Copyright | (c) 2009 2011 Bryan O'Sullivan |
---|---|

License | BSD3 |

Maintainer | bos@serpentine.com |

Stability | experimental |

Portability | portable |

Safe Haskell | None |

Language | Haskell2010 |

Less common mathematical functions.

## Synopsis

- bd0 :: Double -> Double -> Double
- chooseExact :: Int -> Int -> Double
- logChooseFast :: Double -> Double -> Double
- logGammaAS245 :: Double -> Double
- logGammaCorrection :: Double -> Double

# Documentation

logChooseFast :: Double -> Double -> Double Source #

Quickly compute the natural logarithm of *n* `choose`

*k*, with
no checking.

Less numerically stable:

exp $ lg (n+1) - lg (k+1) - lg (n-k+1) where lg = logGamma . fromIntegral

logGammaAS245 :: Double -> Double Source #

Compute the logarithm of the gamma function Γ(*x*). Uses
Algorithm AS 245 by Macleod.

Gives an accuracy of 10-12 significant decimal digits, except
for small regions around *x* = 1 and *x* = 2, where the function
goes to zero. For greater accuracy, use `logGammaL`

.

Returns ∞ if the input is outside of the range (0 < *x* ≤ 1e305).

logGammaCorrection :: Double -> Double Source #

Compute the log gamma correction factor for Stirling
approximation for `x`

≥ 10. This correction factor is
suitable for an alternate (but less numerically accurate)
definition of `logGamma`

:

\[ \log\Gamma(x) = \frac{1}{2}\log(2\pi) + (x-\frac{1}{2})\log x - x + \operatorname{logGammaCorrection}(x) \]