{-|
Module      : Numeric.Combinatorics
Copyright   : Copyright (c) 2017 Vanessa McHale

This provides a few facilities for working with common combinatorial
functions.
-}

module Numeric.Combinatorics ( factorial
                             , choose
                             , doubleFactorial
                             ) where

import           Control.Composition
import           Data.GMP
import           Foreign.C
import           Foreign.Ptr
import           Foreign.Storable

foreign import ccall unsafe factorial_ats :: CInt -> Ptr GMPInt
foreign import ccall unsafe double_factorial_ats :: CInt -> Ptr GMPInt
foreign import ccall unsafe choose_ats :: CInt -> CInt -> Ptr GMPInt

-- | See [here](http://mathworld.wolfram.com/BinomialCoefficient.html).
choose :: Int -> Int -> IO Integer
choose = (gmpToInteger <=<) . (peek .* on choose_ats fromIntegral)

-- | See [here](http://mathworld.wolfram.com/DoubleFactorial.html).
doubleFactorial :: Int -> IO Integer
doubleFactorial = gmpToInteger <=< (peek . double_factorial_ats . fromIntegral)

factorial :: Int -> IO Integer
factorial = gmpToInteger <=< (peek . factorial_ats . fromIntegral)