Fastest code C/C++ to select the median in a set of 27 floating point values

Question

This is the well know select algorithm. see http://en.wikipedia.org/wiki/Selection_algorithm.

I need it to find the median value of a set of 3x3x3 voxel values. Sinc

Answer 1

I'm betting that you could calculate them for zero cost - in a separate thread while loading from disk (or however they're generated).

What I'm really saying is that 'speed' isn't going to come from bit twiddling because 27 values isn't enough for Big O notation to be a real factor.

Answer 2

The selection algorithm is linear time (O(n)). Complexity-wise you can't do better than linear time, because it takes linear time to read in all the data. So you couldn't have made something that is faster complexity-wise. Perhaps you have something that is a constant factor faster on certain inputs? I doubt it would make much of a difference.

C++ already includes the linear-time selection algorithm. Why not just use it?

std::vector<YourType>::iterator first = yourContainer.begin();
std::vector<YourType>::iterator last = yourContainer.end();
std::vector<YourType>::iterator middle = first + (last - first) / 2;
std::nth_element(first, middle, last); // can specify comparator as optional 4th arg
YourType median = *middle;

Edit: Technically, that is only the median for a container of odd length. For one of even length, it will get the "upper" median. If you want the traditional definition of median for even length, you might have to run it twice, once for each of the two "middles" at first + (last - first) / 2 and first + (last - first) / 2 - 1 and then average them or something.

Answer 3

+1 for everybody who mentioned nth_element, but this kind of code is where hand written algorithm is better than STL because you want to generate the most efficient code for that one compiler running on the one CPU with a specific data set. For example, for some CPU/compiler combination std::swap(int, int) maybe slower than hand written swap using XOR (before you reply, i know this is probably true 20 years ago but not anymore). Sometimes performance is gained by hand writing assembly code specific to your CPU. If you plan to take advantage of GPU's stream processors, you may have to design your algorithm accordingly.

You mentioned using 2 heaps and keep track of the median as you insert. That's what i did a while ago in a project. I changed the array inplace and used only one heap. I could not think of any faster algorithm, but i'd like to caution you about memory usage, specifically CPU cache memory. You want to be careful with memory access. CPU cache is swapped in and out by page, so you want your algorithm to touch memory that are close together to minimize CPU cache miss.