Difference between revisions of "Sinc function"
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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. |
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| − | == Sinc function == |
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| + | <haskell> |
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| ⚫ | |||
| − | |||
| − | <pre> |
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epsilon :: RealFloat a => a |
epsilon :: RealFloat a => a |
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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 -} |
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sinc :: (RealFloat a) => a -> a |
sinc :: (RealFloat a) => a -> a |
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| + | sinc x = |
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| − | + | if abs x >= taylor_n_bound |
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| ⚫ | |||
| + | then sin x / x |
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where |
where |
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taylor_n_bound = sqrt $ sqrt epsilon |
taylor_n_bound = sqrt $ sqrt epsilon |
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| − | </ |
+ | </haskell> |
| + | |||
| + | [[Category:Code]] |
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| + | [[Category:Mathematics]] |
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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