# Sinc function

### From HaskellWiki

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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 = | + | epsilon = encodeFloat 1 (fromIntegral $ 1-floatDigits epsilon) |

{- 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 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