-- 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 0.1.1.3


-- | This module defines a storable instance for GMP's <tt>mpz</tt> integer
--   type.
module Data.GMP

-- | The GMP integer type holds information about array size as well as a
--   pointer to an array.
data GMPInt
GMPInt :: Word32 -> Word32 -> Ptr Word64 -> GMPInt

-- | Number of limbs allocated.
[_mp_alloc] :: GMPInt -> Word32

-- | Number of limbs used.
[_mp_size] :: GMPInt -> Word32

-- | Pointer to an array containing the limbs.
[_mp_d] :: GMPInt -> Ptr Word64

-- | Convert a GMP <tt>mpz</tt> to Haskell's <a>Integer</a> type.
gmpToInteger :: GMPInt -> IO Integer
instance Foreign.Storable.Storable Data.GMP.GMPInt


-- | This provides a few facilities for working with common combinatorial
--   functions.
module Numeric.Combinatorics
factorial :: Int -> IO Integer

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


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

-- | O(√n)
isPrime :: Int -> Bool


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

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

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

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


-- | Pure Haskell functions for testing and benchmarking. Specialized for
--   <a>Int</a>s.
module Numeric.Pure
hsIsPrime :: (Integral a) => a -> Bool
hsFactorial :: (Integral a) => a -> a
hsDoubleFactorial :: (Integral a) => a -> a
hsChoose :: (Integral a) => a -> a -> a
hsTotient :: (Integral a) => a -> a
hsTau :: (Integral a) => a -> Int
hsTotientSum :: (Integral a) => a -> a
hsLittleOmega :: (Integral a) => a -> Int
hsIsPerfect :: (Integral a) => a -> Bool