New portion of improvements for Dual-Pivot Quicksort
Goktug Gokdogan
gokdogan at gmail.com
Thu Apr 29 08:18:13 UTC 2010
One quick comment: you can consider moving trivial array check so it will be
executed only if insertion sort threshold check passes:
if (length < INSERTION_SORT_THRESHOLD) {
if (length < 2) {
return;
}
....
On Mon, Apr 26, 2010 at 2:50 PM, Vladimir Iaroslavski <
vladimir.iaroslavski at googlemail.com> wrote:
> 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
>
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