Copyright	(c) Eric Crockett 2011-2017 Chris Peikert 2011-2017
License	GPL-3
Maintainer	ecrockett0@gmail.com
Stability	experimental
Portability	POSIX \( \def\Z{\mathbb{Z}} \) \( \def\R{\mathbb{R}} \)
Safe Haskell	None
Language	Haskell2010

Crypto.Lol.Types.Unsafe.RRq

Description

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.

Synopsis

newtype RRq q r = RRq r

Documentation

newtype RRq q r Source #

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) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.RRq Methods reduce :: r -> RRq q r Source #
TensorPowDec t (RRq q r) => UnCyc t (RRq q r) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods cycPow :: Fact m => CycRep t P m (RRq q r) -> Cyc t m (RRq q r) Source # cycDec :: Fact m => CycRep t D m (RRq q r) -> Cyc t m (RRq q r) Source # unCycPow :: Fact m => Cyc t m (RRq q r) -> CycRep t P m (RRq q r) Source # unCycDec :: Fact m => Cyc t m (RRq q r) -> CycRep t D m (RRq q r) Source #
TensorPowDec t (RRq q r) => ExtensionCyc (Cyc t) (RRq q r) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods embed :: Divides m m' => Cyc t m (RRq q r) -> Cyc t m' (RRq q r) Source # twace :: Divides m m' => Cyc t m' (RRq q r) -> Cyc t m (RRq q r) Source # powBasis :: Divides m m' => Tagged m [Cyc t m' (RRq q r)] Source # coeffsCyc :: Divides m m' => Basis -> Cyc t m' (RRq q r) -> [Cyc t m (RRq q r)] Source #
(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)) Source #
Instance details Defined in Crypto.Lol.Types.IZipVector Associated Types type ProtoType (IZipVector m (RRq q Double, b)) :: Type Source # Methods toProto :: IZipVector m (RRq q Double, b) -> ProtoType (IZipVector m (RRq q Double, b)) Source # fromProto :: MonadError String m0 => ProtoType (IZipVector m (RRq q Double, b)) -> m0 (IZipVector m (RRq q Double, b)) Source #
(Fact m, Reflects q Double) => Protoable (IZipVector m (RRq q Double)) Source #
Instance details Defined in Crypto.Lol.Types.IZipVector Associated Types type ProtoType (IZipVector m (RRq q Double)) :: Type Source # Methods toProto :: IZipVector m (RRq q Double) -> ProtoType (IZipVector m (RRq q Double)) Source # fromProto :: MonadError String m0 => ProtoType (IZipVector m (RRq q Double)) -> m0 (IZipVector m (RRq q Double)) Source #
(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) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Int64 -> RRq q r) -> Cyc t m Int64 -> Cyc t m (RRq q r) Source #
(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) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Double -> RRq q r) -> Cyc t m Double -> Cyc t m (RRq q r) Source #
(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) Source #
Instance details 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) Source #
(Fact m, TensorPowDec t (RRq q r), Foldable (t m)) => FoldableCyc (Cyc t m) (RRq q r) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods foldrCyc :: Maybe Basis -> (RRq q r -> b -> b) -> b -> Cyc t m (RRq q r) -> b Source #
(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 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (RRq q r -> Int64) -> Cyc t m (RRq q r) -> Cyc t m Int64 Source #
(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 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (RRq q r -> Double) -> Cyc t m (RRq q r) -> Cyc t m Double Source #
(Fact m, Functor (t m), UnCyc t (RRq q r)) => FunctorCyc (Cyc t m) (RRq q r) Integer Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (RRq q r -> Integer) -> Cyc t m (RRq q r) -> Cyc t m Integer Source #
(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) Source #
Instance details 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) Source #
(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) Source #	rescale from one modulus to another
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rescaleCyc :: Basis -> Cyc t m (RRq q r) -> Cyc t m (RRq p r) Source #
(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) Source #
Instance details 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) Source #
(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) Source #
Instance details 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) Source #
(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) Source #
Instance details 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) Source #
Eq r => Eq (RRq q r) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rnf :: Cyc t m (RRq q r) -> () #
C r => C (RRq q r) Source #
Instance details 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)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods isZero :: Cyc t m (RRq q r) -> Bool #
RealField r => C (RRq q r) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.RRq Methods lift :: RRq q r -> LiftOf (RRq q r) Source #
(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)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Associated Types type ProtoType (Cyc t m (RRq q Double)) :: Type Source # Methods toProto :: Cyc t m (RRq q Double) -> ProtoType (Cyc t m (RRq q Double)) Source # fromProto :: MonadError String m0 => ProtoType (Cyc t m (RRq q Double)) -> m0 (Cyc t m (RRq q Double)) Source #
(Additive (RRq q r), Additive (RRq p r)) => Rescale (RRq q r) (RRq p r) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.RRq Methods rescale :: RRq q r -> RRq p r Source #
(Reflects q Double, FunctorCyc (Cyc t m) Double (RRq q Double)) => Reduce (Cyc t m Double) (Cyc t m (RRq q Double)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods reduce :: Cyc t m Double -> Cyc t m (RRq q Double) Source #
(ToInteger z, RealField r, Reflects q z, Reflects q r) => Subgroup (ZqBasic q z) (RRq q r) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.RRq Methods fromSubgroup :: ZqBasic q z -> RRq q r Source #
data Cyc t m (RRq q r) Source #	additive group \( K/qR \), limited to powerful- or decoding-basis representation
Instance details 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)) Source #
Instance details Defined in Crypto.Lol.Types.IZipVector type ProtoType (IZipVector m (RRq q Double, b)) = KqProduct
type ProtoType (IZipVector m (RRq q Double)) Source #
Instance details Defined in Crypto.Lol.Types.IZipVector type ProtoType (IZipVector m (RRq q Double)) = KqProduct
type LiftOf (RRq q r) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.RRq type LiftOf (RRq q r) = r
type ProtoType (Cyc t m (RRq q Double)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc type ProtoType (Cyc t m (RRq q Double))