XMP, Krita, KFileMetaInfo and Strigi

[Jos van den Oever]

2007/6/22, Tobias G. Pfeiffer <tgpfeiffer at web.de>:
> On Friday 22 June 2007, 19:09, Jos van den Oever wrote:
> > 2007/6/22, Cyrille Berger <cberger at cberger.net>:
> > > > >  - it lacks some important types like rationals
> > > >
> > > > a double is not a rational? QVariant::Double
> > >
> > > Yes it is, but a rational isn't a double, it's a division between two
> > > integers.
> > > For instance, there is no double representation of the rational 2 / 3
> > > (0.66666666666666666666666666666666 is just an approximation, even if the
> > > mathematical theory says that 0.666 followed only by 6 is equal to 2 / 3,
> > > but there is no way to represent such a thing in double, 2/3 is
> > > represented by 0.666..67 in a double anyway).
> >
> > It is very simple and not expensive to find a nice rational from a
> > double.
>
> What do you mean by "not expensive"? And what by "nice"? For every number that
> is stored as a double, there are infinitely many rational numbers that give
> that result. With both numerator and denominator being represented by a
> finite number of bits, you end up with a finite number of possible
> combinations, yeehaw. Now you don't even want to find a rational that has the
> same value as this double, but something "nice" that has a *similar* value as
> the given double. (Funny: look at 1.001002004008016032064128256, which might
> look very constructed, with powers of 2, but is actually the result of
> 999/998, continuing with digits 513 = 512 + 001024 etc.) -- Maybe this is a
> bit academic, but it seems to me as if storing a pair of integers is waaaay
> less problematic than trying to recreate such a representation from a double.

It is _very_ academic. In the graphic world the number of denominators
is really limited and all are smaller than 1000. So

double d;
int den = 0;
int nom = 0;
while (den++ < 1000) {
    nom = round(den*d);
    double error = abs(1 - nom / d / den);
    if (error < 0.01) break;
}
if (den == 1001) {
    // bad luck
}

is perfectly acceptable for many purposes and usually, a set fixed of
denominators is know, making it even easier.
Note that this algorithm is horrible inefficient, but still quite
cheap for gui purposes.

Cheers,
Jos