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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: February 16, 2019)
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The first scalable multi-threaded Pi-benchmark for multi-core systems...
How fast can your computer compute Pi?
y-cruncher is a program that can compute Pi and other constants to trillions of digits.
It is the first of its kind that is multi-threaded and scalable to multi-core systems. Ever since its launch in 2009, it has become a common benchmarking and stress-testing application for overclockers and hardware enthusiasts.
y-cruncher has been used to set several world records for the most digits of Pi ever computed.
- 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 9497 (Released: February 16, 2019)
Linux : Version 0.7.7 Build 9497 (Released: February 16, 2019)
Official Mersenneforum Subforum (new).
Official HWBOT forum thread.
Version v0.7.7: (January 5, 2019) - permalink
Version 0.7.7 is now out and with it are all mathematical features that I've blogged about here months ago.
- The Custom Formula feature along with about 80 prebuilt formulas and constants.
- 3 new built-in algorithms for Catalan's constant: Guilerra, Pilehrood-short, and Pilehrood-long
- A new built-in algorithm for the Lemniscate constant: AGM-Pi
So for the first time in years, this is a major release with almost nothing on the hardware/optimization front.
The defining feature for this release is obviously the custom formulas. As mentioned in the October blog, it allows y-cruncher to evaluate user-input formulas.
The final list of functions for v0.7.7 is:
- Basic Arithmetic: addition, subtraction, multiplication, division, integer power
- Elementary Functions: square root, arithmetic-geometric mean (AGM), logarithms, ArcCoth() of integer
- Special Functions: ArcSinlemn() of rational, generalized hypergeometric series of rationals
- Constants: Golden Ratio, e, Pi, Zeta(3), Catalan's Constant, Lemniscate, Euler-Mascheroni Constant
The only thing new since the original announcement is that the logarithm has been extended to allow any real input as opposed to just small integers.
All of these operations are fully parallelized and run in quasi-linear time and linear memory. There is also support for swap mode and checkpoint restart. Thus anything that can be represented (or sufficiently approximated) by a reasonably small combination of these operations (subject to restrictions) can be now be feasibly computed to billions or even trillions of digits without being limited by physical memory. This is well beyond the capability of most computer algebra systems. So hopefully it will serve as a useful tool for researchers in search of algorithms for super-high-precision computation of various constants and functions.
The download bundles now include about 80 prebuilt formulas which you can input into y-cruncher to compute. Feel free to contribute more on GitHub.
Documentation for the custom formulas can be found here.
Due to the sheer size and scope of the custom formulas, I expect there to be a lot of bugs. So if you encounter anything that doesn't seem right, let me know either though email or by opening an issue on GitHub.
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: |
| February 16, 2019 | February 16, 2019 | Tizian Hanselmann | Catalan's Constant | 300,000,000,000 | 2 x Intel Xeon X5650 @ 2.67 GHz 240 GB |
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| January 23, 2019 | January 23, 2019 | Oliver Kruse | Zeta(5) | 100,000,000,000 |
Not Verified |
AMD Threadripper 1950X @ 3.4 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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| 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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| December 10, 2018 | December 10, 2018 | Michael Kwok | Log(2) | 600,000,000,000 | Core i7 7700k @ 4.2 GHz - 16 GB Core i7 4790 @ 3.6 GHz - 16 GB |
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| November 30, 2018 | November 30, 2018 | Screen | Alexander Yee | Gamma(1/4) | 100,000,000,000 | Compute: 32.0 hours | Intel Core i7 5960X @ 4.0 GHz 64 GB - 16 x 2TB 7200 RPM |
| 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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| October 6, 2018 | October 6, 2018 | Screen | Alexander Yee | Zeta(5) | 20,000,000,000 | Compute: 25.3 hours | Intel Core i9 7940X @ 3.6 GHz 128 GB DDR4 |
| 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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| August 14, 2017 | August 13, 2017 | Ron Watkins | Zeta(3) - Apery's Constant | 500,000,000,000 | 8 x Xeon 6550 @ 2.0 GHz - 512 GB 2 x Xeon X5690 @ 3.46 GHz - 142 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 |
| July 11, 2016 | July 5, 2016 | "yoyo" | Golden Ratio | 10,000,000,000,000 |
Not Verified |
2 x Intel Xeon E5-2696 v4 @ 2.2 GHz 768 GB |
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| 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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| June 4, 2016 | May 29, 2016 | Ron Watkins | Lemniscate | 250,000,000,000 | 4 x Xeon E5-4660 v3 @ 2.1 GHz - 1TB 4 x Xeon X6550 @ 2 GHz - 512 GB |
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| April 9, 2016 | April 3, 2016 | Ron Watkins | Log(10) | 500,000,000,000 | 2 x Xeon X5690 @ 3.47 GHz 141 GB |
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| February 8, 2016 | February 6, 2016 | Mike A | Catalan's Constant | 500,000,000,000 |
Not Verified |
2 x Intel Xeon E5-2697 v3 @ 2.6 GHz 128 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: (February 16, 2019)
OS Download Link Size Windows
41.6 MB Linux (Static)
27.4 MB Linux (Dynamic)
20.6 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: February 2, 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) | v0.7.6 (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 | 1.539 |
| 50,000,000 | 8.761 | 39.049 | 26.289 | 4.102 | 3.591 | 3.309 |
| 100,000,000 | 19.338 | 87.626 | 65.147 | 9.007 | 7.916 | 7.546 |
| 250,000,000 | 57.716 | 277.711 | 192.473 | 25.444 | 21.959 | 20.011 |
| 500,000,000 | 132.171 | 587.516 | 493.551 | 56.566 | 48.781 | 47.370 |
| 1,000,000,000 | 304.784 | 1,350.868 | 130.055 | 108.108 | 109.754 | |
| 2,500,000,000 | 895.365 | 3,884.838 | 308.514 | 291.586 | ||
| 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 E5-2687W v4 | Xeon E5-2696 v4 | Epyc 7601 | Xeon Gold 6130F | Xeon Platinum 8124M | Xeon Gold 6148 |
| Generation: | Intel Broadwell | Intel Broadwell | AMD Naples | Intel Skylake Purley | Intel Skylake Purley | Intel Skylake Purley |
| Sockets/Cores/Threads: | 2/24/48 | 2/44/88 | 2/64/128 | 2/32/64 | 2/36/72 | 2/40/40 |
| Processor Speed: | 3.0 GHz | 2.2 GHz | 2.2 GHz | 2.1 GHz | 3.0 GHz | 2.4 GHz |
| Memory: | 64 GB | 768 GB - ??? | 256 GB - ?? | 256 GB - ?? | 137 GB - ?? | 188 GB - ?? |
| Program Version: | v0.7.6 (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) |
| Instruction Set: | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX2 + ADX | x64 AVX512-DQ | x64 AVX512-DQ | x64 AVX512-DQ |
| 25,000,000 | 0.490 | 0.715 | 2.459 | 1.150 | 0.540 | 0.329 |
| 50,000,000 | 1.072 | 1.344 | 4.347 | 1.883 | 0.981 | 0.683 |
| 100,000,000 | 2.303 | 2.673 | 6.996 | 3.341 | 1.905 | 1.456 |
| 250,000,000 | 6.196 | 6.853 | 14.258 | 7.731 | 5.085 | 3.737 |
| 500,000,000 | 13.046 | 14.538 | 24.930 | 15.346 | 10.372 | 7.750 |
| 1,000,000,000 | 27.763 | 31.260 | 47.837 | 31.301 | 21.217 | 16.550 |
| 2,500,000,000 | 76.202 | 84.271 | 111.139 | 82.871 | 55.701 | 45.693 |
| 5,000,000,000 | 165.046 | 192.889 | 228.252 | 179.488 | 118.151 | 99.078 |
| 10,000,000,000 | 356.487 | 417.322 | 482.777 | 387.530 | 247.928 | 212.984 |
| 25,000,000,000 | 1,006.131 | 1,186.881 | 1,184.144 | 1,063.850 | 599.653 | |
| 50,000,000,000 | 2,202.558 | 2,601.476 | ||||
| 100,000,000,000 | 6,037.704 | |||||
| 250,000,000,000 | ||||||
| Credit: | Cameron Giesbrecht | "yoyo" | Dave Graham | Jacob Coleman | Oliver Kruse | |
| Processor(s): | Xeon X5482 | Xeon E5-2690 | Xeon E5-2683 v3 | Xeon E7-8880 v3 | |
| Generation: | Intel Penryn | Intel Sandy Bridge | Intel Haswell | Intel Haswell | |
| Sockets/Cores/Threads: | 2/8/8 | 2/16/32 | 2/28/56 | 4/64/128 | |
| Processor Speed: | 3.2 GHz | 3.5 GHz | 2.03 GHz | 2.3 GHz | |
| Memory: | 64 GB - 800 MT/s | 256 GB - ??? | 128 GB - ??? | 2 TB - ??? | |
| 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) |
| Instruction Set: | x64 SSE4.1 | x64 AVX | x64 AVX2 | x64 AVX2 | |
| 25,000,000 | 4.548 | 4.248 | 2.283 | 0.907 | 1.176 |
| 50,000,000 | 9.779 | 9.148 | 4.295 | 1.745 | 2.321 |
| 100,000,000 | 20.834 | 19.580 | 8.167 | 3.317 | 4.217 |
| 250,000,000 | 60.049 | 56.226 | 20.765 | 8.339 | 8.781 |
| 500,000,000 | 134.978 | 126.448 | 42.394 | 17.708 | 15.879 |
| 1,000,000,000 | 308.679 | 286.903 | 89.920 | 37.311 | 32.078 |
| 2,500,000,000 | 874.588 | 824.820 | 239.154 | 102.131 | 78.251 |
| 5,000,000,000 | 1,946.683 | 1,836.808 | 520.977 | 218.917 | 164.157 |
| 10,000,000,000 | 4,317.677 | 4,000.065 | 1,131.809 | 471.802 | 346.307 |
| 25,000,000,000 | 3,341.281 | 1,511.852 | 957.966 | ||
| 50,000,000,000 | 7,355.076 | 2,096.169 | |||
| 100,000,000,000 | 4,442.742 | ||||
| 250,000,000,000 | 17,428.450 | ||||
| Credit: | Shigeru Kondo | Shigeru Kondo | Jacob Coleman | ||
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 |
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| 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!!!
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?
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.