y-cruncher - A Multi-Threaded Pi-Program
From a high-school project that went a little too far...
By Alexander J. Yee
(Last updated: January 10, 2019)
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 0.7.7 Build 9494 (Released: January 10, 2019)
Linux : Version 0.7.7 Build 9494 (Released: January 10, 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.
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:
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:|
|January 6, 2019||January 6, 2019||Tizian Hanselmann||Golden Ratio||3,000,000,000,100||
Intel Xeon X5650 @ 2.67 GHz
|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
|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
|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
|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
|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 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
|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: (January 10, 2019)
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 i9 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||v0.7.6 ~ 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 E5-2687W 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|
|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 ~ Kurumi||v0.7.1 ~ Kurumi||v0.7.3 ~ Yukina||v0.7.3 ~ Kotori||v0.7.5 ~ Kotori||v0.7.6 ~ Kotori|
|Instruction Set:||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX2 + ADX||x64 AVX512-DQ||x64 AVX512-DQ||x64 AVX512-DQ|
|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|
|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 ~ Ushio||v0.7.5 ~ Nagisa||v0.6.2/3 ~ Hina||v0.6.9 ~ Airi||v0.7.1 ~ Airi|
|Instruction Set:||x64 SSE4.1||x64 AVX||x64 AVX2||x64 AVX2|
|Credit:||Shigeru Kondo||Shigeru Kondo||Jacob Coleman|
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:
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.