In the abstract realm of polynomial functions there is exactitude. There is a zero point derivative. But in real world problems(physics) there is not complete exactness. To find a slope you hone in on a infinitely small part of the real world curve but you cannot make it infinitely small. That would require infinite calculations so you cannot reach it.
I don't follow this gibberish, but the subject of accuracy is an interesting and important one.
Currently, accuracy in physical computation is dependent on the digital floating point representation of numbers and currently this is determined by the IEEE 754/854 standard which has been in effect for twenty years or so. This standard sets the precision at roughly 16-bits of decimal or 53-bits of binary.
This standard is already severely outdated, but amazingly there is little impetus for change. Hardware makers such as Intel are taking the multi-core processor concept to higher and higher levels but the floating point registers remain fixed at a paltry 64-bits. These should be bumped to at least 128-bits or even 256 bits. 512-bits would not be an unreasonable requirement.
The current workaround is multi-precision FP software, but, as expected, the software routines are S-L-O-W.
How long will it take for this IEEE bureaucracy to begin to demand higher precision for FP computation? It is certainly feasible so let's get moving now.
On Nov 20, 8:09 pm, BURT <macromi...@yahoo.com> wrote:
> In the abstract realm of polynomial functions there is exactitude. > There is a zero point derivative. But in real world problems(physics) > there is not complete exactness. To find a slope you hone in on a > infinitely small part of the real world curve but you cannot make it > infinitely small. That would require infinite calculations so you > cannot reach it.
> I don't follow this gibberish, but the subject of accuracy > is an interesting and important one.
> Currently, accuracy in physical computation is dependent > on the digital floating point representation of numbers > and currently this is determined by the IEEE 754/854 > standard which has been in effect for twenty years or > so. This standard sets the precision at roughly 16-bits > of decimal or 53-bits of binary.
> This standard is already severely outdated, but amazingly > there is little impetus for change. Hardware makers such > as Intel are taking the multi-core processor concept to > higher and higher levels but the floating point registers > remain fixed at a paltry 64-bits. These should be bumped to > at least 128-bits or even 256 bits. 512-bits would not be > an unreasonable requirement.
> The current workaround is multi-precision FP software, > but, as expected, the software routines are S-L-O-W.
> How long will it take for this IEEE bureaucracy to begin > to demand higher precision for FP computation? It is > certainly feasible so let's get moving now.
Ask why there is little impetus for change and I'll ask you why 512 bits would be a "reasonable" requirement. The paltry 64-bit registers that Intel provides for most users is paralleled by Ford's Model T. If you want 512-bit precision then buy a Cray or Rolls Royce. It may be feasible but I don't need it and neither do MOST people. In fact, MOST people don't use FP at all. If you had a million dollars win on a lottery you would not quibble about it being $1,000,000 and 1 cent, for which 64-bit fixed point is more than adequate. The subject of accuracy is an uninteresting and unimportant one to MOST people. Buy yourself a Cray.
On Nov 20, 7:09 pm, Huang <huangxienc...@yahoo.com> wrote:
> On Nov 20, 8:09 pm, BURT <macromi...@yahoo.com> wrote:
> > In the abstract realm of polynomial functions there is exactitude. > > There is a zero point derivative. But in real world problems(physics) > > there is not complete exactness. To find a slope you hone in on a > > infinitely small part of the real world curve but you cannot make it > > infinitely small. That would require infinite calculations so you > > cannot reach it.
> > Mitch Raemsch
> Ever heard of a thing called the Limit ?
You can't hone in on the curve by the unlimited calculation.
Huang wrote: > On Nov 20, 8:09 pm, BURT <macromi...@yahoo.com> wrote: >> In the abstract realm of polynomial functions there is exactitude. >> There is a zero point derivative. But in real world problems(physics) >> there is not complete exactness. To find a slope you hone in on a >> infinitely small part of the real world curve but you cannot make it >> infinitely small. That would require infinite calculations so you >> cannot reach it.
>> Mitch Raemsch
> Ever heard of a thing called the Limit ?
Burt thinks arithmetical absolute precision is perfection.
> Huang wrote: >> On Nov 20, 8:09 pm, BURT <macromi...@yahoo.com> wrote: >>> In the abstract realm of polynomial functions there is exactitude. >>> There is a zero point derivative. But in real world problems(physics) >>> there is not complete exactness. To find a slope you hone in on a >>> infinitely small part of the real world curve but you cannot make it >>> infinitely small. That would require infinite calculations so you >>> cannot reach it.
>>> Mitch Raemsch
>> Ever heard of a thing called the Limit ?
> Burt thinks arithmetical absolute precision is perfection.
1+1 = 2 absolutely perfectly when I went to school.
> > Huang wrote: > >> On Nov 20, 8:09 pm, BURT <macromi...@yahoo.com> wrote: > >>> In the abstract realm of polynomial functions there is exactitude. > >>> There is a zero point derivative. But in real world problems(physics) > >>> there is not complete exactness. To find a slope you hone in on a > >>> infinitely small part of the real world curve but you cannot make it > >>> infinitely small. That would require infinite calculations so you > >>> cannot reach it.
> >>> Mitch Raemsch
> >> Ever heard of a thing called the Limit ?
> > Burt thinks arithmetical absolute precision is perfection.
> 1+1 = 2 absolutely perfectly when I went to school.
How do you know that one plus one equals two? Who told you?
On Nov 21, 12:49 am, BURT <macromi...@yahoo.com> wrote:
> > > Burt thinks arithmetical absolute precision is perfection.
> > 1+1 = 2 absolutely perfectly when I went to school.
> How do you know that one plus one equals two? > Who told you?
Hey "Mitch" got those two Nobel prizes yet? Algore and Obama have theirs! Bigmouth idiot!
Who says 1 + 1 = 2? Since mathematics is abstract 1+ 1 can equal ANYTHING you say it is! Of course, whatever you say, thus defines a mathematical system which you must then demonstrate to be consistent or it isn't mathematics.
Androcles wrote: > "purple" <pur...@colorme.com> wrote in message > news:7mpaavF3i061sU1@mid.individual.net... >> Huang wrote: >>> On Nov 20, 8:09 pm, BURT <macromi...@yahoo.com> wrote: >>>> In the abstract realm of polynomial functions there is exactitude. >>>> There is a zero point derivative. But in real world problems(physics) >>>> there is not complete exactness. To find a slope you hone in on a >>>> infinitely small part of the real world curve but you cannot make it >>>> infinitely small. That would require infinite calculations so you >>>> cannot reach it.
>>>> Mitch Raemsch >>> Ever heard of a thing called the Limit ? >> Burt thinks arithmetical absolute precision is perfection.
> 1+1 = 2 absolutely perfectly when I went to school.
Did you test it on a one's-complement, two's-complement and three's-complement machine? Did you add 1 and -1 and get a negative or positive zero?
On Nov 21, 3:43 am, rabid_fan <r...@righthere.net> wrote:
> On Fri, 20 Nov 2009 18:09:24 -0800, BURT wrote:
> I don't follow this gibberish, but the subject of accuracy > is an interesting and important one.
> Currently, accuracy in physical computation is dependent > on the digital floating point representation of numbers > and currently this is determined by the IEEE 754/854 > standard which has been in effect for twenty years or > so. This standard sets the precision at roughly 16-bits > of decimal or 53-bits of binary.
Thats precision not an accuracy. A number can be precises up to n bits, but accurate to at most to n bit. In certain rare cases a number which is precise to 53 bits has 0 bits of accuracy.
> This standard is already severely outdated, but amazingly > there is little impetus for change.
You can't change it. You need exact errors in calculation that are guaranteed by said standard.
> Hardware makers such > as Intel are taking the multi-core processor concept to > higher and higher levels but the floating point registers > remain fixed at a paltry 64-bits.
That's nice, but multiplication is O(n^2) algorithm, and the simplest division algorithm which is working is a subtraction algorithm, which requires as many steps as bits of accuracy. While there are also higher radix algorithms, doubling register size means doubling CPU speed requirements for one operation.
> These should be bumped to > at least 128-bits or even 256 bits. 512-bits would not be > an unreasonable requirement.
I do have library for high accuracy computing that doesn't need stuff like NaN or something absurd like that. However when n-body simulation with 100 objects is slow on Doubles, the same simulation would be even slower in SW mode. There is a cut off where higher precession doesn't help much.
FP is basically something which is supposed to help mathematicians to use programming without much hassle, as long as they don't require too accurate results. Real programmers are using i64, or i32 because addition of two whole numbers is an exact modulo 2^n operation, which is extremely efficient for a real world algorithms.
> In the abstract realm of polynomial functions there is exactitude. > There is a zero point derivative. But in real world problems(physics) > there is not complete exactness.
Maybe, but does it matter?
-- Which of the seven heavens / Was responsible her smile / Wouldn't be sure but attested / That, whoever it was, a god / Worth kneeling-to for a while / Had tabernacled and rested.
> That's nice, but multiplication is O(n^2) algorithm, and the simplest > division algorithm which is working is a subtraction algorithm, which > requires as many steps as bits of accuracy. While there are also higher > radix algorithms, doubling register size means doubling CPU speed > requirements for one operation.
Ordinary multiplication is O(n^2) but multiplication using FFT methods is O(nlogn). Already hardware-based FFT methods (implemented in FPGA) are being used on 4096-bit operands. It is not far-fetched at all to expect this kind of performance to appear on desktops.
> FP is basically something which is supposed to help mathematicians to > use programming without much hassle, as long as they don't require too > accurate results. Real programmers are using i64, or i32 because > addition of two whole numbers is an exact modulo 2^n operation, which is > extremely efficient for a real world algorithms.
Integer arithmetic would also benefit from larger registers. The IEEE standard was drafted over a generation ago when hardware was much more limited than it is today. It's time to move forward with the future.
I suppose the gist of this question (or whatever it is) concerns the impossibility of attaining the infinitely small in real world problems.
But physics makes no attempt to deal with the infinitely small. The models of the real world are based on the idea of a differential, which is not an infinitely small quantity but rather a quantity that is small enough to allow the derivative to be approximated by the difference quotient.
How small is "small enough?" The answer depends on the particular experiment or investigation but it is never infinitely small.
For more info on this often overlooked but essential concept, just do a search for "differential."
Aside: When doing a search, try to avoid using Google. Google is not the only search engine but somehow it has become a de facto monopoly. A new verb, "google," a synonym for search, has even arisen in the language. This is not good. Use AltaVista or something else once in a while.
On Sat, 21 Nov 2009 07:32:32 -0500, jmfbahciv wrote:
> Did you test it on a one's-complement, two's-complement and > three's-complement machine? Did you add 1 and -1 and get a negative or > positive zero?
There are 10 kinds of people that post to sci.physics.
On 2009-11-21, rabid_fan <r...@righthere.net> wrote:
> Currently, accuracy in physical computation is dependent on the > digital floating point representation of numbers and currently this > is determined by the IEEE 754/854 standard which has been in effect > for twenty years or so. This standard sets the precision at roughly > 16-bits of decimal or 53-bits of binary.
IEEE 754 already defines a 128-bit floating point type as a basic format. There are some CPUs that have worked with 128-bit floating point types for quite a while, though not many as it is not very useful. Note that "128-bit floating point pipeline" in modern graphics cards actually refers to operations on 4x 32-bit floating point operands.
> This standard is already severely outdated, but amazingly there is > little impetus for change.
That is because there are real costs to increasing the native width of operands, which can be much larger than you might expect. Meanwhile, the benefits are minor: old FPUs had 80-bit operands for intermediate results, but the extra precision over 64 bits was almost never useful.
Any serious algorithm design with floating point numbers addresses error propagation to reduce the effects of finite precision. Moving to even 512-bit numbers cannot remove the need for this analysis: a good algorithm can bound the accuracy to within a few units in the last place. A poor one will often produce useless output with _any_ fixed intermediate precision, 512 bits or not.
So in practice the need for intermediate precision is usually determined by the required final accuracy, which seldom exceeds 15 decimal places. The exceptions tend to be in specialized fields, for which specialized software or hardware can be employed.
When the choice in a mass-market CPU design is between 128-bit FPU pathways vs twice as many 64-bit pathways, the usefulness of the latter overwhelmingly dominates. That's actually conservative in favour of the 128-bit path: complexity of higher-precision operations scales much worse than linearly.
What's more, someone who needs more than 64-bit precision often needs more than 128-bit as well, so designing a 128-bit path may well be in vain. Similar considerations apply to 256 bits or greater.
On 2009-11-21, rabid_fan <r...@righthere.net> wrote:
> Ordinary multiplication is O(n^2) but multiplication using FFT > methods is O(nlogn). Already hardware-based FFT methods > (implemented in FPGA) are being used on 4096-bit operands.
Specialized hardware for specialized tasks. If you need it, you can easily get it. If you don't need it, it's a useless waste of silicon and power across billions of CPUs.
It would be sheer lunacy to fix into mass-market CPUs the designs for everything that has ever been done in FPGAs. That's why they (and ASICs) exist.
> Integer arithmetic would also benefit from larger registers.
Not much. Integer arithmetic would benefit much much more from being able to do more of it per clock cycle. And hey, guess what? That's exactly the direction taken by CPU designers.
64-bit integer registers only became common when a significant fraction of practical operations (such as calculating offsets in large files or memory blocks) needed it. It's an optimization, and you don't optimize the least common cases at the expense of the more common ones. Silicon real estate is a finite resource, so widening registers and all their data paths comes at the expense of other things.
> The IEEE standard was drafted over a generation ago when hardware > was much more limited than it is today. It's time to move forward > with the future.
The current IEEE 754 standard is IEEE 754-2008. Last year, not a generation ago.
the original poster had mentioned 754 and 854, which latter I'd seen mentioned, somewhere on the IEEE website, but I wasn't a member. anyway, 754 is an article in Computer (magazine), from 1980; its implimentation is quite variable, I think.
anyone got a reference to link?
> The current IEEE 754 standard is IEEE 754-2008. Last year, not a
--l'Ouvre: www.wlym.com stop the second cap & trade rip-off; install a tariff on imported oil!
On Nov 20, 9:09 pm, BURT <macromi...@yahoo.com> wrote:
> In the abstract realm of polynomial functions there is exactitude. > There is a zero point derivative. But in real world problems(physics) > there is not complete exactness.
Well, that's mostly because Physics cranks are about the only people who have ever proclaimed the real number systems the unique exemplar of exactness.
The educable people, some time started working on DSP, rather than whip antennas. And today they have HDTV, Home Broadband, Laser Disks, mp3, mpeg, Blue Ray, USB, non AT&T PCM, Multiplexed Fiber Optics Systems, Digital Books, Post ACME Fastener Systems, Self-Assembling Robots, Cyber Batteries, Self-Replicating Machines, Deconvolution Algorithms, Desktop Publishing, All-In-Printers, Mini External Computer Hardisks, Flash Memory, 4D Holographics Research Programs, On-Line Publishing, Reverse Compilers, GPS and Post US Steel Welding Robots, Rapid Prototyping, Digital Terrain Mapping, Weather Satellites, Pv Cell Energy, Data Fusion, Atomic Clock Wristwatches, Light Sticks, Post Watt Turbines and Biodiesel and Hybrid-Electric Energy. Rather than just Newton Apples.
> infinitely small part of the real world curve but you cannot make it > infinitely small. That would require infinite calculations so you > cannot reach it.
I have always meant to study difference equatoipns, alas. anyway, I never googol anything that I am dyscussing online, particualry when using the googol front-end for Usenet at some public terminal. I recently saw who owned altavista.com, but I forgot, though I've used it, when needed.
> A new verb, "google," a synonym for search, has > even arisen in the language. This is not good.
thus: the original poster had mentioned 754 and 854, which latter I'd seen mentioned, somewhere on the IEEE website, but I wasn't a member. anyway, 754 is an article in Computer (magazine), from 1980; its implimentation is quite variable, I think.
anyone got a reference to link?
> The current IEEE 754 standard is IEEE 754-2008. Last year, not a
--l'Ouvre: www.wlym.com Stop the second cap & trade rip-off; install a tariff on imported oil -- dumb-*** "republicans R Them!"
The accuracy, independent of any degree of precision, of Calculus is not questionable from even before Liebniz&|Newton, without the need of any -- advanced or otherwise -- computational limitations, discovered it.
really, and Leibniz made a mechanical computer, demonstrated at the Royal Society, where Clarke made a rather obsequious comment, about having to convert-by-hand to obtain negative numbers (ten's compliment .-)
> The accuracy, independent of any degree of precision, of Calculus is > not questionable from even before Liebniz&|Newton, without the need of > any -- advanced or otherwise -- computational limitations, discovered > it.
thus: the problem with Podolsky, Rosen and Einstein, as refuted by the Aspect experiment & so forth, is that they require the "gedanken" part of it to be a photon; Young conclusively proved, a hundred years after Newton-the-quackologist squeezed-out a corpuscular "theory" of light, that *all* of lights essential properties are those of waves, with the sole exception of the photo-eclectical effect, when Moon hits your eye *like* banana-cream pie. and, all of the important work, by Huyghens, Fresnel, Fizzeau etc. etc. has only improved this comprehension, perhaps best *formulated* by Schroedinger (and, anyway, let us recall, that Newton merely algebraized Kepler's orbital constraints -- if he didn't steal it from Hooke, which he did).
Newton's "theory" was probably about as important as Descartes ridiculous ad hoc explanation for the law of refraction (see l'Ouvre, below .-)
> > By the way, I think I heard that John Bell himself > > expected his theorem to prove EPR /right/. If the
thus: dood said, Numbertheory; if you don't want to know that, you don't want to know any thing in science, vis-a-vu *mathematica* -- not the God-am programme of the Wolframites / KNU Kinda Science; see l'Ouvre, below!
> You have a point of view Marxist, mine is Platonist. What is the
thus: Lord Berty was quite an evil pacifist (see larouchepub.com), but he also made me realize that "silly" must be derived from syllogism; apparently, he was completely fried by Godel's thing, although Whitehead would not have been.
> Gorgias lived 2400 years ago. Maybe Russel borrowed from him :)
thus: I have always meant to study difference equations, alas. anyway, I never googol anything that I am dyscussing online, particualry when using the googol front-end for Usenet at some public terminal. I recently saw who owned altavista.com, but I forgot, though I've used it, when needed.
> A new verb, "google," a synonym for search, has
thus: the original poster had mentioned 754 and 854, which latter I'd seen mentioned, somewhere on the IEEE website, but I wasn't a member. anyway, 754 is an article in Computer (magazine), from 1980; its implimentation is quite variable, I think. anyone got a reference to link?
> The current IEEE 754 standard is IEEE 754-2008. Last year, not a
--l'Ouvre: www.wlym.com Stop the second cap & trade rip-off; install a tariff on imported oil -- dumb-*** "republicans R Them!"
rabid_fan wrote: > On Sat, 21 Nov 2009 07:32:32 -0500, jmfbahciv wrote:
>> Did you test it on a one's-complement, two's-complement and >> three's-complement machine? Did you add 1 and -1 and get a negative or >> positive zero?
> There are 10 kinds of people that post to sci.physics.
> We must all ask ourselves: "Which one am I?"
I haven't been able to answer that question yet.
> 1 + 1 = Overflow and carry out flagged
<grin> Whenever I had to deal with computer arithmetic, my hair hurt (as you probably could tell from my post). I simply intended to whet the curiosity of the poster. If s/he/it had done any investigation of the terms, s/he/it would have had found piles of docs and specs to munch on. We had a math PhD who would teach us how to make the computer add better; it took a lot of research.
> > On Fri, 20 Nov 2009 18:09:24 -0800, BURT wrote:
> > I don't follow this gibberish, but the subject of accuracy > > is an interesting and important one.
> > Currently, accuracy in physical computation is dependent > > on the digital floating point representation of numbers > > and currently this is determined by the IEEE 754/854 > > standard which has been in effect for twenty years or > > so. This standard sets the precision at roughly 16-bits > > of decimal or 53-bits of binary.
> > This standard is already severely outdated, but amazingly > > there is little impetus for change. Hardware makers such > > as Intel are taking the multi-core processor concept to > > higher and higher levels but the floating point registers > > remain fixed at a paltry 64-bits. These should be bumped to > > at least 128-bits or even 256 bits. 512-bits would not be > > an unreasonable requirement.
> > The current workaround is multi-precision FP software, > > but, as expected, the software routines are S-L-O-W.
> > How long will it take for this IEEE bureaucracy to begin > > to demand higher precision for FP computation? It is > > certainly feasible so let's get moving now.
> Ask why there is little impetus for change and I'll ask you > why 512 bits would be a "reasonable" requirement. > The paltry 64-bit registers that Intel provides for most users > is paralleled by Ford's Model T. If you want 512-bit precision > then buy a Cray or Rolls Royce. It may be feasible but I don't > need it and neither do MOST people. In fact, MOST people > don't use FP at all. If you had a million dollars win on a lottery > you would not quibble about it being $1,000,000 and 1 cent, > for which 64-bit fixed point is more than adequate. > The subject of accuracy is an uninteresting and unimportant > one to MOST people. Buy yourself a Cray.- Hide quoted text -
Well, the subject of computer registers, of any kind, is unintering to many people, so that's how distributed processing software came to be.
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