What is the fastest sorting algorithm for a small number of integers?

Question

I am wondering what the fastest algorithm would be for this. I have 8 integers between 0 and 3000 and I need to sort them. Although there are only 8 integers, this operation will be performed millions of times.

Answer 1

Here is an implementation of an odd-even merge sort network in C99 (sorry for the "wrong" language):

#define CMP_SWAP(i, j) if (a[i] > a[j])              \
    { int tmp = a[i]; a[i] = a[j]; a[j] = tmp; }

void sort8_network(int *a)
{
    CMP_SWAP(0, 1); CMP_SWAP(2, 3); CMP_SWAP(4, 5); CMP_SWAP(6, 7);
    CMP_SWAP(0, 2); CMP_SWAP(1, 3); CMP_SWAP(4, 6); CMP_SWAP(5, 7);
    CMP_SWAP(1, 2); CMP_SWAP(5, 6); CMP_SWAP(0, 4); CMP_SWAP(1, 5);
    CMP_SWAP(2, 6); CMP_SWAP(3, 7); CMP_SWAP(2, 4); CMP_SWAP(3, 5);
    CMP_SWAP(1, 2); CMP_SWAP(3, 4); CMP_SWAP(5, 6);
}

I timed it on my machine against insertion sort

void sort8_insertion(int *a)
{
    for (int i = 1; i < 8; i++)
    {
        int tmp = a[i];
        int j = i;
        for (; j && tmp < a[j - 1]; --j)
            a[j] = a[j - 1];
        a[j] = tmp;
    }
}

For about 10 million sorts (exactly 250 times all the 40320 possible permutations), the sort network took 0.39 seconds while insertion sort took 0.88 seconds. Seems to me both are fast enough. (The figures inlcude about 0.04 seconds for generating the permutations.)

Answer 2

The fastest would be to simply write a lot of if statements to compare them to determine their exact order. That will remove the overhead that any sorting algoritm has.

Answer 3

For only 8 integers and given that the range is much greater than 8, insertion sort is probably the best. Try it to start with, and if profiling indicates that it's not the bottleneck then leave it.

(Depending on many factors, the cutoff point at which quick-sort becomes better than insertion sort is usually between 5 and 10 items).