----------------------------------------------------------------------------- -- Copyright 2013, Open Universiteit Nederland. This file is distributed -- under the terms of the GNU General Public License. For more information, -- see the file "LICENSE.txt", which is included in the distribution. ----------------------------------------------------------------------------- -- | -- Maintainer : bastiaan.heeren@ou.nl -- Stability : provisional -- Portability : portable (depends on ghc) -- ----------------------------------------------------------------------------- module Domain.Math.Safe ( -- * Safe division SafeDiv(..), safeDivFractional , -- * Safe power and root SafePower(..) ) where import Control.Monad import Data.Ratio ------------------------------------------------------------------- -- Safe division class Num a => SafeDiv a where safeDiv :: a -> a -> Maybe a safeRecip :: a -> Maybe a -- default definitions safeRecip = safeDiv 1 instance SafeDiv Integer where safeDiv x y | y /= 0 && m == 0 = Just d | otherwise = Nothing where (d, m) = x `divMod` y instance SafeDiv Double where safeDiv = safeDivFractional instance Integral a => SafeDiv (Ratio a) where safeDiv = safeDivFractional safeDivFractional :: (Eq a,Fractional a) => a -> a -> Maybe a safeDivFractional x y | y /= 0 = Just (x / y) | otherwise = Nothing ------------------------------------------------------------------- -- Safe power and root class Num a => SafePower a where safePower :: a -> a -> Maybe a safeSqrt :: a -> Maybe a safeRoot :: a -> a -> Maybe a -- default definitions safeSqrt = (`safeRoot` 2) instance SafePower Integer where safeRoot x y = case fmap round (safeRoot (fromInteger x :: Double) (fromInteger y)) of Just a | safePower a y == Just x -> Just a _ -> Nothing safePower x y | y >= 0 = Just (x ^ y) | otherwise = Nothing instance Integral a => SafePower (Ratio a) where safeRoot x y = do let n = toInteger (numerator y) guard (denominator y == 1) a <- safeRoot (toInteger (numerator x)) n b <- safeRoot (toInteger (denominator x)) n safeDiv (fromInteger a) (fromInteger b) safePower x y | denominator y /= 1 = Nothing | numerator y >= 0 = Just a | otherwise = Just (1/a) where a = x ^ abs (numerator y) instance SafePower Double where safePower x y | x==0 && y<0 = Nothing | otherwise = Just (x**y) safeRoot x y | x >= 0 && y >= 1 = Just (x ** (1/y)) | otherwise = Nothing