New portion of improvements for Dual-Pivot Quicksort

[Vladimir Iaroslavski]

Hello Dmytro,

Please, see file test/java/util/Arrays/Sorting.java in the
JDK repository, It contains unit tests.

Thank you,
Vladimir

2010/4/30 Dmytro Sheyko <dmytro_sheyko at hotmail.com>:
> Hello Vladimir,
>
> Could you remind me where can I find sources for the test suite?
>
> Thanks,
> Dmytro
>
>> Date: Tue, 27 Apr 2010 01:50:08 +0400
>> Subject: New portion of improvements for Dual-Pivot Quicksort
>> From: vladimir.iaroslavski at googlemail.com
>> To: core-libs-dev at openjdk.java.net
>>
>> Hello, everyone!
>>
>> I've investigated the implementation of the Dual-Pivot Quicksort
>> which is used for sorting primitives and here is my result:
>>
>> http://cr.openjdk.java.net/~alanb/6947216/webrev.00
>>
>> New implementation of Dual-Pivot Quicksort is faster
>> than previous one of 12% for client VM and few percents for
>> server VM. Tests on Bentley's test suite (Win XP, JDK 7,
>> build 1.7.0-ea-b84, n = 1000000) show geometry mean 0.88
>> for client VM and 0.98-1.00 for server VM.
>>
>> In compare with sorting from JDK 6 by Jon L. Bentley and
>> M. Douglas McIlroy's (with one pivot) the ratio is 0.61 / 0.50
>> (client / server).
>>
>> See the execution time for sorting array of 2`000`000 int elements
>> 50 times, client / server VM, in milliseconds:
>>
>> random
>> new: 16723 18776
>> jdk7: 17571 18975
>> jdk6: 22241 26524
>>
>> ascendant
>> new: 3541 4702
>> jdk7: 4486 4669
>> jdk6: 8667 7978
>>
>> descendant
>> new: 3854 4907
>> jdk7: 4942 5034
>> jdk6: 8787 8243
>>
>> equal
>> new: 234 281
>> jdk7: 291 230
>> jdk6: 602 1018
>>
>> organ pipes
>> new: 7673 8613
>> jdk7: 8167 8993
>> jdk6: 11902 14044
>>
>> stagger 1
>> new: 7648 8591
>> jdk7: 8161 8979
>> jdk6: 11908 13810
>>
>> stagger 2
>> new: 8349 9299
>> jdk7: 10968 11916
>> jdk6: 12194 14734
>>
>> stagger 4
>> new: 8475 9622
>> jdk7: 9221 9682
>> jdk6: 10523 12006
>>
>> stagger 8
>> new: 9321 10689
>> jdk7: 11125 12387
>> jdk6: 13829 16214
>>
>> period 1..2
>> new: 758 751
>> jdk7: 870 754
>> jdk6: 1038 1227
>>
>> period 1..4
>> new: 1004 963
>> jdk7: 1365 1209
>> jdk6: 1511 1847
>>
>> period 1..8
>> new: 1588 1573
>> jdk7: 1599 1790
>> jdk6: 2602 3045
>>
>> random 1..2
>> new: 1327 1125
>> jdk7: 1362 1496
>> jdk6: 1531 2182
>>
>> random 1..4
>> new: 1830 2118
>> jdk7: 1851 2236
>> jdk6: 2292 3025
>>
>> where stagger(m) is array like a[i] = i * (m + 1) % length.
>>
>> The summary of changes is:
>>
>> 1. For sorting small arrays is used insertion sort with sentinel
>> instead of traditional, which has the structure:
>>
>> for (int i = left + 1; i <= right; i++) {
>> for (j = i; j > left && a[j-1] > a[j]; j--) {
>> swap(a[i], a[j-1]);
>> }
>> }
>>
>> Note that range check j > left is performed on each iteration,
>> but really helps very rare. To avoid this expensive range check,
>> it was suggested to set minimum value (negative infinity) on the
>> first position. This type of suggestion is used in new version:
>>
>> if left bound > 0, we can put sentinel on a[left - 1], do insertion
>> sort without expensive check range, and then restore a[left - 1]
>> value. If left == 0, traditional insertion sort is used. Please,
>> look at the webrev for details.
>>
>> 2. In previous implementation 5 evenly spaced elements
>>
>> sixth = length / 6;
>> a[sixth], a[2 * sixth], a[3 * sixth], a[4 * sixth], a[5 * sixth]
>>
>> were used as candidates of pivots elements. This case is very
>> sensitive for period inputs, especially by 6. The new suggestion
>> is to take 5 center evenly spaced elements like this:
>>
>> int seventh = length / 7;
>> int midpoint = (left + right) >>> 1;
>>
>> a[midpoint - 2 * seventh], a[midpoint - seventh], a[midpoint],
>> a[midpoint + seventh], a[midpoint + 2 * seventh]
>>
>> and moreover, the seventh is calculated inexpensively:
>> seventh = (length >>> 3) + (length >>> 6) + 1;
>>
>> This schema works the same on random, ascendant, descendant, equal
>> inputs, but much better for period / stagger.
>>
>> 3. The whole structure
>>
>> <choose pivots>
>>
>> if (pivotsDiffer) {
>> <do partitioning for two pivots>
>> }
>> else {
>> <do partitioning for one pivot>
>> }
>>
>> <sort left and right parts>
>>
>> if (!pivotsDiffer) {
>> return;
>> }
>> <swap internal pivot values to ends>
>>
>> <sort center part>
>>
>> was modified to:
>> ----------------
>>
>> <choose pivots>
>>
>> if (pivot1 < pivot2) {
>> <do partitioning for two pivots>
>> <swap pivots into their final positions>
>> <sort left and right parts>
>> <swap internal pivot values to ends>
>> <sort center part>
>> }
>> else {
>> <do partitioning for one pivot>
>> <sort left and right parts>
>> }
>>
>> 4. Partitioning for both cases have not been changed at all.
>>
>> 5. Minor javadoc and format changes.
>>
>> Please, review new implementation,
>> any comments / suggestions are welcome!
>>
>> Thank you,
>> Vladimir