Instead of printing log in every function. I (or most of the people) would suggest you to put debug.
To use debug first create breakpoints inside every function you want to check. To apply breakpoints simply left click in the area to the left of your code (refer image the pink circle represents a break-point).

Then to use Debug you have to press this button after successfully running your application.

As soon as the first method is called your application will pause at the break-point, then you can use F8 (or F6 if you are using eclipse settings) to move to next line, to move to next break-point you can press F9(or F8 if you are using eclipse settings). this way to can check all the functions being called.
This break-point method is really helpful if you just want to make sure that a particular function is being called.
Other than this if you still insist to know the details of all the functions you can store the stacktrace.
final StackTraceElement[] trace = new Throwable().getStackTrace())
StackTraceElement STrace = trace[1];
String className = STrace.getMethodName();