[R] Rounding error in seq(...)

[cls59]

Martin Batholdy wrote:
> 
> hum,
> 
> can you explain that a little more detailed?
> Perhaps I miss the background knowledge - but it seems just absurd to  
> me.
> 
> 0.1+0.1+0.1 is 0.3 - there is no rounding involved, is there?
> 
> 

Unfortunately this comes as an utter shock to many people who never take a
Computer Science course. I watch it nail engineering students all the time.

Basically, if you have a fraction and the denominator is not equal to 2^n
for some integer n, that fraction will NEVER be stored as an exact "floating
point" number-- instead it will contain some error due to concessions that
must be made in order to use an efficient binary number scheme.

These errors are generally small, but they do propagate-- especially if you
are carrying the same numbers through a large computation. A good example is
large-scale numerical solutions to nonlinear problems where iterative
algorithms are employed repetitively at each solution step. As the
calculation progresses the roundoff error can rot away the computational
soundness of the algorithm.

If this concerns you, I would suggest reading up on common internal
representations of floating point numbers as well as the propagation of
roundoff error.

At the very least I hope this revelation will instill an appropriate sense
of paranoia concerning the numbers calculated by those magic boxes sitting
on our desks.

-Charlie 

-----
Charlie Sharpsteen
Undergraduate
Environmental Resources Engineering
Humboldt State University
-- 
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