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The Average Case

On average case data where no patterns are detected pdqsort is effectively a quicksort that uses median-of-3 pivot selection, switching to insertion sort if the number of elements to be (recursively) sorted is small. The overhead associated with detecting the patterns for the best case is so small it lies within the error of measurement.

pdqsort gets a great speedup over the traditional way of implementing quicksort when sorting large arrays (1000+ elements). This is due to a new technique described in "BlockQuicksort: How Branch Mispredictions don't affect Quicksort" by Stefan Edelkamp and Armin Weiss. In short, we bypass the branch predictor by using small buffers (entirely in L1 cache) of the indices of elements that need to be swapped. We fill these buffers in a branch-free way that's quite elegant (in pseudocode):

buffer_num = 0; buffer_max_size = 64;
for (int i = 0; i < buffer_max_size; ++i) {
    // With branch:
    if (elements[i] < pivot) { buffer[buffer_num] = i; buffer_num++; }
    // Without:
    buffer[buffer_num] = i; buffer_num += (elements[i] < pivot);