[PATCH] Bug 20837 - libc++ std::sort has O(n^2) worst case, standard mandates O(N log(N))

[Marshall Clow]

On Sep 2, 2014, at 12:05 PM, Orson Peters <orsonpeters at gmail.com> wrote:

> This is a patch for bug 20837 - "libc++ std::sort has O(n^2) worst
> case, standard mandates O(N log(N))" found at
> http://llvm.org/bugs/show_bug.cgi?id=20837 . Description and
> attachments copied in this email as suggested by Hal Finkel.
> 
> 
> The C++ standard mandates that `std::sort` has complexity O(N log(N)),
> but libc++'s implementation takes O(N^2) in the worst case.
> 
> As proof I've attached a program that constructs a worst case input
> for several sizes. It also instruments the number of comparisons used
> to sort these worst cases and prints the results. The technique used
> is described in the 1999 paper "A Killer Adversary for Quicksort" by
> M. D. McIlroy.
> 
> Compiling and running:
> 
> $ clang++ -O2 -m64 -march=native -std=c++11 -stdlib=libc++ main.cpp
> -nodefaultlibs -lc++ -lc++abi -lm -lc -lgcc_s -lgcc && ./a.out
> N: comparisons
> 100: 2479
> 200: 10229
> 400: 40729
> 800: 161729
> 1600: 448698
> 3200: 1413898
> 6400: 5264298
> 
> This is clearly quadratic. To illustrate this defect more, these are
> the comparison counts given by compiling using libstdc++:
> 
> $ clang++ -O2 -m64 -march=native -std=c++11 main.cpp && ./a.out
> N: comparisons
> 100: 1742
> 200: 4260
> 400: 10035
> 800: 22784
> 1600: 51049
> 3200: 112386
> 6400: 244850
> 
> Inspecting the source of <algorithm> shows the cause of the issue:
> there is no introsort implemented, only quicksort (albeit with
> non-trivial optimizations, but nothing preventing the worst case).
> I've written a patch that augments the current implementation to make
> it work as an introspective sort, switching to heapsort if the
> recursion depth exceeds 2*floor(log(N)). The patch is attached to this
> email.
> 
> Having not contributed to libc++ before I'm not 100% familiar with all
> coding styles/(un)written rules. My changes are rather minimal though,
> so I've just followed what style could be found in context. And of
> course I knowingly submit my code under the libc++ licenses, the MIT
> license and the UIUC License.

Thanks for the report and the patch.
I am doing some research and testing on this.

— Marshall