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y-cruncher - A Multi-Threaded Pi-Program |
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From a high-school project that went a little too far...By Alexander J. Yee |
(Last updated: June 23, 2019)
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Apologies for the downtime. Botched a site migration... This is why I do HPC instead of webdev.
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.
- 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 0.7.7 Build 9501 (Released: April 22, 2019)
Linux : Version 0.7.7 Build 9501 (Released: April 22, 2019)
Official Mersenneforum Subforum (new).
Official HWBOT forum thread.
Commercial Use Reminders: (April 22, 2019) - permalink
Due to the amount of publicity that Google's latest computation has generated, there are multiple parties who have expressed interest in doing the same thing - that is to advertise a product or service by setting a world record for Pi.
As unpopular as this will sound, I must remind everyone (including those who have not reached out to me) that y-cruncher is not free for such commercial use. So if you wish to repeat what Google did, you too will need to acquire a commercial use license.
To put it frankly, corporations are not allowed to profit off my work for free unless it falls under one of the exceptions. In the past, I've typically allowed minor violations to slip since I usually don't care and I'm not exactly the kind of person to chase people down. But things are starting to get out of hand now.
Google Cloud Topples the Pi Record: (March 14, 2019) - permalink
Happy Pi Day everyone!
Guess what? Records are meant to be broken and there is a new one!
From September to January, Emma Haruka Iwao of Google (@Yuryu) ran a computation of Pi to 31.4 trillion digits. The exact number of digits that was computed is 31,415,926,535,897 decimal digits and 26,090,362,246,629 hexadecimal digits. (Pop Quiz: Where do those figures come from?)
The details of the computation can be found in the main article. Below are the official Google blogs:
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: |
| June 6, 2019 | May 26, 2019 | Ian Cutress | Zeta(3) - Apery's Constant | 1,000,000,000,000 | 2 x Intel Xeon 8260L @ 2.4 GHz 768 TB + 6 TB Optane 2 x Xeon 8280 @ 2.7 GHz 1.5 TB |
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| May 22, 2019 | May 21, 2019 | Screen | Seungmin Kim |
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 |
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| April 29, 2019 | April 26, 2019 | Jacob Riffee | Log(2) | 1,000,000,000,000 | Compute: 30.9 days | Intel Xeon E5-2660 @ 2.2 GHz 32 GB + 6 x 4 TB HD |
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| April 22, 2019 | April 20, 2019 | Ian Cutress | Gamma(1/4) | 362,560,990,822 | Compute: 3.01 days | ||
| April 15, 2019 | April 14, 2019 | Ian Cutress | Log(10) | 600,000,000,000 | 2 x Intel Xeon 8170M @ 2.1 GHz 384 GB + 2 x 2 TB SSD |
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| March 29, 2019 | March 29, 2019 | Screen | Mike A |
Catalan's Constant | 500,000,000,000 | 2 x Intel Xeon E5-2696 v4 @ 2.2 GHz 768 GB |
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| March 25, 2019 | March 24, 2019 | Oliver Kruse |
Zeta(5) | 100,000,000,000 | AMD Threadripper 1950X @ 3.4 GHz 128 GB |
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| 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 |
| March 3, 2019 | March 3, 2019 | Screen | Alexander Yee | Gamma(1/3) | 200,000,000,000 | Compute: 42.5 hours | Intel Core i7 5960X @ 4.0 GHz 64 GB - 16 x 2TB 7200 RPM |
| January 6, 2019 | January 6, 2019 | Tizian Hanselmann | Golden Ratio | 3,000,000,000,100 | Intel Xeon X5650 @ 2.67 GHz 240 GB |
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| January 3, 2019 | January 3, 2019 | Gerald Hofmann | e | 8,000,000,000,000 | Compute: 28.5 days | 2 x AMD Epyc 7551 @ 2.0 GHz 256 GB |
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| November 30, 2018 | November 27, 2018 | Kevin Humphreys | Golden Ratio | 3,000,000,000,000 | Compute: 10.3 days | Intel Xeon E5-2640 v2 @ 2.0 GHz 48 GB |
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| 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 |
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| January 21, 2019 | January 17, 2019 | Gerald Hofmann | Golden Ratio | 16,180,339,887,498 |
Not Verified |
2 x AMD Epyc 7551 @ 2.0 GHz 200 GB |
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| 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 |
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| 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 |
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| 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
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| Core i7 5960X @ 4.0 GHz - 64 DDR4 @ 2133 MHz - 16 HDs |
Latest Releases: (April 22, 2019)
Downloading any of these files constitutes as acceptance of the license agreement.
OS Download Link Size Windows
41.7 MB Linux (Static)
27.5 MB Linux (Dynamic)
20.9 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 Vista 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: April 6, 2019)
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.
Laptops + Low-Power:
| Processor(s): | Core i7 3630QM | VIA C4650 | Pentium N42001 | Xeon E3-1535M v5 | Core i7 6820HK | Core i7 8850H |
| Generation: | Intel Ivy Bridge | VIA Isaiah | Intel Apollo Lake | Intel Skylake | Intel Skylake | Intel Coffee Lake |
| Cores/Threads: | 4/8 | 4/4 | 4/4 | 4/8 | 4/8 | 6/12 |
| Processor Speed: | 3.2 GHz | 2.0 GHz | 1.1 - 2.5 GHz | 2.9 GHz | 3.2 GHz | ?? GHz |
| Memory: | 16 GB - 1600 MT/s | 16 GB | 4 GB | 16 GB | 48 GB - 2133 MT/s | 16 GB |
| Version: | v0.7.6 (11-SNB) | v0.7.2 (11-SNB) | v0.7.2 (08-NHM) | v0.7.1 (14-BDW) | v0.7.6 (14-BDW) | v0.7.7 (14-BDW) |
| Instruction Set: | x64 AVX | x64 AVX | x64 SSE4.1 | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX2 + ADX |
| 25,000,000 | 3.895 | 17.207 | 11.739 | 1.865 | 1.656 | 1.384 |
| 50,000,000 | 8.761 | 39.049 | 26.289 | 4.102 | 3.591 | 3.032 |
| 100,000,000 | 19.338 | 87.626 | 65.147 | 9.007 | 7.916 | 6.614 |
| 250,000,000 | 57.716 | 277.711 | 192.473 | 25.444 | 21.959 | 19.411 |
| 500,000,000 | 132.171 | 587.516 | 493.551 | 56.566 | 48.781 | 43.391 |
| 1,000,000,000 | 304.784 | 1,350.868 | 130.055 | 108.108 | 96.995 | |
| 2,500,000,000 | 895.365 | 3,884.838 | 308.514 | 290.325 | ||
| 5,000,000,000 | 681.761 | |||||
| 10,000,000,000 | 1,535.329 | |||||
| Credit: | Oliver Kruse | Tralalak | Kaupo Karuse | yoyo | ||
| Processor(s): | Core i3 8121U | ||||||||
| Generation: | Intel Cannon Lake | ||||||||
| Cores/Threads: | 2/4 | ||||||||
| Processor Speed: | 3.1 GHz | 3.0 - 3.1 GHz | 2.5 - 3.0 GHz | 2.6 - 3.1 GHz | 2.5 - 3.0 GHz | 2.3 - 2.9 GHz | |||
| Memory: | 8 GB | ||||||||
| Version: | v0.7.7 (05-A64) | v0.7.7 (08-NHM) | v0.7.7 (11-SNB) | v0.7.7 (13-HSW) | v0.7.7 (14-BDW) | v0.7.7 (17-ZN1) | v0.7.7 (16-KNL) | v0.7.7 (17-SKX) | v0.7.7 (18-CNL) |
| Instruction Set: | x64 SSE3 | x64 SSE4.1 | x64 AVX | x64 AVX2 | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX512-F | x64 AVX512-DQ | x64 AVX512-VBMI |
| 25,000,000 | 8.419 | 7.246 | 6.188 | 3.215 | 3.174 | 3.625 | 3.044 | 2.887 | 2.352 |
| 50,000,000 | 19.081 | 16.509 | 14.303 | 7.308 | 7.226 | 8.209 | 7.014 | 6.584 | 5.319 |
| 100,000,000 | 43.460 | 37.357 | 32.328 | 16.419 | 16.257 | 18.300 | 15.815 | 14.936 | 11.893 |
| 250,000,000 | 129.876 | 115.746 | 99.125 | 49.496 | 50.420 | 55.394 | 49.257 | 45.183 | 34.345 |
| 500,000,000 | 292.674 | 264.631 | 230.130 | 115.856 | 115.005 | 128.041 | 114.936 | 106.493 | 83.882 |
| 1,000,000,000 | 670.319 | 611.136 | 525.670 | 264.095 | 263.852 | 292.807 | 260.168 | 241.327 | 190.027 |
| Credit: | |||||||||
Mainstream Desktops:
| Processor(s): | Core i7 7700K | Ryzen 7 1800X | Core i7 8700K | Core i7 9700K | Core i9 9900K |
| Generation: | Intel Kaby Lake | AMD Zen | Intel Coffee Lake | Intel Coffee Lake | Intel Coffee Lake |
| Cores/Threads: | 4/8 | 8/16 | 6/12 | 8/8 | 8/16 |
| Processor Speed: | 4.9 GHz (OC) | 3.7 GHz | 4.9 - 5.0 GHz (OC) | 4.6 GHz | 4.7 GHz |
| Memory: | 64 GB - 3200 MT/s | 64 GB - 3000 MT/s | 16 GB - 3600 MT/s | 16 GB - 3600 MT/s | 32 GB - 3600 MT/s |
| Program Version: | v0.7.6 (14-BDW) | v0.7.6 (17-ZN1) | v0.7.6 (14-BDW) | v0.7.6 (14-BDW) | v0.7.6 (14-BDW) |
| Instruction Set: | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX2 + ADX |
| 25,000,000 | 1.049 | 1.247 | 0.930 | 0.730 | 0.675 |
| 50,000,000 | 2.314 | 2.655 | 2.023 | 1.630 | 1.496 |
| 100,000,000 | 5.077 | 5.759 | 4.352 | 3.605 | 3.259 |
| 250,000,000 | 14.277 | 16.115 | 11.925 | 10.213 | 9.032 |
| 500,000,000 | 31.878 | 35.783 | 25.883 | 22.960 | 20.018 |
| 1,000,000,000 | 70.806 | 79.345 | 56.387 | 50.819 | 44.175 |
| 2,500,000,000 | 204.042 | 228.840 | 157.515 | 145.464 | 125.223 |
| 5,000,000,000 | 448.258 | 498.923 | 279.321 | ||
| 10,000,000,000 | 976.451 | 1,092.887 | |||
| Credit: | Oliver Kruse | Nehal Prasad | ji lcpd | ||
| Processor(s): | Phenom II X3 720 | Core i7 920 | FX-8350 | Core i7 4770K | Core i7 5775C |
| Generation: | AMD K10 | Intel Nehalem | AMD Piledriver | Intel Haswell | Intel Broadwell |
| Cores/Threads: | 4/4 (unlock from 3/3) | 4/8 | 8/8 | 4/8 | 4/8 |
| Processor Speed: | 2.8 GHz | 3.5 GHz (OC) | 4.0 GHz | 4.0 GHz (OC) | 3.8 GHz (OC) |
| Memory: | 12 GB - 1333 MT/s | 12 GB - 1333 MT/s | 32 GB - 1600 MT/s | 32 GB - 2133 MT/s | 16 GB - 2400 MT/s |
| Program Version: | v0.7.6 (05-A64) | v0.7.6 (08-NHM) | v0.7.6 (11-BD1) | v0.7.6 (13-HSW) | v0.7.1 (14-BDW) |
| Instruction Set: | x64 SSE3 | x64 SSE4.1 | x64 AVX + XOP | x64 AVX2 | x64 AVX2 + ADX |
| 25,000,000 | 9.357 | 4.934 | 3.239 | 1.524 | 1.730 |
| 50,000,000 | 19.678 | 10.935 | 7.167 | 3.365 | 3.940 |
| 100,000,000 | 43.794 | 24.792 | 15.700 | 7.527 | 8.739 |
| 250,000,000 | 127.530 | 73.153 | 43.787 | 20.766 | 25.073 |
| 500,000,000 | 283.572 | 164.107 | 97.843 | 46.358 | 56.343 |
| 1,000,000,000 | 648.422 | 374.590 | 219.344 | 102.451 | 125.967 |
| 2,500,000,000 | 1,832.422 | 633.021 | 291.632 | 369.738 | |
| 5,000,000,000 | 1,408.939 | 645.998 | |||
| 10,000,000,000 | |||||
| Credit: | André Bachmann |
High-End Desktops:
| Processor(s): | Core i7 5820K | Core i7 5960X | Threadripper 1950X | Core i9 7900X | Core i9 7940X |
| Generation: | Intel Haswell | Intel Haswell | AMD Threadripper | Intel Skylake X | Intel Skylake X |
| Cores/Threads: | 6/12 | 8/16 | 16/32 | 10/20 | 14/28 |
| Processor Speed: | 4.5 GHz (OC) | 4.0 GHz (OC) | 3.5 - 3.7 GHz | 4.3/4.0/3.6 GHz* |
4.6/4.0/3.6 GHz* |
| 3.0 GHz cache | 2.8 GHz cache | ||||
| Memory: | 32 GB - 2400 MT/s | 64 GB - 2133 MT/s | 128 GB - 3000 MT/s | 128 GB - 3600 MT/s | 128 GB - 3466 MT/s |
| Program Version: | v0.7.3 (13-HSW) | v0.7.6 (13-HSW) | v0.7.6 (17-ZN1) | v0.7.6 (17-SKX) | v0.7.6 (17-SKX) |
| Instruction Set: | x64 AVX2 | x64 AVX2 | x64 AVX2 + ADX | x64 AVX512-DQ | x64 AVX512-DQ |
| 25,000,000 | 1.287 | 0.812 | 0.747 | 0.522 | 0.520 |
| 50,000,000 | 2.499 | 1.942 | 1.516 | 1.117 | 1.052 |
| 100,000,000 | 5.401 | 4.072 | 3.203 | 2.362 | 2.177 |
| 250,000,000 | 14.732 | 10.991 | 8.733 | 6.209 | 5.409 |
| 500,000,000 | 32.294 | 23.929 | 19.139 | 13.204 | 11.412 |
| 1,000,000,000 | 71.225 | 52.768 | 42.345 | 28.827 | 24.232 |
| 2,500,000,000 | 200.323 | 149.365 | 119.526 | 79.854 | 66.592 |
| 5,000,000,000 | 443.543 | 330.414 | 266.066 | 178.786 | 147.719 |
| 10,000,000,000 | 722.456 | 579.380 | 394.887 | 323.079 | |
| 25,000,000,000 | 1629.994 | 1119.634 | 911.097 | ||
| Credit: | Sean Heneghan | 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 E5-2686 v4 | Xeon E5-2696 v4 | Epyc 7601 | Xeon Gold 6130F | Xeon Platinum 8124M | Xeon Gold 6148 | Xeon Platinum 8175M |
| Generation: | Intel Broadwell | Intel Broadwell | AMD Naples | Intel Skylake Purley | Intel Skylake Purley | Intel Skylake Purley | Intel Skylake Purley |
| Sockets/Cores/Threads: | 2/36/72 | 2/44/88 | 2/64/128 | 2/32/64 | 2/36/72 | 2/40/40 | 2/48/96 |
| Processor Speed: | 2.3 GHz | 2.2 GHz | 2.2 GHz | 2.1 GHz | 3.0 GHz | 2.4 GHz | 2.5 GHz |
| Memory: | 504 GB - ??? | 768 GB - ??? | 256 GB - ?? | 256 GB - ?? | 137 GB - ?? | 188 GB - ?? | ~756 GB - ?? |
| Program Version: | v0.7.7 (14-BDW) | v0.7.1 (14-BDW) | v0.7.3 (17-ZN1) | v0.7.3 (17-SKX) | v0.7.5 (17-SKX) | v0.7.6 (17-SKX) | v0.7.6 (17-SKX) |
| Instruction Set: | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX512-DQ | x64 AVX512-DQ | x64 AVX512-DQ | x64 AVX512-DQ |
| 25,000,000 | 0.494 | 0.715 | 2.459 | 1.150 | 0.540 | 0.329 | 0.294 |
| 50,000,000 | 0.982 | 1.344 | 4.347 | 1.883 | 0.981 | 0.683 | 0.617 |
| 100,000,000 | 2.193 | 2.673 | 6.996 | 3.341 | 1.905 | 1.456 | 1.305 |
| 250,000,000 | 6.044 | 6.853 | 14.258 | 7.731 | 5.085 | 3.737 | 3.591 |
| 500,000,000 | 12.582 | 14.538 | 24.930 | 15.346 | 10.372 | 7.750 | 7.293 |
| 1,000,000,000 | 26.852 | 31.260 | 47.837 | 31.301 | 21.217 | 16.550 | 15.041 |
| 2,500,000,000 | 73.596 | 84.271 | 111.139 | 82.871 | 55.701 | 45.693 | 39.329 |
| 5,000,000,000 | 160.094 | 192.889 | 228.252 | 179.488 | 118.151 | 99.078 | 83.601 |
| 10,000,000,000 | 346.305 | 417.322 | 482.777 | 387.530 | 247.928 | 212.984 | 176.695 |
| 25,000,000,000 | 980.784 | 1,186.881 | 1,184.144 | 1,063.850 | 599.653 | 491.988 | |
| 50,000,000,000 | 2,156.854 | 2,601.476 | 1081.181 | ||||
| 100,000,000,000 | 6,037.704 | ||||||
| 250,000,000,000 | |||||||
| Credit: | newalex | "yoyo" | Dave Graham | Jacob Coleman | Oliver Kruse | newalex | |
| Processor(s): | Xeon X5482 | Xeon E5-2690 | Xeon E5-2683 v3 | Xeon E7-8880 v3 | Xeon E5-2687W v4 | |
| Generation: | Intel Penryn | Intel Sandy Bridge | Intel Haswell | Intel Haswell | Intel Broadwell | |
| Sockets/Cores/Threads: | 2/8/8 | 2/16/32 | 2/28/56 | 4/64/128 | 2/24/48 | |
| Processor Speed: | 3.2 GHz | 3.5 GHz | 2.03 GHz | 2.3 GHz | 3.0 GHz | |
| Memory: | 64 GB - 800 MT/s | 256 GB - ??? | 128 GB - ??? | 2 TB - ??? | 64 GB | |
| Program Version: | v0.7.2 (08-NHM) | v0.7.5 (07-PNR) | v0.6.2/3 (11-SNB) | v0.6.9 (13-HSW) | v0.7.1 (13-HSW) | v0.7.6 (14-BDW) |
| Instruction Set: | x64 SSE4.1 | x64 AVX | x64 AVX2 | x64 AVX2 | x64 AVX2 + ADX | |
| 25,000,000 | 4.548 | 4.248 | 2.283 | 0.907 | 1.176 | 0.490 |
| 50,000,000 | 9.779 | 9.148 | 4.295 | 1.745 | 2.321 | 1.072 |
| 100,000,000 | 20.834 | 19.580 | 8.167 | 3.317 | 4.217 | 2.303 |
| 250,000,000 | 60.049 | 56.226 | 20.765 | 8.339 | 8.781 | 6.196 |
| 500,000,000 | 134.978 | 126.448 | 42.394 | 17.708 | 15.879 | 13.046 |
| 1,000,000,000 | 308.679 | 286.903 | 89.920 | 37.311 | 32.078 | 27.763 |
| 2,500,000,000 | 874.588 | 824.820 | 239.154 | 102.131 | 78.251 | 76.202 |
| 5,000,000,000 | 1,946.683 | 1,836.808 | 520.977 | 218.917 | 164.157 | 165.046 |
| 10,000,000,000 | 4,317.677 | 4,000.065 | 1,131.809 | 471.802 | 346.307 | 356.487 |
| 25,000,000,000 | 3,341.281 | 1,511.852 | 957.966 | 1,006.131 | ||
| 50,000,000,000 | 7,355.076 | 2,096.169 | 2,202.558 | |||
| 100,000,000,000 | 4,442.742 | |||||
| 250,000,000,000 | 17,428.450 | |||||
| Credit: | Shigeru Kondo | Shigeru Kondo | Jacob Coleman | Cameron Giesbrecht | ||
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 don't 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.