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Sinc function

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Sinc function

The sinc function sin(x) / x 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 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 | (abs x) >= taylor_n_bound = (sin x)/x
       | otherwise = 1 - (x^2/6) + (x^4/120)
 where
  taylor_n_bound = sqrt $ sqrt epsilon