(Last updated: December 9, 2018)
This is a table of all the active branches of y-cruncher. As this is just a side-hobby, overall development is slow and there is no formal release cycle. But in recent years, feature releases have been approximately every 4 - 8 months with multiple patches in between.
|Branch||Version #||Changes (from v0.7.6.9490)|
y-cruncher was pretty heavily developed between 2008 - 2013. But I've since left school and found a full-time job. While y-cruncher will probably remain a side-hobby for the near future, it won't get as much attention as it used to get. At the very least, I'll continue to fix whatever bugs that are discovered. And I'll make an effort to keep the program up-to-date with the latest instruction set extensions and development toolchains. But for the most part, the project is done.
Most of the work right now is in cleaning up the code and refactoring it into idiomatic C++ for long-term maintainability. The program was (and still largely is) a fragile mess of unreadable C hackery with little to no documentation. So at the very least, I'd like to get it into a state where someone other than myself can read it.
Nevertheless, it's a never-ending project. So there are things on the to-do list. But it can be a long time before anything gets done.
Provide a way to control y-cruncher through TCP. This will allow 3rd party applications to build a GUI around y-cruncher.
More details here: https://github.com/Mysticial/y-cruncher-GUI
An early version of this was launched with v0.7.6. As of v0.7.7, it theoretically should be complete enough to implement a full GUI for both the stress tester and custom compute options.
Incremental progress will continue to be made. In particular a unified way to express menus and suboptions is still needed.
|Nth Root Radicals||
Add support for nth root radicals.
This will enable the computation of Gamma(1/3).
This was originally slated for v0.7.7 with the first release of the Custom Formula feature. But on further analysis, it isn't as simple as it appears.
A preliminary analysis on the numeric behavior of Newton's Method showed some non-linear effects which warrant further investigation before it can be implemented.
Implementing this efficiently will require a specially optimized power function that y-cruncher currently doesn't have.
Given the sheer number of bugs that were showing up in v0.7.7, this was dropped indefinitely and will be reconsidered for v0.7.8.
Add support for the exponential function.
This will enable the fully generic non-integer power function for real numbers.
This involves inverting log(x) with Newton's Method.
This hasn't really been looked at yet. So it's unknown how many numerical and implementation complications there will be like in the case of the nth root radicals.
At the very least, designing a way to do status printing that is both useful and not overly spammy might be tricky.
|Improved Stress Test||
The current stress-tester has increasingly poor coverage in today's processors. In fact, the program's unit and integration test frameworks are a better stress test than the dedicated stress test itself!
Find a way build a new stress test around these "better" workloads.
The difficulty here is that the "best" stress test requires mixing all the different instruction sets (SSE, AVX, AVX512). But each of y-cruncher's binaries focuses on only one of them and it's not easy to use a "lower" ISA when compiling for a "higher" one since the compiler will try to vectorize the code to use the higher one.
|Optimized Square Root||
The current square root is just the inverse square root followed by a multiply by the input.
It may be possible to do better by merging that multiply in the final iteration - as is the case for division and reciprocal.
|Optimize the AGM||
In the final iterations of the AGM, much of the output is already known. These can be used to skip some of the early iterations of the Newton's Method square root.
The current log(x) implementation is a dumb wrapper around AGM(1,x).
There are ways to make the AGM require fewer iterations that should be investigated.
|Non-Monotonically Convergent Hypergeometric Series||
Extend the SeriesHypergeometric function to allow series that are not monotonically convergent.
This is needed for confluent hypergeometic functions at large inputs where the series initially diverges before eventually converging.
This will allow certain approximation algorithms to be implemented:
This is expected to be very difficult.
Irregular convergence behavior wreaks havoc on the Binary Splitting implementation since a lot of assumptions break down. While the Brent-McMillan formula for the Euler-Mascheroni Constant already exhibits this behavior, it is specially handled.
The most difficult part of this is precision control. In order to do precision control, y-cruncher needs to know:
#1 is complicated, but likely doable.
#2 doesn't seem approachable in the generic case with the mathematical techniques that I know of.
#2 is difficult due to destructive cancellation. Confluent hypergeometric functions are notorious for this behavior. And it is just the simplest case.
Take a series and something as simple as taking its derivative can drastically alter the magnitude of the value that it converges to. (i.e. exp(-x2) and the Error Function for very large x)
It is likely that #2 will require the user to explicitly tell y-cruncher what the final magnitude will be.
These are projects which have either stalled made no recent progress or are so long term that there is no roadmap.
|Rewrite the Radix Conversion||
The current radix conversion code is actually a prototype that ended up in production. It has so many problems that it's basically unsalvageable.
The current code is actually the 3rd radix conversion to be used in y-cruncher (and the 2nd to use the Scaled Remainder Tree). But it's still a prototype since it's the first to combine all of the following features/optimizations:
At the time (2011), this was very ambitious - perhaps a little too ambitious. In the end, it required so many hacks that the thing became a complete mess.
The radix conversion will need to be completely redesigned and rewritten.
Stalled. No progress has been made in years.
Still trying to figure out a way to approach this in a way that will be maintainable without sacrificing any performance...
The existing radix conversion has virtually no internal abstraction. This makes it both very fast and unmaintainable.
No progress has been made in years due to a backlog of higher priority issues.
The only work has been maintenance to keep the current work-in-progress code working with respect to breaking changes in other parts of y-cruncher.
|Reduced Memory Mode||
For Pi Chudnovsky and Ramanujan, add a mode that will allow a computation to be done using less memory/disk at the cost of slower performance.
For a typical computation, most of the work requires very little memory. It's the occasional memory spike that causes y-cruncher to have such a high memory requirement.
There are about 4 large memory spikes in a Pi computation. In approximate descending order of size, they are:
These spikes can be flattened via space-time tradeoffs in the respective algorithms. Since the trade-off only needs to be done at the spikes, the overall performance hit should be reasonably small.
Stalled. No progress has been made in years.
As of v0.6.8, only the first two memory spikes have been suppressed. The overall memory reduction is not enough to be worth enabling the feature publicly.
The last two spikes both involve the radix conversion which is completely blocked pending the rewrite of the radix conversion code.
This partially completed feature was used for the 12.1 trillion digit computation of Pi.
As of 2017, this is low priority due to a backlog of higher priority issues.
MRFM stands for "Multi-Region Far Memory". It is a very large experimental project that will attempt to solve the NUMA problem and more generally, the supercomputer problem.
The current design of MRFM that is planned is a fundamental departure from y-cruncher's battle-tested model of computation. So virtually all high-level code will need new implementations for MRFM.
As a result, the plan calls for two completely new computation modes:
This will bring the total number of modes to 4. But if all goes as planned, Multi-Region Swap will become a no-compromise generalization of the current Swap Mode. So it will be possible to remove the current Swap Mode without losing much functionality.
Due to the sheer scale of this project along with a large number of unknowns, this was expected to be (and has become) a multi-year project with no guarantee of success.
Much of the planning for this began years ago. But actual coding didn't start until around September of 2016.
As of 2018, progress is stalled due to large amounts of technical debt in y-cruncher's high-level code which have been accumulating for years. The radix conversion mentioned above is one such example of this technical debt.
MRFM remains a multi-year project with no end in sight.
Disk I/O is the bane of large number computations. Historically, it was bad only because it is slow. Nowadays, it's also unreliable.
"Unreliability" comes in several forms:
(1) and (2) are easily solved using checkpoint-restart and periodic backups. y-cruncher has supported checkpointing this since v0.5.4 so it isn't really a problem anymore. But (3) is very scary and remains a huge problem today.
Silent data corruption is the worst since it's undetected. It plagues database applications, and unfortunately, y-cruncher is extremely vulnerable as well. If an error manages to slip through y-cruncher's built-in redundancy checks, it will cause a computation to finish with the wrong digits.
Hard drives already use error-correction and CRCs to ensure data integrity. And transfers between the drive to the controller are also protected with CRCs. So you would expect that data corruption would be detected by the operating system right? Nope...
When a hard drive fails to read a sector due to CRC failures, it usually propagates all the way back into the program and manifests as a (1). So that's not a problem. But transfer errors between the drive and the controller are less ideal. Supposedly, transfer errors lead to retransmission. But this isn't always the case.
Throughout the years of developing y-cruncher, transfer errors have also been observed to:
(1) is to be expected if the connection quality is so bad that the data gets stuck in a retransmission loop.
(2) is also be expected if the corrupted data passes a CRC by chance. (I have no idea how long the CRC is, but if it's CRC32, a 1 in 4 billion chance isn't small.)
(3) makes absolutely no sense at all. If the hard drive was able to detect the error, then why the hell doesn't it notify the OS that the operation failed?
In any case, there are other things that don't add up. And in the end, we are forced to accept the reality.
To date, y-cruncher's only defense for silent data corruption is the RAID3. When the swap file configuration is set to use RAID3, (almost) all reads are parity checked. And if the data is bad, it will report a failure. The parity bits are flipped so that zeroing errors that zero everything will fail the parity.
Unfortunately, this is far from sufficient:
To date, silent data corruption has yet to bring down a world-record attempt. But it happens regularly in the development test machines (which contain some very old hard drives). There has also been an instance reported on a forum where a 1 trillion digit computation of Pi failed - presumably due to silent data corruption.
Approximately 80% of the disk I/Os that y-cruncher does are covered by redundancy checks at a higher level. So in the absence of RAID 3, silent data corruption will be detected with 80% probability if we assume uniform distribution. To put it simply, 80% is not good enough. But at the very least, failing a redundancy check should be an immediate and serious red flag.
Use a filesystem designed for data integrity (such ZFS). While this is almost too obvious, there will also be performance trade-offs.
The other approaches involve adding checksumming into y-cruncher's raid-file implementation. But this is easier said than done:
Inlining checksums into the data will break sector-alignment and incur copy-shifting overhead. But perhaps this can be merged with the RAID interleaving. Placing the checksums elsewhere will add seek overhead. Either way, it will be messy.
Due to the poor state of the current raid-file code, any significant change will likely imply a complete rewrite of the entire raid-file implementation.
y-cruncher is currently a shared memory program. So it will run efficiently given the following assumptions:
As of 2016, these assumptions hold for almost all single-socket systems - which include the majority of personal desktop computers and low-end servers.
But due to the laws of physics and the speed of light, assumption #2 does not hold for larger systems. So now we're into the territory of Non-Uniform Memory Access (NUMA), cluster/distributed computing. For now the focus will be on NUMA systems since that's what the majority of the multi-socket systems are.
In short, y-cruncher does not run efficiently on NUMA. While it scales reasonably well onto dual-socket, it all goes downhill after that. There have been numerous reports of non-scaling (and even backwards scaling) on quad-Opteron systems. And all of this is due to the NUMA.
To exacerbate the problem, OS's normally default to a "first-touch" policy for memory allocation. The problem is that y-cruncher allocates all its memory at the start of a computation with a single thread. With the first-touch policy, all the memory will be allocated (or heavily biased) on one NUMA mode. So during the computation, all the cores from all the NUMA nodes will be hammering that one node for memory access. The interconnect going in and out of that one node will be overwhelmed by the traffic which leads to terrible performance.
y-cruncher v0.7.3 adds the ability to interleave memory across nodes. This balances the interconnect traffic and leads to a significant performance on modern dual and quad-socket systems. But ultimately, this doesn't actually solve the problem of NUMA since the memory accesses (which are now randomized) will still be hitting remote nodes over the interconnect.
To be efficient, the program needs to be aware of the NUMA and needs to be designed specifically for it. This is a fairly difficult task which is made worse by the unlimited combinations of NUMA topologies. Long story short, making y-cruncher NUMA aware will require changing the way that memory is fundamentally stored and managed. This means that it will need to be done as a new "mode" much like how "Ram Only" and "Swap Mode" have completely different data storage formats.
Currently, the most promising solution is to generalize the functionality of swap mode in the following ways:
Many binary splitting recursions have a lot of common factors between the fraction numerators and denominators. Implement an optimization that seeks to remove these common factors so that the numbers are smaller in size.
GCD Factorization was first described here (now a dead link). Since then, there have been subsequent publications that describe the method:
The general idea of the optimization is to keep the prime factorization of some of the recursion variables. Then use this factorization to obtain the GCD of the numerator and denominator terms. Obtaining this prime factorization is done using a sieve.
In the context of y-cruncher, this optimization is applicable to the following constants/algorithms:
Even though GCD factorization has been known for years, y-cruncher has yet to use it for a number of reasons:
While (1) and (3) are certainly solvable, (2) is more difficult. All the ideas so far for attacking (2) are either complicated and fragile, or they require breaking out of the current memory model. For now, there's bigger fish to fry.