[PD] Sinesum, cosinesum and cubic interpolation's guard points

[Alexandros Drymonitis]

OK, that's clear, thanks. Still when using [tabread4~] or [tabosc4~] you
still need a copy of the last element in the first index and copies of the
first two elements in the last two indices, right? Even if you're not using
sinesum or cosinesum but some other mathematical function..


On Thu, Sep 5, 2013 at 1:56 PM, IOhannes m zmoelnig <zmoelnig at iem.at> wrote:

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> On 2013-09-05 09:45, Alexandros Drymonitis wrote:
> > OK, index 0 is the negative of index 2,
>
> no not really, they just happen to be the same.
>
> > which can again make sense as it's a sine (supposing that index 0
> > is a copy of the table's last element), but index 512 doesn't have
> > that value, why? And why do indices 1 and 513 have different values
> > too?
>
> do they?
>
> when it comes to floating point, "equality" becomes a little bit fuzzy.
> e.g. "0.1" is really the 'same' as "0.100000001490116119384765625" [1].
>
> comparing the values, you can see that they are not *very* wrong:
>
> array[512]-array[0] = -5.30668e-6 = -0.0000053
> array[513]-array[1] = -5.30718e-6 = -0.0000053
> array[514]-array[2] = -5.30668e-6 = -0.0000053
>
> so the errors are really rather small, and hopefully don't matter so
> much in the interpolation (which is another approximation anyhow).
>
> the reason why the error is not smaller, is that Pd internally
> (src/g_array.c:896) deals with a PI value of 3.14159, which is a
> rather rough estimate and is the reason why the cycle is not exactly
> 512 points long.
>
>
> fgamsdr
> IOhannes
>
> [1]
>
> http://en.wikipedia.org/wiki/Floating_point#Representable_numbers.2C_conversion_and_rounding
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