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Word.hs
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Word.hs
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{-# LANGUAGE FlexibleInstances #-}
module Word (Word, wordMin, wordMax) where
import Prelude hiding (Word)
import Data.Ratio
import Data.Ix
import Trit
type Word = [Trit] -- I'll just have to assert length of 10
-- adds two words together
addWord :: Word -> Word -> Word
addWord = addWord' O
where
addWord' :: Trit -> Word -> Word -> Word
addWord' _ [] [] = []
addWord' _ _ [] = error "Words must be of length 10"
addWord' _ [] _ = error "Words must be of length 10"
addWord' carry (x:xs) (y:ys) =
let (newCarry, res) = addTrit3 carry x y in
res : addWord' newCarry xs ys
-- subtract two words
subWord :: Word -> Word -> Word
subWord = subWord' O
where
subWord' :: Trit -> Word -> Word -> Word
subWord' _ [] [] = []
subWord' _ _ [] = error "Words must be of length 10"
subWord' _ [] _ = error "Words must be of length 10"
subWord' carry (x:xs) (y:ys) =
let (newCarry, res) = subTrit3 carry x y in
res : subWord' newCarry xs ys
instance Num Word where
(+) = addWord
(-) = subWord
fromInteger =
let fromInteger' x = tritFromInt (x `mod` 3) : fromInteger' (x `div` 3) in
take 10 . fromInteger'
x * y = if x == fromInteger 0 then y else y + (x - fromInteger 1) * y
abs = id
signum _ = fromInteger 1
instance Enum Word where
toEnum =
let toEnum' x = tritFromInt (x `mod` 3) : toEnum' (x `div` 3) in
take 10 . toEnum'
fromEnum [] = 0
fromEnum (x:xs) = tritToInt x + 3 * fromEnum xs
succ x = x + [W,O,O,O,O,O,O,O,O,O]
instance Real Word where
toRational [] = 0
toRational (x:xs) = (tritToInt x % 1) + 3 * toRational xs
instance Integral Word where
toInteger [] = 0
toInteger (x:xs) = tritToInt x + 3 * toInteger xs
quotRem x y = if y == fromInteger 0 then error "Divide by 0" else quotRem' x y
where
quotRem' :: Word -> Word -> (Word, Word)
quotRem' x y
| reverse x < reverse y = (fromInteger 0, x)
| otherwise = let (quot, rem) = quotRem' (x-y) y in (quot+1, rem)
instance Ix Word where
range (x,y) = take (1+fromEnum (y-x)) (iterate succ x)
inRange (x,y) z = z' >= x' && z' <= y'
where
x' = reverse x
y' = reverse y
z' = reverse z
index (x,y) z
| inRange (x,y) z = fromEnum (z-x)
| otherwise = error ("Error: " ++ show z ++ "Out of range")
wordMax :: Word
wordMax = [T,T,T,T,T,T,T,T,T,T]
wordMin :: Word
wordMin = [O,O,O,O,O,O,O,O,O,O]