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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

#181

Post by squeaky-clean »

tombert wrote: post #67
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…

That's what I was thinking too; If I do 1 / 3, then of course it will have to truncate, and integration errors would still be inevitable.

I've definitely owned a Casio calculator that worked on fractions rather than decimals and could even work in terms of roots and certain irrational numbers like e and pi.

For example, sqrt(2) + sqrt(8) would print 3 sqrt(2) rather than 4.242640687119286~

I wish I knew how it worked, it's probably something simple like suggested in another comment.

Re: Inventor Claims to Have Solved Floating Point Error Problem

#182

Post by geezerjay »

TallGuyShort wrote: post #89
tombert wrote: post #67

Earlier quoted context omitted.

That's what I was thinking too; If I do 1 / 3, then of course it will have to truncate, and integration errors would still be inevitable.

There is inaccuracy, but the point is that it tracks how much inaccuracy there might be. I picture this as being similar to how computers can't trust time for all sorts of reasons, so Google's Spanner uses time ranges and estimates of potential inaccuracy to make it possible to work with that. It will truncate, so you won't really have 1/3, but you'll know it's approximately 0.333, definitely more than 6/20 but defin…

> but you'll know it's approximately 0.333, definitely more than 6/20 but definitely less than 7/20, for instance

What strikes me as odd is that in my intro course to numerical methods taught how to calculate floating point error bounds when introducing the concept of floating point numbers, including how errors propagated with each flop.

Re: Inventor Claims to Have Solved Floating Point Error Problem

#183

Post by [deleted] »

School-Cotton wrote: post #112
tombert wrote: post #67

Earlier quoted context omitted.

That's what I was thinking too; If I do 1 / 3, then of course it will have to truncate, and integration errors would still be inevitable.

Actually it's possible to represent 1/3 perfectly accurately, but what about all the numbers that it's theoretically impossible to compute? (Almost all real numbers have this property)

[deleted]

Re: Inventor Claims to Have Solved Floating Point Error Problem

#184

Post by LASR »

BFatts wrote: post #162
koonsolo wrote: post #145

Earlier quoted context omitted.

Yes, this is my exact understanding of the article too. So in that case, "[it] allows representation of real numbers accurate to the last digit" doesn't really hold true.

I think you're reading it wrong. I think the intended meaning was that it's accurate for real numbers up to, but not including, the final digit" That's how I read it.

I think you're missing the point. Using the example above. 1/3 has no final digit. 0.333333 repeating infinitely.

So how do you then store this number to the final digit or final -1 digit using this mechanism?

Re: Inventor Claims to Have Solved Floating Point Error Problem

#185

Post by [deleted] »

School-Cotton wrote: post #177
Ma8ee wrote: post #134

Earlier quoted context omitted.

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

I wasn't talking about irrational numbers.

[deleted]

Re: Inventor Claims to Have Solved Floating Point Error Problem

#186

Post by LASR »

craftyguy wrote: post #174
ars wrote: post #168

Earlier quoted context omitted.

> I'm curious, how? As 1/3 - exactly as it's on your screen. All rational numbers can be represented exactly.

Hmm, yes, it can be represented in ASCII. But you still have to approximate when storing it in a way that is actually useful for computation using a finite number of bits.

No. of course not.

A lot of scientific calculators do this. They have a fractional arithmetic mode that keeps numbers you input as fractions as fractions in the output.

Scientific calculators even have irrational modes where they represent irrational numbers such as sqrt(2) as sqrt(2) and can do 100% precise operations on it. Like sqrt(2) * sqrt(2) will give you a result of 2

https://i.imgur.com/l83fwr2.png

Re: Inventor Claims to Have Solved Floating Point Error Problem

#187

Post by sbuttgereit »

sirclueless wrote: post #100
vec wrote: post #56

Earlier quoted context omitted.

I don't expect him to work for free, but I do want Intel (and AMD, ARM, NVIDIA, TI, and anyone else who makes a floating point module) to go "sweet, thanks for the fix" as quickly and, almost more importantly, as collectively as possible. I want this guy to be compensated, but I'd prefer this guy be compensated in a manner that doesn't prevent third parties from fixing their hardware. In general, I think bounties are…

You're living in a fantasy world. You're looking at the status quo: some guy has invented a better floating point circuit, and you think there are two options. 1) The guy releases it to the public for general use, or 2) the guy patents it and holds a monopoly over its use. Obviously 1) is a greater public good than 2), but in reality these are not the only options. Here's some other realistic situations: 3) With no i…

This. I know of someone that invented what appears to be useful medical technology; certain trusted professionals in the field that reviewed the work agreed.

However, some of the case law around what they'd need to patent the turned unfavorable around the time they were pursuing this and looking to turn it into a business. For your reasons 3) and 5), they've shelved it. This was an individual, not a large company, and without sufficient legal protection to reasonably hold large companies at bay, there simply was not sufficient reason to pursue this effort given how questionable the return would be.

Re: Inventor Claims to Have Solved Floating Point Error Problem

#188

Post by [deleted] »

oh_sigh wrote: post #171
jovial_cavalier wrote: post #157

Earlier quoted context omitted.

> 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?

Presumably if you specify that you want more units of precision than are available, then yes. But if you say you only want 1 significant digit, then it can store it.

[deleted]

Re: Inventor Claims to Have Solved Floating Point Error Problem

#189

Post by TallGuyShort »

geezerjay wrote: post #182
TallGuyShort wrote: post #89

Earlier quoted context omitted.

There is inaccuracy, but the point is that it tracks how much inaccuracy there might be. I picture this as being similar to how computers can't trust time for all sorts of reasons, so Google's Spanner uses time ranges and estimates of potential inaccuracy to make it possible to work with that. It will truncate, so you won't really have 1/3, but you'll know it's approximately 0.333, definitely more than 6/20 but defin…

> but you'll know it's approximately 0.333, definitely more than 6/20 but definitely less than 7/20, for instance What strikes me as odd is that in my intro course to numerical methods taught how to calculate floating point error bounds when introducing the concept of floating point numbers, including how errors propagated with each flop.

Yeah I doubt this is anything novel in the purely mathematical realm. It sounds like what's patented is a practical design for doing this on a chip.

Not sure if you were taught a different method, but I envision this being similar to counting "significant digits" in scientific notation, and it sounds like that's very similar to the approach he took. I wonder if that explains there statements about tracking to the last "digit". They obviously can't do that for irrational number, so maybe they mean the last "significant" digit as far as the underlying floating point implementation is concerned.

Re: Inventor Claims to Have Solved Floating Point Error Problem

#190

Post by enedil »

squeaky-clean wrote: post #181
tombert wrote: post #67

Earlier quoted context omitted.

That's what I was thinking too; If I do 1 / 3, then of course it will have to truncate, and integration errors would still be inevitable.

I've definitely owned a Casio calculator that worked on fractions rather than decimals and could even work in terms of roots and certain irrational numbers like e and pi. For example, sqrt(2) + sqrt(8) would print 3 sqrt(2) rather than 4.242640687119286~ I wish I knew how it worked, it's probably something simple like suggested in another comment.

Look at any computer algebra system, for exaple sympy (https://sympy.org) and see how they implement it (it's open source).
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