Is hamlets madness genuine or not

Hamlet may be depressed and a little too uptight over his mother's sexuality but I don't think he was crazy. Here is a case in point. Hamlet wishes to point out that there is method and cunning behind his "madness." The imagery involves bad weather and hunting birds. Beyond the chaos, Hamlet is saying that he knows a hunting hawk from a hunted "handsaw" or heron. Hamlet means that he is able to distinguish his enemies and friends. This pointed comment is meant for his "friends" Rosencrantz and Guildenstern.