y-cruncher - A Multi-Threaded Pi-Program

From a high-school project that went a little too far...

By Alexander J. Yee

(Last updated: July 25, 2023)

 

Shortcuts:

 

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 0.8.1 Build 9517 (Released: July 12, 2023)

Linux      : Version 0.8.1 Build 9517 (Released: July 12, 2023)

 

Official Mersenneforum Subforum (new).

Official HWBOT forum thread.

 

News:

 

Version 0.8.1 Released: (July 11, 2023) - permalink

 

And it's finally here! Part one of the revamp is now complete. This release brings forward the newly rewritten algorithms which will have the most performance impact for in-memory computations.

 

Here are some benchmarks showing the improvements brought by v0.8.1 and AVX512. Because of the large performance swings, HWBOT integration will be withheld until the HWBOT community decides what to do.

10 Billion Digits of Pi - (Times in Seconds)

Intel Core i9 7940X @ 3.6 - 3.9 GHz - 128GB DDR4 @ 3466 MT/s

 

AVX2

(14-BDW)

AVX512

(17-SKX)

AVX2 -> AVX512 Speedup
y-cruncher v0.7.10 413.588 319.901 29%
y-cruncher v0.8.1 388.944 295.546 32%
v0.7.10 -> v0.8.1 Speedup 6% 8%  

25 Billion Digits of Pi - (Times in Seconds)

Intel Core i9 7940X @ 3.6 - 3.9 GHz - 128GB DDR4 @ 3466 MT/s

 

AVX2

(14-BDW)

AVX512

(17-SKX)

AVX2 -> AVX512 Speedup
y-cruncher v0.7.10 1215.584 910.867 33%
y-cruncher v0.8.1 1101.471 824.828 34%
v0.7.10 -> v0.8.1 Speedup 10% 10%  

10 Billion Digits of Pi - (Times in Seconds)

Intel Core i7 11800H @ stock - 64GB DDR4 @ 3200 MT/s

 

AVX2

(14-BDW)

AVX512

(18-CNL)

AVX2 -> AVX512 Speedup
y-cruncher v0.7.10 778.916 588.790 32%
y-cruncher v0.8.1 732.009 474.887 54%
v0.7.10 -> v0.8.1 Speedup 6% 24%  
 

10 Billion Digits of Pi - (Times in Seconds)

AMD Ryzen 9 7950X @ stock - 128GB DDR5 @ 4400 MT/s

 

AVX2

(19-ZN2)

AVX512

(22-ZN4)

AVX2 -> AVX512 Speedup
y-cruncher v0.7.10 317.010 310.648 2%
y-cruncher v0.8.1 291.127 240.954 21%
v0.7.10 -> v0.8.1 Speedup 9% 29%  

25 Billion Digits of Pi - (Times in Seconds)

AMD Ryzen 9 7950X @ stock - 128GB DDR5 @ 4400 MT/s

 

AVX2

(19-ZN2)

AVX512

(22-ZN4)

AVX2 -> AVX512 Speedup
y-cruncher v0.7.10 903.344 893.641 1%
y-cruncher v0.8.1 830.538 682.074 22%
v0.7.10 -> v0.8.1 Speedup 9% 31%  

Last year when I did the Zen 4 optimizations, I was disappointed (but not surprised) that I was only able to gain 1-2% speedup with AVX512. In fact, this was so embarrassingly bad that I couldn't publish any numbers. Sure, Zen 4's AVX512 is "double-pumped" and doesn't have wider units. But there's a lot more to AVX512 than just the 512-bit width.

 

In reality, I was able to achieve around 10% speedup for AVX512 on Zen 4 - but only within cache. Upon scaling it up, it was completely wiped out by the memory inefficiencies in the old algorithm. And it certainly didn't help that Zen 4 set a new record for insufficient memory bandwidth.

 

This memory bottleneck I suspect is the primary reason why the overall benefit of AVX512 remains higher on Intel than AMD even in v0.8.1. y-cruncher has been memory-bound on every high-end chip since 2017 with AMD faring worse due to having twice as many cores and lower memory speeds. While it's also tempting to blame Zen 4's "double-pumped" AVX512 as part of the problem, in reality it isn't much worse than Intel chips that lack the second 512-bit FMA.

 

Memory bandwidth as a whole has been a problem that has gone completely out of control. Since 2015, computational power has increased by more than 5x while memory bandwidth has barely improved by 50%. Needless to say, this trend is completely unsustainable at least for this field of high performance computing.

 

 

Stress Testing:

 

Testing and validation of v0.8.1 was done on 8 computers which were long believed to be stable (most aren't even overclocked). All 8 of these machines held against older versions of y-cruncher during past releases. But for this release, 2 of them were found to be unstable. Neither were overclocked and were completely within spec.

 

Neither machine could be fixed by downclocking or overvolting. One of them (an Intel laptop) had to be retired. The other (a custom-built AMD desktop) was eventually stabilized by changing the motherboard. (Yes, this was a huge headache and a massive distraction from the software development.)

 

What does this mean for stress-testing? While it's tempting to conclude that v0.8.1 is more stressful than older versions, this sample size of 8 really isn't enough. So I'll leave it to the rest of the overclocking community to decide. The specific stress-test you want to run is called "VT3" which is the newly rewritten version of the "VST" test that everyone seems to love. Likewise, any large in-memory computation will be running the new code.

 

 

The Hybrid NTT Algorithm:

 

As promised in the previous announcement, y-cruncher's good old Hybrid NTT algorithm has now been published here. Despite its importance to y-cruncher's early days, it is not as conceptually spectacular as one would assume by modern (adult) standards. But as a kid when I first wrote it, it was amazing.

 

 

 

Anyways, I hope everyone enjoys this new version. As mentioned, this is just part one of the ongoing rewrite of the internal algorithms. While there's still a lot of work to do (including optimizations), development will now shift to swap mode. So in the short term, I don't expect any more performance swings beyond compiler changes and new optimizations for new processors.

 

 

 

 

Upcoming Changes for v0.8.x: (June 7, 2023) - permalink

 

In an effort to clean up and modernize the project, most of the large multiply algorithms are getting either refreshed or removed. Algorithms that are useful on modern processors are getting redesigned and rewritten from scratch while the rest will be completely removed from the codebase.

 

The implication of this will be performance gains on newer processors and regressions on older processors.

 

If this sounds big, it is. More than 400,000 lines of code will be touched. Work actually began more than 3 years ago, but very little progress was made until this year where I'm on garden leave and therefore not working.

 

As of today, enough has been done to get some preliminary in-memory benchmarks:

Processor Architecture Clock Speeds Binary ISA Pi computation Speedup vs. v0.7.10
Core i7 920 Intel Nehalem 2008 3.5 GHz + 3 x 1333 MT/s 08-NHM ~ Ushio x64 SSE4.1 -27%
Core i7 3630QM Intel Ivy Bridge 2012 stock + 2 x 1600 MT/s 11-SNB ~ Hina x64 AVX -10%
FX-8350 AMD Piledriver 2012 stock + 2 x 1600 MT/s 11-BD1 ~ Miyu x64 FMA4 -1%
Core i7 5960X Intel Haswell 2013 4.0 GHz + 4 x 2400 MT/s 13-HSW ~ Airi x64 AVX2 3 - 4%
Core i7 6820HK Intel Skylake 2015 stock + 2 x 2133 MT/s 14-BDW ~ Kurumi x64 AVX2 + ADX 4 - 7%
Ryzen 7 1800X AMD Zen 1 2017 stock + 2 x 2866 MT/s 17-ZN1 ~ Yukina x64 AVX2 + ADX ~1%
Core i9 7900X Intel Skylake X 2017 3.6 GHz (AVX512) + 4 x 3000 MT/s 17-SKX ~ Kotori x64 AVX512-DQ 6 - 9%
Core i9 7940X 3.6 GHz (AVX512) + 4 x 3466 MT/s 10 - 13%
Ryzen 9 3950X AMD Zen 2 2019 stock + 2 x 3000 MT/s 19-ZN2 ~ Kagari x64 AVX2 + ADX 13 - 14%
Core i3 8121U Intel Cannon Lake 2018 stock + 2 x 2400 MT/s 18-CNL ~ Shinoa x64 AVX512-VBMI 16 - 17%
Core i7 1165G7 Intel Tiger Lake 2020 stock + 2 x 2666 MT/s 12 - 22%
Core i7 11800H stock + 2 x 3200 MT/s 23 - 27%
Ryzen 9 7950X AMD Zen 4 2022 stock + 2 x 4400 MT/s 22-ZN4 ~ Kizuna x64 AVX512-GFNI 23 - 31%

The loss of performance for the oldest processors is primarily due to the removal of the Hybrid NTT. Yes, the Hybrid NTT that started the entire y-cruncher project is now gone. While it was the fastest thing in 2008, it unfortunately did not age very well. Stay tuned for a future blog about the algorithm. It will no longer be a secret.

 

Overall, there is still a lot of work to do. For example, swap-mode is still using the old implementations and will need to be revamped as well. But since the new code has reached or exceeded performance parity for the chips I care about, this is a good stopping point for v0.8.1 pending testing and validation.

 

Nevertheless, the benchmarks above are not final and are subject to change. Specifically, there are unresolved toolchain issues where Intel is removing their old compiler while its replacement is still significantly worse. And it's unclear whether it can be fixed before it is no longer possible to keep using their old compiler.

 

A big unknown is how stress-testing will be affected. Despite not being designed for this purpose, y-cruncher's stress-test is notorious for its ability to expose memory instabilities that other (even dedicated) memory testing applications cannot. In other words, it is one of the best memory testers out there. But with so much stuff being rewritten, there's no telling how this will change. Nevertheless, it doesn't make a whole lot of sense to keep around hundreds of thousands of lines of old code if turns out to be the better stress test.

 

So yeah... Out with the old and in with the new. Expect to see Zen 4 gaining up to 20% speedup with AVX512 vs. just AVX2 - no wider execution units needed.

 

 

 

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:
May 13, 2023 May 13, 2023  

Jordan Ranous & Kevin O'Brien

Euler-Mascheroni Constant 700,000,000,000

Compute:  8.80 days

Verify:  6.95 days

2 x AMD Epyc 9654 @ 2.4 GHz

1.5 TB

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
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
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:

 

Download:

Sample Screenshot: 1 trillion digits of Pi

Core i7 5960X @ 4.0 GHz - 64 DDR4 @ 2400 MHz - 16 HDs

 

Latest Releases: (July 11, 2023)

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

OS Download Link Size

Windows

y-cruncher v0.8.1.9317.zip

44.1 MB

Linux (Static)

y-cruncher v0.8.1.9317-static.tar.xz

35.2 MB

Linux (Dynamic)

y-cruncher v0.8.1.9317-dynamic.tar.xz

28.9 MB

 

 

 

 

 

 

 

 

The Linux version comes in both statically and dynamically linked versions. The static version should work on most Linux distributions, but lacks TBB 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:

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:

 

 

Benchmarks:

Comparison Chart: (Last updated: July 11, 2023)

 

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 6820HK Core i7 11800H Core i7 11800H
Generation: Intel Skylake Intel Tiger Lake Intel Tiger Lake
Cores/Threads: 4/8 8/16 8/16
Processor Speed: 3.2 GHz (stock) ~2.5 GHz (45W PL) ~3.0 GHz (60W PL)
Memory: 64 GB @ 2133 MT/s 64 GB @ 3200 MT/s 64 GB @ 3200 MT/s
Version: v0.8.1 (14-BDW) v0.8.1 (18-CNL) v0.8.1 (18-CNL)
Instruction Set: x64 AVX2 + ADX x64 AVX512-VBMI x64 AVX512-VBMI
25,000,000 1.500 0.655 0.530
50,000,000 3.307 1.406 1.125
100,000,000 7.238 3.005 2.447
250,000,000 20.596 8.576 6.855
500,000,000 45.967 19.747 15.356
1,000,000,000 102.885 42.727 34.308
2,500,000,000 290.824 123.523 96.918
5,000,000,000 640.506 247.705 218.782
10,000,000,000 1,391.204 526.212 480.197
Credit:      
Processor(s): Core i3 8121U Core i7 11800H
Generation: Intel Cannon Lake Intel Tiger Lake
Cores/Threads: 2/4 8/16
Processor Speed: ~2.5 - 3.2 GHz (stock) ~2.5 - 2.8 GHz (45W PL)
Memory: 8 GB @ 2400 MT/s 64 GB @ 3200 MT/s
Version: v0.8.1 (14-BDW) v0.8.1 (17-SKX) v0.8.1 (18-CNL) v0.8.1 (14-BDW) v0.8.1 (17-SKX) v0.8.1 (18-CNL)
Instruction Set: x64 AVX2 + ADX x64 AVX512-DQ x64 AVX512-VBMI x64 AVX2 + ADX x64 AVX512-DQ x64 AVX512-VBMI
25,000,000 2.857 2.467 1.988 0.907 0.853 0.655
50,000,000 6.446 5.501 4.392 2.075 1.862 1.406
100,000,000 14.335 12.257 9.490 4.176 3.749 3.005
250,000,000 42.566 36.204 27.137 12.014 10.705 8.576
500,000,000 99.040 85.443 64.359 28.805 24.123 19.747
1,000,000,000 228.863 198.405 151.605 63.898 55.264 42.727
2,500,000,000       187.882 148.423 123.523
5,000,000,000       375.130 327.776 247.705
10,000,000,000       794.573 709.606 526.212
Credit:            

 

 

 

Mainstream Desktops:

Processor(s): Ryzen 7 1800X Ryzen 7 3800X Core i9 11700K Ryzen 9 3950X Ryzen 9 5950X Ryzen 9 7950X
Generation: AMD Zen 1 AMD Zen 2 Intel Rocket Lake AMD Zen 2 AMD Zen 3 AMD Zen 4
Cores/Threads: 8/16 8/16 8/16 16/32 16/32 16/32
Processor Speed: stock stock stock stock stock stock
Memory: 64 GB - 2866 MT/s 32 GB - 3600 MT/s 32 GB - 3200 MT/s 128 GB - 2666 MT/s 64 GB - 3200 MT/s 128 GB - 4400 MT/s
Program Version: v0.8.1 (17-ZN1) v0.8.1 (19-ZN2) v0.8.1 (18-CNL) v0.8.1 (19-ZN2) v0.8.1 (19-ZN2) v0.8.1 (22-ZN4)
Instruction Set: x64 AVX2 + ADX x64 AVX2 + ADX x64 AVX512-VBMI x64 AVX2 + ADX x64 AVX2 + ADX x64 AVX512-GFNI
25,000,000 1.150 0.654 0.501 0.588 0.490 0.312
50,000,000 2.527 1.415 1.114 1.257 1.090 0.679
100,000,000 5.555 3.028 2.223 2.685 2.345 1.517
250,000,000 15.760 8.404 6.220 7.251 6.371 4.157
500,000,000 34.659 18.440 13.573 15.556 13.395 8.883
1,000,000,000 78.690 41.097 30.415 33.925 29.301 18.542
2,500,000,000 220.278 117.788 86.119 96.695 82.204 50.743
5,000,000,000 493.388 266.719 193.718 215.333 181.355 110.379
10,000,000,000 1,078.187     473.958 399.012 241.162
25,000,000,000       1,361.732   680.344
Credit:   Oliver Kruse Oliver Kruse

 

Oliver Kruse  
Processor(s): Core i7 920 FX-8350 Core i7 4770K
Generation: Intel Nehalem AMD Piledriver Intel Haswell
Cores/Threads: 4/8 8/8 4/8
Processor Speed: 3.5 GHz stock 4.0 GHz
Memory: 12 GB - 1333 MT/s 32 GB - 1600 MT/s 32 GB - 2133 MT/s
Program Version: v0.8.1 (08-NHM) v0.8.1 (11-BD1) v0.8.1 (13-HSW)
Instruction Set: x64 SSE4.1 x64 FMA4 x64 AVX2
25,000,000 7.032 3.677 1.546
50,000,000 17.174 7.703 3.259
100,000,000 36.164 16.576 6.987
250,000,000 105.789 46.597 19.588
500,000,000 236.096 103.165 43.197
1,000,000,000 531.676 230.780 96.845
2,500,000,000   669.594 274.336
5,000,000,000   1,460.714 606.605
10,000,000,000      
25,000,000,000      
Credit:      

 

 

 

High-End Desktops:

Processor(s): Core i7 5960X Threadripper 1950X Core i9 7900X Core i9 7940X Threadripper 3990X
Generation: Intel Haswell AMD Zen 1 Intel Skylake X Intel Skylake X Zen 2
Cores/Threads: 8/16 16/32 10/20 14/28 64/128
Processor Speed: 4.0 GHz stock ~3.6 GHz (200W PL) 3.6 GHz (AVX512) 2.9 GHz
Memory: 64 GB - 2400 MT/s 64 GB - 2800 MT/s 128 GB - 3000 MT/s 128 GB - 3466 MT/s ~141 GB
Program Version: v0.8.1 (13-HSW) v0.8.1 (17-ZN1) v0.8.1 (17-SKX) v0.8.1 (17-SKX) v0.8.1 (19-ZN2)
Instruction Set: x64 AVX2 x64 AVX2 + ADX x64 AVX512-DQ x64 AVX512-DQ x64 AVX2 + ADX
25,000,000 0.807 0.756 0.522 0.404 0.584
50,000,000 1.743 1.579 1.028 0.721 1.181
100,000,000 3.647 3.273 2.048 1.451 2.409
250,000,000 10.088 8.990 5.752 4.056 5.724
500,000,000 22.075 19.604 12.830 9.017 10.881
1,000,000,000 49.232 43.014 28.906 20.518 21.496
2,500,000,000 139.404 121.645 82.764 60.636 58.009
5,000,000,000 311.388 271.983 186.233 137.906 126.513
10,000,000,000 669.736 613.450 401.820 302.121 274.050
25,000,000,000     1,125.775 843.498 768.212
Credit:   Oliver Kruse     Paul Underwood

 

 

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:

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:

 

Decimal Digits of Pi - Times in Seconds

Core i9 7940X @ 3.7 GHz AVX512

Memory Frequency: 2666 MT/s 3466 MT/s
25,000,000 0.839 0.758
50,000,000 1.424 1.338
100,000,000 2.701 2.425
250,000,000 6.489 5.877
500,000,000 13.307 11.917
1,000,000,000 27.913 24.915
2,500,000,000 76.837 68.322
5,000,000,000 168.058 148.737
10,000,000,000 365.047 322.115
25,000,000,000 1,037.527 916.039

High core count Skylake X processors are known to be heavily bottlenecked by memory bandwidth.

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:

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.

*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.

 

 

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:


Algorithms and Developments:

 

FAQ:

 

Pi and other Constants:

 

Program Usage:

 

Hardware and Overclocking:

 

Academia:

 

Programming:

 

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.

You can also find me on Twitter as @Mysticial.