{-
	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@]	Defines /QuickCheck/-properties for "Math.Power".
-}

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

import qualified	Data.List
import qualified	Factory.Math.Power	as Math.Power
import qualified	Test.QuickCheck
import			Test.QuickCheck((==>))

-- | Defines invariant properties.
quickChecks :: IO ()
quickChecks =
	Test.QuickCheck.quickCheck `mapM_` [prop_maybeSquareNumber, prop_rewriteRule]
	>> Test.QuickCheck.quickCheckWith Test.QuickCheck.stdArgs {Test.QuickCheck.maxSuccess = 10000} prop_notSquare
	>> Test.QuickCheck.quickCheck `mapM` [prop_squaresFrom, prop_isPerfectPower]
	>> Test.QuickCheck.quickCheck prop_raiseModulo
	where
		prop_maybeSquareNumber, prop_notSquare, prop_rewriteRule :: Integer -> Test.QuickCheck.Property
		prop_maybeSquareNumber i	= Test.QuickCheck.label "prop_maybeSquareNumber" $ Math.Power.maybeSquareNumber (Math.Power.square i) == Just (abs i)

		prop_notSquare i	= abs i > 0	==> Test.QuickCheck.label "prop_notSquare" $ Math.Power.maybeSquareNumber (i ^ (10 {-promote rounding-error using big number-} :: Int) + 1) == Nothing
		prop_rewriteRule i	= Test.QuickCheck.label "prop_rewriteRule" $ Math.Power.isPerfectPower i' == Math.Power.isPerfectPower (fromIntegral i' :: Int)	where
			i'	= abs i

		prop_squaresFrom, prop_isPerfectPower :: Integer -> Integer -> Test.QuickCheck.Property
		prop_squaresFrom from l	= Test.QuickCheck.label "prop_squaresFrom" . (\(x, y) -> y == Math.Power.square x) . Data.List.genericIndex (Math.Power.squaresFrom from) $ abs l

		prop_isPerfectPower b e	= Test.QuickCheck.label "prop_isPerfectPower" . Math.Power.isPerfectPower $ b' ^ e'	where
			b'	= 2 + (b `mod` 10)
			e'	= 2 + (e `mod` 8)

		prop_raiseModulo :: Integer -> Integer -> Integer -> Test.QuickCheck.Property
		prop_raiseModulo b e m	= m /= 0	==> Test.QuickCheck.label "prop_raiseModulo" $ Math.Power.raiseModulo b e' m == (b ^ e') `mod` m	where
			e' :: Integer
			e'	= abs e