How to detect whether a hash change came from the Back or Forward button

back_forward.js

var detectBackOrForward = function(onBack, onForward) {
  hashHistory = [window.location.hash];
  historyLength = window.history.length;

  return function() {
    var hash = window.location.hash, length = window.history.length;
    if (hashHistory.length && historyLength == length) {
      if (hashHistory[hashHistory.length - 2] == hash) {
        hashHistory = hashHistory.slice(0, -1);
        onBack();
      } else {
        hashHistory.push(hash);
        onForward();
      }
    } else {
      hashHistory.push(hash);
      historyLength = length;
    }
  }
};

window.addEventListener("hashchange", detectBackOrForward(
  function() { console.log("back") },
  function() { console.log("forward") }
));

as mentioned by 7cc, this fails: a -> #b -> #a -> back
it also fails if you refresh the page in the middle of history and then press forward or back. this is because you can't tell index of your current history within the actual browser history array - therefore can't tell if next hashchange is forward or backwards (even if all hashes are unique).
so my conclusion: this is a problem impossible to solve.