Optimize QuadF's IsCounterClockwise function

IsCounterClockwise is a busy function,See performance and discussion:
https://groups.google.com/a/chromium.org/forum/#!topic/graphics-dev/aSvAbzcgbos

This patch reduce IsCounterClockwise() from 8mul+3add+4sub to 4mul+2add+2sub,
and performance doubled in real micro-bench.

R=danakj@chromium.org

Review URL: https://codereview.chromium.org/458113002

Cr-Commit-Position: refs/heads/master@{#289138}
git-svn-id: svn://svn.chromium.org/chrome/trunk/src@289138 0039d316-1c4b-4281-b951-d872f2087c98

AUTHORS

@@ -472,3 +472,4 @@ The MathWorks, Inc. <binod.pant@mathworks.com>
 Torchmobile Inc.
 Venture 3 Systems LLC <*@venture3systems.com>
 Yandex LLC <*@yandex-team.ru>
+ARM Holdings <*@arm.com>

ui/gfx/geometry/quad_f.cc

@@ -43,19 +43,23 @@ bool QuadF::IsCounterClockwise() const {
   // counter-clockwise. Note carefully: this is backwards from conventional
   // math because our geometric space uses screen coordiantes with y-axis
   // pointing downards.
-  // Reference: http://mathworld.wolfram.com/PolygonArea.html
+  // Reference: http://mathworld.wolfram.com/PolygonArea.html.
+  // The equation can be written:
+  // Signed area = determinant1 + determinant2 + determinant3 + determinant4
+  // In practise, Refactoring the computation of adding determinants so that
+  // reducing the number of operations. The equation is:
+  // Signed area = element1 + element2 - element3 - element4
+
+  float p24 = p2_.y() - p4_.y();
+  float p31 = p3_.y() - p1_.y();
 
   // Up-cast to double so this cannot overflow.
-  double determinant1 = static_cast<double>(p1_.x()) * p2_.y()
-      - static_cast<double>(p2_.x()) * p1_.y();
-  double determinant2 = static_cast<double>(p2_.x()) * p3_.y()
-      - static_cast<double>(p3_.x()) * p2_.y();
-  double determinant3 = static_cast<double>(p3_.x()) * p4_.y()
-      - static_cast<double>(p4_.x()) * p3_.y();
-  double determinant4 = static_cast<double>(p4_.x()) * p1_.y()
-      - static_cast<double>(p1_.x()) * p4_.y();
-
-  return determinant1 + determinant2 + determinant3 + determinant4 < 0;
+  double element1 = static_cast<double>(p1_.x()) * p24;
+  double element2 = static_cast<double>(p2_.x()) * p31;
+  double element3 = static_cast<double>(p3_.x()) * p24;
+  double element4 = static_cast<double>(p4_.x()) * p31;
+
+  return element1 + element2 < element3 + element4;
 }
 
 static inline bool PointIsInTriangle(const PointF& point,