```{-
-      ``Data/Random/Distribution/Binomial''
-}
{-# LANGUAGE
MultiParamTypeClasses,
FlexibleInstances, FlexibleContexts,
UndecidableInstances
#-}

module Data.Random.Distribution.Binomial where

import Data.Random.Internal.Classification

import Data.Random.Source
import Data.Random.Distribution
import Data.Random.RVar

import Data.Random.Distribution.Beta
import Data.Random.Distribution.Uniform

import Data.Int
import Data.Word

-- algorithm from Knuth's TAOCP, 3rd ed., p 136
-- specific choice of cutoff size taken from gsl source
integralBinomial :: (Integral a, RealFloat b) => a -> b -> RVar a
integralBinomial t p = bin 0 t p
where
bin k t p
| t > 10    = do
let a = 1 + t `div` 2
b = 1 + t - a

x <- realFloatBetaFromIntegral a b
if x >= p
then bin  k      (a - 1) (p / x)
else bin (k + a) (b - 1) ((p - x) / (1 - x))

| otherwise = count k t
where
count k  0    = return k
count k (n+1) = do
x <- realFloatStdUniform
(count \$! (if x < p then k + 1 else k)) n

binomial :: Distribution (Binomial b) a => a -> b -> RVar a
binomial t p = sample (Binomial t p)

class (Classification NumericType t c) => BinomialByClassification c t where
binomialByClassification :: RealFloat a => t -> a -> RVar t

instance (Classification NumericType t IntegralType, Integral t) => BinomialByClassification IntegralType t
where binomialByClassification = integralBinomial
instance (Classification NumericType t FractionalType, RealFrac t) => BinomialByClassification FractionalType t
where binomialByClassification t p = liftM fromInteger (integralBinomial (truncate t) p)

instance (BinomialByClassification c t, RealFloat b) => Distribution (Binomial b) t where
rvar (Binomial t p) = binomialByClassification t p

data Binomial b a = Binomial a b

```