module Number.GaloisField2p32m5 where
import qualified Number.ResidueClass as RC
import qualified Algebra.Module as Module
import qualified Algebra.Field as Field
import qualified Algebra.Ring as Ring
import qualified Algebra.Additive as Additive
import Data.Int (Int64, )
import Data.Word (Word32, Word64, )
import qualified Foreign.Storable.Newtype as SN
import qualified Foreign.Storable as St
import Test.QuickCheck (Arbitrary(arbitrary), )
import PreludeBase
import NumericPrelude
newtype T = Cons {decons :: Word32}
deriving Eq
appPrec :: Int
appPrec = 10
instance Show T where
showsPrec p (Cons x) =
showsPrec p x
instance Arbitrary T where
arbitrary = fmap (Cons . fromInteger . flip mod base) arbitrary
instance St.Storable T where
sizeOf = SN.sizeOf decons
alignment = SN.alignment decons
peek = SN.peek Cons
poke = SN.poke decons
base :: Ring.C a => a
base = 2^325
lift2 :: (Word64 -> Word64 -> Word64) -> (T -> T -> T)
lift2 f (Cons x) (Cons y) =
Cons (fromIntegral (mod (f (fromIntegral x) (fromIntegral y)) base))
lift2Integer :: (Int64 -> Int64 -> Int64) -> (T -> T -> T)
lift2Integer f (Cons x) (Cons y) =
Cons (fromIntegral (mod (f (fromIntegral x) (fromIntegral y)) base))
instance Additive.C T where
zero = Cons zero
(+) = lift2 (+)
xy = x + negate y
negate n@(Cons x) =
if x==0
then n
else Cons (basex)
instance Ring.C T where
one = Cons one
(*) = lift2 (*)
fromInteger =
Cons . fromInteger . flip mod base
instance Field.C T where
(/) = lift2Integer (RC.divide base)
instance Module.C T T where
(*>) = (*)