Fundamental question: How does MATLAB calculate the sine function?
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Ronald LaFleur
on 15 Mar 2017
Commented: Ronald LaFleur
on 15 Mar 2017
Since it is a built-in function there is little information provided and many online Q/A's have to do with using the sine function for particular applications not the fundamental code-level evaluation of the function.
I imagine the modulo function is used to convert a wide range of angles to the 0:2*pi or -pi:pi range prior to sine function mathematics.
If a series expansion is used, what is the highest order term used? If a look-up table is used, what is the number of table entries within the above range?
These questions come up in our discussion of error propagation of functions.
Thank you, Ron LaFleur, Clarkson University
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James Tursa
on 15 Mar 2017
MATLAB doesn't publish all of their function algorithms, but I would guess it would be range reduction followed by a rational function approximation rather than a series expansion. The range reduction is not trivial. E.g., see this link:
https://www.mathworks.com/matlabcentral/answers/195965-taylor-series-cosx-function
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