y-cruncher - A Multi-Threaded Pi-Program

From a high-school project that went a little too far...

By Alexander J. Yee

(Last updated: June 4, 2017)

 

Shortcuts:

 

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.

 

Current Release:

Windows: Version 0.7.2 Build 9469 (Released: June 3, 2017)

Linux      : Version 0.7.2 Build 9469 (Released: June 3, 2017)

 

Official HWBOT thread.

Official XtremeSystems Forums thread.

 

News:

 

Version 0.7.2 and AMD Zen: (March 14, 2017)

 

I went through a lot of trouble to do this in time for Pi day, but here it is. y-cruncher v0.7.2 has a new binary specifically optimized for AMD's Ryzen 7 processors.

 

The performance gain is about 5% over the Broadwell-tuned binary and 15% over v0.7.1. It turns out that the optimizations between v0.7.1 and v0.7.2 happened to be more favorable to AMD Zen than to Intel processors. Nevertheless, this is not enough to make Ryzen beat Haswell-E or Broadwell-E.

 

It's unlikely that any amount of Zen-specific optimizations can make Ryzen beat Haswell/Broadwell-E. The difference in memory bandwidth and 256-bit AVX throughput is simply far too large to overcome. AMD made a conscious decision to sacrifice HPC to focus on mainstream.

 

As for the Ryzen platform itself: It's a bit immature at this point. I went out on launch day to grab the Zen parts. In the end, it took me 3 sets of memory and 2 weeks before I finally found a stable configuration that I could use. From what I've seen on Reddit and various forums, I've been unlucky, but I'm definitely not alone.

 

Slightly more concerning is a system freeze with FMA instructions which appears to be have been confirmed by AMD as a processor errata. Fortunately, the source also says this is fixable via a microcode update. So it won't lead to something catastrophic like a recall or a fix that disables processor features.

 

As for the Zen architecture itself. Here are my (early) observations:

For software developers, compiling code on the 1800X is about as fast as the 5960X at stock clocks. But the 5960X has much more overclocking headroom, so it ends up winning by around 15%. For a $500 processor, the R7 1800X is very impressive.

 

 

 

Older News

 

Records Set by y-cruncher:

y-cruncher has been used to set a number world record size 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:
November 15, 2016 November 11, 2016 Blog
Sponsor
Peter Trueb Pi 22,459,157,718,361 Compute:  105 days

Verify:  28 hours

Validation File

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

Compute:  48.6 days

Verify:  48.7 days

2 x Xeon X5690 @ 3.47 GHz
141 GB
August 14, 2016 June 26, 2016   Ron Watkins Euler-Mascheroni Constant 477,511,832,674

Compute:  34.4 days

Not Verified

4 x Xeon E5-4660 v3 @ 2.1 GHz
1 TB
July 11, 2016 July 5, 2016   "yoyo" Golden Ratio 10,000,000,000,000

Compute:  6.2 days

Not Verified

2 x Intel Xeon E5-2696 v4 @ 2.2 GHz
768 GB
June 28, 2016 June 19, 2016   Ron Watkins Square Root of 2 10,000,000,000,000

Compute:  18.8 days

Verify:  25.2 days

2 x Xeon X5690 @ 3.47 GHz
141 GB
June 4, 2016 May 29, 2016   Ron Watkins Lemniscate 250,000,000,000

Compute:  91.7 hours

Verify:  270 hours

4 x Xeon E5-4660 v3 @ 2.1 GHz - 1TB
4 x Xeon X6550 @ 2 GHz - 512 GB
June 4, 2016 June 2, 2016   "yoyo" Golden Ratio 5,000,000,000,000

Compute:  67.9 hours

Not Verified

2 x Intel Xeon E5-2696 v4 @ 2.2 GHz
768 GB
May 25, 2016 May 18, 2016   Ron Watkins Euler-Mascheroni Constant 250,000,000,000

Compute:  35.9 days

Verify:  30.65 days

2 x Xeon E5-4660 v3 @ 2.1 GHz - 1 TB
4 x Xeon X6550 @ 2.0 GHz - 512 GB
April 24, 2016 April 18, 2016   Ron Watkins Log(2) 500,000,000,000

Compute:  12.8 days

Verify:  14.4 days

4 x Xeon X5690 @ 3.47 GHz - 141 GB
April 17, 2016 April 12, 2016   Ron Watkins Catalan's Constant 250,000,000,000

Compute:  204 hours

Verify:  207 hours

4 x Xeon E5-4660 v3 @ 2.1 GHz
1 TB
April 9, 2016 April 3, 2016   Ron Watkins Log(10) 500,000,000,000

Compute:  14.4 days

Verify:  15.2 days

2 x Xeon X5690 @ 3.47 GHz
141 GB
February 8, 2016 February 6, 2016   Mike A Catalan's Constant 500,000,000,000

Compute:  26.1 days

Not Verified

2 x Intel Xeon E5-2697 v3 @ 2.6 GHz
128 GB
December 21, 2015 December 21, 2015   Dipanjan Nag Zeta(3) - Apery's Constant 400,000,000,000

Compute:  22 days

Verify:  24 days

Xeon E5-2698B @ 2.0 GHz - 224 GB
July 24, 2015 July 22, 2015
July 23, 2015
Source Ron Watkins
Dustin Kirkland
Golden Ratio 2,000,000,000,000

Compute:  77.3 hours

Verify:  76.33 hours

Compute:  79.3 hours

Verify:  80.8 hours

4 x Xeon X6550 @ 2 GHz - 512 GB
Xeon E5-2676 v3 @ 2.4 GHz - 64 GB
October 8, 2014 October 7, 2014   "houkouonchi" Pi 13,300,000,000,000

Compute:  208 days

Verify:  182 hours

Validation File

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

Compute: 94 days

Verify: 46 hours

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 run two computations using different formulas (one to compute, the other to verify). Then send me the validation files, but do not make any attempt to modify them. The validation files are protected with a checksum to prevent tampering/cheating. Yes, people have tried to cheat before.

 

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.

 

Features:

Aside from computing Pi and other constants, y-cruncher is great for stress testing 64-bit systems with lots of ram.

 

 

Download:

Sample Screenshot: 100 billion digits of Pi

Core i7 5960X @ 4.0 GHz - 128GB DDR4 @ 2666 MHz - 16 HDs

 

Latest Releases: (June 3, 2017)

OS Programs Download Link Size

Windows

y-cruncher + HWBOT Submitter

y-cruncher v0.7.2.9469.zip

19.9 MB

Linux (Static)

y-cruncher Only

y-cruncher v0.7.2.9469-static.tar.gz

18.3 MB

Linux (Dynamic)

y-cruncher Only

y-cruncher v0.7.2.9469-dynamic.tar.gz

12.5 MB

Windows

HWBOT Submitter Only

HWBOT Submitter v0.9.6.114.jar

2.53 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. The dynamic version supports Cilk Plus, but is less portable due to the DLL dependency hell.

 

The HWBOT submitter allows y-cruncher benchmarks to be submitted to HWBOT - which is a competitive overclocking site. It is currently only available for Windows.

 

System Requirements:

Windows:

Linux:

All Systems:

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:

 

 

 

 

 

Known Issues:

 

Functionality Issues:

 

Performance Issues:

So while it may be difficult to believe, Windows is currently the more suitable OS for running y-cruncher.

 

 

 

Benchmarks:

Comparison Chart: (Last updated: April 14, 2017)

 

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.

 

 

Laptops + Low-Power:

Processor(s): Core i7 3630QM VIA C46501 Xeon E3-1535M v52 Core i7 6820HK Pentium N42001
Generation: Intel Ivy Bridge VIA Isaiah Intel Skylake Intel Skylake Intel Apollo Lake
Cores/Threads: 4/8 4/4 4/8 4/8 4/4
Processor Speed: 3.2 GHz 2.0 GHz 2.9 GHz 3.2 GHz 1.1 - 2.5 GHz
Memory: 8 GB - 1600 MHz 16 GB 16 GB 48 GB - 2133 MHz 4 GB
Version: v0.7.2 - AVX v0.7.2 - AVX v0.7.1 - ADX v0.7.2 - ADX v0.7.2 - SSE4.1
25,000,000 3.767 17.207 1.865 1.745 11.739
50,000,000 8.496 39.049 4.102 3.833 26.289
100,000,000 19.056 87.626 9.007 8.376 65.147
250,000,000 55.089 277.711 25.444 23.577 192.473
500,000,000 128.311 587.516 56.566 52.134 493.551
1,000,000,000 299.217 1,350.868 130.055 115.661  
2,500,000,000   3,884.838   327.784  
5,000,000,000       727.042  
10,000,000,000       1,602.565  

1Credit to Tralalak.

2Credit to Kaupo Karuse.

 

 

Mainstream Desktops:

Processor(s): Core 2 Quad Q6600 Core i7 920 FX-8350 Core i7 4770K Core i7 5775C1 Core i7 7700K2 Ryzen 7 1800X
Generation: Intel Core Intel Nehalem AMD Piledriver Intel Haswell Intel Broadwell Intel Kaby Lake AMD Zen
Cores/Threads: 4/4 4/8 8/8 4/8 4/8 4/8 8/16
Processor Speed: 2.4 GHz 3.5 GHz (OC) 4.0 GHz 4.0 GHz (OC) 3.8 GHz (OC) 4.8 GHz (OC) 3.7 GHz
Memory: 6 GB - 800 MHz 12 GB - 1333 MHz 32 GB - 1333 MHz 32 GB - 2133 MHz 16 GB - 2400 MHz 64 GB - 3000 MHz 64 GB - 2133 MHz
Version: v0.7.2 - SSE3 v0.7.2 - SSE4.1 v0.7.2 - XOP v0.7.2 - AVX2 v0.7.1 - ADX v0.7.1 - ADX v0.7.2 - ADX
25,000,000 10.591 4.998 3.598 1.678 1.730 1.271 1.566
50,000,000 23.698 11.310 8.070 3.767 3.940 2.817 3.291
100,000,000 53.502 25.268 17.675 8.207 8.739 6.198 7.279
250,000,000 157.269 74.230 50.004 22.695 25.073 17.384 20.124
500,000,000 351.470 166.724 112.364 50.442 56.343 38.176 44.189
1,000,000,000 801.731 381.903 249.087 111.593 125.967 84.432 96.368
2,500,000,000   1,119.114 729.652 316.052 369.738 238.194 273.675
5,000,000,000     1,636.260 700.029   527.186 605.845
10,000,000,000           1,151.396 1327.901

1Credit to André Bachmann.

2Credit to Oliver Kruse.

 

 

High-End Desktops:

Processor(s): Core i7 5960X
Generation: Intel Haswell
Cores/Threads: 8/16
Processor Speed: 4.0 GHz (OC)
Memory: 128 GB - 2666 MHz
Version: v0.7.2 - AVX2
25,000,000 1.044
50,000,000 2.067
100,000,000 4.329
250,000,000 12.145
500,000,000 26.060
1,000,000,000 58.598
2,500,000,000 160.576
5,000,000,000 354.845
10,000,000,000 771.584
25,000,000,000 2,156.038

 

 

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.

 

For example, enabling node-interleaving in the BIOS can improve performance by around 2x. But tweaks like these are often not possible as many of these systems are corporate or university machines that are heavily locked down and do not provide the user with sufficient access privileges. Furthermore, due the exponentially large space of settings and configurations, it's often difficult to find the optimal set of settings.

Processor(s): Xeon X5482 Xeon E5-26901 Xeon E5-2683 v31 Xeon E5-2696 v42 Xeon E7-8880 v33
Generation: Intel Penryn Intel Sandy Bridge Intel Haswell Intel Broadwell Intel Haswell
Sockets/Cores/Threads: 2/8/8 2/16/32 2/28/56 2/44/88 4/64/128
Processor Speed: 3.2 GHz 3.5 GHz 2.03 GHz 2.2 GHz 2.3 GHz
Memory: 64 GB - 800 MHz 256 GB - ??? 128 GB - ??? 768 GB - ??? 2 TB - ???
Version: v0.7.2 - SSE4.1 v0.6.2/3 - AVX v0.6.9 - AVX2 v0.7.1 - ADX v0.7.1 - AVX2
25,000,000 4.548 2.283 0.907 0.715 1.176
50,000,000 9.779 4.295 1.745 1.344 2.321
100,000,000 20.834 8.167 3.317 2.673 4.217
250,000,000 60.049 20.765 8.339 6.853 8.781
500,000,000 134.978 42.394 17.708 14.538 15.879
1,000,000,000 308.679 89.920 37.311 31.260 32.078
2,500,000,000 874.588 239.154 102.131 84.271 78.251
5,000,000,000 1,946.683 520.977 218.917 192.889 164.157
10,000,000,000 4,317.677 1,131.809 471.802 417.322 346.307
25,000,000,000   3,341.281 1,511.852 1,186.881 957.966
50,000,000,000   7,355.076   2,601.476 2,096.169
100,000,000,000       6,037.704 4,442.742
250,000,000,000         17,428.450

1Credit to Shigeru Kondo.

2Credit to "yoyo".

3Credit to Jacob Coleman.

 

 

I've been asked a few times on what benchmarks quality for these tables. But there aren't any specific rules. For the most part, I try to maximize the variety of processors on the list. So I won't put more than one system in each processor line unless they have drastically different capabilities such as core count. I also have a strong preference for systems that are at the top of their line and have as much memory as possible.

 

Perhaps the most important part is that the benchmarks are representative of the hardware. If there is any evidence of interference that may cause the hardware to perform suboptimally, they will be excluded. Examples of this include (but are not limited to), underclocking, disabled cores, disabled hyperthreading, disabled AVX, fewer than all memory channels, background programs, thermal throttling, using an outdated version of y-cruncher, etc... Some leeway is given to multi-processor servers since they are so sensitive to numerous factors.

 

Likewise, absurdly high overclocks will be excluded. These tables are meant to compare systems running at real life speeds. Benchmarks done with extreme overclocks (especially with liquid nitrogen) show go on HWBOT. Just be aware that HWBOT has stringent rules on submissions since it's competitive.

 

 

Fastest Times:

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: 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.


Algorithms and Developments:

 

FAQ:

 

Pi and other Constants:

 

Hardware and Overclocking:

 

Academia:

 

Programming:

 

Program Usage:

 

Other:

 

Links:

Here's some interesting sites dedicated to the computation of Pi and other constants:

 

Questions or Comments

Contact me via e-mail. I'm pretty good with responding unless it gets caught in my school's junk mail filter.