Loop Coalescing

Loop Coalescing

Loop coalescing is a loop optimization that involves flattening two nested loops into one non-nested loop. Typically, loop coalescing will still operate on a 2-dimensional array, whereas flattening both the nested loops and the array is called “loop collapsing.”

As a dummy example, consider a matrix initialization via nested loops:

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            arr[i][j] = 0.0f;
        }
    }

Loop coalescing involves changing to a single loop, but still using two indices i and j, which are calculated from the main linear index.

    int maxx = n * m;
    for (int x = 0; i < maxx; x++) {
        int i = x / n;
        int j = x % m;
        arr[i][j] = 0.0f;
    }

The benefit in speed from loop coalescing can arise by simplifying the loop, which makes it easier to parallelize via hardware acceleration, and also maybe a different data access pattern which might improve data locality and cache freshness.

This optimization is not always possible, as nested loop logic is often quite complicated, and flattening a nested loop may actually worsen data locality in many instances. However, the linear nature of a simple loop can make the code to send off chunks to a GPU much easier.

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