After a nightmarish ordeal of attempting to get the range swap to work, I finally found the two problems causing the code not to work. It's always something simple. I finished the optimized version of my algorithm, and I'm quite happy with the result.

These are some attributes of my sorting algorithm:

• It is a stable sort
  
• Low memory requirement (only a few extra KiB is required)
  
• It's a divide and conquer algorithm, which makes it easy to parallelize
  
• Good performance (not as fast as quick sort, but only a little bit slower than merge sort, and faster than shell sort)
  
• Faster on sorted or partially sorted data
  
• Similar to Timsort, except for the range swap
  
• The range swap is pretty fast at reversing elements in descending order
  
• Minimal risk of stack overflow using tail calls

For greater detail on the sorting algorithm, see my previous blog posts:
Designing a sorting algorithm
Sort Algorithm pt. 2

You can download the source code here. This contains a simple text file as well as an HTML file with syntax highlighting. It contains the source for my sort as well as all of the other algorithms I implemented for scrutinies sake.
Download xinokSort.zip | Mirror

I have also started an open source project to implement this sorting algorithm in many programming languages.
Xinok Sort on SourceForge

---

Now for some benchmarks! The benchmarks of shell sort and quick sort are faster than in previous posts because I further optimized them. The characters on the right are MD5 hashes, to verify the array was sorted correctly.

Shuffled:


Shuffled 4x Larger Array: (To show how well my algorithm scales) (there wasn't enough memory left for radix sort)


Sorted Array:


Partially Sorted Array: (2048 elements were swapped and out of place)


Reversed Array: (elements are in descending order)