Re: on-line calculator

I wrote:

troymius wrote:

[...]

In the code, pi is only defined with a limited
precision (16 digits or
so), so to get a completely correct answer for
tan(pi/2) i would have
to implement some kind of a logic... I am not sure
how to do that
yet.

Easy answer: with (closed) interval arithmetic!

In that realm:

pi = 'exact-pi' +- err

or rather, pi is the (topologically closed)
interval:

pi = ['exact-pi'-err, 'exact-pi'+err]

Please note that that is not so rigorous, but I'd have to get into outwardly directed rounding to properly put that.

-LV


With closed interval arithmetic, then you'd get the
(still closed) interval:

tan(pi/2) = [overflow, infinity]

Hope my "calculation" is correct as I did it from the
top of my head. In any case, the idea behind it
should be clear enough once you also think that, when
graphing your results, you always end up drawing
rectangles...

Let me know if you need further pointers, and also
maybe note that I am myself trying to build (although
in my spare time) a system for
parsing/calculating/graphing, based on closed
interval arithmetic, to eventually put on the web.
Maybe we could join the efforts with an open
source/free software kind of project?

-LV

[...]
.

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