y-cruncher - A Multi-Threaded Pi-Program
From a high-school project that went a little too far...
By Alexander J. Yee
(Last updated: October 19, 2018)
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 0.7.6 Build 9487 (Released: October 14, 2018)
Linux : Version 0.7.6 Build 9487 (Released: October 14, 2018)
Official HWBOT thread.
Official XtremeSystems Forums thread.
Catalan's Constant is No Longer a Slow Constant: (August 23, 2018) - permalink
In what is probably the first major mathematical improvement since the start of the y-cruncher project, there are 3 new formulas for Catalan's Constant.
I was recently made aware of a publication by F. M. S. Lima which directly and indirectly led to 3 new formulas for Catalan's Constant which are faster than the Lupas formula which had been the fastest for more than a decade.
|Name||Formula||Speedup vs. Lupas|
All 3 formulas have been implemented for y-cruncher v0.7.7. But the timing of this with respect to y-cruncher's release cycle (having just released v0.7.6), means it will be months before these formulas see the light of day for y-cruncher. But at the very least, we know that they exist and that they work. All 3 implementations have been tested to 1 billion digits. (which didn't take very long)
Catalan's Constant has historically been one of the slowest mainstream constants to compute - second only to the Euler-Mascheroni Constant. But thanks to these formulas, Catalan's Constant is now almost as fast as Zeta(3).
As only two independent algorithms are needed to establish records, the existing formulas by Lupas and Huvent (as well as Guillera's formula) are now effectively out-of-date. But there are no immediate plans to remove any of the outdated formulas.
Mathematics evolves at a much slower pace than computer hardware. So it is easy to forget that math remains one of the most important parts of high precision computations. Without such formulas and algorithms, large computations would be impossible. So we must never stop thanking the generations of mathemeticians, both past and present, that have made such projects possible.
While we wait for v0.7.7, two new articles have been added to the algorithms page:
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 6, 2018||October 6, 2018||Alexander Yee||Zeta(5)||20,000,000,000||Compute: 25.3 hours||
Intel Core i9 7940X @ 3.6 GHz
128 GB DDR4
|September 23, 2018||September 28, 2018||Tizian Hanselmann||Golden Ratio||2,600,000,000,000||Compute: 9.25 days||
2 x Intel Xeon E5620 @ 2.4 GHz
|August 28, 2018||August 28, 2018||
|Golden Ratio||2,500,000,000,000||Compute: 42.2 hours||
2 x Intel Xeon E5-2696 v4 @ 2.2 GHz
Intel Core i7 7700K @ 4.2 GHz
|August 9, 2018||August 4, 2018||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
|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
|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
|September 3, 2016||August 29, 2016||Ron Watkins||e||5,000,000,000,000||2 x Xeon X5690 @ 3.47 GHz
|July 11, 2016||July 5, 2016||"yoyo"||Golden Ratio||10,000,000,000,000||
|2 x Intel Xeon E5-2696 v4 @ 2.2 GHz
|June 28, 2016||June 19, 2016||Ron Watkins||Square Root of 2||10,000,000,000,000||2 x Xeon X5690 @ 3.47 GHz
|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
|April 24, 2016||April 18, 2016||Ron Watkins||Log(2)||500,000,000,000||4 x Xeon X5690 @ 3.47 GHz - 141 GB|
|April 17, 2016||April 12, 2016||Ron Watkins||Catalan's Constant||250,000,000,000||4 x Xeon E5-4660 v3 @ 2.1 GHz
|April 9, 2016||April 3, 2016||Ron Watkins||Log(10)||500,000,000,000||2 x Xeon X5690 @ 3.47 GHz
|February 8, 2016||February 6, 2016||Mike A||Catalan's Constant||500,000,000,000||
|2 x Intel Xeon E5-2697 v3 @ 2.6 GHz
|July 24, 2015||July 22, 2015
July 23, 2015
|Golden Ratio||2,000,000,000,000||4 x Xeon X6550 @ 2 GHz - 512 GB
Xeon E5-2676 v3 @ 2.4 GHz - 64 GB
|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 wish to set a record, you must:
*The validation files are protected with a checksum to prevent tampering/cheating. People have tried to cheat before - which is why we can't have nice things.
An exception to the "two computations rule" can be made for Pi since it can be verified using BBP formulas.
Note that for anyone attempting to set a Pi world record: Should the attempt succeed, I kindly ask that you make yourself sufficiently available for external requests to access or download the digits in its entirety (at least until it is broken again by someone else). Pi is popular enough that people do actually want to see the digits.
The main computational features of y-cruncher are:
Latest Releases: (October 14, 2018)
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 Vista 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: October 19, 2018)
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|
|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 ~ Hina||v0.7.2 ~ Hina||v0.7.2 ~ Ushio||v0.7.1 ~ Kurumi||v0.7.6 ~ Kurumi||v0.7.6 ~ Kurumi|
|Instruction Set:||x64 AVX||x64 AVX||x64 SSE4.1||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX|
|Credit:||Oliver Kruse||Tralalak||Kaupo Karuse||yoyo|
|Processor(s):||Core i7 7700K||Ryzen 7 1800X||Core i7 8700K||Core i7 9700K||Core i7 9900K|
|Generation:||Intel Kaby Lake||AMD Zen||Intel Coffee Lake||Intel Coffee Lake||Intel Coffee Lake|
|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 ~ Kurumi||v0.7.6 ~ Yukina||v0.7.6 ~ Kurumi||v0.7.6 ~ Kurumi||v0.7.6 ~ Kurumi|
|Instruction Set:||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX|
|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 ~ Kasumi||v0.7.5 ~ Ushio||v0.7.6 ~ Miyu||v0.7.6 ~ Airi||v0.7.1 ~ Kurumi|
|Instruction Set:||x64 SSE3||x64 SSE4.1||x64 AVX + XOP||x64 AVX2||x64 AVX2 + ADX|
|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|
|Processor Speed:||4.5 GHz (OC)||4.0 GHz (OC)||3.5 - 3.7 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 ~ Airi||v0.7.6 ~ Airi||v0.7.6 ~ Yukina||v0.7.6 ~ Kotori||v0.7.6 ~ Kotori|
|Instruction Set:||x64 AVX2||x64 AVX2||x64 AVX2 + ADX||x64 AVX512-DQ||x64 AVX512-DQ|
|Credit:||Sean Heneghan||Oliver Kruse|
*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 E5-2683 v3||Xeon E5-2687W v4||Xeon E5-2696 v4||Xeon E7-8880 v3||Epyc 7601||Xeon Gold 6130F||Xeon Platinum 8124M|
|Generation:||Intel Haswell||Intel Broadwell||Intel Broadwell||Intel Haswell||AMD Naples||Intel Skylake Purley||Intel Skylake Purley|
|Processor Speed:||2.03 GHz||3.0 GHz||2.2 GHz||2.3 GHz||2.2 GHz||2.1 GHz||3.0 GHz|
|Memory:||128 GB - ???||64 GB||768 GB - ???||2 TB - ???||256 GB - ??||256 GB - ??||137 GB - ??|
|Program Version:||v0.6.9 ~ Airi||v0.7.4 ~ Kurumi||v0.7.1 ~ Kurumi||v0.7.1 ~ Airi||v0.7.3 ~ Yukina||v0.7.3 ~ Kotori||v0.7.5 ~ Kotori|
|Instruction Set:||x64 AVX2||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2||x64 AVX2 + ADX||x64 AVX512-DQ||x64 AVX512-DQ|
|Credit:||Shigeru Kondo||Cameron Giesbrecht||"yoyo"||Jacob Coleman||Dave Graham||Jacob Coleman|
|Processor(s):||Xeon X5482||Xeon E5-2690|
|Generation:||Intel Penryn||Intel Sandy Bridge|
|Processor Speed:||3.2 GHz||3.5 GHz|
|Memory:||64 GB - 800 MT/s||256 GB - ???|
|Program Version:||v0.7.2 ~ Ushio||v0.7.5 ~ Nagisa||v0.6.2/3 ~ Hina|
|Instruction Set:||x64 SSE4.1||x64 AVX|
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: firstname.lastname@example.org
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|
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:
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.