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

A sorting network generated using the Bose-Nelson algorithm will find the median directly with no loops/recursion using 173 comparisons. If you have the facility to perform comparisions in parallel such as usage of vector-arithmetic instructions then you may be able to group the comparisions into as few as 28 parallel operations.

If you are sure that the floats are normalized and not (qs)NaN's, then you can use integer operations to compare IEEE-754 floats which can perform more favorably on some CPU's.

A direct conversion of this sorting network to C (gcc 4.2) yields a worst-case of 388 clock cycles on my Core i7.

Sorting Networks