Sort arrays of primitive types in descending order

I think it would be best not to re-invent the wheel and use Arrays.sort().

Yes, I saw the "descending" part. The sorting is the hard part, and you want to benefit from the simplicity and speed of Java's library code. Once that's done, you simply reverse the array, which is a relatively cheap O(n) operation. Here's some code I found to do this in as little as 4 lines:

for (int left=0, right=b.length-1; left<right; left++, right--) {
    // exchange the first and last
    int temp = b[left]; b[left]  = b[right]; b[right] = temp;
}

Java Primitive includes functionality for sorting primitive arrays based on a custom comparator. Using it, and Java 8, your sample could be written as:

double[] array = new double[1048576];
...
Primitive.sort(array, (d1, d2) -> Double.compare(d2, d1), false);

If you're using Maven, you can include it with:

<dependency>
    <groupId>net.mintern</groupId>
    <artifactId>primitive</artifactId>
    <version>1.2.1</version>
</dependency>

When you pass false as the third argument to sort, it uses an unstable sort, a simple edit of Java's built-in dual-pivot quicksort. This means that the speed should be close to that of built-in sorting.

Full disclosure: I wrote the Java Primitive library.