Difference between revisions of "Sinc function"
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| − | + | The sinc function, <math>\frac{\sin(x)}{x}</math>, is a useful function that is a little tricky to implement because it becomes <math>\frac{0}{0}</math> as x approaches <math>0</math>. Here is an implementation taken from the [http://www.boost.org/boost/math/special_functions/sinc.hpp Boost] library. | |
| − | + | <haskell> | |
| − | |||
| − | |||
epsilon :: RealFloat a => a | epsilon :: RealFloat a => a | ||
epsilon = encodeFloat 1 (fromIntegral $ 1-floatDigits epsilon) | epsilon = encodeFloat 1 (fromIntegral $ 1-floatDigits epsilon) | ||
| Line 9: | 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 | + | sinc x = |
| − | + | 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 | ||
| − | </ | + | </haskell> |
| + | |||
| + | [[Category:Code]] | ||
| + | [[Category:Mathematics]] | ||
Latest revision as of 16:35, 15 November 2006
The sinc function, 
, is a useful function that is a little tricky to implement because it becomes 
as x approaches 
. 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