y-cruncher - A Multi-Threaded Pi-Program

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

By Alexander J. Yee

(Last updated: November 18, 2024)

 

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 0.8.5 Build 9543 (Released: July 21, 2024)

Linux      : Version 0.8.5 Build 9543 (Released: July 21, 2024)

 

Official Mersenneforum Subforum.

Official HWBOT forum thread.

 

News:

 

Version 0.8.6 Preview: (October 26, 2024) - permalink

 

Officially, I don't plan on releasing v0.8.6 until next year since there isn't a whole lot of new stuff yet. I've since started a new job so the amount of free time I have has essentially dropped to zero. But I will pull it forward if some of the new and upcoming hardware (9800X3D or Arrow Lake) manages to find its way to my desk.

 

I am particularly interested in building optimized profiles for the Ryzen 9700X and 9800X3D to see how much they differ due to the extra cache. Though as of this writing, I do not have either chip.

 

In the event that does happen, here's what has so far made it into v0.8.6...

 

 

 

Tuning Profiles:

The Zen4 binary will have 2 trained profiles. Generic profiles also exist in case the trained profiles do not run well on a particular system.

 

As you all know, y-cruncher has about a dozen different binaries which are optimized for differnet CPUs going back almost 2 decades. But while this goes a long way to maximizing performance of every processor line, it fails to handle variations within the same processor line.

 

For example, a Zen4 laptop, Zen4 desktop, and Zen4 server are all very different. While the CPU architecture itself is the same, the cache and memory topologies are completely different. What is optimal for one is not optimal for the others. As of today, most of the binaries are optimized for the top-end desktop of that generation - which may or may not be efficient on laptops or servers of that same generation.

 

To help combat that problem, v0.8.6 will add support for tuning profiles. These are profiles within each binary that you can select from. For example, the Zen4 binary (22-ZN4) has two main profiles: One for the desktop 7950X and one for the laptop 7940HS.

 

The table below shows how each CPU runs faster on its own profile than on the other (incorrect) profile:

10 Billion Digits of Pi - (times in seconds)
CPU / Profile "Kizuna" (Raphael 7950X) "Saki" (Phoenix 7940HS)

Ryzen 9 7950X @ stock

128 GB @ 4800 MT/s

235.082 275.812

Ryzen 9 7940HS* @ stock

96 GB @ 5600 MT/s

463.296 395.041

 

 

 

 

 

 

 

 

 

 

*Huge thanks to Framework Computer for providing me this amazing review sample of their Framework 16 laptop.)

 

For this initial release of the tuning profiles, there will only be a set of hard-coded profiles that are tuned for the various machines in my laboratory. Which means there will be no server profiles since I currently do not have server hardware. Currently, it's not possible to allow others to generate their own profiles since the process is not fully automated and requires compiling y-cruncher itself which is closed sourced.

 

Oh... and if it isn't obvious enough already, yes v0.8.6 will come with performance changes - potentially large ones. So competitive overclockers should be prepared to re-bench everything. Though as of now, it's too early for me to give any numbers yet since the new tuning model hasn't been finalized yet.

 

 

 

Core Affinity:

 

One of the various complaints/requests I've received recently is that y-cruncher cannot be taskset or bound to specific cores on the system. The reason for this is that most of the parallel frameworks that it use set their own core affinities - thus overriding what the user specifies.

 

Starting from v0.8.6, the Task Queue and Push Pool frameworks will support setting explicit core affinities. Additionally, there will be QoL options to quickly enable/disable hyper-thread cores as well as entire ranges of cores.

 

This may prove useful for systems where SMT is detrimental to performance as the only way to disable SMT is in the BIOS which requires rebooting.

 

The core affinities is part of a larger internal refactor that could potentially improve performance on larger Windows systems with multiple processor groups. But that remains untested for now.

 

 

 

Integration Improvements:

 

Being a fairly popular benchmark and stress-test, it is wrapped by other programs like BenchMate for HWBOT and CoreCycler (and possibly others).

 

The problem is that y-cruncher was never really intended for this type of integration, so the developers of such wrappers had to go to extensive lengths to "hack" their way into the program to properly intercept the output and send commands. Because these hacks were... hacks, they had issues supporting non-standard console manipulation such as the console colors and refreshing status lines. Furthermore, each time I changed how those worked, it would break the integration.

 

Starting from v0.8.6, there will be new options to control the following:

In addition to the above, v0.8.6 will have proper output logging. This solves the problem where piping or redirecting y-cruncher's output to a file will result in garbled output from terminal escape sequences.

 

 

 

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:
October 20, 2024 October 19, 2024 Source Gerd Lamprecht Gamma(1/5) 3,000,000,010 Compute:  48.5 minutes

Verified by Alexander Yee

Intel Core i9 7900X

32 GB

October 20, 2024 July 31, 2024   Mamdouh Barakat Gamma(1/4) 1,001,001,001,001

Compute:  149 days

Verify:  6.45 days

AMD Ryzen 7900X

128 GB

AMD Threadripper 5965WX

256 GB

June 28, 2024 May 20, 2024 Source

Jordan Ranous

Kevin O’Brien

Brian Beeler

(StorageReview)

Pi 202,112,290,000,000

Compute:  104 days

Verify:  4 days

Validation File

2 x Intel Xeon Platinum 8592+
1.0 TB
1.6 PB storage

May 12, 2024 May 11, 2024   Dmitriy Grigoryev Zeta(5) 260,000,000,000 Compute:  5.11 days
Verify:  6.93 days
Intel Xeon W7-3465X
1 TB
March 14, 2024 February 27, 2024 Source

Jordan Ranous

Kevin O’Brien

Brian Beeler

(StorageReview)

Pi 105,000,000,000,000

Compute:  75 days

Verify:  4 days

Validation File

2 x AMD Epyc 9754
1.5 TB
960 TB storage

February 13, 2024 February 12, 2024   Jordan Ranous Log(2) 3,000,000,000,000

Compute:  42.7 hours
Verify:  58.3 hours

2 x Intel Xeon Platinum 8460H
512 GB
December 26, 2023 December 24, 2023   Jordan Ranous e 35,000,000,000,000

Compute:  94.5 hours

Verify:  92.5 hours

2 x Intel Xeon Platinum 8460H
512 GB

December 26, 2023 December 25, 2023   Jordan Ranous Square Root of 2 20,000,000,000,000

Compute:  29.2 hours

Verify:  21.6 hours

Intel Xeon Platinum 8450H
512 GB
Intel Xeon Platinum 8460H
512 GB
December 26, 2023 December 22, 2023  

Andrew Sun

Zeta(3) - Apery's Constant 2,020,569,031,595 Compute:  5.61 days

Verify:  5.93 days

Intel Xeon Platinum 8347C
505 GB
Intel Xeon Platinum 8347C
507 GB
December 18, 2023 December 15, 2023   Jordan Ranous Gamma(1/3) 1,000,000,000,000

Compute:  17.5 hours

Verify:  23.3 hours

2 x Intel Xeon Platinum 8450H

512 GB

December 2, 2023 November 27, 2023   Jordan Ranous Golden Ratio 20,000,000,000,000

Compute:  76.1 hours

Verify:  30.0 hours

AMD Epyc 9654 - 1.5 TB

Intel Xeon Platinum 8450H

September 9, 2023 September 7, 2023  

Andrew Sun

Euler-Mascheroni Constant 1,337,000,000,000

Compute:  28.5 days

Verify:  41.3 days

Intel Xeon Platinum 83470C

400 GB

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
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 x Intel Xeon E5-2680 v3

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
1 TB
34 + 4 Hard Drives
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
756 GB
2 x Intel Xeon Gold 5220
754 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

315 GB

48 Hard Drives

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
> 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
1.25 TB DDR4
20 x 6 TB 7200 RPM Seagate
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
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
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 21, 2024)

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

OS Download Link Size

Windows

y-cruncher v0.8.5.9543.zip

42.9 MB

Linux (Static)

y-cruncher v0.8.5.9543-static.tar.xz

33.7 MB

Linux (Dynamic)

y-cruncher v0.8.5.9543-dynamic.tar.xz

26.7 MB

 

 

 

 

 

 

 

 

Downloads can also be found on GitHub. Use this if you prefer HTTPS.

 

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.

 

HWBOT submission is back with this release. So I expect the leaderboards to be rewritten soon.

 

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 8, 2024)

 

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 i3 8121U Core i7 11800H Ryzen 9 7940HS
Generation: Intel Cannon Lake Intel Tiger Lake AMD Zen4
Cores/Threads: 2/4 8/16 8/16
Processor Speed: ~2.5 - 3.2 GHz (stock) ~2.5 - 2.8 GHz (60W PL) ~4.1 - 4.8 GHz (50W PL)
Memory: 8 GB @ 2400 MT/s 64 GB @ 3200 MT/s 96 GB - 5600 MT/s
Program Version: v0.8.5 (18-CNL) v0.8.5 (18-CNL) v0.8.5 (22-ZN4)
Instruction Set: x64 AVX512-VBMI x64 AVX512-VBMI x64 AVX512-GFNI
25,000,000 1.951 0.490 0.410
50,000,000 4.279 1.083 0.910
100,000,000 9.272 2.372 2.041
250,000,000 26.129 6.585 5.662
500,000,000 62.364 14.750 12.486
1,000,000,000 142.219 32.271 27.654
2,500,000,000   92.021 79.921
5,000,000,000   203.953 199.153
10,000,000,000   446.934 501.327
Credit:      
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:      

 

 

 

Mainstream Desktops:

Processor(s): Ryzen 7 1800X Ryzen 9 3950X Ryzen 9 7950X Ryzen 9 9950X Ultra 9 285K
Generation: AMD Zen 1 AMD Zen 2 AMD Zen 4 AMD Zen 5 Intel Arrow lake
Cores/Threads: 8/16 16/32 16/32 16/32 24/24
Processor Speed: stock stock stock PBO 5.5/4.9 GHz P/E-core
Memory: 64 GB - 2866 MT/s 32 GB - 3200 MT/s 128 GB - 5200 MT/s 48 GB - 6000 MT/s 32 GB - 8200 MT/s
Program Version: v0.8.5 (17-ZN1) v0.8.5 (17-ZN2) v0.8.5 (22-ZN4) v0.8.5 (24-ZN5) v0.8.5 (14-BDW)
Instruction Set: x64 AVX2 x64 AVX2 x64 AVX512-GFNI x64 AVX512-GFNI x64 AVX2
25,000,000 1.092 0.527 0.287 0.207 0.211
50,000,000 2.393 1.112 0.615 0.474 0.454
100,000,000 5.337 2.387 1.365 1.107 0.979
250,000,000 15.340 6.302 3.813 3.209 2.769
500,000,000 34.074 13.519 7.985 6.829 6.218
1,000,000,000 76.415 29.470 16.841 14.670 13.796
2,500,000,000 218.467 84.116 45.703 40.091 39.733
5,000,000,000 495.367 187.272 100.214 89.030 88.031
10,000,000,000 1,112.598 412.102 218.732 197.779  
25,000,000,000     615.070    
Credit:       muziqaz 曾 铮
Processor(s): Ryzen 5 7600 Core i9 11700K Ryzen 9 3950X Ryzen 9 5950X Core i9 13900KS Ryzen 9 7950X
Generation: AMD Zen 4 Intel Rocket Lake AMD Zen 2 AMD Zen 3 Intel Raptor Lake AMD Zen 4
Cores/Threads: 6/12 8/16 16/32 16/32 24/32 16/32
Processor Speed:   stock stock stock 5.7/4.5 GHz stock
Memory: 32 GB 32 GB - 3200 MT/s 128 GB - 2666 MT/s 64 GB - 3200 MT/s 96 GB - 8000 MT/s 128 GB - 4400 MT/s 128 GB - 5200 MT/s
Program Version: v0.8.1 (22-ZN4) v0.8.1 (18-CNL) v0.8.1 (19-ZN2) v0.8.1 (19-ZN2) v0.8.1 (14-BDW) v0.8.1 (22-ZN4)
Instruction Set: x64 AVX512-GFNI x64 AVX512-VBMI x64 AVX2 + ADX x64 AVX2 + ADX x64 AVX2 + ADX x64 AVX512-GFNI
25,000,000 0.439 0.501 0.588 0.490 0.241 0.312 0.307
50,000,000   1.114 1.257 1.090 0.525 0.679 0.654
100,000,000   2.223 2.685 2.345 1.132 1.517 1.410
250,000,000   6.220 7.251 6.371 3.185 4.157 3.820
500,000,000 13.378 13.573 15.556 13.395 7.065 8.883 8.062
1,000,000,000 29.497 30.415 33.925 29.301 15.901 18.542 17.039
2,500,000,000 83.421 86.119 96.695 82.204 44.888 50.743 46.467
5,000,000,000 181.647 193.718 215.333 181.355 99.566 110.379 101.345
10,000,000,000     473.958 399.012   241.162 220.522
25,000,000,000     1,361.732     680.344 623.493
Credit: Joel Rufin Oliver Kruse

 

Oliver Kruse 曾 铮    
Processor(s): Core i7 920 FX-8350 Core i7 4770K Ryzen 7 1800X Ryzen 7 3800X
Generation: Intel Nehalem AMD Piledriver Intel Haswell AMD Zen 1 AMD Zen 2
Cores/Threads: 4/8 8/8 4/8 8/16 8/16
Processor Speed: 3.5 GHz stock 4.0 GHz stock stock
Memory: 12 GB - 1333 MT/s 32 GB - 1600 MT/s 32 GB - 2133 MT/s 64 GB - 2866 MT/s 32 GB - 3600 MT/s
Program Version: v0.8.1 (08-NHM) v0.8.1 (11-BD1) v0.8.1 (13-HSW) v0.8.1 (17-ZN1) v0.8.1 (19-ZN2)
Instruction Set: x64 SSE4.1 x64 FMA4 x64 AVX2 x64 AVX2 + ADX x64 AVX2 + ADX
25,000,000 7.032 3.677 1.546 1.150 0.654
50,000,000 17.174 7.703 3.259 2.527 1.415
100,000,000 36.164 16.576 6.987 5.555 3.028
250,000,000 105.789 46.597 19.588 15.760 8.404
500,000,000 236.096 103.165 43.197 34.659 18.440
1,000,000,000 531.676 230.780 96.845 78.690 41.097
2,500,000,000   669.594 274.336 220.278 117.788
5,000,000,000   1,460.714 606.605 493.388 266.719
10,000,000,000       1,078.187  
25,000,000,000          
Credit:         Oliver Kruse

 

 

 

High-End Desktops:

Processor(s): Core i7 5960X Core i9 7900X Core i9 10980XE Xeon W7-2495X
Generation: Intel Haswell Intel Skylake X Intel Cascake Lake Intel Sapphire Rapids
Cores/Threads: 8/16 10/20 18/36 24/48
Processor Speed: 4.0 GHz ~3.6 GHz (200W PL) 3.3 GHz (AVX512) 4.1 GHz (AVX512)
Memory: 64 GB - 2400 MT/s 128 GB - 3000 MT/s 128 GB - 3600 MT/s 64 GB - 6400 MT/s
Program Version: v0.8.5 (13-HSW) v0.8.5 (17-SKX) v0.8.5 (17-SKX) v0.8.5 (18-CNL)
Instruction Set: x64 AVX2 x64 AVX512-DQ x64 AVX512-DQ x64 AVX512-VBMI
25,000,000 0.727 0.409 0.286 0.134
50,000,000 1.626 0.885 0.567 0.278
100,000,000 3.524 1.916 1.245 0.612
250,000,000 10.089 5.488 3.541 1.787
500,000,000 22.546 12.419 7.976 3.989
1,000,000,000 50.538 27.822 17.822 8.824
2,500,000,000 146.103 78.850 50.888 25.490
5,000,000,000 314.891 174.063 113.511 56.102
10,000,000,000 681.296 380.010 245.876 124.008
25,000,000,000   1,064.718 676.923  
Credit:       曾铮
Processor(s): Core i7 5960X Threadripper 1950X Core i9 7900X Core i9 7940X Threadripper 3990X Xeon W7-2495X Xeon W9-3475X
Generation: Intel Haswell AMD Zen 1 Intel Skylake X Intel Skylake X AMD Zen 2 Intel Sapphire Rapids Intel Sapphire Rapids
Cores/Threads: 8/16 16/32 10/20 14/28 64/128 24/48 36/72
Processor Speed: 4.0 GHz stock ~3.6 GHz (200W PL) 3.6 GHz (AVX512) 2.9 GHz 4.1-4.9 GHz 4.2-4.9 GHz
Memory: 64 GB - 2400 MT/s 64 GB - 2800 MT/s 128 GB - 3000 MT/s 128 GB - 3466 MT/s ~141 GB - 2666 MT/s 64 GB - 6400 MT/s 128 GB - 6400 MT/s
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) v0.8.1 (18-CNL) v0.8.3 (18-CNL)
Instruction Set: x64 AVX2 x64 AVX2 + ADX x64 AVX512-DQ x64 AVX512-DQ x64 AVX2 + ADX x64 AVX512-VBMI x64 AVX512-VBMI
25,000,000 0.807 0.756 0.522 0.404 0.584 0.170 0.201
50,000,000 1.743 1.579 1.028 0.721 1.181 0.340 0.321
100,000,000 3.647 3.273 2.048 1.451 2.409 0.726 0.586
250,000,000 10.088 8.990 5.752 4.056 5.724 2.068 1.413
500,000,000 22.075 19.604 12.830 9.017 10.881 4.588 2.627
1,000,000,000 49.232 43.014 28.906 20.518 21.496 10.190 5.924
2,500,000,000 139.404 121.645 82.764 60.636 58.009 28.881 16.345
5,000,000,000 311.388 271.983 186.233 137.906 126.513 64.158 36.139
10,000,000,000 669.736 613.450 401.820 302.121 274.050 124.826 78.816
25,000,000,000     1,125.775 843.498 768.212   225.482
Credit:   Oliver Kruse     Paul Underwood 曾 铮

 

 

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 8375C

(AWS x2iedn.32xlarge)

Xeon Platinum 8488C

(AWS m7i.48xlarge)

Epyc 9R14

(AWS m7a.48xlarge)

Epyc 9R14

(AWS hpc7a.96xlarge)

Epyc 9754
Generation: Intel Sapphire Rapids Intel Sapphire Rapids AMD Genoa AMD Bergamo
Cores/Threads: 64/128 96/192 192/192 128/256 128/128
Processor Speed: 2.9 GHz 2.4 GHz 2.6 GHz 2.25 - 3.1 GHz
Memory: 4 TB 744 GB 740 GB 768 GB - 4800 MT/s
Program Version: v0.8.1 (18-CNL) v0.8.1 (18-CNL) v0.8.1 (22-ZN4) v0.8.1 (22-ZN4)
Instruction Set: x64 AVX512-VBMI x64 AVX512-VBMI x64 AVX512-GFNI x64 AVX512-GFNI
25,000,000 0.250 0.163 0.216 0.213 0.245 0.229
50,000,000 0.454 0.289 0.285 0.279 0.350 0.433
100,000,000 0.844 0.531 0.642 0.635 0.853 0.876
250,000,000 1.976 1.288 1.776 1.716 2.224 2.133
500,000,000 3.794 2.499 3.728 3.621 4.186 3.850
1,000,000,000 7.650 5.149 6.547 6.265 7.063 6.495
2,500,000,000 20.425 13.633 13.554 12.500 15.338 14.477
5,000,000,000 45.675 29.655 25.334 22.377 29.072 28.133
10,000,000,000 101.468 64.026 51.134 44.059 58.797 59.007
25,000,000,000 297.622 182.920 140.286 120.282 156.797 164.281
50,000,000,000 678.016 410.842 321.970 275.297 350.391 368.548
100,000,000,000 1,549.991 943.182 771.266 672.558 829.957 853.717
250,000,000,000 4,488.317          
500,000,000,000 9,685.971          
Credit: Greg Hogan Tim Wesley

 

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.