Basement.Bounded

Description

Types to represent ℤ/nℤ.

ℤ/nℤ is a finite field and is defined as the set of natural number: {0, 1, ..., n − 1}.

Synopsis

Documentation

A type level bounded natural backed by a Word64

Instances

Eq (Zn64 n) Source #
Methods (==) :: Zn64 n -> Zn64 n -> Bool # (/=) :: Zn64 n -> Zn64 n -> Bool #
Ord (Zn64 n) Source #
Methods compare :: Zn64 n -> Zn64 n -> Ordering # (<) :: Zn64 n -> Zn64 n -> Bool # (<=) :: Zn64 n -> Zn64 n -> Bool # (>) :: Zn64 n -> Zn64 n -> Bool # (>=) :: Zn64 n -> Zn64 n -> Bool # max :: Zn64 n -> Zn64 n -> Zn64 n # min :: Zn64 n -> Zn64 n -> Zn64 n #
Show (Zn64 n) Source #
Methods showsPrec :: Int -> Zn64 n -> ShowS # show :: Zn64 n -> String # showList :: [Zn64 n] -> ShowS #
From (Zn64 n) Word256 Source #
Methods from :: Zn64 n -> Word256 Source #
From (Zn64 n) Word128 Source #
Methods from :: Zn64 n -> Word128 Source #
From (Zn64 n) Word64 Source #
Methods from :: Zn64 n -> Word64 Source #
(KnownNat n, NatWithinBound Word32 n) => From (Zn64 n) Word32 Source #
Methods from :: Zn64 n -> Word32 Source #
(KnownNat n, NatWithinBound Word16 n) => From (Zn64 n) Word16 Source #
Methods from :: Zn64 n -> Word16 Source #
(KnownNat n, NatWithinBound Word8 n) => From (Zn64 n) Word8 Source #
Methods from :: Zn64 n -> Word8 Source #
(KnownNat n, NatWithinBound Word64 n) => From (Zn n) (Zn64 n) Source #
Methods from :: Zn n -> Zn64 n Source #
KnownNat n => From (Zn64 n) (Zn n) Source #
Methods from :: Zn64 n -> Zn n Source #

A type level bounded natural

Instances

Eq (Zn n) Source #
Methods (==) :: Zn n -> Zn n -> Bool # (/=) :: Zn n -> Zn n -> Bool #
Ord (Zn n) Source #
Methods compare :: Zn n -> Zn n -> Ordering # (<) :: Zn n -> Zn n -> Bool # (<=) :: Zn n -> Zn n -> Bool # (>) :: Zn n -> Zn n -> Bool # (>=) :: Zn n -> Zn n -> Bool # max :: Zn n -> Zn n -> Zn n # min :: Zn n -> Zn n -> Zn n #
Show (Zn n) Source #
Methods showsPrec :: Int -> Zn n -> ShowS # show :: Zn n -> String # showList :: [Zn n] -> ShowS #
(KnownNat n, NatWithinBound Word256 n) => From (Zn n) Word256 Source #
Methods from :: Zn n -> Word256 Source #
(KnownNat n, NatWithinBound Word128 n) => From (Zn n) Word128 Source #
Methods from :: Zn n -> Word128 Source #
(KnownNat n, NatWithinBound Word64 n) => From (Zn n) Word64 Source #
Methods from :: Zn n -> Word64 Source #
(KnownNat n, NatWithinBound Word32 n) => From (Zn n) Word32 Source #
Methods from :: Zn n -> Word32 Source #
(KnownNat n, NatWithinBound Word16 n) => From (Zn n) Word16 Source #
Methods from :: Zn n -> Word16 Source #
(KnownNat n, NatWithinBound Word8 n) => From (Zn n) Word8 Source #
Methods from :: Zn n -> Word8 Source #
(KnownNat n, NatWithinBound Word64 n) => From (Zn n) (Zn64 n) Source #
Methods from :: Zn n -> Zn64 n Source #
KnownNat n => From (Zn64 n) (Zn n) Source #
Methods from :: Zn64 n -> Zn n Source #

Create an element of ℤ/nℤ from a Word64

If the value is greater than n, then the value is normalized by using the integer modulus n

zn :: forall n. KnownNat n => Natural -> Zn n Source #

Create an element of ℤ/nℤ from a Natural.

If the value is greater than n, then the value is normalized by using the integer modulus n

Create an element of ℤ/nℤ from a type level Nat

znNat :: forall m n. (KnownNat m, KnownNat n, CmpNat m n ~ LT) => Proxy m -> Zn n Source #

Create an element of ℤ/nℤ from a type level Nat