Primality.hs

{-# LANGUAGE CPP #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
{-
	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@]	Implements 'Test.QuickCheck.Arbitrary' and defines /QuickCheck/-properties for "Math.Implementations.Primality".
-}

module Factory.Test.QuickCheck.Primality(
-- * Functions
	quickChecks
) where

import			Control.Applicative((<$>))
import			Factory.Test.QuickCheck.PrimeFactorisation()
import qualified	Data.List
import qualified	Data.Numbers.Primes
import qualified	Factory.Math.Implementations.Primality		as Math.Implementations.Primality
import qualified	Factory.Math.Implementations.PrimeFactorisation	as Math.Implementations.PrimeFactorisation
import qualified	Factory.Math.Primality				as Math.Primality
import qualified	Test.QuickCheck
import			Test.QuickCheck((==>))

instance Test.QuickCheck.Arbitrary factorisationAlgorithm => Test.QuickCheck.Arbitrary (Math.Implementations.Primality.Algorithm factorisationAlgorithm)	where
	arbitrary	= Test.QuickCheck.oneof [
		Math.Implementations.Primality.AKS <$> Test.QuickCheck.arbitrary,
		return {-to Gen-monad-} Math.Implementations.Primality.MillerRabin
	 ]
#if !(MIN_VERSION_QuickCheck(2,1,0))
	coarbitrary	= undefined	--CAVEAT: stops warnings from ghc.
#endif

-- | Defines invariant properties.
quickChecks :: IO ()
quickChecks
	= Test.QuickCheck.quickCheck prop_prime
	>> Test.QuickCheck.quickCheck prop_composite
	>> Test.QuickCheck.quickCheck prop_consistency
	where
		prop_prime :: Math.Implementations.Primality.Algorithm Math.Implementations.PrimeFactorisation.Algorithm -> Integer -> Test.QuickCheck.Property
		prop_prime primalityAlgorithm i	= Test.QuickCheck.label "prop_prime" $ Math.Primality.isPrime primalityAlgorithm prime	where
			normalise n
				| primalityAlgorithm == Math.Implementations.Primality.MillerRabin	= n `mod` 1000000	--Limited by the efficiency of 'Data.Numbers.Primes.primes'.
				| otherwise								= n `mod` 59

			prime :: Integer
			prime	= Data.List.genericIndex Data.Numbers.Primes.primes $ normalise i

		prop_composite :: Math.Implementations.Primality.Algorithm Math.Implementations.PrimeFactorisation.Algorithm -> [Integer] -> Test.QuickCheck.Property
		prop_composite primalityAlgorithm l	= length l > 1	==> Test.QuickCheck.label "prop_composite" . not $ Math.Primality.isPrime primalityAlgorithm composite	where
			normalise n
				| primalityAlgorithm == Math.Implementations.Primality.MillerRabin	= n `mod` 1000000
				| otherwise								= n `mod` 10

			composite :: Integer
			composite	= product . map (Data.List.genericIndex Data.Numbers.Primes.primes . normalise) $ take 8 l

		prop_consistency :: Math.Implementations.Primality.Algorithm Math.Implementations.PrimeFactorisation.Algorithm -> Math.Implementations.Primality.Algorithm Math.Implementations.PrimeFactorisation.Algorithm -> Integer -> Test.QuickCheck.Property
		prop_consistency l r i	= l /= r	==> Test.QuickCheck.label "prop_consistency" $ Math.Primality.isPrime l i' == Math.Primality.isPrime r i'	where
			i'	= i `mod` 512