{-
Copyright (C) 2011 Dr. Alistair Ward
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see .
-}
{- |
[@AUTHOR@] Dr. Alistair Ward
[@DESCRIPTION@] Exports a common interface for implementations of /prime-number/ generators.
-}
module Factory.Math.Primes(
-- * Types-classes
Algorithmic(..),
-- * Functions
primorial,
mersenneNumbers
) where
import qualified Control.DeepSeq
import qualified Data.Array.IArray
-- | Defines the methods expected of a /prime-number/ generator.
class Algorithmic algorithm where
primes :: (Control.DeepSeq.NFData i, Data.Array.IArray.Ix i, Integral i) => algorithm -> [i] -- ^ Returns the constant, infinite, list of primes.
{- |
* Returns the constant list, defining the /Primorial/.
* .
* .
-}
primorial :: (
Algorithmic algorithm,
Control.DeepSeq.NFData i,
Data.Array.IArray.Ix i,
Integral i
) => algorithm -> [i]
primorial = scanl (*) 1 . primes
{- |
* Returns the constant ordered infinite list of /Mersenne numbers/.
* Only the subset composed from a prime exponent is returned; which is a strict superset of the /Mersenne Primes/.
* .
*
-}
mersenneNumbers :: (Algorithmic algorithm, Integral i) => algorithm -> [i]
mersenneNumbers algorithm = map (pred . (2 ^)) (primes algorithm :: [Int]) -- Whilst the exponentiation could be parallelised, not all values are known to be required.