OT : Approximate / fast math libraries ?
Chris Jones
jonesc at hep.phy.cam.ac.uk
Sat Sep 1 10:23:38 UTC 2007
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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