y-cruncher - A Multi-Threaded Pi-Program
	From a high-school project that went a little too far... By Alexander J. Yee

(Last updated: October 13, 2022)

 

 

The first scalable multi-threaded Pi-benchmark for multi-core systems...

 

How fast can your computer compute Pi?

 

y-cruncher is a program that can compute Pi and other constants to trillions of digits.

It is the first of its kind that is multi-threaded and scalable to multi-core systems. Ever since its launch in 2009, it has become a common benchmarking and stress-testing application for overclockers and hardware enthusiasts.

 

y-cruncher has been used to set several world records for the most digits of Pi ever computed.

• 100 trillion digits - June 2022 (Emma Haruka Iwao)
• 62.8 trillion digits - August 2021 (UAS Grisons)
• 50 trillion digits - January 2020 (Timothy Mullican)
• 31.4 trillion digits - January 2019 (Emma Haruka Iwao)
• 22.4 trillion digits - November 2016 (Peter Trueb)
• 13.3 trillion digits - October 2014 (Sandon Van Ness "houkouonchi")
• 12.1 trillion digits - December 2013 (Shigeru Kondo)
• 10 trillion digits - October 2011 (Shigeru Kondo)
• 5 trillion digits - August 2010 (Shigeru Kondo)

 

Current Release:

Windows: Version 0.7.10 Build 9513 (Released: August 31, 2022)

Linux      : Version 0.7.10 Build 9513 (Released: August 31, 2022)

 

Official Mersenneforum Subforum (new).

Official HWBOT forum thread.

 

News:

 

Zen4's AVX512: (Sepember 26, 2022) - permalink

 

Now that the embargos have lifted, I have published my breakdown of Zen4's AVX512 over on Mersenneforum.

So if you're a SIMD programmer or just curious about architecture in general, this might be worth a read.

 

 

 

Version 0.7.10 and AMD Zen4: (August 31, 2022) - permalink

 

Zen4 is set to be AMD's first processor to support AVX512. You know what that means - a new y-cruncher binary for it!

 

AMD has graciously provided me a pre-release sample of their Ryzen 9 7950X. And using that, I'm able to produce a Zen4-optimized binary - well ahead of launch and in time for the hardware reviewers to pick up.

 

Since most information about Zen4 is still under embargo, I cannot say anything about it at this time. If you happen to have access to a Zen4 system, feel free to try out this new release.

 

If you are a hardware reviewer who uses y-cruncher as one of your benchmarks, you will need to grab this latest version of y-cruncher to get the best results on Zen4.

 

The existing Intel-optimized AVX512 binaries for Skylake and Tiger Lake do not run optimally on Zen4, so you will need the new binary. Fortunately, the performance of the other binaries remain unchanged in v0.7.10. So Zen4 benchmarks on v0.7.10 can be directly compared with those of other processors using y-cruncher v0.7.9. Thus you do not need to redo your benchmarks for competing processors if they are already done with v0.7.9.

 

Overall, this was a very fun project which I enjoyed. Being pre-release meant that all the usual optimization and architectural resources that I usually rely on do not exist yet. So I had to do all the reverse engineering myself to figure out enough of architecture to where I could optimize for it. Unless someone beats me to it (via leaks), I intend to publish my findings as soon as is allowed.

 

AMD's support for AVX512 may be the trigger that finally breaks AVX512's chicken-egg problem. For better part of the last decade, nobody used AVX512 because of poor support. And since nobody used it, it received poor support. Now with AMD's backing, adoption of AVX512 may finally start to increase and perhaps put Intel at a competitive disadvantage until they bring it back to the consumer market.

 

 

I mentioned earlier this year that Zen4 and Sapphire Rapids X were the other two chips I wanted to test and optimize for. Now with Zen4 fulfilled (for now), that leaves Sapphire Rapids - which looks like it's having its fair share of delays. So I obviously have no timeline for that and I may end up skipping it if it ends being cost prohibitive. Just in case if anyone from Intel is paying attention...

 

 

 

100 Trillion Digits of Pi: (June 8, 2022) - permalink

 

I'm glad to announce that Google has reclaimed the Pi world record by computing 100 trillion digits of Pi!

 

This computation took 158 days from October 14 to March 21. Like last time, it was run on the Google Cloud platform, but with newer and improved hardware for both compute and storage.

 

Hardware Specs:

• 128 vCPU Ice Lake Xeon (2.6 - 3.1 GHz)
• 864 GB ram
• 663 TB of total storage

For more details check out Google's blog here. If you are interested in the digits, you can download them from here.

 

 

Older News

 

Records Set by y-cruncher:

y-cruncher has been used to set a number of world record sized computations.

 

Blue: Current World Record

Green: Former World Record

Red: Unverified computation. Does not qualify as a world record until verified using an alternate formula.

Date Announced	Date Completed:	Source:	Who:	Constant:	Decimal Digits:	Time:	Computer:
July 17, 2022	July 15, 2022		Seungmin Kim	Lemniscate	1,200,000,000,100	Compute:  32.2 days Verify:  46.5 days	2 x Intel Xeon Gold 6140 @ 2.30 GHz 377 GB
June 8, 2022	March 21, 2022		Emma Haruka Iwao	Pi	100,000,000,000,000	Compute:  158 days Verify:  12.6 hours Validation File	128 vCPU Intel Ice Lake (GCP) 864 GB 663 TB storage
March 14, 2022	March 9, 2022		Seungmin Kim	Catalan's Constant	1,200,000,000,100	Compute:  48.6 days Verify:  47.3 days	2 x Intel Xeon Gold 6140 @ 2.30 GHz 2 x Intel Xeon E5-2680 v3 @ 2.50 GHz
January 5, 2022	November 12, 2021		Tizian Hanselmann	Square Root of 2	10,000,000,001,000	Compute:  18.4 days Verify:  18.5 days	Intel Xeon E7-4870 @ 2.4 GHz 896 GB
October 4, 2021	September 30, 2021		Chris Danneil	Zeta(5)	200,000,000,000	Compute:  28.2 days Verify:  33.0 days	Intel Xeon E5-268v4 @ 2.1 GHz 256 GB
October 4, 2021	September 9, 2021		William Echols	Log(2)	1,500,000,000,000	Compute:  98.9 days Verify:  61.7 days	2 x Intel Xeon E5-2690 v3 @ 2.6 GHz 256 GB
August 17, 2021	August 14, 2021	Source	UAS Grisons	Pi	62,831,853,071,796	Compute:  108 days Verify:  34.4 hours	AMD Epyc 7542 @ 2.9 GHz 1 TB 34 + 4 Hard Drives
February 14, 2021	February 12, 2021		Clifford Spielman	Golden Ratio	10,000,000,000,000	Compute:  14.3 days Verify:  7.40 days	AMD Threadripper 3995WX @ 2.7 GHz 512 GB
December 5, 2020	November 22, 2020		David Christle	e	31,415,926,535,897	Compute:  53.8 days Verify:  46.0 days	2 x Intel Xeon E5-2680 v2 @ 2.8 GHz 252 GB
September 13, 2020	September 6, 2020		Seungmin Kim	Log(10)	1,200,000,000,100	Compute:  14.5 days Verify:  22.5 days	2 x Intel Xeon E5-2699 v3 @ 2.3 GHz 756 GB 2 x Intel Xeon Gold 5220 @ 2.2 GHz 754 GB
August 9, 2020	July 26, 2020		Seungmin Kim	Zeta(3) - Apery's Constant	1,200,000,000,100	Compute:  31.7 days Verify:  32.6 days	2 x Intel Xeon E5-2670 v3 @ 2.3 GHz 503 GB 2 x Intel Xeon Gold 5220 @ 2.2 GHz 754 GB
August 9, 2020	July 23, 2020		Andrew Sun	Gamma(1/3)	500,000,001,337	Compute:  17.3 days Verify:  4.07 days	2 x Intel Xeon E5-2690 v4 @ 2.6 GHz 315 GB
June 28, 2020	June 22, 2020		Seungmin Kim	Zeta(3) - Apery's Constant	1,200,000,000,000	Compute:  31.7 days Not Verified	2 x Xeon E5-2670 v3 @ 2.3 GHz 503 GB
June 28, 2020	May 27, 2020		Andrew Sun	Gamma(1/4)	500,000,000,000	Compute:  20.0 days Verify:  14.9 days	2 x Intel Xeon E5-2690 v4 @ 2.6 GHz 315 GB
May 28, 2020	May 26, 2020		Seungmin Kim Ian Cutress	Euler-Mascheroni Constant	600,000,000,100	Compute:  145 days Verify:  104 days	2 x Intel Xeon Gold 6140 @ 2.3 GHz 187 GB Intel Xeon 8280 @ 2.7 GHz 768 GB
January 29, 2020	January 29, 2020	Blog	Timothy Mullican	Pi	50,000,000,000,000	Compute:  303 days Verify:  17.2 hours Validation File	4 x Intel Xeon E7-4880 v2 @ 2.5 GHz 315 GB 48 Hard Drives
December 4, 2019	November 13, 2019		Christophe Patris de Broe & Alexandre Gouy & Cyril Hsu	Golden Ratio	20,000,000,000,000	Compute:  6.94 days Not Verified	2 x Intel Xeon Platinum 8268 @ 2.9 GHz 768 GB
October 21, 2019	October 17, 2019		Marco Julian Hummel	Gamma(1/3)	274,877,906,944	Compute:  11.2 days Verify:  30.7 days	2 x Intel Xeon E5-2651 v2 @ 1.8 GHz 192 GB
March 14, 2019	January 21, 2019	Blogs 1 + 2	Emma Haruka Iwao	Pi	31,415,926,535,897	Compute:  121 days Verify:  20.0 hours Validation File	2 x Undisclosed Intel Xeon @ 2.00 GHz > 1.40 TB DDR4 > 240 TB SSD
August 24, 2017	August 23, 2017		Ron Watkins	Euler-Mascheroni Constant	477,511,832,674	Compute:  34.4 days Verify:  141 days	4 x Xeon E5-4660 v3 @ 2.1 GHz - 1 TB 2 x Xeon X5690 @ 3.47 GHz - 128 GB
November 15, 2016	November 11, 2016	Blog Sponsor	Peter Trueb	Pi	22,459,157,718,361	Compute:  105 days Verify:  28 hours Validation File	4 x Xeon E7-8890 v3 @ 2.50 GHz 1.25 TB DDR4 20 x 6 TB 7200 RPM Seagate
June 28, 2016	June 19, 2016		Ron Watkins	Square Root of 2	10,000,000,000,000	Compute:  18.8 days Verify:  25.2 days	2 x Xeon X5690 @ 3.47 GHz 141 GB
October 8, 2014	October 7, 2014		Sandon Van Ness (houkouonchi)	Pi	13,300,000,000,000	Compute:  208 days Verify:  182 hours Validation File	2 x Xeon E5-4650L @ 2.6 GHz 192 GB DDR3 @ 1333 MHz 24 x 4 TB + 30 x 3 TB
December 28, 2013	December 28, 2013	Source	Shigeru Kondo	Pi	12,100,000,000,050	Compute: 94 days Verify: 46 hours	2 x Xeon E5-2690 @ 2.9 GHz 128 GB DDR3 @ 1600 MHz 24 x 3 TB

See the complete list including other notably large computations. If you want to set a record yourself, the rules are in that link.

 

 

Features:

 

The main computational features of y-cruncher are:

• Able to compute Pi and other constants to trillions of digits.
• Two algorithms are available for most constants. One for computation and one for verification.
• Multi-Threaded - Multi-threading can be used to fully utilize modern multi-core processors without significantly increasing memory usage.
• Vectorized - Able to fully utilize the SIMD capabilities for most processors. (SSE, AVX, AVX512, etc...)
• Swap Space management for large computations that require more memory than there is available.
• Multi-Hard Drive - Multiple hard drives can be used for faster disk swapping.
• Semi-Fault Tolerant - Able to detect and correct for minor errors that may be caused by hardware instability or software bugs.

 

Download:

 

Latest Releases: (August 31, 2022)

Downloading any of these files constitutes as acceptance of the license agreement.

OS	Download Link	Size
Windows	y-cruncher v0.7.10.9513.zip	45.1 MB
Linux (Static)	y-cruncher v0.7.10.9513-static.tar.xz	34.1 MB
Linux (Dynamic)	y-cruncher v0.7.10.9513-dynamic.tar.xz	28.0 MB

 

 

 

 

 

 

 

 

The Linux version comes in both statically and dynamically linked versions. The static version should work on most Linux distributions, but lacks Cilk Plus and NUMA binding. The dynamic version supports all features, but is less portable due to the DLL dependency hell.

 

The Windows download comes bundled with the HWBOT submitter which allows benchmarks to be submitted to HWBOT.

 

System Requirements:

Windows:

• Windows 7 or later.
• The HWBOT submitter requires the Java 8 Runtime.

Linux:

• 64-bit Linux is required. There is no support for 32-bit.
• The dynamic version has been tested on Ubuntu 22.04.

All Systems:

• An x86 or x64 processor.

Very old systems that don't meet these requirements may be able to run older versions of y-cruncher. Support goes all the way back to even before Windows XP.

 

Version History:

• y-cruncher
• HWBOT Submitter

 

Other Downloads (for C++ programmers):

• Source code for the Digit Viewer
• Mini-Pi: A tiny self-contained Pi program

 

Advanced Documentation:

• Multi-Threading
• Memory Allocation
• Swap Mode
• Custom Formulas

 

 

Benchmarks:

Comparison Chart: (Last updated: October 12, 2022)

 

Computations of Pi to various sizes. All times in seconds. All computations done entirely in ram.

The timings include the time needed to convert the digits to decimal representation, but not the time needed to write out the digits to disk.

 

Blue: Benchmarks are up-to-date with the latest version of y-cruncher.

Green: Benchmarks were done with an old version of y-cruncher that is comparable in performance with the current release.

Red: Benchmarks are significantly out-of-date due to being run with an old version of y-cruncher that is no longer comparable with the current release.

Purple: Benchmarks are from unreleased internal builds that are not speed comparable with the current release.

 

 

Laptops + Low-Power:

Processor(s):	Core i7 8565U	Core i7 9750H	Core i7 1065G7		Core i7 1065G7	Core i7 1165G7	Core i9 11900KB
Generation:	Intel Kaby Lake R	Intel Coffee Lake	Intel Ice Lake		Intel Ice Lake	Intel Tiger Lake	Intel Tiger Lake
Cores/Threads:	4/8	6/12	4/8		4/8	4/8	8/16
Processor Speed:	2.3 - 4.6 GHz	3.1 - 3.9 GHz	2.1 - 3.0 GHz (25W)		???	3.6 - 4.0 GHz (45W)	3.3 - 4.5 GHz
Memory:	8 GB	16 GB - 2666 MT/s	16 GB @ 3200 MT/s		16 GB @ 3733 MT/s	32 GB @ 3200 MT/s	32 GB @ 3200 MT/s
Version:	v0.7.8 (14-BDW)	v0.7.8 (14-BDW)	v0.7.7 (18-CNL)		v0.7.8 (18-CNL)	v0.7.8 (18-CNL)	v0.7.8 (18-CNL)
Instruction Set:	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX512-DQ	x64 AVX512-VBMI	x64 AVX512-VBMI	x64 AVX512-VBMI	x64 AVX512-VBMI
25,000,000	1.584	1.463	1.596	1.243	1.046	0.868	0.575
50,000,000	3.523	3.123	3.552	2.718	2.318	1.825	1.301
100,000,000	7.837	6.585	7.903	5.870	5.150	3.888	2.866
250,000,000	23.336	18.378	22.520	16.531	14.745	10.813	7.997
500,000,000	54.403	40.028	50.683	37.778	32.856	23.769	17.560
1,000,000,000	127.177	87.298	114.539	85.426	73.918	52.930	38.525
2,500,000,000		251.637	332.819	249.579	222.515	156.696	111.600
5,000,000,000						348.512	247.368
10,000,000,000
Credit:		ji lcpd	ji lcpd		Gnyueh	ji lcpd	ji lcpd

Processor(s):	Core i7 3630QM	Core i7 4610M	Core i3 8121U (Windows*)			Core i7 6560U	Core i7 6700HQ
Generation:	Intel Ivy Bridge	Intel Haswell	Intel Cannon Lake			Intel Skylake	Intel Skylake
Cores/Threads:	4/8	2/4	2/4			4/8	4/8
Processor Speed:	3.2 GHz	3.0 GHz	2.6 - 3.0 GHz	2.6 - 3.0 GHz	2.4 - 2.9 GHz	2.21 GHz	2.6 GHz ?
Memory:	16 GB - 1600 MT/s	8 GB	8 GB			8 GB	16 GB
Version:	v0.7.8 (11-SNB)	v0.7.8 (13-HSW)	v0.7.8 (14-BDW)	v0.7.8 (17-SKX)	v0.7.8 (18-CNL)	v0.7.8 (14-BDW)	v0.7.8 (14-BDW)
Instruction Set:	x64 AVX	x64 AVX2	x64 AVX2 + ADX	x64 AVX512-DQ	x64 AVX512-VBMI	x64 AVX2 + ADX	x64 AVX2 + ADX
25,000,000	3.688	3.372	2.984	2.685	2.189	3.165	2.140
50,000,000	8.460	7.634	6.795	6.079	4.879	7.212	4.634
100,000,000	18.817	17.037	15.173	13.654	10.725	16.008	10.168
250,000,000	56.097	48.912	45.801	41.775	31.268	46.491	29.298
500,000,000	129.173	109.82	106.192	97.429	75.072	105.889	65.509
1,000,000,000	302.003	244.751	241.978	222.909	170.715	233.860	144.395
2,500,000,000	848.475						429.748
5,000,000,000
10,000,000,000
Credit:	Oliver Kruse	Marco Julian Hummel				Sebastien Davies	Marco Julian Hummel

 

 

Mainstream Desktops:

Processor(s):	Ryzen 7 1800X	Ryzen 7 3700X	Ryzen 7 5800X3D	Core i9 11900K	Ryzen 9 3950X	Ryzen 9 5950X	Core i9 12900K	Ryzen 9 7950X
Generation:	AMD Zen	AMD Zen 2	AMD Zen 3	Intel Rocket Lake	AMD Zen 2	AMD Zen 3	Intel Alder Lake	AMD Zen 4
Cores/Threads:	8/16	8/16	8/16	8/16	16/32	16/32	8/16 + 8/8	16/32
Processor Speed:	3.7 GHz	4.3 GHz		5.3 GHz			5.1 GHz
Memory:	64 GB - 2866 MT/s	64 GB - 3600 MT/s	32 GB	64 GB - 3733 MT/s	64 GB - 3200 MT/s	64 GB	64 GB - 6400 MT/s	128 GB - 4400 MT/s
Program Version:	v0.7.8 (17-ZN1)	v0.7.8 (17-ZN1)	v0.7.9 (20-ZN3)	v0.7.8 (18-CNL)	v0.7.8 (17-ZN1)	v0.7.8 (19-ZN2)	v0.7.9 (14-BDW)	v0.7.10 (22-ZN4)
Instruction Set:	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX512-VBMI	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX512-GFNI
25,000,000	1.247	0.681	0.580	0.461	0.701	0.559	0.399	0.434
50,000,000	2.623	1.427	1.220	1.027	1.422	1.171	0.744	0.901
100,000,000	5.655	2.975	2.693	2.223	2.870	2.403	1.622	1.875
250,000,000	16.053	8.135	7.435	6.350	7.279	6.162	4.529	4.953
500,000,000	35.607	17.666	16.713	14.133	15.037	12.725	9.930	10.620
1,000,000,000	78.961	39.007	36.338	31.235	32.306	27.277	21.550	23.431
2,500,000,000	226.557	112.849	104.964	91.316	91.836	77.652	61.097	65.561
5,000,000,000	498.824	250.157	232.368	202.208	204.570	171.633	134.698	144.664
10,000,000,000	1,084.855	549.067		447.487	460.548	382.39		317.490
25,000,000,000								914.088
Credit:		Sebastien Davies	Marc Beste	O-EtaIXVII	Marc Beste	Sebastien Davies	曾 铮

Processor(s):	FX-8350	Core i7 4770K	Core i7 7700K
Generation:	AMD Piledriver	Intel Haswell	Intel Kaby Lake
Cores/Threads:	8/8	4/8	4/8
Processor Speed:	4.0 GHz	4.0 GHz (OC)	4.9 GHz (OC)
Memory:	32 GB - 1600 MT/s	32 GB - 2133 MT/s	64 GB - 3200 MT/s
Program Version:	v0.7.8 (11-BD1)	v0.7.8 (13-HSW)	v0.7.8 (14-BDW)
Instruction Set:	x64 AVX + XOP	x64 AVX2	x64 AVX2 + ADX
25,000,000	3.070	1.482	1.149
50,000,000	6.845	3.396	2.489
100,000,000	15.130	7.385	5.482
250,000,000	43.077	20.610	15.419
500,000,000	96.327	45.964	33.986
1,000,000,000	214.870	101.692	74.021
2,500,000,000	623.521	292.899	209.412
5,000,000,000	1,384.689	643.534	451.414
10,000,000,000			966.710
Credit:			Oliver Kruse

 

 

 

High-End Desktops:

Processor(s):	Core i9 9980XE	Core i9 10980XE	Threadripper 3955WX	Threadripper 3970X		Threadripper 3990X
Generation:	Intel Skylake X	Intel Cascade Lake X	AMD Zen 2	AMD Zen 2		AMD Zen 2
Cores/Threads:	18/18	18/36	16/32	32/64		64/128
Processor Speed:		2.8 GHz	3.9 GHz	3.7 GHz		4.0 GHz (OC)
Memory:	128 GB - 3600 MT/s	128 GB - 3600 MT/s	512 GB - 3200 MT/s	64 GB		256 GB - 3200 MT/s
Program Version:	v0.7.8 (17-SKX)	v0.7.8 (17-SKX)	v0.7.8 (19-ZN2)	v0.7.8 (17-ZN1)	v0.7.8 (19-ZN2)	v0.7.8 (19-ZN2)
Instruction Set:	x64 AVX512-DQ	x64 AVX512-DQ	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX2 + ADX
25,000,000	0.262	0.394	0.531	0.458	0.431	0.694
50,000,000	0.556	0.837	1.070	0.910	0.890	1.011
100,000,000	1.203	1.814	2.015	1.763	1.734	2.203
250,000,000	3.492	4.885	5.072	4.258	4.070	5.618
500,000,000	7.703	10.198	10.423	8.699	7.896	10.474
1,000,000,000	16.923	21.633	22.386	18.427	15.939	21.872
2,500,000,000	48.896	59.536	63.115	50.338	44.058	54.171
5,000,000,000	108.179	129.954	138.574	109.537	95.645	116.739
10,000,000,000	236.789	282.091	304.391	237.537	208.484	245.579
25,000,000,000	675.992	799.543	846.597			682.885
50,000,000,000			1,960.563			1672.776
100,000,000,000			4,450.366
Credit:	Shigeru Kondo	ji lcpd	Michael Makovi	Tainus		Bennet Huch

Processor(s):	Core i7 5960X	Threadripper 1950X	Core i9 7940X
Generation:	Intel Haswell	AMD Threadripper	Intel Skylake X
Cores/Threads:	8/16	16/32	14/28
Processor Speed:	4.0 GHz (OC)	3.5 - 3.7 GHz	3.8 GHz	3.6 GHz
			2.8 GHz cache
Memory:	64 GB - 2133 MT/s	128 GB - 2933 MT/s	128 GB - 3466 MT/s
Program Version:	v0.7.8 (13-HSW)	v0.7.8 (17-ZN1)	v0.7.8 (14-BDW)	v0.7.8 (17-SKX)
Instruction Set:	x64 AVX2	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX512-DQ
25,000,000	0.853	0.721	0.503	0.482
50,000,000	1.769	1.500	1.090	0.994
100,000,000	3.828	3.173	2.407	1.974
250,000,000	10.807	8.666	6.575	5.145
500,000,000	23.523	18.926	14.026	10.791
1,000,000,000	51.930	41.762	29.989	22.974
2,500,000,000	149.081	119.06	84.231	64.586
5,000,000,000	326.022	264.191	189.510	143.051
10,000,000,000	713.146	572.900	410.372	316.622
25,000,000,000		1642.184	1,185.891	903.586
50,000,000,000
Credit:		Oliver Kruse

 

*All-core non-AVX/AVX/AVX512 CPU frequency.

 

 

Multi-Processor Workstation/Servers:

 

Due to high core count and the effect of NUMA (Non-Uniform Memory Access), performance on multi-processor systems are extremely sensitive to various settings. Therefore, these benchmarks may not be entirely representative of what the hardware is capable of.

Processor(s):	Xeon Platinum 8124M	Xeon Gold 6148	Xeon Platinum 8175M	Xeon Platinum 8275CL	Epyc 7742	Epyc 7B12	Epyc 7742
Generation:	Intel Skylake Purley	Intel Skylake Purley	Intel Skylake Purley	Intel Cascade Lake	AMD Rome	AMD Rome	AMD Rome
Sockets/Cores/Threads:	2/36/72	2/40/40	2/48/96	2/48/96	2/128/256	2/112/224	2/128/256
Processor Speed:	3.0 GHz	2.4 GHz	2.5 GHz	3.0 GHz		2.25 GHz	2.25 GHz
Memory:	137 GB - ??	188 GB - ??	~756 GB - ??	192 GB	~504 GB	~882 GB	2 TB
Program Version:	v0.7.5 (17-SKX)	v0.7.6 (17-SKX)	v0.7.6 (17-SKX)	v0.7.8 (17-SKX)	v0.7.7 (17-ZN1)	v0.7.8 (19-ZN2)	v0.7.8 (19-ZN2)
Instruction Set:	x64 AVX512-DQ	x64 AVX512-DQ	x64 AVX512-DQ	x64 AVX512-DQ	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX2 + ADX
25,000,000	0.540	0.329	0.294	0.283	0.534	0.439	0.513
50,000,000	0.981	0.683	0.617	0.544	1.027	0.838	0.920
100,000,000	1.905	1.456	1.305	1.169	2.298	1.796	1.887
250,000,000	5.085	3.737	3.591	3.125	5.854	4.509	4.650
500,000,000	10.372	7.750	7.293	6.309	10.502	8.196	8.066
1,000,000,000	21.217	16.550	15.041	13.042	17.836	14.252	13.246
2,500,000,000	55.701	45.693	39.329	34.028	35.485	30.592	27.011
5,000,000,000	118.151	99.078	83.601	71.777	62.432	58.405	49.940
10,000,000,000	247.928	212.984	176.695	153.169	115.543	116.900	98.156
25,000,000,000		599.653	491.988	425.442	307.995	314.907	258.081
50,000,000,000			1,081.181		690.662	741.633	598.716
100,000,000,000						1715.123	1,370.714
250,000,000,000							3,872.397
Credit:	Jacob Coleman	Oliver Kruse	newalex	Xinyu Miao	Carsten Spille	Greg Hogan	Song Pengei

Processor(s):	Xeon E5-2683 v3	Xeon E7-8880 v3	Xeon E5-2687W v4	Xeon E5-2686 v4	Xeon E5-2696 v4	Epyc 7601	Xeon Gold 6130F
Generation:	Intel Haswell	Intel Haswell	Intel Broadwell	Intel Broadwell	Intel Broadwell	AMD Naples	Intel Skylake Purley
Sockets/Cores/Threads:	2/28/56	4/64/128	2/24/48	2/36/72	2/44/88	2/64/128	2/32/64
Processor Speed:	2.03 GHz	2.3 GHz	3.0 GHz	2.3 GHz	2.2 GHz	2.2 GHz	2.1 GHz
Memory:	128 GB - ???	2 TB - ???	64 GB	504 GB - ???	768 GB - ???	256 GB - ??	256 GB - ??
Program Version:	v0.6.9 (13-HSW)	v0.7.1 (13-HSW)	v0.7.6 (14-BDW)	v0.7.7 (14-BDW)	v0.7.1 (14-BDW)	v0.7.3 (17-ZN1)	v0.7.3 (17-SKX)
Instruction Set:	x64 AVX2	x64 AVX2	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX2 + ADX	x64 AVX512-DQ
25,000,000	0.907	1.176	0.490	0.494	0.715	2.459	1.150
50,000,000	1.745	2.321	1.072	0.982	1.344	4.347	1.883
100,000,000	3.317	4.217	2.303	2.193	2.673	6.996	3.341
250,000,000	8.339	8.781	6.196	6.044	6.853	14.258	7.731
500,000,000	17.708	15.879	13.046	12.582	14.538	24.930	15.346
1,000,000,000	37.311	32.078	27.763	26.852	31.260	47.837	31.301
2,500,000,000	102.131	78.251	76.202	73.596	84.271	111.139	82.871
5,000,000,000	218.917	164.157	165.046	160.094	192.889	228.252	179.488
10,000,000,000	471.802	346.307	356.487	346.305	417.322	482.777	387.530
25,000,000,000	1,511.852	957.966	1,006.131	980.784	1,186.881	1,184.144	1,063.850
50,000,000,000		2,096.169	2,202.558	2,156.854	2,601.476
100,000,000,000		4,442.742			6,037.704
250,000,000,000		17,428.450
Credit:	Shigeru Kondo	Jacob Coleman	Cameron Giesbrecht	newalex	"yoyo"	Dave Graham

 

 

Fastest Times:

The full chart of rankings for each size can be found here:

• Rankings: 25m
• Rankings: 50m
• Rankings: 100m
• Rankings: 250m
• Rankings: 500m
• Rankings: 1b
• Rankings: 2.5b
• Rankings: 5b
• Rankings: 10b
• Rankings: 25b
• Rankings: 50b
• Rankings: 100b
• Rankings: 250b
• Rankings: 500b
• Rankings: 1t

These fastest times may include unreleased betas.

Got a faster time? Let me know: a-yee@u.northwestern.edu

Note that I usually do not respond to these emails. I simply put them into the charts which I update periodically (typically within 2 weeks).

 

 

Performance Tips:

 

Memory Bandwidth:

 

Because of the memory-intensive nature of computing Pi and other constants, y-cruncher needs a lot of memory bandwidth to perform well. In fact, the program has been noticably memory bound on nearly all high-end desktops since 2012 as well as the majority of multi-socket systems since at least 2006.

 

Recommendations:

• Make sure all memory channels are populated. This is by far the most important since bandwidth scales almost linearly with the # of channels.
• Run your memory at as high a frequency as possible to maximize bandwidth.
• Memory timings are usually less important. Long memory latencies are hidden away fairly well by Hyperthreading.
• On Skylake X processors, L3 cache bandwidth is also a bottleneck. So overclock the cache as much as possible.

Don't be surprised if y-cruncher exposes instabilities that other applications and stress-tests do not. y-cruncher is unusual in that it simultaneously places a heavy load on both the CPU and the entire memory subsystem.

 

 

 

Parallel Performance:

 

y-cruncher has a lot of settings for tuning parallel performance. By default, it makes a best effort to analyze the hardware and pick the best settings. But because of the virtually unlimited combinations of processor topologies, it's difficult for y-cruncher to optimally pick the best settings for everything. So sometimes the best performance can only be achieved with manual settings.

• Try both the Push Pool and Cilk Plus frameworks. While the Push Pool is faster in most cases, Cilk Plus may be better for extremely small computations as well as on machines with many (> 64) cores.*
• Experiment with larger task decomposition sizes. This may alleviate problems with load-imbalance.*
• On Windows, if the system has more than 64 logical cores, make sure node-interleaving is disabled in the BIOS. Otherwise, it would lead to imbalanced processor groups which will lead to load-imbalance.

*These are advanced settings that cannot be changed if you're using the benchmark option in the console UI. To change them, you will need to either run benchmark mode from the command line or use the custom compute menu.

 

Load imbalance is a faily common problem in y-cruncher. The usual causes are:

1. The number of logical cores is not a power-of-two.
2. The cores are not homogenous. Common reasons include:
   • The cores are clocked at different speeds.
   • The cores have access to different amounts of memory bandwidth due an imbalanced NUMA topology.
   • The cores are different generation cores hidden behind a virtual machine.
3. CPU-intensive background processes are interfering with y-cruncher's ability to use all the hardware. This applies to all forms of system jitter.

 

 

Large Pages:

 

Large pages used to not matter in the past, but they do now in the post-Spectre/Meltdown world. Mitigations for the Meltdown vulnerability can have a noticeable performance drop for y-cruncher (up to 5% has been observed). It turns out that turning on large pages can mitigate the penalty for this mitigation. (pun intended)

 

Refer to the memory allocation guide on how to turn on large pages.

 

 

Swap Mode:

 

This is probably one of the most complicated features in y-cruncher.

• Read the guide so you know how to use it.
• Depending on the CPU capability of your system, chances are you will either need multiple NVMe SSDs or many hard drives to avoid bottlenecking on disk I/O.
• Don't use hardware or software RAID. y-cruncher usually does a better job if you let it manage each drive separately.
• Don't use SSDs if you care about their lifespan. y-cruncher can and will destroy SSDs if you sustain it long enough.

 

 

Known Issues:

 

Everything in this section is in the process of being re-verified and moved to: https://github.com/Mysticial/y-cruncher/issues

 

 

Performance Issues:

• Swap computations on the latest Ubuntu (15.10) and possibly everything else with the same kernel version have very poor performance in swap mode. This is because the OS does excessive and unnecessary disk swapping to the pagefile. The solution is to disable the swap file so that no paging is possible. It may also suffice to set the "swappiness" value to zero. y-cruncher will also attempt to lock pages in memory to prevent the OS from shooting itself with paging.

Algorithms and Developments:

• Algorithms and Internals
• Current and Future Developments
• Technology Wishlist

 

FAQ:

 

Pi and other Constants:

• Where can I download the digits for Pi and other constants that are featured in the various record computations?
• Can you search for XXX in the digits of Pi for me?
• Can you add support for more constants? I want to compute e^Pi, Khinchin, Glaisher, etc...
• I have found an amazing new algorithm for X that's better than the rest!

 

Program Usage:

• What's with the warning, "Unable to acquire the permission, "SeLockMemoryPrivilege". Large pages and page locking may not be possible."?
• What's the difference between "Total Computation Time" and "Total Time"? Which is relevant for benchmarks?
• Why does y-cruncher need administrator privileges in Windows to run Swap Mode computations?
• Why is the performance so poor for small computations? The program only gets xx% CPU utilization on my xx core machine for small sizes!!!
• I've found a bug! How do I report it? Can you fix it?

 

Hardware and Overclocking:

• My computer is completely stable. But I keep getting errors such as, "Redundancy Check Failed: Coefficient is too large".
• Why is y-cruncher so much slower on AMD processors than Intel processors?

 

Academia:

• Is there a version that can use the GPU?
• Why can't you use distributed computing to set records?
• Is there a distributed version that performs better on NUMA and HPC clusters?
• Why have recent Pi records used desktops instead of supercomputers?
• Why do desktops use the Chudnovsky formula while supercomputers use the AGM? Isn't the AGM faster?

 

Programming:

• What is the technical explanation for the notorious, "Coefficient is too large" error?
• Is there a publicly available library for the multi-threaded arithmetic that y-cruncher uses?
• Is y-cruncher open-sourced?

 

Other:

• What about support for other platforms? Mac, ARM, etc...

 

Links:

Here's some interesting sites dedicated to the computation of Pi and other constants:

• Mathematical Constants and Computation
• Shigeru Kondo's Pi pages (dead)
• Stu's Pi page (dead)

 

Questions or Comments

Contact me via e-mail. I'm pretty good with responding unless it gets caught in my school's junk mail filter.

You can also find me on Twitter as @Mysticial.