Re: How to use floating point in a module?

[Hugo Mills <hugo-lkml@carfax.org.uk>]

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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.

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