Sinc function
From HaskellWiki
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(Category:Mathematics) |
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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]] | ||
Current revision
The sinc function, 
, is a useful function that is a little tricky to implement because it becomes 
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
