function doQuickSort(ary, comparator, p, r) {
  // If our lower bound is less than our upper bound, we (1) partition the
  // array into two pieces and (2) recurse on each half. If it is not, this is
  // the empty array and our base case.

  if (p < r) {
    // (1) Partitioning.
    //
    // The partitioning chooses a pivot between `p` and `r` and moves all
    // elements that are less than or equal to the pivot to the before it, and
    // all the elements that are greater than it after it. The effect is that
    // once partition is done, the pivot is in the exact place it will be when
    // the array is put in sorted order, and it will not need to be moved
    // again. This runs in O(n) time.

    // Always choose a random pivot so that an input array which is reverse
    // sorted does not cause O(n^2) running time.
    var pivotIndex = randomIntInRange(p, r);
    var i = p - 1;

    swap(ary, pivotIndex, r);
    var pivot = ary[r];

    // Immediately after `j` is incremented in this loop, the following hold
    // true:
    //
    //   * Every element in `ary[p .. i]` is less than or equal to the pivot.
    //
    //   * Every element in `ary[i+1 .. j-1]` is greater than the pivot.
    for (var j = p; j < r; j++) {
      if (comparator(ary[j], pivot) <= 0) {
        i += 1;
        swap(ary, i, j);
      }
    }

    swap(ary, i + 1, j);
    var q = i + 1;

    // (2) Recurse on each half.

    doQuickSort(ary, comparator, p, q - 1);
    doQuickSort(ary, comparator, q + 1, r);
  }
}
The Quick Sort algorithm.

@param {Array} ary
       An array to sort.
@param {function} comparator
       Function to use to compare two items.
@param {Number} p
       Start index of the array
@param {Number} r
       End index of the array