Revert "Revert of Divorce PaintInvalidationState from LayoutState (https://codereview.chromium.org/360833002/), and"

This reverts commit 487e91013d29e3d9283a833fbe1ed48416dbf81a.

These patches were incorrectly reverted to fix a DrMemory issue. The revert
landed in r177725, but the DrMemory bots recovered in r177712:
http://build.chromium.org/p/chromium.memory.fyi/builders/Windows%20Content%20Browser%20%28DrMemory%20full%29%20%283%29/builds/294

TBR=yutak
BUG=363834

Review URL: https://codereview.chromium.org/396453002

git-svn-id: svn://svn.chromium.org/blink/trunk@178125 bbb929c8-8fbe-4397-9dbb-9b2b20218538