# Sinc function

### From HaskellWiki

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(Category:Mathematics) |
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− | == Sinc function == |
+ | 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. |

− | The sinc function <math>\frac{sin(x)}{x}</math> 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. |
+ | <haskell> |

− | |||

− | <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 | (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 |
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+ | else 1 - x^2/6 + x^4/120 |
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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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− | </pre> |
+ | </haskell> |

+ | |||

+ | [[Category:Code]] |
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+ | [[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 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