throw vs throw ex vs wrap and throw in c-sharp

I've come across the throw vs throw ex 'debate' a few times, even as an interview question, and it's always bugged me because it's never something I've worried about in my own c# code.

background

So here's a typical example of the throw vs throw ex thing: https://stackoverflow.com/questions/730250/is-there-a-difference-between-throw-and-throw-ex

Basically it revolves around either messing up the line numbers in your stack trace (throw ex;) or losing an chunk of your stack entirely (throw;) - exception1 and 2 respectively in this nice clear answer http://stackoverflow.com/a/776756/10245

the third option

I've just figured out why.

Because in my own code, whenever I catch and re-throw I always wrap another exception to add more context before rethrowing, and this means you don't have either of the above problems. For example:

private static void ThrowException3() {
try {
DivByZero(); // line 43
} catch (Exception ex) {
throw new Exception("doh", ex); // line 45
}
}

Exception 3:

System.Exception: doh ---> System.DivideByZeroException: Division by zero

  at puke.DivByZero () [0x00002] in /home/tim/repo/puker/puke.cs:51 

  at puke.ThrowException3 () [0x00000] in /home/tim/repo/puker/puke.cs:43 

  --- End of inner exception stack trace ---

  at puke.ThrowException3 () [0x0000b] in /home/tim/repo/puker/puke.cs:45 

  at puke.Main (System.String[] args) [0x00040] in /home/tim/repo/puker/puke.cs:18 

Obviously 'doh' would be something meaningful about the state of that function ThrowException3 in the real world.

Full example with output at https://gist.github.com/timabell/78610f588961bd0a0b95

This makes life much easier when tracking down bugs / state problems later on. Particularly if you string.format() the new message and add some useful state info.