How To Check If The Digest Cycles Have Stabilized (aka "has Angular Finished Compilation?")

tl;dr: The initial question was 'How to trigger a callback every digest cycle?' but the underlying question is much more interesting and since this answers both, I went ahead and m

Solution 1:

I actually do not know if my advice will answer your question, but you could simply pass a listener to the $watch function which will be called on each iteration:

$rootScope.$watch(function(oldVal, newVal){
    // add some logic here which will be called on each digest cycle
});

Have a look here: http://docs.angularjs.org/api/ng/type/$rootScope.Scope#$watch