Thanks for your reply.
Actually, I want to make unicode string comparasion robust. So I need to compare both Canonical equivalance as well as Compatibility equivalance. I can mention one example where these two equivalance makes difference. The half-width and full-width katakana characters have same compatibility equivalents, but they are not canonical equivalent.
So, is it fine to compare canonical equivalance first and then compatibility equivalance?
TIA
-Pijush