Re: Floating point: sine, cosine etc.

Search for Taylor expansions or Taylor series. I found a website this
morning that tells you how to calculate the coefficients. Unfortunately,
you have to keep differentiating the original function for each term you
require.

I remember having to do this at school and college many, many years ago...

Dave

On Fri, 30 Sept 2022, 06:47 Baltissen, GJPAA (Ruud), <ruud.baltissen_at_apg.nl>
wrote:

> Hallo Michał,
>
>
> > arFacTan[7] := 17/315
> >
> > What goes further, I would have to calculate since it's been like 20
> years since I have last done this stuff. But it shouldn't be hard.
>
> I even had not heard of Bernoulli numbers before. But that are sons for 😊
>
>
> > One more: If the "s" variable from the previous step is the same as the
> one from the current step, ...
>
> Very good tip, thank you!
>
>
> > That is kinda neat.
>
> Thank you. I may not be a good mathematician but I consider my self at
> least a good programmer. (what others think.....)
>
>
> > I'll be glad to help too!
>  +
> David: > From what I remember, any continuous function can be expressed as
> a power series. ....
>
> I found a site on Wikipedia that showed a lot of these expressions stacked
> together  but unfortunately I cannot find it anymore. But that isn't a
> problem, when looking for the individual functions like "natural
> logarithm", you can find the formulas there is well. So what seemed to be a
> neat trick to calculate sine and cosine is growing into a nice tool for
> calculating other functions as well. Using tables has one advantage: speed.
> But the downside: they occupy space. So I will program two versions: one
> with tables and one where all needed values are calculated. But that leads
> to another question: I think Bernoulli numbers can be calculated but that
> will cost space as well. And TAN = SIN / COS so no calculations for the
> Bernoulli numbers needed at all. FYI: that's how GWBASIC and Commodore do
> it.
>
>
> With kind regards / Met vriendelijke groet, Ruud Baltissen
>
> http://www.baltissen.org
>
>
>
>
>
>
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