# 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
```