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Re: OT : Approximate / fast math libraries ?



On Saturday 1 September 2007 9:36:02 am Mogens Kjaer wrote:
> Chris Jones wrote:
> ...
>
> > for the profiler output. atan2 is taking 50% of the time of this method.
> > Not here I don't need that much precision on the result - say +-
> > O(2*pi/100).
>
> Can't you use a Taylor expansion of arctan?

Talyor expansions are valid when your argument is 'small' i.e.

sin(x) ~ x
tan(x) ~ x
cos(x) ~ (1-(x)*(x)/2)

etc. only work when x is small, and the error increases as x does (since the 
size of the truncated terms become more important). Yes you can include more 
terms but that only allows you to go to large x before the errors explode.

I'm well aware of these series, and already use them when appropriate. In this 
case, I need tan(x) with fixed errors, between 0 and 2pi, the whole range.

for instance, a really course estimate for atan2(x,y) can be made, by just 
comparing the signs of x and y, i.e. if x>0 and y>0, atan2(x,y) is between 0 
and pi/2 ...

Chris


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