Re: How to use floating point in a module?
From: Hugo Mills (hugo-lkml_at_carfax.org.uk)
Date: 05/31/04
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Date: Mon, 31 May 2004 21:23:09 +0100 To: Michal Jaegermann <michal@harddata.com>
On Mon, May 31, 2004 at 02:12:53PM -0600, Michal Jaegermann wrote:
> On Mon, May 31, 2004 at 01:44:40PM +0800, Ian Kent wrote:
> >
> > Why not scaled longs (or bigger), scalled to number of significant
> > digits. The Taylor series for the trig functions might be a painfull.
>
> Taylor series usually are painful for anything you want to calculate
> by any practical means. Slow convergence but, for a change, quickly
> growing roundup errors and things like that. An importance and uses
> of Taylor series lie elsewhere.
>
> OTOH polynomial approximations, or rational ones (after all division
> is quite quick on modern processors), can be fast and surprisingly
> precise; especially if you know bounds for your arguments and that
> that range is not too wide. Of course when doing that in a fixed
> point one needs to pay attention to possible overflows and
> structuring calculations to guard against a loss of precision is
> always a good idea.
It's also worth pointing out that there are other, much
faster-converging, polynomial series that can be used to approximate
trig functions. Chebyshev polynomials are, I believe, pretty
well-behaved. IIRC, they are what the Sinclair Spectrum used to use.
Hugo.
-- === Hugo Mills: hugo@... carfax.org.uk | darksatanic.net | lug.org.uk === PGP key: 1C335860 from wwwkeys.eu.pgp.net or http://www.carfax.org.uk --- Hey, Virtual Memory! Now I can have a *really big* ramdisk! ---
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