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Inventor Claims to Have Solved Floating Point Error Problem

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Re: Inventor Claims to Have Solved Floating Point Error Problem

#151

Post by enedil »

Ma8ee wrote: post #134
mcny wrote: post #120

Earlier quoted context omitted.

> Almost all real numbers have this property > Almost all I love this comment because it brings back memories of school. In a layman's terms, I think almost all in this case means all but a finite amount can we say almost all real numbers are irrational? 1 1/1 2/1 3/1 4/1 5/1 ... 2 1/2 2/2 3/2 4/2 5/2 ... 3 ... so clearly we can count all the rational numbers but how many irrational numbers are there? are there (many…

The rational numbers are clearly countable. The irrational numbers are uncountable, which means that for every rational number there are infinitely many irrational numbers.

For every rational, there are infinitely many rational numbers too, since finite cartesian product of countable sets is countable.

Re: Inventor Claims to Have Solved Floating Point Error Problem

#152

Post by pps43 »

JoeAltmaier wrote: post #78
agar wrote: post #20

Considering the over-the-top language ("a game changer for the computing industry") and questionable or imprecise comments like, "[it] allows representation of real numbers accurate to the last digit" (um, who reads that without thinking of irrational numbers?) it sounds too much like a sales pitch and not like serious research. I could be wrong, but based on the similarities to interval arithmetic everyone has alrea…

Briefly read, it looks like an idea and not an 'apparatus'. Yes, carrying error bound information along with the number is interesting. How is that implemented in real time? How is accumulated error calculated (how do we know the floating values we are calculating with are not perfectly precise e.g. 3.0000... and not 3.000...1)?

That's easy, always round down and also carry max possible error (calculated by rounding up and subtracting the rounded down value). For example, 1/3 can be represented as 0.333 with error 0.001. Multiply it by 3 and get 0.999 with error 0.003.

You won't need many bits for the error, and operations can be made reasonably fast as only several lowest bits are affected.

Re: Inventor Claims to Have Solved Floating Point Error Problem

#153

Post by kbenson »

HarryHirsch wrote: post #33
api wrote: post #14

Earlier quoted context omitted.

I understand the downside, but how else would he ever get paid for this?

They could have used trade secrets. Konrad Zuse tells the story that back then, optical equipment manufacturers used to contract him for computations. Instead of rooms full of mechanical calculators operated by humans (the original "computers") they would supply his company with data and algorithms and he would reply back with results. Apparently, there were design reasons why for electronic calculations a different…

This is meant to be implemented in a processor. I'm not sure how you would keep it secret from end users, much less from the company tasked with implementing it at the chip level, and their engineers, which might find employment at different companies in the future. This seems like a very poor for for a trade secret if you ask me.

Re: Inventor Claims to Have Solved Floating Point Error Problem

#155

Post by mrob »

Spivak wrote: post #79
bringtheaction wrote: post #25

Earlier quoted context omitted.

Because the whole patent system is broken and everyone who partakes in it shares blame.

If he didn't patent his work someone else will and collect the royalties resulting in 0 additional freedom. There is nothing gained by not playing.

If he publicly discloses it then (theoretically) nobody else can patent it.

Re: Inventor Claims to Have Solved Floating Point Error Problem

#156

Post by kbenson »

api wrote: post #130
Tenobrus wrote: post #29

Earlier quoted context omitted.

Under a different system that doesn't incentivize holding back global progress for small amounts of individual enrichment. There's a reason Linux and GNU utilities are so massively widely used, and overall they've probably provided billions in economic value. They do that freely, for any human to use, and in fact that's part of their main value proposition. Both were born out of the legal nightmare that was UNIX at t…

I agree with the sentiment but unfortunately we've never found a way to implement real socialism without creating a massive permanent welfare underclass that does nothing and a sclerotic self-serving bureaucracy to support them. Most people are not little philosopher kings who work to advance a grand vision of life's unfolding in the universe. Most people just want to do the minimum to get by until they can get their…

> Social democracy (Europe, USA to a lesser extent) is a hybrid that basically works but you still have to make money in that system.

Whether it's capitalism with a large dose of socialism of socialism or socialism with a large dose of capitalism, neither extreme seems to work as well as approaches that adopt portions of both.

> Most people are not little philosopher kings who work to advance a grand vision of life's unfolding in the universe. Most people just want to do the minimum to get by until they can get their next dose of entertainment. I hate to be such a cynic, but I have eyes.

I think the only people that actually work to advance understanding of the universe do so for selfish reasons, and we all just get to benefit from the byproduct of their self interest. If I had to guess whether Einstein of Newton did what they did because they wanted every human to be better of, or if it was primarily because that's what they enjoyed doing and they were lucky enough to be in circumstances that allowed them to live doing that (and become famous as well), I know where I'd place my bet.

It's the same for child rearing. There's a sense of happiness and contentment when your children are happy and safe (or at a minimum there's usually uneasiness and dread when your children are unhappy or unsafe), so you try to make that the situation the one that makes you the most comfortable happy. It's an instinctual and emotional response, but doesn't necessarily make sense from a purely rational self-interest point of view.

We aren't saints, we're machines with wacky firmware that imparts interesting and had to evaluate value functions.

Re: Inventor Claims to Have Solved Floating Point Error Problem

#157

Post by jovial_cavalier »

shmolyneaux wrote: post #70

The floating point error problem has not been solved. This patent describes a floating-point representation that includes fields for storing error information. The standard IEEE floating-point representation has three fields: a sign field, an exponent field, and a mantissa (or significand). This patent proposes reducing the size of other fields and adding additional fields to store error information. The error inform…

> If an operation exceeds this limit, an insufficient significant bits signal "sNaN(isb)" would be raised.

What about for binary repeating decimals like 0.3? Wouldn't it always raise that signal?

Re: Inventor Claims to Have Solved Floating Point Error Problem

#159

Post by tomxor »

Terrible title with a terrible description of the invention.

What he is doing appears so be interval arithmetic: https://en.wikipedia.org/wiki/Interval_arithmetic

Because we don't have infinite computer memory or processing power numbers have to be finite, so no one will ever "solve the floating point error problem" however being able to quantify the error is both extremely useful and extremely complex because you have to try to determine how the error propagates through all of the operations applied over the original input values.

In science this is also done based on the precision of the raw data... roughly through selecting a sensible number of significant figures in final calculation. In other words they omit all of the digits they deem to be potentially outside of the precision provided by the raw data, e.g your inputs a:123.456 and b:789.012 but your result from some multistep calculation is 12.714625243422799, obviously the extra precision is artificial and should be reduced to something slightly less than the input precision (because it will have been rounded).

For floating point math this is about going a step further by calculating the propagation of error from the end of the maximum length significand provided by IEEE 754 (where anything longer causes rounding and thus error), and trying to quantify how that window opens wider and wider as those rounding errors propagate towards more significant digits as more operations are performed. With interval arithmetic this is done by keeping track of the upper and lower bounds of that window (the real number existing somewhere within that window).

This doesn't solve any of the many issues that floating point math has, but it allows whatever is consuming it to potentially assign significance to the output of a calculation more precisely. i.e so that you can say 1369.462628234m is actually 1.4e3m (implying ± 100m) perhaps translating into understanding that your trajectory calculation isn't actually as accurate accurate as the output looks, but instead the target has a variance of up to 100x100 meters.

I expect the patent details a hardware implementation to make this practical at the instruction level rather than a likely very slow software implementation.

Re: Inventor Claims to Have Solved Floating Point Error Problem

#160

Post by everybodyknows »

payne92 wrote: post #94

Here’s the issued patent: https://www.google.com/patents/US9817662 Note that it’s a claim on the processing unit implementation (e.g. the FPU), not the method. Nonetheless, I’d be very surprised if this stands the test of interval arithmetic prior art.

The beauty of the patent is that it will never be tested, being of no practical value, for numerous reasons already mentioned in other comments, plus a few more not worth the bother of going into.

So the inventor gets a patent number for his LinkedIn profile, and USPTO get their fee, and that's the end of it. A win-win for all involved.

Earlier HN discussion of the phenomenon: https://news.ycombinator.com/item?id=16015371

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