# Sinc function

(Difference between revisions)
 Revision as of 17:56, 25 February 2006 (edit)← Previous diff Current revision (16:35, 15 November 2006) (edit) (undo) (Category:Mathematics) (4 intermediate revisions not shown.) Line 1: Line 1: - == Sinc function == + 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 [http://www.boost.org/boost/math/special_functions/sinc.hpp Boost] library. - The sinc function sin(x)/x[/itex] is a useful function that is a little tricky to use because it becomes 0/0 as x tends to 0. Here is an implementation taken from the [http://www.boost.org/boost/math/special_functions/sinc.hpp Boost] library. + - + -
+
epsilon :: RealFloat a => a                                                                                                                                                                                                                                                                                                                 epsilon :: RealFloat a => a
epsilon = encodeFloat 1 (fromIntegral $1-floatDigits epsilon) epsilon = encodeFloat 1 (fromIntegral$ 1-floatDigits epsilon)
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{- 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]]

## Current revision

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