Short version: I\'d like to know whether there are implementations of the standard trigonometric functions that are faster than the ones included in math.h
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Here are some good slides on how to do power series approximations (NOT Taylor series though) of trig functions: Faster Math Functions.
It's geared towards game programmers, which means accuracy gets sacrificed for performance, but you should be able to add another term or two to the approximations to get some of the accuracy back.
The nice thing about this is that you should also be able to extend it to SIMD easily, so that you could compute the sin or cos of 4 values at one (2 if you're using double precision).
Hope that helps...