performance - Fast algorithm implementation to sort very small list

Question

This is the problem I ran into long time ago. I thought I may ask your for your ideas. assume I have very small list of numbers (integers), 4 or 8 elements, that need to be sorted, fast. what would be the best approach/algorithm?

my approach was to use the max/min functions (10 functions to sort 4 numbers, no branches, iirc).

// s(i,j) == max(i,j), min(i,j)
i,j = s(i,j)
k,l = s(k,l)
i,k = s(i,k) // i on top
j,l = s(j,l) // l on bottom
j,k = s(j,k)

I guess my question pertains more to implementation, rather than type of algorithm.

At this point it becomes somewhat hardware dependent , so let us assume Intel 64-bit processor with SSE3 .

Thanks

Answer 1

For small arrays like this, you should probably look into sorting networks. As you can see on that page, insertion sort can be expressed as a sorting network. However, if you know the size of the array beforehand, you can devise an optimal network. Take a look at this site that can help you to find optimal sorting networks for a given size of array (though optimal is only guaranteed up to a size of 16 I believe). The comparators are even grouped together in operations that can be done in parallel. The comparators are essentially the same as your s(x,y) function though if you really want this to be fast, you shouldn't be using min and max because then you're doing twice the number of comparisons that are necessary.

If you need this sorting algorithm to work on a wide range of sizes, then you should probably just go with insertion sort as others have suggested.