Update (04/28/14): Check out the GrailSort project on GitHub for a similar algorithm based on a paper by Huang and Langston. It's actually faster than WikiSort for the Random and RandomFew tests when you remove the 512-item cache! It goes to show that this is still an open area of research that could use your expertise.
WikiSort is an implementation of "block merge sort", or "block sort" for short, which is a stable merge sort based on the work described in "Ratio based stable in-place merging", by Pok-Son Kim and Arne Kutzner [PDF].
WikiSort is generally as fast as a standard merge sort while using O(1) memory, and is even faster when the input is partially ordered or as the arrays get larger. It can also be modified to use any additional memory optionally provided to it, which can further improve its speed.
C, C++, and Java versions are currently available, and you have permission from me and the authors of the paper (Dr. Kim and Dr. Kutzner) to do whatever you want with this code.
If you want to learn how it works, check out the documentation:
• Chapter 1: Tools
• Chapter 2: Merging
• Chapter 3: In-Place
• Chapter 4: Faster!
Or you can check out the Wikipedia page that is now up and running! Technically block sort is still a merge sort despite requiring the use of some other sorting algorithm like insertion sort to function properly, but it was too detailed to justify putting in the existing in-place merge sort page.
WikiSort vs. std::stable_sort()
(clang++ version 3.2, sorting 0 to 1.5 million items)
Using a 512-item fixed-size cache for O(1) memory:
Test Fast comparisons Slow comparisons 150,000,000 items 0-32 items
Random 6% faster 95% as fast 35% faster 45% faster
RandomFew 5% faster 16% faster 20% faster 45% faster
MostlyDescending 97% as fast 13% faster 99% as fast 53% faster
MostlyAscending 149% faster 117% faster 286% faster 47% faster
Ascending 1280% faster 518% faster 1101% faster 242% faster
Descending 23% faster 121% faster 12% faster 164% faster
Equal 1202% faster 418% faster 1031% faster 227% faster
Jittered 526% faster 298% faster 733% faster 70% faster
MostlyEqual 15% faster 57% faster 10% faster 42% faster
Append 153% faster 90% faster 348% faster 112% faster
Using a dynamically allocated half-size cache:
Test Fast comparisons Slow comparisons
Random 11% faster 3% faster
RandomFew 10% faster 5% faster
MostlyDescending 19% faster 26% faster
MostlyAscending 98% faster 79% faster
Ascending 861% faster 463% faster
Descending 39% faster 142% faster
Equal 837% faster 460% faster
Jittered 326% faster 243% faster
MostlyEqual 15% faster 2% faster
Append 159% faster 94% faster
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