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Sinc function

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== 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.
   
The sinc function <math>\frac{sin(x)}{x}</math> is a useful function that is a little tricky to implement 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.
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<haskell>
 
<pre>
 
 
epsilon :: RealFloat a => a
 
epsilon :: RealFloat a => a
 
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 -}
 
sinc :: (RealFloat a) => a -> a
 
sinc :: (RealFloat a) => a -> a
sinc x | (abs x) >= taylor_n_bound = (sin x)/x
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sinc x =
| otherwise = 1 - (x^2/6) + (x^4/120)
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if abs x >= taylor_n_bound
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then sin x / x
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else 1 - x^2/6 + x^4/120
 
where
 
where
 
taylor_n_bound = sqrt $ sqrt epsilon
 
taylor_n_bound = sqrt $ sqrt epsilon
</pre>
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</haskell>
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[[Category:Code]]
  +
[[Category:Mathematics]]

Latest revision as of 16:35, 15 November 2006

The sinc function, \frac{\sin(x)}{x}, is a useful function that is a little tricky to implement because it becomes \frac{0}{0} 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