How can the following simple implementation of sum be faster?

private long sum( int [] a, int begin, int end ) {
    if( a == null   ) {
        return 0;
    }
    long r = 0;
    for( int i =  begin ; i < end ; i++ ) {
       r+= a[i];
    }
    return r;
}

EDIT

Background is in order.

Reading latest entry on coding horror, I came to this site: http://codility.com which has this interesting programming test.

Anyway, I got 60 out of 100 in my submission, and basically ( I think ) is because this implementation of sum, because those parts where I failed are the performance parts. I'm getting TIME_OUT_ERROR's

So, I was wondering if an optimization in the algorithm is possible.

So, no built in functions or assembly would be allowed. This my be done in C, C++, C#, Java or pretty much in any other.

EDIT

As usual, mmyers was right. I did profile the code and I saw most of the time was spent on that function, but I didn't understand why. So what I did was to throw away my implementation and start with a new one.

This time I've got an optimal solution [ according to San Jacinto O(n) -see comments to MSN below - ]

This time I've got 81% on Codility which I think is good enough. The problem is that I didn't take the 30 mins. but around 2 hrs. but I guess that leaves me still as a good programmer, for I could work on the problem until I found an optimal solution:

Here's my result.

I never understood what is those "combinations of..." nor how to test "extreme_first"