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Old 5th October 2015, 15:55   #41  |  Link
feisty2
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*That precision could be calculated, and this is the one of the first things you do when you start doing physics lab in school (when you're starting to apply math to the real world).
That stuff is actually hard, so it's not surprising that no one bothers with it. Just throw more precision, and hope that it helps.
AND,
errors produced by computers due to finite precision are OBVIOUSLY "Systematic Errors" (these errors are constant, you repeat the calculation like a billion times, and the error stays the same, not something fluctuating)
and the page you linked to showed us some basic stuff of "Estimating Random Errors" (fluctuating as you repeat the experiment)

what's your point
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Old 5th October 2015, 16:13   #42  |  Link
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Originally Posted by bxyhxyh View Post
Don't computers already work this way?

EDIT: One thing I can't understand is that what's the point of debating on two things that does exactly same thing on the screen?
Floating point numbers you said? Not even close.
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Old 5th October 2015, 16:22   #43  |  Link
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Originally Posted by vivan View Post
Input data also has limited precision.
If you perform calculations with precision higher* than the precision of your data - then you're not losing any data.
There's no point in calculating 10 + 20 with 256-bit precision just because you can if you're not even sure if first number is actually 10 or 7 or 13.
Agree, but the input can have infinite precision like natural logarithm. Euler's number is not a ratio of integers and it is not a root of any non-zero polynomial with rational coefficients. Like log (param).

EDIT. Forget it... you always think that the input is only 'param'.
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Last edited by Khanattila; 5th October 2015 at 16:28.
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Old 5th October 2015, 16:28   #44  |  Link
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Originally Posted by bxyhxyh View Post
Don't computers already work this way?

EDIT: One thing I can't understand is that what's the point of debating on two things that does exactly same thing on the screen?
the topic has turned academic for a while
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Old 5th October 2015, 16:47   #45  |  Link
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@vivan
you and I have different perceptions of "lossless", I can live with that
but please don't drag physics stuff here, computers do mathematical calculations, not physical experiments
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Old 5th October 2015, 19:27   #46  |  Link
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Originally Posted by Khanattila View Post
Agree, but the input can have infinite precision like natural logarithm. Euler's number is not a ratio of integers and it is not a root of any non-zero polynomial with rational coefficients. Like log (param).

EDIT. Forget it... you always think that the input is only 'param'.
No, in computers it cannot. Computers don't do infinite precision. The input will always have finite precision.

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@vivan
you and I have different perceptions of "lossless", I can live with that
but please don't drag physics stuff here, computers do mathematical calculations, not physical experiments
Vivan's point was a mathematical one, not a physical one.

If you can only output integers there is a point where keeping track of extra precision cannot change the result at all. This point depends on the equation(s), of course, but it can be calculated with certainty. In physics/chemistry it is based on the precision of your measurements while in computers it is based on the precision of your input and output.
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Old 5th October 2015, 19:45   #47  |  Link
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I'd just implement the real infinite precision if I had time to be wasted on "precision calculation"
Like, ln (Pi) stays ln (Pi), not 1.144729885849400
And that's the infinite precision
And that's the real deal
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Old 5th October 2015, 21:27   #48  |  Link
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Maybe my previous post which included word "physics" may confused people.
It is my bad for using wrong words and meaning. But that is still valid for mathematics.

Especially for this case if input and output are the same, it means that it IS mathematically lossless.

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I'd just implement the real infinite precision if I had time to be wasted on "precision calculation"
Like, ln (Pi) stays ln (Pi), not 1.144729885849400
And that's the infinite precision
And that's the real deal
I think that's not possible for programming level numbers. Well for Pi example, 4*atan(1) can do that. But it will be still limited by bit precision (memory). It can't be irrational number with infinite digit.

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Originally Posted by Khanattila View Post
Floating point numbers you said? Not even close.
Ah, my memory was mixed then lol. I have some vague memory of that fractal numbers are precised that way. Then it wasn't floating point numbers.

EDIT: TBH, I personally think this thread needs to be locked. Because we're arguing like "this method is more accurate because it calculates correctly" while both results the same. It is just meaningless.

Last edited by bxyhxyh; 5th October 2015 at 22:42.
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Old 6th October 2015, 01:52   #49  |  Link
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@bxyhxyh
It's possible
Don't convert Pi to 3.1415926.... just use "Pi" to represent the number
Like what you did in math
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Old 6th October 2015, 06:36   #50  |  Link
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@bxyhxyh
It's possible
Don't convert Pi to 3.1415926.... just use "Pi" to represent the number
Like what you did in math
Well even if you save some math numbers as representations in CPU, memory or whatever place, It will end up being rational numbers, when you use it in REAL calculation.
You can use any kind of trick to make it accurate as possible. But in the end the calculation still will be limited by bits.

Maybe for some cases even precise calculation might end up being more accurate. Who knows.
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Old 6th October 2015, 06:46   #51  |  Link
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and define "REAL calculation"
the area of a 1cm radius circle is Pi cm^2, "Pi cm^2" is the output, the result of the calculation
that's real calculation
I don't get it, who on earth said you have to convert everything to decimals to be the "REAL calculation"
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Old 6th October 2015, 07:14   #52  |  Link
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I think you don't really understand what Pi and 3.14159265.... stand for
both of them are just different representations of the same objective existence of some certain information, like, simply the distance of some constant dot (dot "Pi") and dot "0" on the axis
it's just this piece of information will need infinite characters if you wanna represent it within the decimal system, BUT, it can be represented with finite characters by other systems, like "Pi"
like, 0.3333... (1/3) is an infinite decimal under the decimal system, but, it's just "0.1", 2 characters under the trinary system
if you're still confused, think about 15(dec) and 0xF

EDIT: corrected a calculation mistake

Last edited by feisty2; 6th October 2015 at 07:29.
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Old 6th October 2015, 07:16   #53  |  Link
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Originally Posted by feisty2 View Post
and define "REAL calculation"
the area of a 1cm radius circle is Pi cm^2, "Pi cm^2" is the output, the result of the calculation
that's real calculation
I don't get it, who on earth said you have to convert everything to decimals to be the "REAL calculation"
I don't wanna argue about what is the real calculation or not.
In this case Pi is more like operation. We already have represented operations. For example divide is same as Pi

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Originally Posted by feisty2 View Post
I think you don't really understand what Pi and 3.14159265.... stand for
both of them are just different representations of the same objective existence of some certain information, like, simply the distance of some constant dot (dot "Pi") and dot "0" on the axis
it's just this piece of information will need infinite characters if you wanna represent it within the decimal system, BUT, it can be represented with finite characters by other systems, like "Pi"
like, 0.3333... (1/3) is an infinite decimal under the decimal system, but, it's just "1", a single character under the trinary system
if you're still confused, think about 15(dec) and 0xF
Computer only work in binary.

Last edited by bxyhxyh; 6th October 2015 at 07:28.
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Old 6th October 2015, 07:34   #54  |  Link
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Originally Posted by bxyhxyh View Post

Computer only work in binary.
and yet you can do decimal calculations on computers
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Old 6th October 2015, 07:49   #55  |  Link
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computers are just like those little kids, they do whatever you tell them to
like, a 6 yrs old kid is calculating the area of a 1cm radius circle, and he's gonna ask like, "I will need Pi, what am I going to do about it?"
you can either tell him, Pi is approximately 3.14, and you just make it 3.14,
and he will tell you the area is 3.14 cm^2, which is imprecise, cuz you told him to do the wrong stuff
or you tell him, Pi is a constant number just like 1,2,3,4.... you can just keep it Pi,
and he will tell you the area is Pi cm^2, which is precise and correct
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Old 6th October 2015, 09:22   #56  |  Link
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Originally Posted by feisty2 View Post
and yet you can do decimal calculations on computers
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Originally Posted by feisty2 View Post
computers are just like those little kids, they do whatever you tell them to
like, a 6 yrs old kid is calculating the area of a 1cm radius circle, and he's gonna ask like, "I will need Pi, what am I going to do about it?"
you can either tell him, Pi is approximately 3.14, and you just make it 3.14,
and he will tell you the area is 3.14 cm^2, which is imprecise, cuz you told him to do the wrong stuff
or you tell him, Pi is a constant number just like 1,2,3,4.... you can just keep it Pi,
and he will tell you the area is Pi cm^2, which is precise and correct
I think you're asking user level calculation. There are high-end programs that can do such stuffs. Heck, even calculators can do that.
In machine level calculations it won't work that way.

Lets say for example in 8 bit unsigned float numbers
4 is 0100.0000, 3 is 0011.0000
In mathematics decimal Pi is 3.14159265359...
Then how much is Pi? It will be something like 0011.0010.
How much is it in decimal? 3.125.

Lets imagine you have converted Pi into something like 1. Then how much is decimal 4?
It will be RATIONAL number bit higher than 1, since memory isn't limitless.
Exactly same as computer we work today.

Memory has limit. Real calculation is limited by it.
Real calculation means calculation going in machine language.

It doesn't know and can't learn any other languages.
WE translate it into language that human can understand.

Last edited by bxyhxyh; 6th October 2015 at 09:30.
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Old 6th October 2015, 09:36   #57  |  Link
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and you just mixed all the concepts up
it's 100% pointless to care about how the calculation is working at the machine code level
like, will you ever care what's going on with the neurons inside someone's brain when he's doing some math?

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I think you're asking user level calculation. There are high-end programs that can do such stuffs. Heck, even calculators can do that.
that's my point, it should stop being just high end programs, it should be universal thru all programs
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Then how much is Pi?
obviously "Pi" is a string (some special symbol) at the machine code level, so it's still precise and finite, and how much is a string is pointless, that's something the higher level program will take care of
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Old 6th October 2015, 09:47   #58  |  Link
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it should stop being just high end programs, it should be universal thru all programs
It just can't.

Machine has only 2 symbol 1 and 0. Then read the previous post's later part please.

Last edited by bxyhxyh; 6th October 2015 at 09:55.
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Old 6th October 2015, 09:53   #59  |  Link
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Originally Posted by bxyhxyh View Post
It just can't.


Machine has only 2 symbol 1 and 0. Then read the previous post's later part please.
special symbol = a certain string
like if you gonna set "Pi" as the special symbol for that number
the symbol will be the binary of the ANSI text of "Pi" at the machine code level

I think you have problems understanding English apparently
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Old 6th October 2015, 10:54   #60  |  Link
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I think you have problems understanding English apparently
Yes.

And you're still asking user level program. Such things already exist. If they don't, someone can create them.
I think there are plenty of programs that does math on physics, chemicals or any science.

But those high-end programs' results don't saved as exact number in memory. It is just displayed that way on screen.
Also they're still not limitless, still not perfectly accurate, still uses precision even in high level calculations.

I think we separated too much from main topic here

Last edited by bxyhxyh; 6th October 2015 at 11:30.
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