrix generation for convex path renderer

src/gpu/GrPathUtils.cpp

Index: src/gpu/GrPathUtils.cpp
diff --git a/src/gpu/GrPathUtils.cpp b/src/gpu/GrPathUtils.cpp
index 81348ec239995a5a5645a1f553d8e1930b2dc869..b7039a9ac62a5834170307ea99efaaa8b380b567 100644
--- a/src/gpu/GrPathUtils.cpp
+++ b/src/gpu/GrPathUtils.cpp
@@ -187,8 +187,6 @@ int GrPathUtils::worstCasePointCount(const SkPath& path, int* subpaths,
 }
 
 void GrPathUtils::QuadUVMatrix::set(const GrPoint qPts[3]) {
-    // can't make this static, no cons :(
-    SkMatrix UVpts;
 #ifndef SK_SCALAR_IS_FLOAT
     GrCrash("Expected scalar is float.");
 #endif
@@ -197,18 +195,23 @@ void GrPathUtils::QuadUVMatrix::set(const GrPoint qPts[3]) {
     // We know M * control_pts = [0  1/2 1]
     //                           [0  0   1]
     //                           [1  1   1]
+    // And control_pts = [x0 x1 x2]
+    //                   [y0 y1 y2]
+    //                   [1  1  1 ]
     // We invert the control pt matrix and post concat to both sides to get M.
-    UVpts.setAll(0,   SK_ScalarHalf,  SK_Scalar1,
-                 0,               0,  SK_Scalar1,
-                 SkScalarToPersp(SK_Scalar1),
-                 SkScalarToPersp(SK_Scalar1),
-                 SkScalarToPersp(SK_Scalar1));
-    m.setAll(qPts[0].fX, qPts[1].fX, qPts[2].fX,
-             qPts[0].fY, qPts[1].fY, qPts[2].fY,
-             SkScalarToPersp(SK_Scalar1),
-             SkScalarToPersp(SK_Scalar1),
-             SkScalarToPersp(SK_Scalar1));
-    if (!m.invert(&m)) {
+    // Using the known form of the control point matrix and the result, we can
+    // optimize and improve precision.
+
+    double x0 = qPts[0].fX;
+    double y0 = qPts[0].fY;
+    double x1 = qPts[1].fX;
+    double y1 = qPts[1].fY;
+    double x2 = qPts[2].fX;
+    double y2 = qPts[2].fY;
+    double det = x0*y1 - y0*x1 + x2*y0 - y2*x0 + x1*y2 - y1*x2;
+
+    if (!sk_float_isfinite(det) 
+        || SkScalarNearlyZero((float)det, SK_ScalarNearlyZero * SK_ScalarNearlyZero)) {
         // The quad is degenerate. Hopefully this is rare. Find the pts that are
         // farthest apart to compute a line (unless it is really a pt).
         SkScalar maxD = qPts[0].distanceToSqd(qPts[1]);
@@ -247,7 +250,35 @@ void GrPathUtils::QuadUVMatrix::set(const GrPoint qPts[3]) {
             fM[3] = 0; fM[4] = 0; fM[5] = 100.f;
         }
     } else {
-        m.postConcat(UVpts);
+        double scale = 1.0/det;
+
+        // order swapped around to minimize stalls

[mtklein, 2013/12/03 20:52:28]

Interesting!  Does this actually generate significantly different code?  I'd
imagine a smart compiler will go in there and do this anyway, but you never
really know how smart they will be.  Is there a bench for this and is it
affected by the order here?

[jvanverth1, 2013/12/04 19:51:20]

I looked into this, and it appears that on Linux, if you store the temporary
adjugate matrix in an array, that the order may matter (because of noise it's
inconclusive). However, I removed the matrix and replaced it with multiple
variables, and in that case the order doesn't appear to matter (again, somewhat
inconclusive).

+        double adjugate[9];
+        adjugate[6] = y0-y1;
+        adjugate[7] = x1-x0;
+        adjugate[8] = x0*y1-y0*x1;

[mtklein, 2013/12/03 20:52:28]

Just a nit.  All the others have x*y except this y0*x1.

+
+        adjugate[3] = y2-y0;
+        adjugate[4] = x0-x2;
+        adjugate[5] = x2*y0-x0*y2;
+
+        adjugate[0] = y1-y2;
+        adjugate[1] = x2-x1;
+        adjugate[2] = x1*y2-x2*y1;
+
+        // this performs the uv_pts*adjugate(control_pts) multiply, 
+        // then does the scale by 1/det afterwards to improve precision
+        m[SkMatrix::kMSkewY] = (float)(adjugate[6]*scale);

[mtklein, 2013/12/03 20:52:28]

This is again a nit, but it'd help me read with an extra space in front of the =
for the skews, so it all lines up pretty-like.

+        m[SkMatrix::kMScaleY] = (float)(adjugate[7]*scale);
+        m[SkMatrix::kMTransY] = (float)(adjugate[8]*scale);
+
+        m[SkMatrix::kMScaleX] = (float)((0.5*adjugate[3] + adjugate[6])*scale);
+        m[SkMatrix::kMSkewX] = (float)((0.5*adjugate[4] + adjugate[7])*scale);
+        m[SkMatrix::kMTransX] = (float)((0.5*adjugate[5] + adjugate[8])*scale);
+
+        m[SkMatrix::kMPersp0] = (float)((adjugate[0] + adjugate[3] + adjugate[6])*scale);
+        m[SkMatrix::kMPersp1] = (float)((adjugate[1] + adjugate[4] + adjugate[7])*scale);
+        m[SkMatrix::kMPersp2] = (float)((adjugate[2] + adjugate[5] + adjugate[8])*scale);
 
         // The matrix should not have perspective.
         SkDEBUGCODE(static const SkScalar gTOL = 1.f / 100.f);