[avr-gcc-list] Trig functions ... accuracy vs speed

[Bernd Felsche]

In a past life, which is not to say that I have one now, I used
Taylor series expansions of as few as 3 terms to drive a graphical
output device (Microangelo - if you must ask). That sped up vector
plotting and arc drawing so much, I went back to the code to make
sure that it was actually running.

Each term of the Taylor series increases accuracy. A 1 in a 1000
error can be achieved with 5 terms or less IIRC, which means a heck
of a lot faster calculation than the "true" function; FPU or not!
That makes the Taylor series expansions useful for for driving
discrete-resolution outputs.

Similarly for inverse functions.

However; if you will be using the calculated result for further
calculations, keep in mind that errors can increase rapidly.
Consider the results "quick-and-dirty". :-)

See any of the thousands of web references for further details.
e.g. http://www.efunda.com/math/taylor_series/taylor_series.cfm

-- 
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