y-cruncher - A Multi-Threaded Pi-Program
From a high-school project that went a little too far...
By Alexander J. Yee
(Last updated: May 28, 2020)
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.
Windows: Version 0.7.8 Build 9503 (Released: October 27, 2019)
Linux : Version 0.7.8 Build 9503 (Released: October 27, 2019)
Official Mersenneforum Subforum (new).
Official HWBOT forum thread.
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.
The Pi Record Returns to the Personal Computer: (January 29, 2020) - permalink
After a grueling 10 months of computation running from April of last year to today, the world record for Pi has once again fallen. This time to Timothy Mullican who computed 50 trillion digits of Pi on a dated (but still powerful) personal computer.
As the previous record was set by Google using their cloud platform, this computation marks the return of the Pi record to single machine personal computers.
Timothy used a 2012-era computer (Ivy Bridge) along with a very large array of 48 modern hard drives. While the processing power was significantly less than that of Google's computation, it had a better balance of computing power and storage bandwidth - thus leading to a computation of comparable speed to Google's.
Full details of the computation can be found on Tim's blog.
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:|
|May 28, 2020||May 26, 2020||Euler-Mascheroni Constant||600,000,000,100||
2 x Intel Xeon Gold 6140 @ 2.3 GHz
Intel Xeon 8280 @ 2.7 GHz
|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
48 Hard Drives
|December 4, 2019||November 13, 2019||
Christophe Patris de Broe
& Alexandre Gouy
& Cyril Hsu
2 x Intel Xeon Platinum 8268 @ 2.9 GHz
|November 26, 2019||August 31, 2019||Hiroyuki Oodaira (大平 寛之)||Log(10)||1,000,000,000,000||Compute: 8.73 days||
AMD Ryzen 3700X @ 3.6 GHz
|September 23, 2019||Hiroyuki Oodaira (大平 寛之)||Golden Ratio||5,000,000,000,000||Compute: 46.9 hours||
AMD Ryzen 3700X @ 3.6 GHz
|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
|July 21, 2019||July 16, 2019||Catalan's Constant||600,000,000,100||
2 x Intel Xeon Gold 6140 @ 2.3 GHz
|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
|May 22, 2019||May 21, 2019||Screen||Lemniscate||600,000,000,000||
2 x Intel Xeon Gold 6140 @ 2.3 GHz
2 x Intel Xeon 8260L @ 2.4 GHz
768 TB + 6 TB Optane
|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
|April 22, 2019||April 20, 2019||Ian Cutress||Gamma(1/4)||362,560,990,822||Compute: 3.01 days|
|March 25, 2019||March 24, 2019||
AMD Threadripper 1950X @ 3.4 GHz
|March 14, 2019||January 21, 2019||
|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
|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
|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
|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
|October 8, 2014||October 7, 2014||
Sandon Van Ness
|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:
Latest Releases: (March 1, 2020)
Downloading any of these files constitutes as acceptance of the license agreement.
OS Download Link Size
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.
- Windows 7 or later.
- The HWBOT submitter requires the Java 8 Runtime.
- 64-bit Linux is required. There is no support for 32-bit.
- The dynamic version has been tested on Ubuntu 18.04.
- 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.
Other Downloads (for C++ programmers):
Comparison Chart: (Last updated: March 12, 2020)
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|
|Generation:||Intel Skylake||Intel Skylake||Intel Kaby Lake R||Intel Coffee Lake||Intel Ice Lake||Intel Ice Lake|
|Processor Speed:||2.21 GHz||2.6 GHz ?||2.3 - 4.6 GHz||3.1 - 3.9 GHz||2.1 - 3.0 GHz (25W)||???|
|Memory:||8 GB||16 GB||8 GB||16 GB - 2666 MT/s||16 GB @ 3200 MT/s||16 GB @ 3733 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)|
|Instruction Set:||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX512-DQ||x64 AVX512-VBMI||x64 AVX512-VBMI|
|Credit:||Sebastien Davies||Marco Julian Hummel||ji lcpd||ji lcpd||Gnyueh|
|Processor(s):||Core i7 3630QM||Core i7 4610M||Core i3 8121U (Windows*)|
|Generation:||Intel Ivy Bridge||Intel Haswell||Intel Cannon Lake|
|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|
|Credit:||Oliver Kruse||Marco Julian Hummel|
|Processor(s):||Ryzen 7 1800X||Ryzen 7 2700||Ryzen 7 3700X||Core i7 8700K||Core i7 9700K||Core i9 9900K||AMD Ryzen 9 3950X|
|Generation:||AMD Zen||AMD Zen+||AMD Zen 2||Intel Coffee Lake||Intel Coffee Lake||Intel Coffee Lake||AMD Zen 2|
|Processor Speed:||3.7 GHz||3.2 GHz||4.3 GHz||4.9 - 5.0 GHz (OC)||4.6 GHz||4.7 GHz|
|Memory:||64 GB - 3000 MT/s||64 GB - 2866 MT/s||64 GB - 2400 MT/s||64 GB - 3600 MT/s||16 GB - 3600 MT/s||16 GB - 3600 MT/s||32 GB - 3600 MT/s||16 GB - 3200 MT/s|
|Program Version:||v0.7.6 (17-ZN1)||v0.7.8 (17-ZN1)||v0.7.7 (17-ZN1)||v0.7.8 (17-ZN1)||v0.7.6 (14-BDW)||v0.7.6 (14-BDW)||v0.7.6 (14-BDW)||v0.7.8 (17-ZN1)|
|Instruction Set:||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX|
|Sebastien Davies||Nehal Prasad||ji lcpd||
|Processor(s):||Core i7 920||FX-8350||Core i7 4770K||Core i7 5775C||Core i7 7700K||AMD Ryzen 5 3600|
|Generation:||Intel Nehalem||AMD Piledriver||Intel Haswell||Intel Broadwell||Intel Kaby Lake||AMD Zen 2|
|Processor Speed:||3.5 GHz (OC)||4.0 GHz||4.0 GHz (OC)||3.8 GHz (OC)||4.9 GHz (OC)|
|Memory:||12 GB - 1333 MT/s||32 GB - 1600 MT/s||32 GB - 2133 MT/s||16 GB - 2400 MT/s||64 GB - 3200 MT/s||16 GB|
|Program Version:||v0.7.6 (08-NHM)||v0.7.6 (11-BD1)||v0.7.8 (11-BD1)||v0.7.6 (13-HSW)||v0.7.8 (13-HSW)||v0.7.1 (14-BDW)||v0.7.8 (14-BDW)||v0.7.7 (17-ZN1)|
|Instruction Set:||x64 SSE4.1||x64 AVX + XOP||x64 AVX + XOP||x64 AVX2||x64 AVX2||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX|
|Credit:||André Bachmann||Oliver Kruse||Yusuke Kamui|
|Processor(s):||Core i9 7900X||Core i9 7940X||Core i9 9980XE||Core i9 10980XE||Threadripper 3970X|
|Generation:||Intel Skylake X||Intel Skylake X||Intel Skylake X||Intel Cascade Lake X||AMD Threadripper|
|3.8 GHz||3.6 GHz||4.7/4.2/3.7||2.8 GHz||3.7 GHz|
|3.0 GHz cache||2.8 GHz cache|
|Memory:||128 GB - 3600 MT/s||128 GB - 3466 MT/s||64 GB - 3600 MT/s||128 GB - 3600 MT/s||64 GB|
|Program Version:||v0.7.6 (17-SKX)||v0.7.8 (14-BDW)||v0.7.8 (17-SKX)||v0.7.8 (17-SKX)||v0.7.8 (17-SKX)||v0.7.8 (17-ZN1)|
|Instruction Set:||x64 AVX512-DQ||x64 AVX2 + ADX||x64 AVX512-DQ||x64 AVX512-DQ||x64 AVX512-DQ||x64 AVX2 + ADX|
|Credit:||曾 铮||ji lcpd||Tainus|
|Processor(s):||Core i7 5960X||Threadripper 1950X|
|Generation:||Intel Haswell||AMD Threadripper|
|Processor Speed:||4.0 GHz (OC)||3.5 - 3.7 GHz|
|Memory:||64 GB - 2133 MT/s||128 GB - 2933 MT/s|
|Program Version:||v0.7.6 (13-HSW)||v0.7.8 (13-HSW)||v0.7.8 (17-ZN1)|
|Instruction Set:||x64 AVX2||x64 AVX2||x64 AVX2 + ADX|
*All-core non-AVX/AVX/AVX512 CPU frequency.
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|
|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|
|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|
|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|
|Credit:||Shigeru Kondo||Jacob Coleman||Cameron Giesbrecht||newalex||"yoyo"||Dave Graham|
The full chart of rankings for each size can be found here:
These fastest times may include unreleased betas.
Got a faster time? Let me know: email@example.com
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|
High core count Skylake X processors are known to be heavily bottlenecked by 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.
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.
y-cruncher has a lot of settings for tuning parallel performance. By default, it makes a best effort to analyze the hardware and pick the best settings. But because of the virtually unlimited combinations of processor topologies, it's difficult for y-cruncher to optimally pick the best settings for everything. So sometimes the best performance can only be achieved with manual settings.
*These are advanced settings that cannot be changed if you're using the benchmark option in the console UI. To change them, you will need to either run benchmark mode from the command line or use the custom compute menu.
Load imbalance is a faily common problem in y-cruncher. The usual causes are:
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.
This is probably one of the most complicated features in y-cruncher.
Everything in this section is in the process of being re-verified and moved to: https://github.com/Mysticial/y-cruncher/issues
Pi and other Constants:
Hardware and Overclocking:
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.