Algorithms. Irrational numer storage.Playing with 6 axis robot.

[skyzoframe[hun] 4]

Hi all. How to solve, one kind of irrational number storage in float? (For example Pi value) ( second reason. I want to solve a movement over an axis, in the most precious way over an help of pascal programing.) Regards k.z.

Edited August 29, 2023 by skyzoframe[hun]

[David Heffernan 2303]

You can't store pi exactly in a float. What is the motivation for the question?

[skyzoframe[hun] 4]

4 minutes ago, David Heffernan said:

You can't store pi exactly in a float. What is the motivation for the question?

I want 0.1 micron precious movement over 6axis robot.

[skyzoframe[hun] 4]

I got one MASTER coordinate system. After that 6 slave. That depends of each other in one kind of linear way. My problem is the first axis movement. (Because of reverse engineering)

Edited August 29, 2023 by skyzoframe[hun]

[Leif Uneus 40]

41 minutes ago, skyzoframe[hun] said:

I want 0.1 micron precious movement over 6axis robot.

First of all, precision depends on the hardware. If you have a 6 axis movement, how accurate is the movement of all those axis?

Secondly, how is the movement controlled? Resolution? Error in the resolution?

Last in that chain comes the controlling equipment, speed and other things that might concern the precision.

 

Edited August 29, 2023 by Leif Uneus

[skyzoframe[hun] 4]

8 minutes ago, Leif Uneus said:

First of all, precision depends on the hardware. If you have a 6 axis movement, how accurate is the movement of all those axis?

Secondly, how is the movement controlled? Resolution? Error in the resolution?

Last in that chain comes the controlling equipment, speed and other things that might concern the precision.

 

I want to adapt to the maximum software possibilities within the limits of Pascal.  The hardware constans in this case.( One kind of parameter)

Edited August 29, 2023 by skyzoframe[hun]

[DelphiUdIT 132]

Apart from the controller hardware (an element that should not be underestimated), on the numerical calculation part currently in hardware the precision you can obtain is in EXTENDED (80 bit) for 32 bit software and DOUBLE (64 bit) for 64 bit software .

If you want to go beyond these limits you have to use libraries that take advantage of HW + SW to increase calculation precision.

I can point this out to you, even though I've never used it.

 

https://github.com/TurboPack/RudysBigNumbers

 

Good luck

[Leif Uneus 40]

We have equipment for linear movement that is controlled by 4 nanometer precision. All controlled by stepper motors with the help of integers.

Even though it is pascal, the programming language is not important. 

[David Heffernan 2303]

The things you are discussing now seem unrelated to storing pi in a float. I don't feel as though we understand the problem domain yet. 

[Sherlock 636]

I feel like the size of the structures or movements are almost irrelevant as long as you don't change magnitudes. As @Leif Uneus said, integers could be enough. Any calculations could be done on the fly, as movements are almost always slower than calculating speed.

[DelphiUdIT 132]

In my applications (even with robot guides) I also tend to use only integers (for example managing the vector of the last movement section precisely with integers), but having carried out several applications with robots I must say that often the float calculations are unavoidable, for example if you have to perform non-linear movements, perhaps using "quaternions".

So it could be that the request made by @skyzoframe[hun] in this thread is legitimate and that its use is also a necessity.

 

Bye

[David Heffernan 2303]

2 hours ago, DelphiUdIT said:

 

So it could be that the request made by @skyzoframe[hun] in this thread is legitimate and that its use is also a necessity.

You mean the request to store pi exactly in a float ? 

[DelphiUdIT 132]

1 hour ago, David Heffernan said:

You mean the request to store pi exactly in a float ? 

Pi was an example, I meant using an "irrational" number with a float, i.e. increasing the number of significant digits in the calculation...at least I think that's what @skyzoframe[hun] wanted suggestions on.

[David Heffernan 2303]

Even rational numbers aren't exactly representable. Examples include 1/3 and 1/10.

[skyzoframe[hun] 4]

19 hours ago, David Heffernan said:

Even rational numbers aren't exactly representable. Examples include 1/3 and 1/10.

Cube face diagonal or cube space diagonal. Irracional numbers also. (Cube edge 1 integer) 

Edited August 31, 2023 by skyzoframe[hun]

[David Heffernan 2303]

34 minutes ago, skyzoframe[hun] said:

Cube face diagonal or cube space diagonal. Irracional numbers also. (Cube edge 1 integer) 

I don't know what this means 

[skyzoframe[hun] 4]

19 minutes ago, David Heffernan said:

I don't know what this means 

https://en.m.wikipedia.org/wiki/Cube

 

Here check the formulas thread

 

[David Heffernan 2303]

Yes but it's hard to see the relevance. Representable numbers have the form k*2^n. Perhaps you don't actually need exact representability. We don't know what your requirements are. 

Edited August 31, 2023 by David Heffernan

[skyzoframe[hun] 4]

45 minutes ago, David Heffernan said:

Yes but it's hard to see the relevance. Representable numbers have the form k*2^n. Perhaps you don't actually need exact representability. We don't know what your requirements are. 

Many irrational numbers must be used in 3D space. my problem is that it has to be stored in memory. usually in float value. which causes an error if I work in six axes

[David Heffernan 2303]

Just now, skyzoframe[hun] said:

Many irrational numbers must be used in 3D space. my problem is that it has to be stored in memory. usually in float value.

You can see that it's impossible to store irrational numbers in floats. Indeed even rationals can't be stored exactly in floats, unless they can be expressed as above, k*2^n.

[skyzoframe[hun] 4]

4 minutes ago, David Heffernan said:

You can see that it's impossible to store irrational numbers in floats. Indeed even rationals can't be stored exactly in floats, unless they can be expressed as above, k*2^n.

if I slice 3D into 2D surface. What do you mean about [k*2^n] What do you mean?

[skyzoframe[hun] 4]

Please give me one kind of example.

[David Heffernan 2303]

K and n are integers. All representable floats are of the form k*2^n. So 1/3, 1/10 aren't of that for, and aren't representable. 

 

I doubt that you need to store these numbers exactly. But we don't know your requirements. 

Edited August 31, 2023 by David Heffernan

[skyzoframe[hun] 4]

Should I have to check every coordinate value in every runtime because of the main coordinate array what I use? I am confused right now...

[David Heffernan 2303]

I've no idea what your requirement is and what the problem is. You don't seem to understabd how floats work. I don't think this is going to be productive.