{- 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 <http://www.gnu.org/licenses/>. -} {- | [@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/. * <http://en.wikipedia.org/wiki/Primorial>. * <http://mathworld.wolfram.com/Primorial.html>. -} 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/. * <http://en.wikipedia.org/wiki/Mersenne_prime>. * <http://mathworld.wolfram.com/MersenneNumber.html> -} 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.