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 15, 2017)

 

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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.

 

Current Release:

Windows: Version 0.7.4 Build 9477 (Released: October 14, 2017)

Linux      : Version 0.7.4 Build 9477 (Released: October 14, 2017)

 

Official HWBOT thread.

Official XtremeSystems Forums thread.

 

News:

 

Version 0.7.4: (October 14, 2017)

 

A new version is out with some changes aimed at addressing the memory bottleneck on Ryzen 7 and Skylake X.

While the changes in this release help alleviate the memory bottleneck, they fall well short of actually solving it. The memory bandwidth problem is here to stay and is expected to get worse if hardware trends continue as they have been for the past decade.

 

The memory bandwidth problem has actually been an ongoing cat-and-mouse game since the very first version of y-cruncher. Whenever the memory bottleneck catches up in a new generation of hardware, an optimization in y-cruncher is made to push it away again. But it looks like the cat is finally winning on the latest generation of desktop processors - especially the HCC Skylake X line.

 

 

 

Older News

 

Records Set by y-cruncher:

y-cruncher has been used to set a number world record size 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:
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
August 14, 2017 August 13, 2017   Ron Watkins Zeta(3) - Apery's Constant 500,000,000,000

Compute:  19.7 days

Verify:  29.8 days

8 x Xeon 6550 @ 2.0 GHz - 512 GB

2 x Xeon X5690 @ 3.46 GHz - 142 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
September 3, 2016 August 29, 2016   Ron Watkins e 5,000,000,000,000

Compute:  48.6 days

Verify:  48.7 days

2 x Xeon X5690 @ 3.47 GHz
141 GB
July 11, 2016 July 5, 2016   "yoyo" Golden Ratio 10,000,000,000,000

Compute:  6.2 days

Not Verified

2 x Intel Xeon E5-2696 v4 @ 2.2 GHz
768 GB
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
June 4, 2016 May 29, 2016   Ron Watkins Lemniscate 250,000,000,000

Compute:  91.7 hours

Verify:  270 hours

4 x Xeon E5-4660 v3 @ 2.1 GHz - 1TB
4 x Xeon X6550 @ 2 GHz - 512 GB
June 4, 2016 June 2, 2016   "yoyo" Golden Ratio 5,000,000,000,000

Compute:  67.9 hours

Not Verified

2 x Intel Xeon E5-2696 v4 @ 2.2 GHz
768 GB
April 24, 2016 April 18, 2016   Ron Watkins Log(2) 500,000,000,000

Compute:  12.8 days

Verify:  14.4 days

4 x Xeon X5690 @ 3.47 GHz - 141 GB
April 17, 2016 April 12, 2016   Ron Watkins Catalan's Constant 250,000,000,000

Compute:  204 hours

Verify:  207 hours

4 x Xeon E5-4660 v3 @ 2.1 GHz
1 TB
April 9, 2016 April 3, 2016   Ron Watkins Log(10) 500,000,000,000

Compute:  14.4 days

Verify:  15.2 days

2 x Xeon X5690 @ 3.47 GHz
141 GB
February 8, 2016 February 6, 2016   Mike A Catalan's Constant 500,000,000,000

Compute:  26.1 days

Not Verified

2 x Intel Xeon E5-2697 v3 @ 2.6 GHz
128 GB
July 24, 2015 July 22, 2015
July 23, 2015
Source Ron Watkins
Dustin Kirkland
Golden Ratio 2,000,000,000,000

Compute:  77.3 hours

Verify:  76.33 hours

Compute:  79.3 hours

Verify:  80.8 hours

4 x Xeon X6550 @ 2 GHz - 512 GB
Xeon E5-2676 v3 @ 2.4 GHz - 64 GB
October 8, 2014 October 7, 2014   "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 wish to set a record, you must run two computations using different formulas (one to compute, the other to verify). Then send me the validation files, but do not make any attempt to modify them. The validation files are protected with a checksum to prevent tampering/cheating. Yes, people have tried to cheat before.

 

An exception to the "two computations rule" can be made for Pi since it can be verified using BBP formulas.

 

Note that for anyone attempting to set a Pi world record: Should the attempt succeed, I kindly ask that you make yourself sufficiently available for external requests to access or download the digits in its entirety (at least until it is broken again by someone else). Pi is popular enough that people do actually want to see the digits.

 

Features:

Aside from computing Pi and other constants, y-cruncher is great for stress testing 64-bit systems with lots of ram.

 

 

Download:

Sample Screenshot: 100 billion digits of Pi

Core i7 5960X @ 4.0 GHz - 128GB DDR4 @ 2666 MHz - 16 HDs

 

Latest Releases: (October 14, 2017)

OS Programs Download Link Size

Windows

y-cruncher + HWBOT Submitter

y-cruncher v0.7.4.9477.zip

31.1 MB

Linux (Static)

y-cruncher Only

y-cruncher v0.7.4.9477-static.tar.gz

28.6 MB

Linux (Dynamic)

y-cruncher Only

y-cruncher v0.7.4.9477-dynamic.tar.gz

21.5 MB

Windows

HWBOT Submitter Only

HWBOT Submitter v0.9.8.118.jar

2.53 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 HWBOT submitter allows y-cruncher benchmarks to be submitted to HWBOT - which is a competitive overclocking site. It is currently only available for Windows.

 

System Requirements:

Windows:

Linux:

All Systems:

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:

 

Other Downloads (for C++ programmers):

 

Advanced Documentation:

 

 

 

 

 

Known Issues:

 

Functionality Issues:

 

Performance Issues:

 

 

 

Benchmarks:

Comparison Chart: (Last updated: October 14, 2017)

 

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.

 

 

Laptops + Low-Power:

Processor(s): Core i7 3630QM VIA C46501 Xeon E3-1535M v52 Core i7 6820HK Pentium N42001
Generation: Intel Ivy Bridge VIA Isaiah Intel Skylake Intel Skylake Intel Apollo Lake
Cores/Threads: 4/8 4/4 4/8 4/8 4/4
Processor Speed: 3.2 GHz 2.0 GHz 2.9 GHz 3.2 GHz 1.1 - 2.5 GHz
Memory: 8 GB - 1600 MHz 16 GB 16 GB 48 GB - 2133 MHz 4 GB
Version: v0.7.2 - AVX v0.7.2 - AVX v0.7.1 - ADX v0.7.2 - ADX v0.7.2 - SSE4.1
25,000,000 3.767 17.207 1.865 1.745 11.739
50,000,000 8.496 39.049 4.102 3.833 26.289
100,000,000 19.056 87.626 9.007 8.376 65.147
250,000,000 55.089 277.711 25.444 23.577 192.473
500,000,000 128.311 587.516 56.566 52.134 493.551
1,000,000,000 299.217 1,350.868 130.055 115.661  
2,500,000,000   3,884.838   327.784  
5,000,000,000       727.042  
10,000,000,000       1,602.565  

1Credit to Tralalak.

2Credit to Kaupo Karuse.

 

 

Mainstream Desktops:

Processor(s): Core 2 Quad Q6600 Core i7 920 FX-8350 Core i7 4770K Core i7 5775C1 Core i7 7700K2 Ryzen 7 1800X
Generation: Intel Core Intel Nehalem AMD Piledriver Intel Haswell Intel Broadwell Intel Kaby Lake AMD Zen
Cores/Threads: 4/4 4/8 8/8 4/8 4/8 4/8 8/16
Processor Speed: 2.4 GHz 3.5 GHz (OC) 4.0 GHz 4.0 GHz (OC) 3.8 GHz (OC) 4.8 GHz (OC) 3.8 GHz
Memory: 6 GB - 800 MHz 12 GB - 1333 MHz 32 GB - 1600 MHz 32 GB - 2133 MHz 16 GB - 2400 MHz 64 GB - 3000 MHz 64 GB - 2666 MHz
Version: v0.7.2 - SSE3 v0.7.2 - SSE4.1 v0.7.4 - XOP v0.7.4 - AVX2 v0.7.1 - ADX v0.7.1 - ADX v0.7.4 - ADX
25,000,000 10.591 4.998 3.462 1.684 1.730 1.271 1.388
50,000,000 23.698 11.310 7.820 3.583 3.940 2.817 3.062
100,000,000 53.502 25.268 16.605 7.788 8.739 6.198 6.267
250,000,000 157.269 74.230 46.492 21.897 25.073 17.384 17.508
500,000,000 351.470 166.724 104.300 48.260 56.343 38.176 37.949
1,000,000,000 801.731 381.903 227.527 107.177 125.967 84.432 84.630
2,500,000,000   1,119.114 700.176 302.159 369.738 238.194 240.341
5,000,000,000     1,703.810 669.735   527.186 530.135
10,000,000,000           1,151.396 1,152.426

1Credit to André Bachmann.

2Credit to Oliver Kruse.

 

 

High-End Desktops:

Processor(s): Core i7 5820K1 Core i7 5960X Threadripper 1950X2 Core i9 7900X
Generation: Intel Haswell Intel Haswell AMD Threadripper Intel Skylake X
Cores/Threads: 6/12 8/16 16/32 10/20
Processor Speed: 4.5 GHz (OC) 4.0 GHz (OC) 4.0 GHz (OC)

4.5/4.1/3.8 GHz

(all-cores non-AVX/AVX/AVX512)

2.4 GHz cache 3.0 GHz cache
Memory: 32 GB - 2400 MHz 64 GB - 2400 MHz 128 GB - 2800-3200 MHz 128 GB - 2666 MHz 128 GB - 3800 MHz
Version: v0.7.3 - AVX2 v0.7.4 - AVX2 v0.7.3 - ADX v0.7.4 - AVX512-DQ
25,000,000 1.287 0.881 0.975 0.648 0.583
50,000,000 2.499 2.038 1.997 1.372 1.218
100,000,000 5.401 4.209 3.697 2.910 2.564
250,000,000 14.732 11.461 9.602 7.917 6.967
500,000,000 32.294 25.153 20.710 17.077 15.022
1,000,000,000 71.225 55.194 45.496 37.108 32.622
2,500,000,000 200.323 154.758 127.040 105.028 91.305
5,000,000,000 443.543 342.364 279.979 231.662 201.697
10,000,000,000   745.234 612.269 506.444 438.074
25,000,000,000     1,910.832 1,442.809 1,239.754

1Credit to Sean Heneghan.

2Credit to Oliver Kruse.

 

 

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.

 

For example, enabling node-interleaving in the BIOS can improve performance by around 2x. But tweaks like these are often not possible as many of these systems corporate or university machines that are heavily locked down and do not provide the user with sufficient access privileges. Furthermore, due the exponentially large space of settings and configurations, it's often difficult to find the optimal set of settings.

Processor(s): Xeon X5482 Xeon E5-26901 Xeon E5-2683 v31 Xeon E5-2687W v42 Xeon E5-2696 v43 Xeon E7-8880 v34 Epyc 76015 Xeon Gold 6130F5
Generation: Intel Penryn Intel Sandy Bridge Intel Haswell Intel Broadwell Intel Broadwell Intel Haswell AMD Naples Intel Skylake Purley
Sockets/Cores/Threads: 2/8/8 2/16/32 2/28/56 2/24/48 2/44/88 4/64/128 2/64/128 2/32/64
Processor Speed: 3.2 GHz 3.5 GHz 2.03 GHz 3.0 GHz 2.2 GHz 2.3 GHz 2.2 GHz 2.1 GHz
Memory: 64 GB - 800 MHz 256 GB - ??? 128 GB - ??? 64 GB 768 GB - ??? 2 TB - ??? 256 GB - ?? 256 GB - ??
Version: v0.7.2 - SSE4.1 v0.6.2/3 - AVX v0.6.9 - AVX2 v0.7.3 - ADX v0.7.1 - ADX v0.7.1 - AVX2 v0.7.3 - ADX v0.7.3 - AVX512-DQ
25,000,000 4.548 2.283 0.907 0.774 0.715 1.176 2.459 1.150
50,000,000 9.779 4.295 1.745 1.586 1.344 2.321 4.347 1.883
100,000,000 20.834 8.167 3.317 3.300 2.673 4.217 6.996 3.341
250,000,000 60.049 20.765 8.339 8.480 6.853 8.781 14.258 7.731
500,000,000 134.978 42.394 17.708 18.029 14.538 15.879 24.930 15.346
1,000,000,000 308.679 89.920 37.311 38.038 31.260 32.078 47.837 31.301
2,500,000,000 874.588 239.154 102.131 103.353 84.271 78.251 111.139 82.871
5,000,000,000 1,946.683 520.977 218.917 224.376 192.889 164.157 228.252 179.488
10,000,000,000 4,317.677 1,131.809 471.802 485.640 417.322 346.307 482.777 387.530
25,000,000,000   3,341.281 1,511.852   1,186.881 957.966 1,184.144 1,063.850
50,000,000,000   7,355.076     2,601.476 2,096.169    
100,000,000,000         6,037.704 4,442.742    
250,000,000,000           17,428.450    

1Credit to Shigeru Kondo.

2Credit to Cameron Giesbrecht.

3Credit to "yoyo".

4Credit to Jacob Coleman.

5Credit to Dave Graham.

 

 

I've been asked a few times on what benchmarks quality for these tables. But there aren't any specific rules. For the most part, I try to maximize the variety of processors on the list. So I won't put more than one system in each processor line unless they have drastically different capabilities such as core count. I also have a strong preference for systems that are at the top of their line and have as much memory as possible.

 

Perhaps the most important part is that the benchmarks are representative of the hardware. If there is any evidence of interference that may cause the hardware to perform suboptimally, they will be excluded. Examples of this include (but are not limited to), underclocking, disabled cores, disabled hyperthreading, disabled AVX, fewer than all memory channels, background programs, thermal throttling, using an outdated version of y-cruncher, etc... Some leeway is given to multi-processor servers since they are so sensitive to numerous factors.

 

Likewise, absurdly high overclocks will be excluded. These tables are meant to compare systems running at real life speeds. Benchmarks done with extreme overclocks (especially with liquid nitrogen) should go on HWBOT. Just be aware that HWBOT has stringent rules on submissions since it's competitive.

 

 

Fastest Times:

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

These fastest times may include unreleased betas.


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

Note that I usually don't respond to these emails. I simply put them into the charts which I update periodically.


Algorithms and Developments:

 

FAQ:

 

Pi and other Constants:

 

Hardware and Overclocking:

 

Academia:

 

Programming:

 

Program Usage:

 

Other:

 

Links:

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

 

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.