Revert of Revert of Forward input and compositing tasks to the Blink scheduler

content/renderer/gpu/render_widget_compositor.cc

Index: content/renderer/gpu/render_widget_compositor.cc
diff --git a/content/renderer/gpu/render_widget_compositor.cc b/content/renderer/gpu/render_widget_compositor.cc
index b0931771d4afc8706a6eac1a17a5451f2cf13c6c..8e31fa046eb7a18579e4b8b5a0775f5675d0665e 100644
--- a/content/renderer/gpu/render_widget_compositor.cc
+++ b/content/renderer/gpu/render_widget_compositor.cc
@@ -515,6 +515,8 @@
 
 void RenderWidgetCompositor::Initialize(cc::LayerTreeSettings settings) {
   scoped_refptr<base::MessageLoopProxy> compositor_message_loop_proxy;
+  scoped_refptr<base::SingleThreadTaskRunner>
+      main_thread_compositor_task_runner(base::MessageLoopProxy::current());
   RenderThreadImpl* render_thread = RenderThreadImpl::current();
   cc::SharedBitmapManager* shared_bitmap_manager = NULL;
   // render_thread may be NULL in tests.
@@ -522,21 +524,23 @@
     compositor_message_loop_proxy =
         render_thread->compositor_message_loop_proxy();
     shared_bitmap_manager = render_thread->shared_bitmap_manager();
+    main_thread_compositor_task_runner =
+        render_thread->main_thread_compositor_task_runner();
   }
   if (compositor_message_loop_proxy.get()) {
-    layer_tree_host_ = cc::LayerTreeHost::CreateThreaded(
-        this,
-        shared_bitmap_manager,
-        settings,
-        base::MessageLoopProxy::current(),
-        compositor_message_loop_proxy);
+    layer_tree_host_ =
+        cc::LayerTreeHost::CreateThreaded(this,
+                                          shared_bitmap_manager,
+                                          settings,
+                                          main_thread_compositor_task_runner,
+                                          compositor_message_loop_proxy);
   } else {
     layer_tree_host_ = cc::LayerTreeHost::CreateSingleThreaded(
         this,
         this,
         shared_bitmap_manager,
         settings,
-        base::MessageLoopProxy::current());
+        main_thread_compositor_task_runner);
   }
   DCHECK(layer_tree_host_);
 }