How can I know the algorithm that MATLAB uses to approximate values of the sine function?

Hi, I try to understand and study the algorithms that MATLAB uses to evaluate sin(x). Since sin(.) is a built-in function, in general, I cannot access the source code. Would that be possible to find that source code somewhere else? Thank you

Answer 1

[Steven Lord]

Take a look at this Cleve's Corner article from Feb. 2002.

If you wanted to see the built-in source code for sin, the first step is to go here.

[James Tursa]

A related discussion can be found here:

http://www.mathworks.com/matlabcentral/answers/195965-taylor-series-cosx-function

Answer 2

[John D'Errico]

Cleve's article is a good one. It discusses range reduction, a tremendously valuable method for special function evaluation. exp, sin, cos, all benefit from that. There are also methods I discuss in the documentation for HPF, where I explain how to get hundreds or thousands of digits for these problems. There are also tricks one can use to minimize the number of divides, useful in environments where a divide costs more time than a multiply.

Another great source of ideas can be found in Hart's book, "Computer Approximations", a superb text that may be difficult to find anymore. And of course, Abramowitz & Stegun is the classic reference for virtually anything in this domain.

[Thai Nhan]

Thank you, John D'Errico. Your answer is very helpful. Also, your HPF article is great. Thank you.