# Sinc function

(Difference between revisions)
 Revision as of 16:34, 15 November 2006 (edit) (Category:Mathematics)← Previous diff Current revision (16:35, 15 November 2006) (edit) (undo) (Category:Mathematics) Line 7: Line 7: {- Boosted from Boost http://www.boost.org/boost/math/special_functions/sinc.hpp -} {- Boosted from Boost http://www.boost.org/boost/math/special_functions/sinc.hpp -} sinc :: (RealFloat a) => a -> a sinc :: (RealFloat a) => a -> a - sinc x | (abs x) >= taylor_n_bound = (sin x)/x + sinc x = - | otherwise = 1 - (x^2/6) + (x^4/120) + if abs x >= taylor_n_bound + then sin x / x + else 1 - x^2/6 + x^4/120 where where taylor_n_bound = sqrt $sqrt epsilon taylor_n_bound = sqrt$ sqrt epsilon + [[Category:Code]] [[Category:Mathematics]] [[Category:Mathematics]]
The sinc function, $\frac{\sin(x)}{x}$, is a useful function that is a little tricky to implement because it becomes $\frac{0}{0}$ as x approaches 0. Here is an implementation taken from the Boost library.
epsilon :: RealFloat a => a
epsilon = encodeFloat 1 (fromIntegral $1-floatDigits epsilon) {- Boosted from Boost http://www.boost.org/boost/math/special_functions/sinc.hpp -} sinc :: (RealFloat a) => a -> a sinc x = if abs x >= taylor_n_bound then sin x / x else 1 - x^2/6 + x^4/120 where taylor_n_bound = sqrt$ sqrt epsilon