(Last updated: February 4, 2019)
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Where can I download the digits for Pi and other constants that are featured in the various record computations?
There is currently no reliable place to get the digits. Due to the large sizes of the data, it simply isn't feasible to move them around.
Personally, I have an archive of some of the digits including all 22.4 trillion digits of Pi that have been computed. But because I'm on a consumer internet connection with rate and possibly bandwidth limits, it simply isn't possible for me to upload them. When I was still in school, I was able to seed some torrents since university connections are very fast. But that isn't possible anymore.
To answer the question directly, your best bet at getting the digits is to:
Under extreme circumstances (if you're a famous professor trying to do research), I may make special arrangements to run research code locally on my machine. But this has happened only once and I was dealing with some pretty amazing professors which I didn't want to let down.
It's worth noting that Bittorrent is a viable way to distribute large files like the digits of Pi. And this is something I actually did for about 2 years while I was in school. But I can't really do that anymore because USbased consumer ISPs suck and they will come after you if you use too much bandwidth.
Can you search for XXX in the digits of Pi for me?
In short no. Not because I don't want to, but because I can't. 22.4 trillion digits is a lot of digits. It takes several days just to read all of it. So searching requires too much time and computational resources. I'm not Google and I don't have the ability to search index something that large.
Can you add support for more constants? I want to compute e^{Pi}, Khinchin, Glaisher^{}, etc...
In the past, the answer was no. But starting from v0.7.7, the custom formula feature will let you build formulas which ycruncher can evaluate to high precision.
However, the set of functionality in the custom formulas is quite limited. And as a general rule, everything must run in quasilinear runtime and linear memory. Thus you will not be able to run hard to compute things like Glaisher and Khinchin's Constant as there are no known algorithms for them that meet the above criteria.
I have found an amazing new algorithm for X that's better than the rest!
This is a loaded question that I get more often than I expect. I used to do these in private over email, but there's now a subforum for ycruncher where these can go. And now, starting from ycruncher v0.7.7, the custom formula feature will allow some algorithms/formulas to be tested and benchmarked with ycruncher's full capability.
The computation of Pi and other constants is a pretty wellstudied topic that has already been attacked by generations of mathematicians. So rarely are there things that are genuinely new. Likewise, the bar is set very high for anything new to be a "breakthrough" or to make it into ycruncher.
The majority of the inquiries I get will fall into these categories:
Only once has something gotten all the way through. And it led the new algorithms for Catalan's Constant in v0.7.7.
#1 is relatively rare and I typically just ignore them.
#2 is more common. Depending on the merits of the proposed idea/algorithm, it may lead to a long and interesting discussion. But so far it has yet to lead to anything groundbreaking.
#3 is the most common. Often times people will present an algorithm that works and looks fast on paper. But a deeper analysis reveals that it's either unworkable or is not anywhere near as efficient as predicted.
Here are the common pitfalls that lead to #3:
What's with the warning, "Unable to acquire the permission, "SeLockMemoryPrivilege". Large pages and page locking may not be possible."?
This warning shows up when ycruncher doesn't have permission to use large pages.
Large pages is an optional feature that may improve performance especially in the presence of KPTI for Meltdown mitigation. Since it is optional, ycruncher can run correctly without it. But it will print out a warning if it can't enable it.
Refer to the memory allocation guide on how to turn on large pages. Be aware that even if you make this warning go away, it doesn't mean that large pages are actually working. Details are in the linked guide.
What's the difference between "Total Computation Time" and "Total Time"? Which is relevant for benchmarks?
"Total Computation Time" is the total time required to compute the constant. It does not include the time needed to write the digits to disk nor does it include the time needed to verify the base conversion. "Total Time" is the endtoend time of the entire computation which includes everything.
The CPU utilization measurements cover the same thing as the "Total Computation Time". It does not include the output or the base convert verify.
For benchmarking, it's better to use the "Total Computation Time". A slow disk that takes a long time to write out the digits will affect neither the computation time nor the CPU utilization measurements. Most other Piprograms measure time the same way, so ycruncher does the same for better comparability. All the benchmark charts on this website as well as any forum threads run by myself will use the "Total Computation Time".
For world record size computations, we use the "Total Time" since everything is relevant  including down time. If the computation was done in several phases, the runtime that is put in the charts is the difference between the start and end dates.
There's currently no "standard" for extremely longrunning computations that are neither benchmarks nor world record sized.
Why does ycruncher need administrator privileges in Windows to run Swap Mode computations?
Privilege elevation is needed to workaround a security feature that would otherwise hurt performance.
In Swap Mode, ycruncher creates large files and writes to them nonsequentially. When you create a new file and write to offset X, the OS will zero the file from the start to X. This zeroing is done for security reasons to prevent the program from reading data that has been leftover from files that have been deleted.
The problem is that this zeroing incurs a huge performance hit  especially when these swap files could be terabytes large. The only way to avoid this zeroing is to use the SetFileValidData() function which requires privilege elevation.
Linux doesn't have this problem since it implicitly uses sparse files.
Why is the performance so poor for small computations? The program only gets xx% CPU utilization on my xx core machine for small sizes!!!
For small computations, there isn't much that can be parallelized. In fact, spawning N threads for an N core machine may actually take longer than the computation itself! In these cases, the program will decide not to use all available cores. Therefore, parallelism is really only helpful when there is a lot of work to be done.
For those who prefer academic terminology, ycruncher has weak scalability, but not strong scalability. For a fixed computation size, is it not possible to sustain a fixed efficiency while increasing the number of processors. But it is possible if you increase the computation size as well.
My computer is completely stable. But I keep getting errors such as, "Redundancy Check Failed: Coefficient is too large."
The notorious "Coefficient is too large" error is a common error that can be caused by many things. A full technical explanation is here.
Because of the nature of error, it can be caused by literally anything. But below are the two most common causes.
The hardware is not "AVX stable" or "AVX512 stable":
If your "stable" overclock is hitting the "Coefficient is too large" error on the standard benchmark sizes, then your overclock is not as stable as you think it is.
This error is most commonly seen on overclocks with an unstable AVX or AVX512 configuration. It first became common on Haswell, but is now seen on nearly all Intel processors  especially those with AVX512.
ycruncher makes heavy use of AVX and AVX512 instructions if the processor supports them. So in order to successfully run a ycruncher benchmark, your system needs to be stable with these heavier workloads. The problem is that the vast majority of programs don't use AVX. So many "rockstable" overclocks are actually not stable when running AVX. To make matters worse, most of the early BIOS versions for Skylake X improperly implemented the AVX/AVX512 offsets  thus causing systems to be unstable even at stock settings!
If you search around overclocking forums, you'll find that there are numerous complaints about Prime95 and other AVX workloads being "unrealistic". And for that reason, many overclockers will skip these stresstests. While this allows for significantly higher overclocks, it sacrifices stability for AVXoptimized applications. So it's common for overclocked systems to be perfectly stable for months, and then immediately crash and burn when attempting to run Prime95 or ycruncher.
If you fall into this category, lower your overclock. Recent processors (since Kaby Lake) have AVX and AVX512 "offsets" which will automatically downclock the CPU under those respective workloads. Use them! They will let you keep your very high nonAVX overclock without sacrificing stability for AVX and AVX512 workloads.
While ycruncher isn't quite as stressful as latest Prime95, the workload is very similar. So if you cannot pass Prime95 small FFTs (with AVX) for at least a few seconds, you stand no chance of running any large benchmark or computation with ycruncher.
AMD processors (up through Zen+) don't have this problem since they don't have native AVX hardware anyway. This may change with Zen 2.
Memory Instability:
The other common cause is memory instability. ycruncher has a reputation of being notoriously stressful on the memory subsystem. If you read around overclocking forums, there are countless reports of ycruncher being able to uncover subtle memory instabilities where all other applications and stresstests will pass.
This doesn't just happen with overclocking. It has been observed on server hardware as well. To date, I've had 4 bug reports on server hardware:
In all 4 of these cases, the users reported that ycruncher is the only application that managed to fail. Personally, I've had one error on server hardware believed to be caused by an overheating northbridge.
Naturally, one would do a double take since server hardware has ECC memory. But ECC only protects against bit flips in the memory. It doesn't guard against instability in the memory controller or general memory incompatibilities.
It's worth noting that ycruncher was never designed to be a memory stresstest. And to date, it is still unclear why it often seems to be better at testing memory than even dedicated tests such as MemTest64.
Disk I/O Instability:
In swap mode computations, disk I/O instability is a major cause of errors. Most storage errors are "visible" (such as CRC errors, unreadable sector, drive dismounted, etc...). But a sizable portion of I/O errors are silent and only get caught by ycruncher's redundency checks.
Silent disk I/O errors tend to be more common on old and aging hard drives. But overall, there isn't enough data to point out any specific causes. Swap mode isn't a heavily used feature. And those that use it tend to have more stable systems. (The overclocking community doesn't really use swap mode.)
Why is ycruncher so much slower on AMD processors than Intel processors?
ycruncher is more than 2x slower on AMD Bulldozer processors compared to Intel Haswell and Skylake. And AMD's Zen processor is still about 50% slower than Intel's 8core Haswell and Broadwell HEDT processors. What's going on here? Is ycruncher another one of those "Intelbiased" benchmarks?
Short Answer:
It boils down to the raw SIMD throughput. Intel processors have 256bit and 512bit wide vector units while AMD processors are only 128bits wide.
ycruncher is one of the few applications that can utilize the AVX to get the full benefit of the vector units. This gives Intel processors a very large advantage.
Long Answer:
Here's a data dump of the performance throughput of various vector operations. Higher is better.
Pink entries mark data that is not yet known. Data in them are merely educated guesses.
Hardware  Throughput Per Cycle  
Processor  Year  Unit  ISA  Vector Width  Vector Units  Integer  FloatingPoint (Double Precision)  Shuffle  
Logic  Add  Mul  Add  Mul  Add or Mul  FMA  
Intel Sandy Bridge  2011  1 core  AVX  256 bit  3  3 x 128  2 x 128  1 x 128  1 x 256  2 x 256    2 x 128 1 x 256 

Intel Ivy Bridge  2012  
Intel Haswell  2013  1 core  AVX2  256 bit  3  3 x 256  2 x 256  1 x 256  1 x 256  2 x 256  1 x 256  
Intel Broadwell  2014  
Intel Skylake  2015  1 core  AVX2  256 bit  3  3 x 256  2 x 256*  1 x 256  
Intel Kaby Lake  2017  
Intel Coffee Lake  2017  
Intel Skylake Purley  2017  1 core  AVX2  256 bit  
AVX512  512 bit  2 (1 x FMA)  2 x 512  1 x 512*  1 x 512  
2 (2 x FMA) 
2 x 512*  
Intel Cannon Lake  2018  1 core  AVX2  256 bit  3  3 x 256  2 x 256*  1 x 256  
AVX512  512 bit  2 (1 x FMA) 
2 x 512  1 x 512*  1 x 512  
Intel Ice Lake  2019  1 core  AVX2  256 bit  3  3 x 256  2 x 256*  2 x 256  
AVX512  512 bit  ? (1 x FMA)  2 x 512  1 x 512*  ? x 512  
? (2 x FMA) 
2 x 512*  
Intel Knights Landing  2016  1 core  AVX512  512 bit  2  2 x 512  2 x 512*  1 x 512  
Intel Knights Mill  2017  1 core  AVX512  512 bit  2  1 x 512  
AMD Bulldozer  2011  1 module  AVX  128 bit  2  2 x 128  1 x 128  2 x 128*  1 x 128  
AMD Piledriver  2012  
AMD Steamroller  2014  
AMD Excavator  2015  AVX2  
AMD Zen  2017  1 core  AVX2  128 bit  4  4 x 128  2 x 128  1 x 128  2 x 128  4 x 128  2 x 128  2 x 128  
AMD Zen 2  2019  1 core  AVX2  256 bit  4  2 x 256  4 x 256  2 x 256 
There really isn't much that needs to be said. Intel chips currently have much better SIMD throughput.
*These processors appear to have monolithic FMA hardware that can do all floatingpoint arithmetic with the same latency and throughput. In the case of Intel processors, this also includes integer multiplication.
Is there a version that can use the GPU?
Currently no. But if there were one:
A GPU implementation must overcome several hurtles before it can challenge a modern CPU.
The GPU must beat the CPU in at least one of 3 workloads.
The GPU must beat the CPU in at least one of these categories by a wide margin. Furthermore, it cannot suck too much in the others.
These correspond to the 3 different classes of large integer multiplication algorithms that are suitable for highprecision arithmetic. In the past, any of the 3 was sufficient for record setting. But in the modern era, #3 alone is no longer adequate. And we are within an order of magnitude of hitting the limit of #1based algorithms. Thus #2 will be required in the long term.
As of 2018, all 3 of these operations are efficient on CPUs. None of them are efficient on consumer grade GPUs. But #1 is efficient on highend HPCoriented GPUs.
To be clear, singleprecision is not viable. Large number arithmetic isn't like deeplearning where you can get away with arbitrarily small precision. There is a genuine need for highprecision datatypes. If they don't exist or are inefficient, they must be emulated.
With #1 becoming inadequate soon (~10 years?), the window for GPUs to win here seems to be closing.
GPUs require massive vectorization. Large number arithmetic code is not that easy to vectorize.
GPUs require massive vectorization or otherwise very uniform (and independent) computation with little branching. Unfortunately, there are some important things in bignum arithmetic that don't fall into this category.
The only thing that's really vectorizable in bignum arithmetic are the FFTbased algorithms for large multiplication. But even that is not without complications. Certain (important) memoryrelated optimizations will place limits on how large the SIMD vector can be. AVX512 is already pushing at these limits in the context of Skylake X processors. It's possible this problem will be worse on GPUs. More investigation is needed, though it shouldn't be a problem since there already exist GPU FFT implementations that outperform CPUs.
It's worth mentioning that Intel's Xeon Phi (co)processor line was interesting for some time as it was (in some sense) a GPU with CPU instructions. But initial benchmarks on Knights Landing were somewhat disappointing. Intel has since refocused the entire line away from general HPC and specialized it for deeplearning. In doing so, they have also nerfed the operations that are important ycruncher. Thus the Xeon Phi line is no longer useful nor interesting for ycruncher.
Large computations of Pi and other constants are not limited by computing power. The bottleneck is in the data communication.
This one is the most serious problem that is the final nail in the coffin for current generation GPUs.
GPUs, when properly utilized, can provide an amazing amount of performance  much more than CPUs. But the problem is that computation isn't even the bottleneck. The bottleneck is memory bandwidth and data communication in general. In other words, throwing GPUs at the problem isn't going to help.
How bad is the communication bottleneck?
ycruncher is already memorybound on the CPU. Put it on a GPU over the PCIe, and it gets worse. So much for all that computing power! The solution here is to use the (large amount of) onboard GPU memory as a cache for the main memory in a manner similar to how ycruncher currently uses main memory as a cache for disk. But this is an additional level of design complexity that will not be easy to do.
Let's assume we do that anyway. Yay! The GPU crushes the CPU for inmemory computations and we get some amazing benchmarks. But that doesn't help you in Swap Mode where you're running off the disk. And the disk sure as hell won't be faster the PCIe  even if you're saturating the system with NVMe drives. (Not that SSDs are a great idea anyway...)
To put this into perspective, I often get asked about how long it would take to set a record for Pi (or some other constant) using X hardware. I typically tell them something on the lines of:
"Given infinite computing power, it will take Y months with your storage configuration".
In other words, computation doesn't even matter anymore. It's all about the disk I/O and the storage. The most economical way to set a record nowadays is to get a machine with the fastest storage configuration, largest memory configuration, and... a mediocre CPU.
Why can't you use distributed computing to set records?
No for more or less the same reasons that GPUs aren't useful.
Follow up question: "I don't understand. If you're computing a trillion digits, why can't you just assign different parts of it to different computers. Then they can all run in parallel and be combined at the end."
Layman Answer: That's not how it works. Computing the digits of Pi is like building a skyscraper. You cannot just assign different floors to different contractors to build at the same time and combine them at the end. You need to finish each floor before you can build the floor above it. The only way to parallelize is to have the different contractors work together within each floor. In other words, the parallelism is horizontal, not vertical.
Technical Answer: Computing all the digits of Pi from 1 to N in an efficient manner is a coarsegrained parallelizable task. At the very top level, it is not parallelizable at all. All the parallelism is at the lower levels. Therefore, communication between all workers is very frequent  enough to become a bottleneck.
There exist algorithms like BBP to directly compute arbitrary binary digits without the memory cost of computing all the digits before it. These are called "digitextraction" algorithms. However, these algorithms require roughly O(N*log(N)) time to compute a small number of digits at offset N. Using this approach to compute all the digits from 1 to N will result in a quadratic runtime algorithm. This alone makes it unsuitable for large N.*
To make things worse, the currently known digitextraction algorithms for bases other than binary are much slower. And a radix conversion runs into the same alltoall communication problem as the current methods to compute Pi.
*While there exists some potential ways that can make the algorithm subquadratic, they haven't been researched since because they don't solve the problem of the radix conversion.
Is there a distributed version that performs better on NUMA and HPC clusters?
No, but it is a current research topic.
Starting from v0.7.3, ycruncher has had the ability to detect the NUMA configuration and automatically interleave the memory across all the nodes. This goes a long way to countering the interconnect traffic imbalance that results from the operating system firsttouch NUIMA policies. But nevertheless, this isn't a scalable solution.
Maintaining scalability across larger and larger systems will require the program and algorithms to be developed specifically for NUMA. The MRFM project will attempt to do this. But this hasn't made much progress over several years and there is no end in sight.
Why have recent Pi records used desktops instead of supercomputers?
While the rest of the world is trending towards more parallelism, computations of Pi seems to have gone the other way.
The only recent Pi record which has "gone the other way" is Fabrice Bellard's computation of 2.7 trillion digits back in 2009. That was the major leap from supercomputer to... a single desktop computer. But since then, all the records have been done using increasingly larger (commodity) server hardware. Nevertheless, the hardware used in these computations are still pretty far removed from actual supercomputers.
So the real question is: Why aren't we using supercomputers anymore?
Unfortunately, I don't have a good answer for it. Sure ycruncher has been dominating the recent Pi records using singlenode computer systems. But that doesn't explain why nobody from the supercomputer field has joined in. Some possible contributing factors are:
What is the technical explanation for the notorious, "Coefficient is too large" error?
The "Coefficient is too large" error is one of many redundancy checks which ycruncher uses. To understand what this redundancy check is at the technical level, it helps to have a basic understanding of large multiplication via Fast Fourier Transform (FFT).
In this algorithm, each of the input operands are broken up into coefficients of a polynomial. FFT is then used to multiply the polynomials together. Based on the size of the input polynomial and its coefficients, it is possible to prove certain limits for the coefficients of the output polynomial.
ycruncher has a redundancy check that checks all the coefficients to make sure they are all less than the limit. If any are above this limit, then it knows that a computational error has occurred and it throws the "Coefficient is too large" error.
The reason why the "Coefficient is too large" error is so common is a combination of various factors:
ycruncher uses this coefficient check because it has high coverage with minimal computational overhead. But this high coverage also makes the error almost useless in helping to track down the source of the error since it's basically the same as, "something went wrong".
Is there a publicly available library for the multithreaded arithmetic that ycruncher uses?
Yes. But it isn't as stable as a library should be. Support only exists for 64bit Windows and backwards compatibility breaks on a regular basis.
For all practical purposes, ycruncher is closed source. Only about 5% of the code is opensourced and available to see on GitHub under varying licenses.
The 5% includes the Launcher, the Digit Viewer, and their dependencies. Also, a very outofdate version of the object library headers can be found in a NumberFactory sideproject. This sideproject has been abandoned for quite some time.
None of the mathematical or computational code is opensourced. So if that's what you're looking for, you will not find it.
What about support for other platforms? Mac, ARM, etc...
Short answer: Not right now. There's little to gain for a lot of effort.
While it would be nice to have ycruncher running everywhere, the time and resource commitment is simply too high. So the best I can do is cover the most important platforms and call it day.
ycruncher currently supports 3 platforms:
Either of the x64 platforms is sufficient for ycruncher's purpose. x86Windows is there because the program started that way and it's easy to maintain it alongside x64Windows. On the other hand, x64Linux is a completely different platform with different compilers and system APIs. For this reason, it takes a signifcant amount of time and effort to keep ycruncher working on x64Linux.
My experience with just Linux has basically convinced me to stay away from any additional platforms for the time being.
What about Mac/x64?
There are several things here:
What about ARM?
While ARM is rapidly improving, it's unlikely to be supported until it achieves significant market share in the highend and highperformance server market.
Translation: Support for ARM will not be considered until:
In other words, ARM will not be supported until it "beats" x64. And I'm not gonna try to guess at if and when this will happen. This applies not just to ARM, but also to any other suitable computer architecture.