On Thu, 20 Nov 2003, William Chops Westfield wrote:

> On Thursday, Nov 20, 2003, at 15:51 US/Pacific, Russell McMahon wrote:
> >
> > For small angles sine(X) = X (in radians) to a good approximation.
> >
> Hmm.  Is there a "sweet spot" for number and/or placement of points for
> a linear interpolation table for trig tables?  Or a general mechanism
> for computing lookup points for a given level of accuracy?

In general, the first derivative of the function that your trying to
interpolate gives you some idea of the interpolation error. Smooth,
monotonic functions (like arctan for angles less than 45 degrees) are easy
to compute with look up tables. The error introduced by lookup tables for
computing the sine function is discussed here:

http://www.dattalo.com/technical/theory/sinewave.html

Scott

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