The new optimized version of Dual-Pivot Quicksort

[Tagir Valeev]

Hello!

By the way why not using radix sort, at least for int[] arrays? The
implementation is much simpler, it uses constant-size additional
buffer (1024 ints) and performance should be better than DPQS, at
least for large arrays. Here's sample implementation written by me
several years ago (reusing merge sort part from JDK) which degrades to
merge sort if array is nearly sorted.
http://cr.openjdk.java.net/~tvaleev/patches/radix/RadixSort.java

With best regards,
Tagir Valeev.

On Fri, Jan 19, 2018 at 8:38 PM Vladimir Yaroslavskiy
<vlv.spb.ru at mail.ru> wrote:
>
> Hi team,
>
> In Sept 2009 Josh Bloch, Jon Bentley and I introduced new sorting
> algorithm, Dual-Pivot Quicksort, for primitives in JDK 7 and later
> I suggested several improvements of Dual-Pivot Quicksort, which
> were integrated into JDK 8.
>
> Now I have more optimized and faster version of Dual-Pivot Quicksort.
> I have been working on it for the last 5 years. Please, find the
> summary of changes below and sources / diff at webrev [1].
>
> All tests and benchmarking were run on the most recent build of JDK 10,
> jdk-10-ea+39. The new version shows the better performance on different
> inputs and guarantees n*log(n) on any data.
>
> The new implementation of Dual-Pivot Quicksort is 'all-in-one' version:
> it contains one code for both parallel and sequential sorting algorithms.
>
> Suggested version is 10-20% faster on random data, 1.5-4 times faster
> on nearly structured arrays, 1.5-2 times faster on period inputs.
>
> Parallel Dual-Pivot Quicksort is 1.5-3 times faster than current
> algorithm based on merge sort.
>
> Benchmarking on the test suite, suggested by Jon Bentley, shows the
> boost of performance in 1.4 times. This test suite contains several
> types of inputs, such as random data, nearly structured arrays, data
> with period and so on. Also there are several modifications of inputs
> and parameters which are used in data building. We run sorting on all
> combinations to compare two algorithms.
>
> Please let me know if you have any questions / comments.
>
> Summary of changes:
>
> DualPivotQuicksort class
> ------------------------
> * Pivots are chosen with another step, the 1-st and 5-th candidates
>    are taken as pivots instead of 2-nd and 4-th.
> * Splitting into parts is related to the golden ratio
> * Pivot candidates are sorted by combination of 5-element
>    network sorting + insertion sort
> * New backwards partitioning is simpler and more efficient
> * Quicksort tuning parameters were updated
> * Merging sort is invoked on each iteration from Quicksort
> * Additional steps for float/double were fully rewritten
> * Heap sort is invoked on the leftmost part
> * Heap sort is used as a guard against quadratic time
> * Parallel sorting is based on Dual-Pivot Quicksort
>    instead of merge sort
>
> SortingAlgorithms class
> -----------------------
> * Merging sort and pair insertion sort were moved from
>    DualPivotQuicksort class
> * Pair insertion sort was simplified and optimized
> * New nano insertion sort was introduced for tiny arrays
> * Merging sort was fully rewritten
> * Optimized merging partitioning is used
> * Merging parameters were updated
> * Merging of runs was fully rewritten
> * Fast version of heap sort was introduced
> * Parallel merging sort was also provided
>
> Sorting / ParallelSorting classes
> ---------------------------------
> * New test cases were added
> * Sources of these classes were unified
>
> Arrays class
> ------------
> * Calls of Dual-Pivot Quicksort were updated
> * Parallel sorting of primitives was switched to parallel
>    Dual-Pivot Quicksort
> * Javadoc was modified
>
> ArraysParallelSortHelpers class
> -------------------------------
> * Old implementation of parallel sorting for primitives was removed
> * Javadoc was updated
>
> Thank you,
> Vladimir
>
> --------------------------------------------------------------------
> [1] http://cr.openjdk.java.net/~alanb/DualPivotSortUpdate/webrev.01/
> --------------------------------------------------------------------