[music-dsp] Optimizing trigonometric functions

[Xavier Amatriain]

>well, i'd be interested in a comparison between a table lookup
>algorithm
>using a decent table size / interpolation and a taylor approximation ...
>in terms of quality vs. speed

>a taylor approximation can be coded with simd instructions, which should
>make them pretty efficient (no memory lookups) but it would require a
>higher order to be as precise as lookup algorithm ...
>for waveshaping functions, i've been using taylor approximations with
>very good results, concerning speed, not sure, how precise they are (i'm
>usually going up to 8th or 10th order)

Are you talking about Taylor or about other kind of polynomial like Minimax? 
In the reference I pointed to, you can read the following (which I think it is pretty
conclusive;) :

"Taylor series as a technique for generating fast polynomial approximations is flawed from
beginning to end" (pg.8)