How did they get to Singapore in Pirates of the Caribbean At World's End?

I imagine it's safe to assume Pirates of the Caribbean is based in the Caribbean.

Do we assume that when they go to Singapore at the beginning of the film that they sailed all the way down around the bottom of South America?

Just wondering as this seems like an awful long way for a pirate ship to travel.

• Next What university is Monsters University modeled after?
• Previous etymology - Use of prefixes mis- and mal-