It seems to be similar to our second assignment, except that here we are doing point in triangle check.
From my point of view, here "early out test" and "early in test" may be first check whether the four corner points is within the triangle, if the answer is no, other points within this chunk can be ignored.
Besides, one way to determine the "right side" of each line of the triangle is to use the left point and the formula of line. The "right side" of each line is the same side with the left point. eg. use P1 to determine the "right side" of line P0P1.