Crypto.Lol.Types.Unsafe.RRq

An implementation of the additive quotient group \(\R/(q\Z)\). This module is "unsafe" because it exports the RRq constructor. This module should only be used to make tensor-specific instances for RRq. The safe way to use this type is to import Crypto.Lol.Types.

Documentation

newtype RRq q r

The additive group \( \R/(q\Z) \) of reals modulo q, using underlying floating-point type r.

Constructors

RRq r

Instances

(Reflects q r, RealField r) => Reduce r (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

reduce :: r -> RRq q r

TensorPowDec t (RRq q r) => UnCyc t (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

cycPow :: Fact m => CycRep t P m (RRq q r) -> Cyc t m (RRq q r)

cycDec :: Fact m => CycRep t D m (RRq q r) -> Cyc t m (RRq q r)

unCycPow :: Fact m => Cyc t m (RRq q r) -> CycRep t P m (RRq q r)

unCycDec :: Fact m => Cyc t m (RRq q r) -> CycRep t D m (RRq q r)

TensorPowDec t (RRq q r) => ExtensionCyc (Cyc t) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

embed :: Divides m m' => Cyc t m (RRq q r) -> Cyc t m' (RRq q r)

twace :: Divides m m' => Cyc t m' (RRq q r) -> Cyc t m (RRq q r)

powBasis :: Divides m m' => Tagged m [Cyc t m' (RRq q r)]

coeffsCyc :: Divides m m' => Basis -> Cyc t m' (RRq q r) -> [Cyc t m (RRq q r)]

(Protoable (IZipVector m (RRq q Double)), ProtoType (IZipVector m (RRq q Double)) ~ KqProduct, Protoable (IZipVector m b), ProtoType (IZipVector m b) ~ KqProduct) => Protoable (IZipVector m (RRq q Double, b))

Defined in Crypto.Lol.Types.IZipVector

Associated Types

type ProtoType (IZipVector m (RRq q Double, b)) :: Type

Methods

toProto :: IZipVector m (RRq q Double, b) -> ProtoType (IZipVector m (RRq q Double, b))

fromProto :: MonadError String m0 => ProtoType (IZipVector m (RRq q Double, b)) -> m0 (IZipVector m (RRq q Double, b))

(Fact m, Reflects q Double) => Protoable (IZipVector m (RRq q Double))

Defined in Crypto.Lol.Types.IZipVector

Associated Types

type ProtoType (IZipVector m (RRq q Double)) :: Type

Methods

toProto :: IZipVector m (RRq q Double) -> ProtoType (IZipVector m (RRq q Double))

fromProto :: MonadError String m0 => ProtoType (IZipVector m (RRq q Double)) -> m0 (IZipVector m (RRq q Double))

(Fact m, UnCyc t Int64, UnCyc t (RRq q r), IFunctor t, IFElt t Int64, IFElt t (RRq q r)) => FunctorCyc (Cyc t m) Int64 (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (Int64 -> RRq q r) -> Cyc t m Int64 -> Cyc t m (RRq q r)

(Fact m, UnCyc t Double, UnCyc t (RRq q r), IFunctor t, IFElt t Double, IFElt t (RRq q r)) => FunctorCyc (Cyc t m) Double (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (Double -> RRq q r) -> Cyc t m Double -> Cyc t m (RRq q r)

(Fact m, UnCyc t (a, b), UnCyc t (RRq q r), IFunctor t, IFElt t (a, b), IFElt t (RRq q r)) => FunctorCyc (Cyc t m) (a, b) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> ((a, b) -> RRq q r) -> Cyc t m (a, b) -> Cyc t m (RRq q r)

(Fact m, TensorPowDec t (RRq q r), Foldable (t m)) => FoldableCyc (Cyc t m) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

foldrCyc :: Maybe Basis -> (RRq q r -> b -> b) -> b -> Cyc t m (RRq q r) -> b

(Fact m, UnCyc t (RRq q r), UnCyc t Int64, IFunctor t, IFElt t (RRq q r), IFElt t Int64) => FunctorCyc (Cyc t m) (RRq q r) Int64

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> Int64) -> Cyc t m (RRq q r) -> Cyc t m Int64

(Fact m, UnCyc t (RRq q r), UnCyc t Double, IFunctor t, IFElt t (RRq q r), IFElt t Double) => FunctorCyc (Cyc t m) (RRq q r) Double

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> Double) -> Cyc t m (RRq q r) -> Cyc t m Double

(Fact m, Functor (t m), UnCyc t (RRq q r)) => FunctorCyc (Cyc t m) (RRq q r) Integer

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> Integer) -> Cyc t m (RRq q r) -> Cyc t m Integer

(Fact m, UnCyc t (RRq q r), UnCyc t (a, b), IFunctor t, IFElt t (RRq q r), IFElt t (a, b)) => FunctorCyc (Cyc t m) (RRq q r) (a, b)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> (a, b)) -> Cyc t m (RRq q r) -> Cyc t m (a, b)

(Fact m, Rescale (RRq q r) (RRq p r), TensorPowDec t (RRq q r), TensorPowDec t (RRq p r)) => RescaleCyc (Cyc t m) (RRq q r) (RRq p r)

rescale from one modulus to another

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

rescaleCyc :: Basis -> Cyc t m (RRq q r) -> Cyc t m (RRq p r)

(Fact m, UnCyc t (ZqBasic q z), UnCyc t (RRq q r), IFunctor t, IFElt t (ZqBasic q z), IFElt t (RRq q r)) => FunctorCyc (Cyc t m) (ZqBasic q z) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (ZqBasic q z -> RRq q r) -> Cyc t m (ZqBasic q z) -> Cyc t m (RRq q r)

(Fact m, UnCyc t (RRq q r), UnCyc t (ZqBasic q z), IFunctor t, IFElt t (RRq q r), IFElt t (ZqBasic q z)) => FunctorCyc (Cyc t m) (RRq q r) (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> ZqBasic q z) -> Cyc t m (RRq q r) -> Cyc t m (ZqBasic q z)

(Fact m, UnCyc t (RRq q r), UnCyc t (RRq q r), IFunctor t, IFElt t (RRq q r), IFElt t (RRq q r)) => FunctorCyc (Cyc t m) (RRq q r) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> RRq q r) -> Cyc t m (RRq q r) -> Cyc t m (RRq q r)

Eq r => Eq (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

(==) :: RRq q r -> RRq q r -> Bool

(/=) :: RRq q r -> RRq q r -> Bool

Show r => Show (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

showsPrec :: Int -> RRq q r -> ShowS

show :: RRq q r -> String

showList :: [RRq q r] -> ShowS

Show (t m (RRq q r)) => Show (Cyc t m (RRq q r))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

showsPrec :: Int -> Cyc t m (RRq q r) -> ShowS

show :: Cyc t m (RRq q r) -> String

showList :: [Cyc t m (RRq q r)] -> ShowS

Random (RRq q Double)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

randomR :: RandomGen g => (RRq q Double, RRq q Double) -> g -> (RRq q Double, g)

random :: RandomGen g => g -> (RRq q Double, g)

randomRs :: RandomGen g => (RRq q Double, RRq q Double) -> g -> [RRq q Double]

randoms :: RandomGen g => g -> [RRq q Double]

randomRIO :: (RRq q Double, RRq q Double) -> IO (RRq q Double)

randomIO :: IO (RRq q Double)

Random (t m (RRq q r)) => Random (Cyc t m (RRq q r))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

randomR :: RandomGen g => (Cyc t m (RRq q r), Cyc t m (RRq q r)) -> g -> (Cyc t m (RRq q r), g)

random :: RandomGen g => g -> (Cyc t m (RRq q r), g)

randomRs :: RandomGen g => (Cyc t m (RRq q r), Cyc t m (RRq q r)) -> g -> [Cyc t m (RRq q r)]

randoms :: RandomGen g => g -> [Cyc t m (RRq q r)]

randomRIO :: (Cyc t m (RRq q r), Cyc t m (RRq q r)) -> IO (Cyc t m (RRq q r))

randomIO :: IO (Cyc t m (RRq q r))

NFData r => NFData (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

rnf :: RRq q r -> ()

(Fact m, forall (m' :: Factored). Fact m' => NFData (t m' (RRq q r))) => NFData (Cyc t m (RRq q r))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

rnf :: Cyc t m (RRq q r) -> ()

C r => C (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

isZero :: RRq q r -> Bool

ZeroTestable (t m (RRq q r)) => C (Cyc t m (RRq q r))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

isZero :: Cyc t m (RRq q r) -> Bool

RealField r => C (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

zero :: RRq q r

(+) :: RRq q r -> RRq q r -> RRq q r

(-) :: RRq q r -> RRq q r -> RRq q r

negate :: RRq q r -> RRq q r

(Additive (RRq q r), TensorPowDec t (RRq q r), IFunctor t, Fact m) => C (Cyc t m (RRq q r))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

zero :: Cyc t m (RRq q r)

(+) :: Cyc t m (RRq q r) -> Cyc t m (RRq q r) -> Cyc t m (RRq q r)

(-) :: Cyc t m (RRq q r) -> Cyc t m (RRq q r) -> Cyc t m (RRq q r)

negate :: Cyc t m (RRq q r) -> Cyc t m (RRq q r)

(Reflects q r, Field r, Reduce r (RRq q r)) => Lift' (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

lift :: RRq q r -> LiftOf (RRq q r)

(Fact m, CRTElt t Double, TensorPowDec t (RRq q Double), Protoable (CycRep t D m (RRq q Double))) => Protoable (Cyc t m (RRq q Double))

Defined in Crypto.Lol.Cyclotomic.Cyc

Associated Types

type ProtoType (Cyc t m (RRq q Double)) :: Type

Methods

toProto :: Cyc t m (RRq q Double) -> ProtoType (Cyc t m (RRq q Double))

fromProto :: MonadError String m0 => ProtoType (Cyc t m (RRq q Double)) -> m0 (Cyc t m (RRq q Double))

(Additive (RRq q r), Additive (RRq p r)) => Rescale (RRq q r) (RRq p r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

rescale :: RRq q r -> RRq p r

(Reflects q Double, FunctorCyc (Cyc t m) Double (RRq q Double)) => Reduce (Cyc t m Double) (Cyc t m (RRq q Double))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

reduce :: Cyc t m Double -> Cyc t m (RRq q Double)

(ToInteger z, RealField r, Reflects q z, Reflects q r) => Subgroup (ZqBasic q z) (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

fromSubgroup :: ZqBasic q z -> RRq q r

data Cyc t m (RRq q r)

additive group \( K/qR \), limited to powerful- or decoding-basis representation

Defined in Crypto.Lol.Cyclotomic.Cyc

data Cyc t m (RRq q r)

• = PowRRq !(CycRep t P m (RRq q r))
• | DecRRq !(CycRep t D m (RRq q r))

type ProtoType (IZipVector m (RRq q Double, b))

Defined in Crypto.Lol.Types.IZipVector

type ProtoType (IZipVector m (RRq q Double, b)) = KqProduct

type ProtoType (IZipVector m (RRq q Double))

Defined in Crypto.Lol.Types.IZipVector

type ProtoType (IZipVector m (RRq q Double)) = KqProduct

type LiftOf (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

type LiftOf (RRq q r) = r

type ProtoType (Cyc t m (RRq q Double))

Defined in Crypto.Lol.Cyclotomic.Cyc

type ProtoType (Cyc t m (RRq q Double))