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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: November 18, 2024)
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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.
- 202 trillion digits - May 2024 (Jordan Ranous, Kevin O’Brien, and Brian Beeler - StorageReview)
- 105 trillion digits - February 2024 (Jordan Ranous, Kevin O’Brien, and Brian Beeler - StorageReview)
- 100 trillion digits - June 2022 (Emma Haruka Iwao)
- 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 0.8.5 Build 9543 (Released: July 21, 2024)
Linux : Version 0.8.5 Build 9543 (Released: July 21, 2024)
Official Mersenneforum Subforum.
Official HWBOT forum thread.
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:
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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.
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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:
- How y-cruncher does manipulates the console. (WinAPI or Virtual Terminal escape sequences)
- How y-cruncher does the refreshing status lines. (overwrite the line, or don't refresh at all)
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.
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 | Intel Core i9 7900X 32 GB |
| October 20, 2024 | July 31, 2024 | Mamdouh Barakat | Gamma(1/4) | 1,001,001,001,001 | AMD Ryzen 7900X 128 GB AMD Threadripper 5965WX 256 GB |
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| June 28, 2024 | May 20, 2024 | Source | Jordan Ranous Kevin O’Brien Brian Beeler (StorageReview) |
Pi | 202,112,290,000,000 | 2 x Intel Xeon Platinum 8592+ |
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| 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 |
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| March 14, 2024 | February 27, 2024 | Source | Jordan Ranous Kevin O’Brien Brian Beeler (StorageReview) |
Pi | 105,000,000,000,000 | 2 x AMD Epyc 9754 |
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| February 13, 2024 | February 12, 2024 | Jordan Ranous | Log(2) | 3,000,000,000,000 | 2 x Intel Xeon Platinum 8460H 512 GB |
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| December 26, 2023 | December 24, 2023 | Jordan Ranous | e | 35,000,000,000,000 | 2 x Intel Xeon Platinum 8460H |
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| December 26, 2023 | December 25, 2023 | Jordan Ranous | Square Root of 2 | 20,000,000,000,000 | Intel Xeon Platinum 8450H 512 GB Intel Xeon Platinum 8460H 512 GB |
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| December 26, 2023 | December 22, 2023 | Andrew Sun |
Zeta(3) - Apery's Constant | 2,020,569,031,595 | Compute: 5.61 days | Intel Xeon Platinum 8347C 505 GB Intel Xeon Platinum 8347C 507 GB |
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| December 18, 2023 | December 15, 2023 | Jordan Ranous | Gamma(1/3) | 1,000,000,000,000 | 2 x Intel Xeon Platinum 8450H 512 GB |
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| December 2, 2023 | November 27, 2023 | Jordan Ranous | Golden Ratio | 20,000,000,000,000 | AMD Epyc 9654 - 1.5 TB Intel Xeon Platinum 8450H |
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| September 9, 2023 | September 7, 2023 | Andrew Sun |
Euler-Mascheroni Constant | 1,337,000,000,000 | Intel Xeon Platinum 83470C 400 GB |
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| July 17, 2022 | July 15, 2022 | Seungmin Kim | Lemniscate | 1,200,000,000,100 | 2 x Intel Xeon Gold 6140 |
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| June 8, 2022 | March 21, 2022 | Emma Haruka Iwao | Pi | 100,000,000,000,000 | 128 vCPU Intel Ice Lake (GCP) |
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| March 14, 2022 | March 9, 2022 | Seungmin Kim | Catalan's Constant | 1,200,000,000,100 | Compute: 48.6 days | 2 x Intel Xeon Gold 6140 |
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| 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 | 2 x Intel Xeon E5-2699 v3 756 GB 2 x Intel Xeon Gold 5220 754 GB |
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| January 29, 2020 | January 29, 2020 | Blog | Timothy Mullican | Pi | 50,000,000,000,000 | 4 x Intel Xeon E7-4880 v2 315 GB 48 Hard Drives |
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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 > 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 | 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 | 2 x Xeon E5-4650L 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 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 @ 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
42.9 MB Linux (Static)
33.7 MB Linux (Dynamic)
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:
- 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 24.04.
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: 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 |
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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 | |
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, 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?- Why is y-cruncher faster 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.