8266431: Dual-Pivot Quicksort improvements (Radix sort)

[VladimirIaroslavski]

The goal of the PR is to improve both, sequential and parallel, sorting of primitives.

The main achievements

• introduced Radix in parallel sorting which shows several times boost of performance and has linear complexity instead of n*ln(n)

• improved mixed insertion sort (makes whole sorting faster)

• improved merging sort for almost sorted data

• optimized parallel sorting

• improved step for pivot candidates and pivot partitioning

• suggested better buffer allocation: if no memory, it is switched to in-place sorting with no OutOfMemoryError

• minor javadoc and comment changes

• extended existing tests

• added tests for radix sort, heap sort, insertion sort

• added benchmarking JMH tests

• improved test coverage

The summary of benchmarking:

Sequential sorting (Arrays.sort)

byte: up to 50% faster
char: 4-7 times faster
short: 2-6 times faster
int: 1.2-5 times faster
long: 1.2-5 times faster
float: 1.2-5 times faster
double: 1.2-4 times faster

Parallel sorting (Arrays.parallelSort)

int: 1.2-9 times faster
long: 1.2-9 times faster
float: 1.2-4 times faster
double: 1.2-4 times faster

AVX512 support

Vamsi Parasa suggested faster sort routines by taking advantage of AVX512 instructions, see #14227, sources of sorting were modified. Therefore, I performed benchmarking of the final version (which includes optimizations by Vamsi Parasa and optimizations from my side) on a server with CPUs supported AVX512 instructions, no regression of performance was found, see detailed benchmarking results.

High-level chart showing how the actual sorting algorithm is selected
based on parallel/sequential and input size

int/long/float/double

if size < MAX_INSERTION_SORT_SIZE(=51) => [ mixed ] insertion sort
if array is almost sorted and size > MIN_MERGING_SORT_SIZE(=512) => merging sort
if recursion depth > MAX_RECURSION_DEPTH(=64) => heap sort
if random data => two pivots quicksort, else => one pivot quicksort

byte

if size < MAX_INSERTION_SORT_SIZE(=51) => insertion sort
else => counting sort

char/short

if size > MIN_COUNTING_SORT_SIZE(640) => counting sort
if size < MAX_INSERTION_SORT_SIZE(=51) => insertion sort
if recursion depth > MAX_RECURSION_DEPTH(=64) => counting sort
if random data => two pivots quicksort, else => one pivot quicksort

parallel sorting (int/long/float/double)

if size < MIN_PARALLEL_SORT_SIZE(3K) => sequential sort
invoke parallel merge sort, depth depends on parallelism level
then switch to parallel quicksort.

---

Progress

• Change must be properly reviewed (1 review required, with at least 1 Reviewer)
• Change must not contain extraneous whitespace
• Commit message must refer to an issue

Issue

• JDK-8266431: Dual-Pivot Quicksort improvements (Radix sort) (Enhancement - P4)

Reviewers

• Tagir F. Valeev (@amaembo - Committer)

Reviewing

Using git

Checkout this PR locally:
$ git fetch https://git.openjdk.org/jdk.git pull/27411/head:pull/27411
$ git checkout pull/27411

Update a local copy of the PR:
$ git checkout pull/27411
$ git pull https://git.openjdk.org/jdk.git pull/27411/head

Using Skara CLI tools

Checkout this PR locally:
$ git pr checkout 27411

View PR using the GUI difftool:
$ git pr show -t 27411

Using diff file

Download this PR as a diff file:
https://git.openjdk.org/jdk/pull/27411.diff

Using Webrev

Link to Webrev Comment

[bridgekeeper]

👋 Welcome back VladimirIaroslavski! A progress list of the required criteria for merging this PR into master will be added to the body of your pull request. There are additional pull request commands available for use with this pull request.

[openjdk]

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See the Progress checklist in the description for automated requirements.

[openjdk]

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[VladimirIaroslavski]

Sorting on a server with AVX512 instructions

OS name: Fedora Linux 38 (Workstation Edition)
Model name: Intel(R) Xeon(R) Gold 6338 CPU @ 2.00GHz
CPU family: 6
Model: 106
Thread(s) per core: 2
Core(s) per socket: 32
Socket(s): 2

OpenJDK version "24-beta" 2025-03-18
OpenJDK Runtime Environment Zulu24+53-CA (build 24-beta+22)
OpenJDK 64-Bit Server VM Zulu24+53-CA (build 24-beta+22, mixed mode, sharing)

Sequential sorting

Benchmark	Data Type	Array Size	Baseline (us/op)	New version (us/op)	Speedup
byte	RANDOM	600	1,105	1,096	1.01
byte	RANDOM	3000	3,315	3,015	1.10
byte	RANDOM	40000	41,283	36,735	1.12
byte	RANDOM	800000	472,986	371,946	1.27
byte	RANDOM	5000000	2958,884	2359,100	1.25
byte	SHUFFLE	600	1,025	1,025	1.00
byte	SHUFFLE	3000	3,110	2,995	1.04
byte	SHUFFLE	40000	37,507	34,698	1.08
byte	SHUFFLE	800000	440,601	353,063	1.25
byte	SHUFFLE	5000000	2645,334	2220,906	1.19
byte	STAGGER	600	0,682	0,696	0.98
byte	STAGGER	3000	2,473	2,498	0.99
byte	STAGGER	40000	16,892	17,167	0.98
byte	STAGGER	800000	340,018	334,596	1.02
byte	STAGGER	5000000	2171,872	2180,550	1.00
byte	REPEATED	600	0,824	0,840	0.98
byte	REPEATED	3000	2,435	2,448	0.99
byte	REPEATED	40000	29,167	29,168	1.00
byte	REPEATED	800000	592,413	592,667	1.00
byte	REPEATED	5000000	3792,008	3791,389	1.00
---	---	---	---	---	---
char	RANDOM	600	8,076	5,811	1.39
char	RANDOM	3000	127,738	18,471	6.92
char	RANDOM	40000	466,992	464,783	1.00
char	RANDOM	800000	1962,639	2007,212	0.98
char	RANDOM	5000000	6608,751	6730,025	0.98
char	SHUFFLE	600	4,713	3,574	1.32
char	SHUFFLE	3000	86,595	10,962	7.90
char	SHUFFLE	40000	116,087	103,458	1.12
char	SHUFFLE	800000	802,059	747,908	1.07
char	SHUFFLE	5000000	3527,583	3273,802	1.08
char	STAGGER	600	9,146	5,651	1.62
char	STAGGER	3000	88,480	9,888	8.95
char	STAGGER	40000	140,569	129,855	1.08
char	STAGGER	800000	694,116	701,170	0.99
char	STAGGER	5000000	3685,380	3667,346	1.00
char	REPEATED	600	1,775	1,745	1.02
char	REPEATED	3000	87,272	17,176	5.08
char	REPEATED	40000	116,472	88,054	1.32
char	REPEATED	800000	789,963	660,936	1.20
char	REPEATED	5000000	4373,931	3907,108	1.12
---	---	---	---	---	---
short	RANDOM	600	8,433	5,455	1.55
short	RANDOM	3000	95,889	9,871	9.71
short	RANDOM	40000	526,723	457,268	1.15
short	RANDOM	800000	1991,657	2011,202	0.99
short	RANDOM	5000000	6592,367	6745,836	0.98
short	SHUFFLE	600	4,706	3,597	1.31
short	SHUFFLE	3000	44,413	11,895	3.73
short	SHUFFLE	40000	137,088	139,490	0.98
short	SHUFFLE	800000	851,142	813,856	1.05
short	SHUFFLE	5000000	3605,340	3642,393	0.99
short	STAGGER	600	8,932	5,088	1.76
short	STAGGER	3000	54,740	11,432	4.79
short	STAGGER	40000	141,403	104,327	1.36
short	STAGGER	800000	739,105	755,126	0.98
short	STAGGER	5000000	3613,685	3649,485	0.99
short	REPEATED	600	1,787	1,646	1.09
short	REPEATED	3000	41,117	17,711	2.32
short	REPEATED	40000	67,597	62,072	1.09
short	REPEATED	800000	725,665	635,773	1.14
short	REPEATED	5000000	3961,620	3910,409	1.01
---	---	---	---	---	---
int	RANDOM	600	10,062	6,263	1.61
int	RANDOM	3000	106,288	81,867	1.30
int	RANDOM	40000	2706,821	2409,536	1.12
int	RANDOM	800000	70786,294	63018,686	1.12
int	RANDOM	5000000	513654,721	448534,136	1.15
int	SHUFFLE	600	5,554	3,832	1.45
int	SHUFFLE	3000	34,681	23,799	1.46
int	SHUFFLE	40000	810,646	675,154	1.20
int	SHUFFLE	800000	17786,842	13394,929	1.33
int	SHUFFLE	5000000	103972,483	89292,885	1.16
int	STAGGER	600	10,912	1,919	5.69
int	STAGGER	3000	16,805	8,743	1.92
int	STAGGER	40000	221,680	119,119	1.86
int	STAGGER	800000	4439,270	2646,225	1.68
int	STAGGER	5000000	28206,856	18989,937	1.49
int	REPEATED	600	1,600	1,401	1.14
int	REPEATED	3000	8,333	8,166	1.02
int	REPEATED	40000	366,056	338,253	1.08
int	REPEATED	800000	8381,340	7163,611	1.17
int	REPEATED	5000000	57009,039	49579,605	1.15
---	---	---	---	---	---
long	RANDOM	600	9,526	5,500	1.73
long	RANDOM	3000	106,262	81,212	1.31
long	RANDOM	40000	2642,178	2380,290	1.11
long	RANDOM	800000	71082,533	60574,668	1.17
long	RANDOM	5000000	497591,181	441894,477	1.13
long	SHUFFLE	600	5,003	3,666	1.36
long	SHUFFLE	3000	39,157	24,116	1.62
long	SHUFFLE	40000	731,785	653,146	1.12
long	SHUFFLE	800000	18055,584	14313,625	1.26
long	SHUFFLE	5000000	122763,113	85477,515	1.44
long	STAGGER	600	8,668	2,020	4.29
long	STAGGER	3000	59,460	9,874	6.02
long	STAGGER	40000	888,697	142,874	6.22
long	STAGGER	800000	19205,162	3480,767	5.52
long	STAGGER	5000000	123337,211	26088,945	4.73
long	REPEATED	600	1,764	1,618	1.09
long	REPEATED	3000	9,284	8,147	1.14
long	REPEATED	40000	370,378	320,390	1.16
long	REPEATED	800000	8546,204	7641,426	1.12
long	REPEATED	5000000	57714,600	50890,207	1.13
---	---	---	---	---	---
float	RANDOM	600	9,229	6,824	1.35
float	RANDOM	3000	98,336	94,386	1.04
float	RANDOM	40000	2737,466	2626,643	1.04
float	RANDOM	800000	71064,995	67788,935	1.05
float	RANDOM	5000000	511617,741	483790,193	1.06
float	SHUFFLE	600	5,356	4,482	1.20
float	SHUFFLE	3000	32,069	27,485	1.17
float	SHUFFLE	40000	803,721	786,535	1.02
float	SHUFFLE	800000	17475,458	15571,843	1.12
float	SHUFFLE	5000000	104055,032	103707,582	1.00
float	STAGGER	600	9,823	2,259	4.35
float	STAGGER	3000	21,148	10,721	1.97
float	STAGGER	40000	280,128	145,725	1.92
float	STAGGER	800000	5625,923	3227,219	1.74
float	STAGGER	5000000	35646,533	22611,370	1.58
float	REPEATED	600	2,489	2,273	1.10
float	REPEATED	3000	14,390	11,444	1.26
float	REPEATED	40000	537,690	456,280	1.18
float	REPEATED	800000	11733,707	10678,972	1.10
float	REPEATED	5000000	78247,675	58791,233	1.33
---	---	---	---	---	---
double	RANDOM	600	9,209	6,879	1.34
double	RANDOM	3000	100,158	89,748	1.12
double	RANDOM	40000	2744,205	2589,135	1.06
double	RANDOM	800000	71450,447	67051,035	1.07
double	RANDOM	5000000	518599,968	482903,685	1.07
double	SHUFFLE	600	5,424	4,574	1.19
double	SHUFFLE	3000	31,738	27,942	1.14
double	SHUFFLE	40000	787,763	776,840	1.01
double	SHUFFLE	800000	17492,549	16081,350	1.09
double	SHUFFLE	5000000	107874,866	107086,811	1.01
double	STAGGER	600	9,883	2,206	4.48
double	STAGGER	3000	19,615	10,908	1.80
double	STAGGER	40000	270,368	151,057	1.79
double	STAGGER	800000	5504,383	3658,210	1.50
double	STAGGER	5000000	37996,995	29044,386	1.31
double	REPEATED	600	2,548	2,260	1.13
double	REPEATED	3000	14,333	12,515	1.15
double	REPEATED	40000	544,588	459,425	1.19
double	REPEATED	800000	11791,047	10734,706	1.10
double	REPEATED	5000000	79668,645	62098,296	1.28

Parallel sorting

Benchmark	Data Type	Array Size	Baseline (us/op)	New version (us/op)	Speedup
int	RANDOM	600	9,724	6,154	1.58
int	RANDOM	3000	96,070	85,794	1.12
int	RANDOM	40000	414,904	282,580	1.47
int	RANDOM	800000	4743,790	1429,808	3.32
int	RANDOM	5000000	23981,879	13549,869	1.77
int	SHUFFLE	600	6,029	3,632	1.66
int	SHUFFLE	3000	37,097	22,772	1.63
int	SHUFFLE	40000	193,044	97,703	1.98
int	SHUFFLE	800000	1769,768	900,230	1.97
int	SHUFFLE	5000000	11040,155	7635,319	1.45
int	STAGGER	600	10,948	2,366	4.63
int	STAGGER	3000	15,728	11,559	1.36
int	STAGGER	40000	76,648	65,278	1.17
int	STAGGER	800000	912,780	532,419	1.71
int	STAGGER	5000000	5528,946	2886,539	1.92
int	REPEATED	600	2,000	1,588	1.26
int	REPEATED	3000	10,518	8,022	1.31
int	REPEATED	40000	153,249	101,689	1.51
int	REPEATED	800000	2564,321	1102,722	2.33
int	REPEATED	5000000	16141,658	6440,913	2.51
---	---	---	---	---	---
long	RANDOM	600	9,392	5,974	1.57
long	RANDOM	3000	119,022	72,486	1.64
long	RANDOM	40000	446,894	327,094	1.37
long	RANDOM	800000	4618,046	2157,313	2.14
long	RANDOM	5000000	26806,347	17064,431	1.57
long	SHUFFLE	600	5,037	3,991	1.26
long	SHUFFLE	3000	39,226	28,969	1.35
long	SHUFFLE	40000	188,613	117,552	1.60
long	SHUFFLE	800000	2203,806	1436,670	1.53
long	SHUFFLE	5000000	15363,291	10869,309	1.41
long	STAGGER	600	10,616	2,506	4.24
long	STAGGER	3000	15,545	13,073	1.19
long	STAGGER	40000	94,714	71,397	1.33
long	STAGGER	800000	1263,737	933,039	1.35
long	STAGGER	5000000	8534,961	5804,477	1.47
long	REPEATED	600	1,726	1,640	1.05
long	REPEATED	3000	10,035	7,876	1.27
long	REPEATED	40000	168,700	110,725	1.52
long	REPEATED	800000	2845,738	1504,553	1.89
long	REPEATED	5000000	18759,763	9377,812	2.00
---	---	---	---	---	---
float	RANDOM	600	9,931	6,936	1.43
float	RANDOM	3000	119,779	99,573	1.20
float	RANDOM	40000	476,756	392,104	1.22
float	RANDOM	800000	4930,482	2919,610	1.69
float	RANDOM	5000000	29463,322	17644,605	1.67
float	SHUFFLE	600	5,459	4,543	1.20
float	SHUFFLE	3000	32,297	27,887	1.16
float	SHUFFLE	40000	235,827	181,163	1.30
float	SHUFFLE	800000	2428,839	1791,028	1.36
float	SHUFFLE	5000000	15353,423	10433,192	1.47
float	STAGGER	600	9,779	2,415	4.05
float	STAGGER	3000	18,693	11,581	1.61
float	STAGGER	40000	117,526	79,751	1.47
float	STAGGER	800000	1744,397	1160,997	1.50
float	STAGGER	5000000	10651,683	7002,571	1.52
float	REPEATED	600	2,651	2,262	1.17
float	REPEATED	3000	15,812	11,984	1.32
float	REPEATED	40000	270,629	155,697	1.74
float	REPEATED	800000	5450,441	1741,966	3.13
float	REPEATED	5000000	34499,266	10705,402	3.22
---	---	---	---	---	---
double	RANDOM	600	9,183	6,965	1.32
double	RANDOM	3000	97,578	94,393	1.03
double	RANDOM	40000	468,966	410,451	1.14
double	RANDOM	800000	5202,712	3569,054	1.46
double	RANDOM	5000000	32081,048	22927,051	1.40
double	SHUFFLE	600	5,462	4,438	1.23
double	SHUFFLE	3000	31,924	27,371	1.17
double	SHUFFLE	40000	263,423	199,992	1.32
double	SHUFFLE	800000	2826,594	2387,148	1.18
double	SHUFFLE	5000000	19212,580	16573,293	1.16
double	STAGGER	600	9,803	2,558	3.83
double	STAGGER	3000	19,258	13,093	1.47
double	STAGGER	40000	133,250	107,261	1.24
double	STAGGER	800000	2027,997	1561,934	1.30
double	STAGGER	5000000	14387,512	10943,813	1.31
double	REPEATED	600	2,553	2,266	1.13
double	REPEATED	3000	14,479	11,995	1.21
double	REPEATED	40000	274,235	167,220	1.64
double	REPEATED	800000	5378,801	2182,560	2.46
double	REPEATED	5000000	35181,974	14323,815	2.46

[VladimirIaroslavski]

Sorting on a computer without AVX512 support

OS name: Edition Windows 10 Pro
Processor: Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz
System type: 64-bit operating system, x64-based processor
Version: 22H2

OpenJDK 26-ea 2026-03-17
OpenJDK Runtime Environment (build 26-ea+13-1333)
OpenJDK 64-Bit Server VM (build 26-ea+13-1333, mixed mode, sharing)

Sequential sorting

Benchmark	Data Type	Array Size	Baseline (us/op)	New version (us/op)	Speedup
byte	RANDOM	600	1,336	1,341	1.00
byte	RANDOM	3000	3,775	3,813	0.99
byte	RANDOM	40000	30,852	31,590	0.98
byte	RANDOM	800000	526,780	526,931	1.00
byte	RANDOM	5000000	3427,225	3466,470	0.99
byte	SHUFFLE	600	1,253	1,260	0.99
byte	SHUFFLE	3000	3,456	3,526	0.98
byte	SHUFFLE	40000	30,739	31,153	0.99
byte	SHUFFLE	800000	506,622	507,776	1.00
byte	SHUFFLE	5000000	3358,144	3340,962	1.01
byte	STAGGER	600	0,926	0,903	1.03
byte	STAGGER	3000	2,463	2,489	0.99
byte	STAGGER	40000	26,155	25,906	1.01
byte	STAGGER	800000	501,954	504,353	1.00
byte	STAGGER	5000000	3264,418	3268,509	1.00
byte	REPEATED	600	0,978	0,634	1.54
byte	REPEATED	3000	2,870	2,532	1.13
byte	REPEATED	40000	30,026	28,714	1.05
byte	REPEATED	800000	571,674	571,686	1.00
byte	REPEATED	5000000	3740,136	3744,403	1.00
---	---	---	---	---	---
char	RANDOM	600	11,029	6,696	1.65
char	RANDOM	3000	106,682	11,737	9.09
char	RANDOM	40000	518,084	509,866	1.02
char	RANDOM	800000	2251,095	2296,499	0.98
char	RANDOM	5000000	8126,281	8208,779	0.99
char	SHUFFLE	600	6,646	4,382	1.52
char	SHUFFLE	3000	91,039	12,664	7.19
char	SHUFFLE	40000	163,862	162,688	1.01
char	SHUFFLE	800000	991,965	981,299	1.01
char	SHUFFLE	5000000	4388,959	4477,596	0.98
char	STAGGER	600	11,344	6,691	1.70
char	STAGGER	3000	74,156	12,469	5.95
char	STAGGER	40000	138,021	138,125	1.00
char	STAGGER	800000	905,072	869,419	1.04
char	STAGGER	5000000	5075,574	5076,498	1.00
char	REPEATED	600	1,796	1,675	1.07
char	REPEATED	3000	72,315	17,109	4.23
char	REPEATED	40000	100,150	99,830	1.00
char	REPEATED	800000	788,861	728,818	1.08
char	REPEATED	5000000	4534,875	4417,603	1.03
---	---	---	---	---	---
short	RANDOM	600	11,147	6,657	1.67
short	RANDOM	3000	97,153	14,013	6.93
short	RANDOM	40000	536,996	533,115	1.01
short	RANDOM	800000	2214,721	2236,256	0.99
short	RANDOM	5000000	8129,979	8305,536	0.98
short	SHUFFLE	600	6,466	4,328	1.49
short	SHUFFLE	3000	37,262	14,628	2.55
short	SHUFFLE	40000	151,558	151,465	1.00
short	SHUFFLE	800000	952,759	961,413	0.99
short	SHUFFLE	5000000	4392,945	4481,849	0.98
short	STAGGER	600	11,456	6,737	1.70
short	STAGGER	3000	42,934	14,630	2.93
short	STAGGER	40000	122,307	120,126	1.02
short	STAGGER	800000	837,886	858,188	0.98
short	STAGGER	5000000	5099,399	5063,530	1.01
short	REPEATED	600	1,797	1,673	1.07
short	REPEATED	3000	36,409	18,124	2.01
short	REPEATED	40000	68,712	64,305	1.07
short	REPEATED	800000	748,089	676,263	1.11
short	REPEATED	5000000	4509,726	4354,061	1.04
---	---	---	---	---	---
int	RANDOM	600	12,799	8,529	1.50
int	RANDOM	3000	168,717	151,504	1.11
int	RANDOM	40000	3053,482	2663,760	1.15
int	RANDOM	800000	77058,078	68039,633	1.13
int	RANDOM	5000000	553486,331	483191,027	1.15
int	SHUFFLE	600	7,091	5,090	1.39
int	SHUFFLE	3000	57,823	37,976	1.52
int	SHUFFLE	40000	982,797	804,192	1.22
int	SHUFFLE	800000	20170,567	15124,860	1.33
int	SHUFFLE	5000000	119944,448	101314,175	1.18
int	STAGGER	600	12,372	2,332	5.31
int	STAGGER	3000	18,185	11,073	1.64
int	STAGGER	40000	263,148	149,947	1.75
int	STAGGER	800000	5206,958	3003,595	1.73
int	STAGGER	5000000	33070,195	20196,353	1.64
int	REPEATED	600	1,850	1,689	1.10
int	REPEATED	3000	19,935	16,725	1.19
int	REPEATED	40000	427,379	426,491	1.00
int	REPEATED	800000	8780,449	8693,568	1.01
int	REPEATED	5000000	59041,332	53085,389	1.11
---	---	---	---	---	---
long	RANDOM	600	12,759	8,332	1.53
long	RANDOM	3000	170,641	153,686	1.11
long	RANDOM	40000	3102,722	2702,462	1.15
long	RANDOM	800000	76062,436	68565,859	1.11
long	RANDOM	5000000	550540,619	488863,464	1.13
long	SHUFFLE	600	7,482	5,153	1.45
long	SHUFFLE	3000	53,436	39,168	1.36
long	SHUFFLE	40000	980,789	803,654	1.22
long	SHUFFLE	800000	20833,103	15763,843	1.32
long	SHUFFLE	5000000	122366,475	104073,072	1.18
long	STAGGER	600	12,709	2,299	5.53
long	STAGGER	3000	19,001	11,054	1.72
long	STAGGER	40000	275,147	165,269	1.66
long	STAGGER	800000	5466,681	3912,351	1.40
long	STAGGER	5000000	37297,708	29582,068	1.26
long	REPEATED	600	2,107	1,681	1.25
long	REPEATED	3000	16,612	9,562	1.74
long	REPEATED	40000	426,694	421,148	1.01
long	REPEATED	800000	8904,279	8561,931	1.04
long	REPEATED	5000000	60695,788	54597,570	1.11
---	---	---	---	---	---
float	RANDOM	600	12,991	9,693	1.34
float	RANDOM	3000	175,275	167,552	1.05
float	RANDOM	40000	3138,437	2962,572	1.06
float	RANDOM	800000	79635,198	75467,573	1.06
float	RANDOM	5000000	572424,359	536613,819	1.07
float	SHUFFLE	600	7,568	6,270	1.21
float	SHUFFLE	3000	54,735	43,874	1.25
float	SHUFFLE	40000	992,473	912,560	1.09
float	SHUFFLE	800000	20273,495	17291,888	1.17
float	SHUFFLE	5000000	120219,159	113983,042	1.05
float	STAGGER	600	13,936	2,911	4.79
float	STAGGER	3000	23,105	13,149	1.76
float	STAGGER	40000	307,735	179,749	1.71
float	STAGGER	800000	22328,783	3838,253	5.82
float	STAGGER	5000000	143354,475	27434,381	5.23
float	REPEATED	600	2,952	2,551	1.16
float	REPEATED	3000	41,605	16,208	2.57
float	REPEATED	40000	650,424	530,244	1.23
float	REPEATED	800000	13124,335	11077,583	1.18
float	REPEATED	5000000	85949,114	64994,047	1.32
---	---	---	---	---	---
double	RANDOM	600	13,226	9,674	1.37
double	RANDOM	3000	174,235	168,003	1.04
double	RANDOM	40000	3143,176	2969,988	1.06
double	RANDOM	800000	80122,032	75624,728	1.06
double	RANDOM	5000000	574170,519	541634,681	1.06
double	SHUFFLE	600	7,350	6,258	1.17
double	SHUFFLE	3000	54,996	47,801	1.15
double	SHUFFLE	40000	997,654	910,188	1.10
double	SHUFFLE	800000	20885,588	17842,091	1.17
double	SHUFFLE	5000000	124954,149	117951,053	1.06
double	STAGGER	600	13,905	3,104	4.48
double	STAGGER	3000	24,836	14,530	1.71
double	STAGGER	40000	315,874	208,873	1.51
double	STAGGER	800000	7174,689	4755,320	1.51
double	STAGGER	5000000	48635,918	34536,380	1.41
double	REPEATED	600	2,963	2,577	1.15
double	REPEATED	3000	29,148	16,343	1.78
double	REPEATED	40000	634,175	525,211	1.21
double	REPEATED	800000	13132,082	11342,063	1.16
double	REPEATED	5000000	88391,737	67412,676	1.31

Parallel sorting

Benchmark	Data Type	Array Size	Baseline (us/op)	New version (us/op)	Speedup
int	RANDOM	600	12,794	8,505	1.50
int	RANDOM	3000	168,675	151,334	1.11
int	RANDOM	40000	987,834	425,065	2.32
int	RANDOM	800000	19055,172	6019,487	3.17
int	RANDOM	5000000	138748,345	37177,898	3.73
int	SHUFFLE	600	7,072	5,122	1.38
int	SHUFFLE	3000	55,693	39,086	1.42
int	SHUFFLE	40000	448,901	210,483	2.13
int	SHUFFLE	800000	7086,518	1789,933	3.96
int	SHUFFLE	5000000	33432,965	17881,627	1.87
int	STAGGER	600	12,467	2,348	5.31
int	STAGGER	3000	18,100	11,108	1.63
int	STAGGER	40000	185,856	91,566	2.03
int	STAGGER	800000	4237,095	1092,863	3.88
int	STAGGER	5000000	91703,510	9672,080	9.48
int	REPEATED	600	2,039	1,693	1.20
int	REPEATED	3000	19,928	16,955	1.18
int	REPEATED	40000	435,095	179,503	2.42
int	REPEATED	800000	8667,204	2280,028	3.80
int	REPEATED	5000000	46503,601	16295,285	2.85
---	---	---	---	---	---
long	RANDOM	600	12,683	8,324	1.52
long	RANDOM	3000	170,779	151,285	1.13
long	RANDOM	40000	1049,755	517,177	2.03
long	RANDOM	800000	19114,558	8186,756	2.33
long	RANDOM	5000000	136592,625	50122,188	2.73
long	SHUFFLE	600	7,507	5,317	1.41
long	SHUFFLE	3000	53,452	38,660	1.38
long	SHUFFLE	40000	456,876	235,079	1.94
long	SHUFFLE	800000	7104,711	3026,515	2.35
long	SHUFFLE	5000000	36215,812	31943,545	1.13
long	STAGGER	600	12,726	2,314	5.50
long	STAGGER	3000	19,204	11,076	1.73
long	STAGGER	40000	188,118	117,579	1.60
long	STAGGER	800000	15883,497	1604,405	9.90
long	STAGGER	5000000	30772,348	19823,240	1.55
long	REPEATED	600	1,958	1,681	1.16
long	REPEATED	3000	19,457	9,782	1.99
long	REPEATED	40000	447,956	201,816	2.22
long	REPEATED	800000	8709,853	2817,039	3.09
long	REPEATED	5000000	47701,874	27042,182	1.76
---	---	---	---	---	---
float	RANDOM	600	12,957	9,760	1.33
float	RANDOM	3000	174,859	168,011	1.04
float	RANDOM	40000	1088,187	593,148	1.83
float	RANDOM	800000	19946,194	8786,492	2.27
float	RANDOM	5000000	143259,840	52053,455	2.75
float	SHUFFLE	600	7,524	6,261	1.20
float	SHUFFLE	3000	55,272	49,120	1.13
float	SHUFFLE	40000	475,746	263,484	1.81
float	SHUFFLE	800000	7241,135	2634,484	2.75
float	SHUFFLE	5000000	35411,419	21196,612	1.67
float	STAGGER	600	13,950	2,942	4.74
float	STAGGER	3000	23,098	13,183	1.75
float	STAGGER	40000	237,012	128,761	1.84
float	STAGGER	800000	4591,090	1751,410	2.62
float	STAGGER	5000000	32436,076	14446,905	2.25
float	REPEATED	600	2,885	2,549	1.13
float	REPEATED	3000	40,168	16,392	2.45
float	REPEATED	40000	660,494	237,183	2.78
float	REPEATED	800000	12950,842	3223,258	4.02
float	REPEATED	5000000	72413,630	22049,544	3.28
---	---	---	---	---	---
double	RANDOM	600	13,141	9,722	1.35
double	RANDOM	3000	173,583	167,573	1.04
double	RANDOM	40000	1094,277	693,851	1.58
double	RANDOM	800000	20258,598	11422,502	1.77
double	RANDOM	5000000	149441,199	66982,876	2.23
double	SHUFFLE	600	7,350	6,198	1.19
double	SHUFFLE	3000	54,795	48,204	1.14
double	SHUFFLE	40000	486,034	292,594	1.66
double	SHUFFLE	800000	7493,063	3994,888	1.88
double	SHUFFLE	5000000	38662,773	38459,203	1.01
double	STAGGER	600	14,004	3,095	4.52
double	STAGGER	3000	24,786	14,442	1.72
double	STAGGER	40000	265,910	166,051	1.60
double	STAGGER	800000	5161,371	2329,184	2.22
double	STAGGER	5000000	37595,716	25195,029	1.49
double	REPEATED	600	2,958	2,575	1.15
double	REPEATED	3000	24,794	16,353	1.52
double	REPEATED	40000	645,872	257,590	2.51
double	REPEATED	800000	13011,569	3817,908	3.41
double	REPEATED	5000000	73640,263	33488,503	2.20

[bourgesl]

Nice work, Vladimir!

Congratulations for all the hard work, needed to upgrade DPQS once again!

I will look at this new PR.

[bourgesl]

Please check your file encoding (windows vs jnix) see jcheck report!

[mlbridge]

Webrevs

• 02: Full - Incremental (bcd2fa3f)
• 01: Full - Incremental (a6cc6a09)
• 00: Full (496b89df)

[amaembo]

Do we need an outcommented line of code?

[VladimirIaroslavski]

            boolean isLargeRandom =
//              size > MIN_RADIX_SORT_SIZE && (sorter == null || bits > 0) &&
                size > MIN_RADIX_SORT_SIZE && (sorter != null && bits > 0) &&
                (a[e1] > a[e2] || a[e2] > a[e3] || a[e3] > a[e4] || a[e4] > a[e5]);

This code runs Radix sort during parallel sort only.
If you want to use Radix sort during sequential or parallel sort also,
you need to switch to the first line.

Agree, both lines should contain explanations.

If we agree to move Radix sort out from this PR, these lines go away from here.

[vlsi]

Have you considered a private static final boolean USE_RADIX_SORT_WITH_PARALLEL = false;? Then we don't need to comment the code, and one could flip the behavior by altering the flag

[VladimirIaroslavski]

Nice suggestion, will apply in the next PR if Radix sort is introduced.

[AlanBateman]

Do you have any sense on if parallelSort is widely used? There is a lot of code and complexity in this proposal and I think important to understand if it is worth it.

[amaembo]

It would be nice to have a high-level chart showing how the actual sorting algorithm is selected based on parallel/sequential, input size and whatever else. For an outsider, it's hard to grasp the whole picture. Is radix sort used for parallel sorting only? Sorry if such a chart already exists and I missed it.

If improvements of parallel sorting and sequential sorting are at least partially independent, I think it may make sense to deliver them in separate PRs. This would really simplify the review process.

[VladimirIaroslavski]

Alan, Tagir,

Thank you for your comments!

New version of sources contains optimizations of sequential and parallel sorts, such as, improvements of insertion sort, better partitioning, better pivot selection, merging sort and counting sort (for byte/char/short).
At the same time Radix sort is introduced. And of course, these parts are independent.

I think also it makes sense to separate this PR into two pull requests.

Do you agree, if I move Radix sort out from this PR and re-run benchmarking?
And later, after integration of these optimizations, we will return to discussion of Radix sort,
what do you think?

[AlanBateman]

Do you agree, if I move Radix sort out from this PR and re-run benchmarking? And later, after integration of these optimizations, we will return to discussion of Radix sort, what do you think?

Yes, splitting this into two would be good as it allow both proposals to be discussed/reviewed on their own merit.

[VladimirIaroslavski]

It would be nice to have a high-level chart showing how the actual sorting algorithm is selected based on parallel/sequential, input size and whatever else. For an outsider, it's hard to grasp the whole picture. Is radix sort used for parallel sorting only? Sorry if such a chart already exists and I missed it.

If improvements of parallel sorting and sequential sorting are at least partially independent, I think it may make sense to deliver them in separate PRs. This would really simplify the review process.

I added the chart to the first post, thank you for advice!

[VladimirIaroslavski]

I moved Radix sort out from sources and re-run benchmarking of parallel sorting.
We can see that new parallel sorting is still faster than existing version in JDK,
no degradation.

Parallel sorting (without Radix sort)

Benchmark	Data Type	Array Size	Baseline (us/op)	New version (us/op)	Speedup
int	RANDOM	600	12,852	8,507	1.51
int	RANDOM	3000	168,764	152,866	1.10
int	RANDOM	40000	987,272	647,195	1.53
int	RANDOM	800000	19120,539	13251,660	1.44
int	RANDOM	5000000	133598,983	90992,272	1.47
int	SHUFFLE	600	7,165	5,136	1.40
int	SHUFFLE	3000	56,363	39,100	1.44
int	SHUFFLE	40000	454,965	233,097	1.95
int	SHUFFLE	800000	7087,698	3153,941	2.25
int	SHUFFLE	5000000	32361,302	22618,240	1.43
int	STAGGER	600	12,499	2,351	5.32
int	STAGGER	3000	18,045	11,093	1.63
int	STAGGER	40000	177,705	91,101	1.95
int	STAGGER	800000	3735,779	1078,546	3.46
int	STAGGER	5000000	25432,573	9705,696	2.62
int	REPEATED	600	1,835	1,696	1.08
int	REPEATED	3000	19,594	16,612	1.18
int	REPEATED	40000	433,101	181,605	2.38
int	REPEATED	800000	8680,406	2206,406	3.93
int	REPEATED	5000000	46452,021	16940,200	2.74
--	--	--	--	--	--
long	RANDOM	600	12,967	8,352	1.55
long	RANDOM	3000	170,926	150,999	1.13
long	RANDOM	40000	1048,627	666,233	1.57
long	RANDOM	800000	19057,260	13713,901	1.39
long	RANDOM	5000000	140089,309	93820,320	1.49
long	SHUFFLE	600	7,284	5,401	1.35
long	SHUFFLE	3000	54,013	39,516	1.37
long	SHUFFLE	40000	454,804	255,803	1.78
long	SHUFFLE	800000	7222,403	3670,639	1.97
long	SHUFFLE	5000000	33815,535	31767,738	1.06
long	STAGGER	600	12,821	2,311	5.55
long	STAGGER	3000	19,027	11,073	1.72
long	STAGGER	40000	188,118	111,978	1.68
long	STAGGER	800000	4763,922	1630,149	2.92
long	STAGGER	5000000	32556,841	19882,107	1.64
long	REPEATED	600	1,961	1,770	1.11
long	REPEATED	3000	19,678	9,766	2.01
long	REPEATED	40000	439,893	201,826	2.18
long	REPEATED	800000	8725,427	2817,883	3.10
long	REPEATED	5000000	47688,415	26917,131	1.77
--	--	--	--	--	--
float	RANDOM	600	13,048	10,256	1.27
float	RANDOM	3000	175,047	167,967	1.04
float	RANDOM	40000	1089,859	740,659	1.47
float	RANDOM	800000	19919,657	15086,025	1.32
float	RANDOM	5000000	143704,590	105425,171	1.36
float	SHUFFLE	600	7,526	6,214	1.21
float	SHUFFLE	3000	54,785	49,150	1.11
float	SHUFFLE	40000	475,588	289,907	1.64
float	SHUFFLE	800000	7221,754	4124,313	1.75
float	SHUFFLE	5000000	35369,094	28281,396	1.25
float	STAGGER	600	13,956	2,936	4.75
float	STAGGER	3000	23,035	13,192	1.75
float	STAGGER	40000	230,380	133,386	1.73
float	STAGGER	800000	4614,573	1736,213	2.66
float	STAGGER	5000000	34053,504	14692,088	2.32
float	REPEATED	600	2,910	2,554	1.14
float	REPEATED	3000	40,965	16,641	2.46
float	REPEATED	40000	654,329	237,761	2.75
float	REPEATED	800000	13094,558	3234,352	4.05
float	REPEATED	5000000	71522,839	23208,431	3.08
--	--	--	--	--	--
double	RANDOM	600	13,103	9,628	1.36
double	RANDOM	3000	174,936	168,750	1.04
double	RANDOM	40000	1094,699	780,827	1.40
double	RANDOM	800000	20205,605	15304,877	1.32
double	RANDOM	5000000	147620,455	107560,209	1.37
double	SHUFFLE	600	7,359	6,191	1.19
double	SHUFFLE	3000	55,208	48,141	1.15
double	SHUFFLE	40000	485,528	311,081	1.56
double	SHUFFLE	800000	7525,265	4723,622	1.59
double	SHUFFLE	5000000	38030,224	38159,739	1.00
double	STAGGER	600	14,019	3,120	4.49
double	STAGGER	3000	24,778	14,510	1.71
double	STAGGER	40000	241,340	151,728	1.59
double	STAGGER	800000	5367,318	2353,046	2.28
double	STAGGER	5000000	38446,590	25241,014	1.52
double	REPEATED	600	2,986	2,586	1.15
double	REPEATED	3000	32,133	16,018	2.01
double	REPEATED	40000	659,864	256,873	2.57
double	REPEATED	800000	13045,124	3823,682	3.41
double	REPEATED	5000000	75177,194	33156,316	2.27

[amaembo]

Was this change justified by benchmarking? Why was the best value different before? Due to hardware changes or due to HotSpot/JIT changes or due to algorithmic changes below?

[VladimirIaroslavski]

These changes are due to algorithmic changes - more optimized insertion sort (combination of mixed, pin and simple insertion sortings), therefore we can run insertion sort on larger arrays.

[amaembo]

Why do we need this method? Offset and elemType are not used here. Probably it could be inlined?

[VladimirIaroslavski]

These methods sort() and partition() were introduced in PR #14227 where intrinsics for sorting and partitioning based on AVX512 instructions were added. The signature of these methods are in sync with native implementations from linux/native/libsimdsort package.

[amaembo]

Thank you for your comments and improvements. In general, looks good to me, but please note that I'm not really an expert in this area. It would be great to get the comments from more relevant people.

[bourgesl]

I also sponsor this effort, I helped on benchmarking this DPQS 2 years ago...

LGTM

[VladimirIaroslavski]

Hi expert/reviewers,

@stuart-marks Stuart Marks
@Martin-Buchholz: Martin Buchholz
@RogerRiggs Roger Riggs
@rgiulietti Raffaello Giulietti
@DougLea Doug Lea
@PaulSandoz Paul Sandoz
@sviswa7 Sandhya Viswanathan
@jatin-bhateja Jatin Bhateja

I'd appreciate it if you find a time to review this PR related to optimization of sorting. Of course, there are a lot of changes, but each sorting of primitive was modified in the same way, so actually ~1/7 of sources should be reviewed only.

If you need, we can set up a meeting at any time where I can provide an explanation for better understanding of new sources, I'm reached by mail vlv.spb.ru gmail com

Paul, Sandhya, Jatin, you reviewed AVX512 optimization for sorting a few years ago, maybe you have time now, please, to review this optimization?

Thank you in advance,
Vladimir