Parallel operations in array with dependency

Question

I need help to solve this problem, I have a code with operations being performed on the previous element of the array, and I need to parallelize using openmp tasks, however I know how to remove this depency. My teacher says that in this case it is not interesting to use depend (in, out). How would I remove that depended on this then?

void sum_sequential(float a[N]) {
        a[0] = 1.0;

    for (int i = 1; i < N; i++)
        a[i] = 2 * a[i-1] + 1;
}

Answer 1

You are quite right that there is is a data dependency. The value to be computed for each element is expressed in terms of the value previously computed for the preceding element, so this algorithm is inherently serial. There is no practical advantage in parallelizing it, as successfully dealing with the dependencies leaves no room for any concurrency.

HOWEVER, if you study the computation carefully, it is possible to re-express it in an algebraically equivalent way that does not have such dependencies -- an altogether different algorithm that produces the same results and is trivially parallelizable. At the risk of providing too big a hint, try writing out the first several terms of the results by hand, and see whether you recognize a simple pattern.