Maths: Geometry limits based on 64-bit FP

[D3K]

Precisely.

Awesome.

Now to reassure myself that all those FP numbers I see in FEA matrices are not deviating by more than 10^16 It's a massive number, but feels like it could cause restriction in some of the small to large unit calculations.

 

[Mr Jack]

Awesome.

Now to reassure myself that all those FP numbers I see in FEA matrices are not deviating by more than 10^16 It's a massive number, but feels like it could cause restriction in some of the small to large unit calculations.

I wouldn't worry about it.

The point of the 10^6 margin between the required final precision and the precision required in the software by the 100m limit is to buffer you against this kind of error.

Floating point is never accurate*, you need only worry about whether the degree of inaccuracy is harmful.


* - To be pedantic there are certain, precisely defined, circumstances where it is but for functional purposes treat it as if it never is. Simply using 0.1 anywhere will render it inaccurate for example (0.1 cannot be represented in a finite number of binary bits, it's a recurring binary number).

 

[D3K]

I wouldn't worry about it.

The point of the 10^6 margin between the required final precision and the precision required in the software by the 100m limit is to buffer you against this kind of error.

Floating point is never accurate*, you need only worry about whether the degree of inaccuracy is harmful.


* - To be pedantic there are certain, precisely defined, circumstances where it is but for functional purposes treat it as if it never is. Simply using 0.1 anywhere will render it inaccurate for example (0.1 cannot be represented in a finite number of binary bits, it's a recurring binary number).

I'm starting to wonder if it is limited to that in the interests of calculation.

Vectors run on x^2 for parabolas, x^3 for inflections, x^4 for loops, etc, so that takes the internal numbering to 10^14, leaving a factor of 10 for error. (nb. I'm using the 1d range of 10^10 as their stated range of precision)

 

[BusError]

That's why everyone dealing with these kind of problems will have a tendency to come up with an arbitrarily smallest unit possible, and then use arbitrarily large integer values (with a multiplier) as a working space.
FP sucks for many things; for example comparing values that 'ought' to be the same from two different calculations will likely give you the wrong answer. You have to end up comparing values using a threshold of matching range etc.