-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Fast functions on integers.
--   
--   Fast functions for number theory and combinatorics with a high level
--   of safety guaranteed by <a>ATS</a>. This package also provides a
--   <a>Storable</a> instance for GMP's <tt>mpz</tt> type.
@package fast-arithmetic
@version 0.3.2.6


-- | This provides a few facilities for working with common combinatorial
--   functions.
module Numeric.Combinatorics

-- | See <a>here</a>.
choose :: Int -> Int -> IO Integer

-- | See <a>here</a>.
doubleFactorial :: Int -> IO Integer

-- | The <tt>n</tt>th Catalan number, with indexing beginning at
--   <tt>0</tt>. See <a>here</a>.
--   
--   <pre>
--   λ:&gt; mapM catalan [0..9]
--   [1,1,2,5,14,42,132,429,1430,4862]
--   </pre>
catalan :: Int -> IO Integer
factorial :: Int -> IO Integer


-- | This module provides a fast primality check.
module Numeric.Integer

-- | O(√n)
isPrime :: Int -> Bool

-- | Indexed starting at <tt>0</tt>.
fibonacci :: Int -> IO Integer


-- | This module provides fast number theoretic functions when possible.
module Numeric.NumberTheory

-- | Euler totient function. Experimental.
totient :: Int -> Int

-- | Number of distinct divisors.
tau :: Int -> Int
littleOmega :: Int -> Int

-- | See <a>here</a>
isPerfect :: Int -> Bool

-- | Sum of proper divisors.
sumDivisors :: Int -> Int


-- | Pure Haskell functions. These tend to be more general than the
--   equivalents in ATS.
module Numeric.Pure

-- | See <a>here</a>.
--   
--   <pre>
--   λ:&gt; fmap derangement [0..10] :: [Integer]
--   [1,0,1,2,9,44,265,1854,14833,133496,1334961]
--   </pre>
derangement :: (Integral a) => Int -> a
hsIsPrime :: (Integral a) => a -> Bool
hsFibonacci :: (Integral a) => Int -> a