Re: How to use floating point in a module?

[Peter Williams <peterw@aurema.com>]

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.
> 
> My guess is that finding some fixed-point libraries, at least to use
> as a starting point, should be not too hard.

See the "Handbook of Mathematical Functions" by Abromawitz and Stegun, 
Dover Publications (ISBN 486-61272-2, Library of Congress number 
65-12253) which has some small but accurate polynomial approximations 
for many functions.


-- 
Dr Peter Williams, Chief Scientist                peterw@aurema.com
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