How do I retrieve if the popstate event comes from back or forward actions with the HTML5 pushstate?

You must implement it yourself which is quite easy.

• When invoking pushState give the data object a unique incrementing id (uid).
• When onpopstate handler is invoked; check the state uid against a persistent variable containing the last state uid.
• Update the persistent variable with the current state uid.
• Do different actions depending on if state uid was greater or less than last state uid.