 |
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 6, 2021)
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.
- 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 0.7.8 Build 9507 (Released: September 14, 2020)
Linux : Version 0.7.8 Build 9507 (Released: September 14, 2020)
Official Mersenneforum Subforum (new).
Official HWBOT forum thread.
62.8 Trillion Digits of Pi: (August 19, 2021) - permalink
This took a bit longer to announce than usual since the verification hadn't been completed when the media got word of the news. But now it is done and verified. Therefore, I'd like to congratulate UAS Grisons for setting a new world record for the digits of Pi!
This new record continues the recent trend of computations using more and more optimized storage systems with less emphasis on computational power.
More details here.
Version 0.7.8 Patch with Zen 2 Optimizations: (March 1, 2020) - permalink
A new patch for v0.7.8 has been released. Aside from the usual bug fixes, this release includes a new binary optimized for AMD Zen 2 processors.
I don't usually add new features to patch releases. However, my priorities in recent months have largely shifted away from y-cruncher. As such, very little progress has been made on v0.7.9. With no timeline for when the next feature release will happen, I decided to pull the Zen 2 optimizations into the v0.7.8 branch.
That aside, the new Zen 2 binary seems bring about 10% performance improvement. This is far greater than the 1-2% that I had expected.
This may be a bit of a shocker, but I have no idea why the improvement is so large nor do I have the time to investigate. Most of the tuning is automated by a superoptimizer. So all I did was run the superoptimizer, wait a week for it to finish, then copy-paste the results into the code.
In other words, I have no idea what it did or what it found that is so significant. But it worked, and I'll take it - no questions asked.
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 4, 2021 | September 30, 2021 | Chris Danneil |
Zeta(5) | 200,000,000,000 | Intel Xeon E5-268v4 @ 2.1 GHz |
||
| October 4, 2021 | September 9, 2021 | William Echols | Log(2) | 1,500,000,000,000 | 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 | AMD Threadripper 3995WX @ 2.7 GHz 512 GB |
||
| December 5, 2020 | November 22, 2020 | David Christle | e | 31,415,926,535,897 | 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 | 2 x Intel Xeon E5-2699 v3 @ 2.3 GHz 756 GB 2 x Intel Xeon Gold 5220 @ 2.2 GHz 754 GB |
||
| September 13, 2020 | September 6, 2020 | Andrew Sun | Catalan's Constant | 1,000,000,001,337 | Compute: 17.5 days | 2 x Intel Xeon E5-2690 v4 @ 2.6 GHz 315 GB |
|
| August 9, 2020 | July 26, 2020 | Seungmin Kim | Zeta(3) - Apery's Constant | 1,200,000,000,100 | Compute: 31.7 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 | 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 |
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 | 2 x Intel Xeon E5-2690 v4 @ 2.6 GHz 315 GB |
||
| May 28, 2020 | May 26, 2020 | Euler-Mascheroni Constant | 600,000,000,100 | 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 | 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 |
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 | 2 x Intel Xeon E5-2651 v2 @ 1.8 GHz 192 GB |
|
| May 22, 2019 | May 21, 2019 | Screen | Lemniscate | 600,000,000,000 | 2 x Intel Xeon Gold 6140 @ 2.3 GHz 187 GB 2 x Intel Xeon 8260L @ 2.4 GHz 768 TB + 6 TB Optane |
||
| March 14, 2019 | January 21, 2019 | Blogs |
Emma Haruka Iwao | Pi | 31,415,926,535,897 | Compute: 121 days | 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 | 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 | 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 | 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 | 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 | 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.
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.
Sample Screenshot: 1 trillion digits of Pi
|
| Core i7 5960X @ 4.0 GHz - 64 DDR4 @ 2400 MHz - 16 HDs |
Latest Releases: (September 14, 2020)
Downloading any of these files constitutes as acceptance of the license agreement.
OS Download Link Size Windows
43.4 MB Linux (Static)
29.2 MB Linux (Dynamic)
22.8 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 18.04.
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:
Other Downloads (for C++ programmers):
Advanced Documentation:
Comparison Chart: (Last updated: May 31, 2021)
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 6560U | Core i7 6700HQ | Core i7 8565U | Core i7 9750H | Core i7 1065G7 | Core i7 1065G7 | Core i7 1165G7 | |
| Generation: | Intel Skylake | Intel Skylake | Intel Kaby Lake R | Intel Coffee Lake | Intel Ice Lake | Intel Ice Lake | Intel Tiger Lake | |
| Cores/Threads: | 4/8 | 4/8 | 4/8 | 6/12 | 4/8 | 4/8 | 4/8 | |
| Processor Speed: | 2.21 GHz | 2.6 GHz ? | 2.3 - 4.6 GHz | 3.1 - 3.9 GHz | 2.1 - 3.0 GHz (25W) | ??? | 3.6 - 4.0 GHz (45W) | |
| Memory: | 8 GB | 16 GB | 8 GB | 16 GB - 2666 MT/s | 16 GB @ 3200 MT/s | 16 GB @ 3733 MT/s | 32 GB @ 3200 MT/s | |
| Version: | v0.7.8 (14-BDW) | v0.7.8 (14-BDW) | 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) | |
| Instruction Set: | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX512-DQ | x64 AVX512-VBMI | x64 AVX512-VBMI | x64 AVX512-VBMI |
| 25,000,000 | 3.165 | 2.140 | 1.584 | 1.463 | 1.596 | 1.243 | 1.046 | 0.868 |
| 50,000,000 | 7.212 | 4.634 | 3.523 | 3.123 | 3.552 | 2.718 | 2.318 | 1.825 |
| 100,000,000 | 16.008 | 10.168 | 7.837 | 6.585 | 7.903 | 5.870 | 5.150 | 3.888 |
| 250,000,000 | 46.491 | 29.298 | 23.336 | 18.378 | 22.520 | 16.531 | 14.745 | 10.813 |
| 500,000,000 | 105.889 | 65.509 | 54.403 | 40.028 | 50.683 | 37.778 | 32.856 | 23.769 |
| 1,000,000,000 | 233.860 | 144.395 | 127.177 | 87.298 | 114.539 | 85.426 | 73.918 | 52.930 |
| 2,500,000,000 | 429.748 | 251.637 | 332.819 | 249.579 | 222.515 | 156.696 | ||
| 5,000,000,000 | 348.512 | |||||||
| 10,000,000,000 | ||||||||
| Credit: | Sebastien Davies | Marco Julian Hummel | ji lcpd | ji lcpd | Gnyueh | ji lcpd | ||
| Processor(s): | Core i7 3630QM | Core i7 4610M | Core i3 8121U (Windows*) | ||
| Generation: | Intel Ivy Bridge | Intel Haswell | Intel Cannon Lake | ||
| Cores/Threads: | 4/8 | 2/4 | 2/4 | ||
| Processor Speed: | 3.2 GHz | 3.0 GHz | 2.6 - 3.0 GHz | 2.6 - 3.0 GHz | 2.4 - 2.9 GHz |
| Memory: | 16 GB - 1600 MT/s | 8 GB | 8 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) |
| Instruction Set: | x64 AVX | x64 AVX2 | x64 AVX2 + ADX | x64 AVX512-DQ | x64 AVX512-VBMI |
| 25,000,000 | 3.688 | 3.372 | 2.984 | 2.685 | 2.189 |
| 50,000,000 | 8.460 | 7.634 | 6.795 | 6.079 | 4.879 |
| 100,000,000 | 18.817 | 17.037 | 15.173 | 13.654 | 10.725 |
| 250,000,000 | 56.097 | 48.912 | 45.801 | 41.775 | 31.268 |
| 500,000,000 | 129.173 | 109.82 | 106.192 | 97.429 | 75.072 |
| 1,000,000,000 | 302.003 | 244.751 | 241.978 | 222.909 | 170.715 |
| 2,500,000,000 | 848.475 | ||||
| 5,000,000,000 | |||||
| 10,000,000,000 | |||||
| Credit: | Oliver Kruse | Marco Julian Hummel | |||
Mainstream Desktops:
| Processor(s): | FX-8350 | Core i7 4770K | Core i7 7700K | Ryzen 7 1800X | Ryzen 7 3700X | Core i9 11900K | Ryzen 9 3950X | Ryzen 9 5950X |
| Generation: | AMD Piledriver | Intel Haswell | Intel Kaby Lake | AMD Zen | AMD Zen 2 | Intel Rocket Lake | AMD Zen 2 | AMD Zen 3 |
| Cores/Threads: | 8/8 | 4/8 | 4/8 | 8/16 | 8/16 | 8/16 | 16/32 | 16/32 |
| Processor Speed: | 4.0 GHz | 4.0 GHz (OC) | 4.9 GHz (OC) | 3.7 GHz | 4.3 GHz | 5.3 GHz | ||
| Memory: | 32 GB - 1600 MT/s | 32 GB - 2133 MT/s | 64 GB - 3200 MT/s | 64 GB - 2866 MT/s | 64 GB - 3600 MT/s | 64 GB - 3733 MT/s | 16 GB - 3200 MT/s | 64 GB |
| Program Version: | v0.7.8 (11-BD1) | v0.7.8 (13-HSW) | v0.7.8 (14-BDW) | v0.7.8 (17-ZN1) | v0.7.8 (17-ZN1) | v0.7.8 (18-CNL) | v0.7.8 (17-ZN1) | v0.7.8 (19-ZN2) |
| Instruction Set: | x64 AVX + XOP | x64 AVX2 | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX512-VBMI | x64 AVX2 + ADX | x64 AVX2 + ADX |
| 25,000,000 | 3.070 | 1.482 | 1.149 | 1.247 | 0.681 | 0.461 | 0.701 | 0.559 |
| 50,000,000 | 6.845 | 3.396 | 2.489 | 2.623 | 1.427 | 1.027 | 1.422 | 1.171 |
| 100,000,000 | 15.130 | 7.385 | 5.482 | 5.655 | 2.975 | 2.223 | 2.870 | 2.403 |
| 250,000,000 | 43.077 | 20.610 | 15.419 | 16.053 | 8.135 | 6.350 | 7.279 | 6.162 |
| 500,000,000 | 96.327 | 45.964 | 33.986 | 35.607 | 17.666 | 14.133 | 15.037 | 12.725 |
| 1,000,000,000 | 214.870 | 101.692 | 74.021 | 78.961 | 39.007 | 31.235 | 32.306 | 27.277 |
| 2,500,000,000 | 623.521 | 292.899 | 209.412 | 226.557 | 112.849 | 91.316 | 91.836 | 77.652 |
| 5,000,000,000 | 1,384.689 | 643.534 | 451.414 | 498.824 | 250.157 | 202.208 | 204.570 | 171.633 |
| 10,000,000,000 | 966.710 | 1,084.855 | 549.067 | 447.487 | 460.548 | 382.39 | ||
| Credit: | Oliver Kruse | Sebastien Davies | O-EtaIXVII | Marc Beste |
Sebastien Davies |
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 | |
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).
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:
- 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:
- The number of logical cores is not a power-of-two.
- 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.
- 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.
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.
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 ePi, 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:
Here's some interesting sites dedicated to the computation of Pi and other constants:
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.