Safe Haskell	None
Language	Haskell2010

Numeric.Rounded.Hardware

Synopsis

newtype Rounded (r :: RoundingMode) a = Rounded {
- getRounded :: a
}
data RoundingMode
- = ToNearest
- | TowardNegInf
- | TowardInf
- | TowardZero
class Rounding (r :: RoundingMode)
class Ord a => RoundedRing a
class RoundedRing a => RoundedFractional a
class RoundedRing a => RoundedSqrt a

Documentation

newtype Rounded (r :: RoundingMode) a Source #

A type tagged with a rounding direction.

The rounding direction is effective for a single operation. You won't get the correctly-rounded result for a compound expression like (a - b * c) :: Rounded 'TowardInf Double.

In particular, a negative literal like -0.1 :: Rounded r Double doesn't yield the correctly-rounded value for -0.1. To get the correct value, call fromRational explicitly (i.e. fromRational (-0.1) :: Rounded r Double) or use NegativeLiterals extension.

Constructors

Rounded
Fields getRounded :: a

Instances

Instances details

Unbox a => Vector Vector (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Rounded r a) -> m (Vector (Rounded r a)) # basicUnsafeThaw :: PrimMonad m => Vector (Rounded r a) -> m (Mutable Vector (PrimState m) (Rounded r a)) # basicLength :: Vector (Rounded r a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Rounded r a) -> Vector (Rounded r a) # basicUnsafeIndexM :: Monad m => Vector (Rounded r a) -> Int -> m (Rounded r a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Rounded r a) -> Vector (Rounded r a) -> m () # elemseq :: Vector (Rounded r a) -> Rounded r a -> b -> b #
Unbox a => MVector MVector (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods basicLength :: MVector s (Rounded r a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Rounded r a) -> MVector s (Rounded r a) # basicOverlaps :: MVector s (Rounded r a) -> MVector s (Rounded r a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Rounded r a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Rounded r a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Rounded r a -> m (MVector (PrimState m) (Rounded r a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Rounded r a) -> Int -> m (Rounded r a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Rounded r a) -> Int -> Rounded r a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Rounded r a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Rounded r a) -> Rounded r a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Rounded r a) -> MVector (PrimState m) (Rounded r a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Rounded r a) -> MVector (PrimState m) (Rounded r a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Rounded r a) -> Int -> m (MVector (PrimState m) (Rounded r a)) #
Functor (Rounded r) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods fmap :: (a -> b) -> Rounded r a -> Rounded r b # (<$) :: a -> Rounded r b -> Rounded r a #
Eq a => Eq (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods (==) :: Rounded r a -> Rounded r a -> Bool # (/=) :: Rounded r a -> Rounded r a -> Bool #
(Rounding r, Num a, RoundedFractional a) => Fractional (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Class Methods (/) :: Rounded r a -> Rounded r a -> Rounded r a # recip :: Rounded r a -> Rounded r a # fromRational :: Rational -> Rounded r a #
(Rounding r, Num a, RoundedRing a) => Num (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Class Methods (+) :: Rounded r a -> Rounded r a -> Rounded r a # (-) :: Rounded r a -> Rounded r a -> Rounded r a # (*) :: Rounded r a -> Rounded r a -> Rounded r a # negate :: Rounded r a -> Rounded r a # abs :: Rounded r a -> Rounded r a # signum :: Rounded r a -> Rounded r a # fromInteger :: Integer -> Rounded r a #
Ord a => Ord (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods compare :: Rounded r a -> Rounded r a -> Ordering # (<) :: Rounded r a -> Rounded r a -> Bool # (<=) :: Rounded r a -> Rounded r a -> Bool # (>) :: Rounded r a -> Rounded r a -> Bool # (>=) :: Rounded r a -> Rounded r a -> Bool # max :: Rounded r a -> Rounded r a -> Rounded r a # min :: Rounded r a -> Rounded r a -> Rounded r a #
(Rounding r, Real a, RoundedFractional a) => Real (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Class Methods toRational :: Rounded r a -> Rational #
(Rounding r, RealFrac a, RoundedFractional a) => RealFrac (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Class Methods properFraction :: Integral b => Rounded r a -> (b, Rounded r a) # truncate :: Integral b => Rounded r a -> b # round :: Integral b => Rounded r a -> b # ceiling :: Integral b => Rounded r a -> b # floor :: Integral b => Rounded r a -> b #
Show a => Show (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods showsPrec :: Int -> Rounded r a -> ShowS # show :: Rounded r a -> String # showList :: [Rounded r a] -> ShowS #
Generic (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Associated Types type Rep (Rounded r a) :: Type -> Type # Methods from :: Rounded r a -> Rep (Rounded r a) x # to :: Rep (Rounded r a) x -> Rounded r a #
Storable a => Storable (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods sizeOf :: Rounded r a -> Int # alignment :: Rounded r a -> Int # peekElemOff :: Ptr (Rounded r a) -> Int -> IO (Rounded r a) # pokeElemOff :: Ptr (Rounded r a) -> Int -> Rounded r a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Rounded r a) # pokeByteOff :: Ptr b -> Int -> Rounded r a -> IO () # peek :: Ptr (Rounded r a) -> IO (Rounded r a) # poke :: Ptr (Rounded r a) -> Rounded r a -> IO () #
NFData a => NFData (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods rnf :: Rounded r a -> () #
Unbox a => Unbox (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding
newtype MVector s (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding newtype MVector s (Rounded r a) = MV_Rounded (MVector s a)
type Rep (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding type Rep (Rounded r a) = D1 ('MetaData "Rounded" "Numeric.Rounded.Hardware.Internal.Rounding" "rounded-hw-0.2.0-G2mMTdTBXOG87Ub6xfZ4rG" 'True) (C1 ('MetaCons "Rounded" 'PrefixI 'True) (S1 ('MetaSel ('Just "getRounded") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
newtype Vector (Rounded r a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding newtype Vector (Rounded r a) = V_Rounded (Vector a)

data RoundingMode Source #

The type for IEEE754 rounding-direction attributes.

Constructors

ToNearest	Round to the nearest value (IEEE754 roundTiesToEven)
TowardNegInf	Round downward (IEEE754 roundTowardNegative)
TowardInf	Round upward (IEEE754 roundTowardPositive)
TowardZero	Round toward zero (IEEE754 roundTowardZero)

Instances

Instances details

Bounded RoundingMode Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods minBound :: RoundingMode # maxBound :: RoundingMode #
Enum RoundingMode Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods succ :: RoundingMode -> RoundingMode # pred :: RoundingMode -> RoundingMode # toEnum :: Int -> RoundingMode # fromEnum :: RoundingMode -> Int # enumFrom :: RoundingMode -> [RoundingMode] # enumFromThen :: RoundingMode -> RoundingMode -> [RoundingMode] # enumFromTo :: RoundingMode -> RoundingMode -> [RoundingMode] # enumFromThenTo :: RoundingMode -> RoundingMode -> RoundingMode -> [RoundingMode] #
Eq RoundingMode Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods (==) :: RoundingMode -> RoundingMode -> Bool # (/=) :: RoundingMode -> RoundingMode -> Bool #
Ord RoundingMode Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods compare :: RoundingMode -> RoundingMode -> Ordering # (<) :: RoundingMode -> RoundingMode -> Bool # (<=) :: RoundingMode -> RoundingMode -> Bool # (>) :: RoundingMode -> RoundingMode -> Bool # (>=) :: RoundingMode -> RoundingMode -> Bool # max :: RoundingMode -> RoundingMode -> RoundingMode # min :: RoundingMode -> RoundingMode -> RoundingMode #
Read RoundingMode Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods readsPrec :: Int -> ReadS RoundingMode # readList :: ReadS [RoundingMode] # readPrec :: ReadPrec RoundingMode # readListPrec :: ReadPrec [RoundingMode] #
Show RoundingMode Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods showsPrec :: Int -> RoundingMode -> ShowS # show :: RoundingMode -> String # showList :: [RoundingMode] -> ShowS #
Generic RoundingMode Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Associated Types type Rep RoundingMode :: Type -> Type # Methods from :: RoundingMode -> Rep RoundingMode x # to :: Rep RoundingMode x -> RoundingMode #
NFData RoundingMode Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods rnf :: RoundingMode -> () #
type Rep RoundingMode Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding type Rep RoundingMode = D1 ('MetaData "RoundingMode" "Numeric.Rounded.Hardware.Internal.Rounding" "rounded-hw-0.2.0-G2mMTdTBXOG87Ub6xfZ4rG" 'False) ((C1 ('MetaCons "ToNearest" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "TowardNegInf" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "TowardInf" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "TowardZero" 'PrefixI 'False) (U1 :: Type -> Type)))

class Rounding (r :: RoundingMode) Source #

This class allows you to recover the runtime value from a type-level rounding mode.

See rounding.

Minimal complete definition

roundingT

Instances

Instances details

Rounding 'ToNearest Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods roundingT :: Tagged 'ToNearest RoundingMode
Rounding 'TowardNegInf Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods roundingT :: Tagged 'TowardNegInf RoundingMode
Rounding 'TowardInf Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods roundingT :: Tagged 'TowardInf RoundingMode
Rounding 'TowardZero Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods roundingT :: Tagged 'TowardZero RoundingMode

class Ord a => RoundedRing a Source #

Rounding-controlled version of Num.

Minimal complete definition

roundedAdd, roundedSub, roundedMul, roundedFusedMultiplyAdd, backendNameT

Instances

Instances details

RoundedRing Double Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.Default Methods roundedAdd :: RoundingMode -> Double -> Double -> Double Source # roundedSub :: RoundingMode -> Double -> Double -> Double Source # roundedMul :: RoundingMode -> Double -> Double -> Double Source # roundedFusedMultiplyAdd :: RoundingMode -> Double -> Double -> Double -> Double Source # roundedFromInteger :: RoundingMode -> Integer -> Double Source # intervalAdd :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double) Source # intervalSub :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double) Source # intervalMul :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double) Source # intervalMulAdd :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double) Source # intervalFromInteger :: Integer -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double) Source # backendNameT :: Tagged Double String Source #
RoundedRing Float Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.Default Methods roundedAdd :: RoundingMode -> Float -> Float -> Float Source # roundedSub :: RoundingMode -> Float -> Float -> Float Source # roundedMul :: RoundingMode -> Float -> Float -> Float Source # roundedFusedMultiplyAdd :: RoundingMode -> Float -> Float -> Float -> Float Source # roundedFromInteger :: RoundingMode -> Integer -> Float Source # intervalAdd :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float) Source # intervalSub :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float) Source # intervalMul :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float) Source # intervalMulAdd :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float) Source # intervalFromInteger :: Integer -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float) Source # backendNameT :: Tagged Float String Source #
RoundedRing Integer Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Class Methods roundedAdd :: RoundingMode -> Integer -> Integer -> Integer Source # roundedSub :: RoundingMode -> Integer -> Integer -> Integer Source # roundedMul :: RoundingMode -> Integer -> Integer -> Integer Source # roundedFusedMultiplyAdd :: RoundingMode -> Integer -> Integer -> Integer -> Integer Source # roundedFromInteger :: RoundingMode -> Integer -> Integer Source # intervalAdd :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer) Source # intervalSub :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer) Source # intervalMul :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer) Source # intervalMulAdd :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer) Source # intervalFromInteger :: Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer) Source # backendNameT :: Tagged Integer String Source #
RoundedRing LongDouble Source #	Only available on x86/x86_64 systems. Note that `LongDouble` may not work correctly on Win64.
Instance details Defined in Numeric.Rounded.Hardware.Backend.X87LongDouble Methods roundedAdd :: RoundingMode -> LongDouble -> LongDouble -> LongDouble Source # roundedSub :: RoundingMode -> LongDouble -> LongDouble -> LongDouble Source # roundedMul :: RoundingMode -> LongDouble -> LongDouble -> LongDouble Source # roundedFusedMultiplyAdd :: RoundingMode -> LongDouble -> LongDouble -> LongDouble -> LongDouble Source # roundedFromInteger :: RoundingMode -> Integer -> LongDouble Source # intervalAdd :: Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> (Rounded 'TowardNegInf LongDouble, Rounded 'TowardInf LongDouble) Source # intervalSub :: Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> (Rounded 'TowardNegInf LongDouble, Rounded 'TowardInf LongDouble) Source # intervalMul :: Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> (Rounded 'TowardNegInf LongDouble, Rounded 'TowardInf LongDouble) Source # intervalMulAdd :: Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> (Rounded 'TowardNegInf LongDouble, Rounded 'TowardInf LongDouble) Source # intervalFromInteger :: Integer -> (Rounded 'TowardNegInf LongDouble, Rounded 'TowardInf LongDouble) Source # backendNameT :: Tagged LongDouble String Source #
RoundedRing CDouble Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.C Methods roundedAdd :: RoundingMode -> CDouble -> CDouble -> CDouble Source # roundedSub :: RoundingMode -> CDouble -> CDouble -> CDouble Source # roundedMul :: RoundingMode -> CDouble -> CDouble -> CDouble Source # roundedFusedMultiplyAdd :: RoundingMode -> CDouble -> CDouble -> CDouble -> CDouble Source # roundedFromInteger :: RoundingMode -> Integer -> CDouble Source # intervalAdd :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalSub :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalMul :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalMulAdd :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalFromInteger :: Integer -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # backendNameT :: Tagged CDouble String Source #
RoundedRing CFloat Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.C Methods roundedAdd :: RoundingMode -> CFloat -> CFloat -> CFloat Source # roundedSub :: RoundingMode -> CFloat -> CFloat -> CFloat Source # roundedMul :: RoundingMode -> CFloat -> CFloat -> CFloat Source # roundedFusedMultiplyAdd :: RoundingMode -> CFloat -> CFloat -> CFloat -> CFloat Source # roundedFromInteger :: RoundingMode -> Integer -> CFloat Source # intervalAdd :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat) Source # intervalSub :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat) Source # intervalMul :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat) Source # intervalMulAdd :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat) Source # intervalFromInteger :: Integer -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat) Source # backendNameT :: Tagged CFloat String Source #
RoundedRing CDouble Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.FastFFI Methods roundedAdd :: RoundingMode -> CDouble -> CDouble -> CDouble Source # roundedSub :: RoundingMode -> CDouble -> CDouble -> CDouble Source # roundedMul :: RoundingMode -> CDouble -> CDouble -> CDouble Source # roundedFusedMultiplyAdd :: RoundingMode -> CDouble -> CDouble -> CDouble -> CDouble Source # roundedFromInteger :: RoundingMode -> Integer -> CDouble Source # intervalAdd :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalSub :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalMul :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalMulAdd :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalFromInteger :: Integer -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # backendNameT :: Tagged CDouble String Source #
Integral a => RoundedRing (Ratio a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Class Methods roundedAdd :: RoundingMode -> Ratio a -> Ratio a -> Ratio a Source # roundedSub :: RoundingMode -> Ratio a -> Ratio a -> Ratio a Source # roundedMul :: RoundingMode -> Ratio a -> Ratio a -> Ratio a Source # roundedFusedMultiplyAdd :: RoundingMode -> Ratio a -> Ratio a -> Ratio a -> Ratio a Source # roundedFromInteger :: RoundingMode -> Integer -> Ratio a Source # intervalAdd :: Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a)) Source # intervalSub :: Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a)) Source # intervalMul :: Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a)) Source # intervalMulAdd :: Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a)) Source # intervalFromInteger :: Integer -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a)) Source # backendNameT :: Tagged (Ratio a) String Source #
(RealFloat a, Num a, RealFloatConstants a) => RoundedRing (ViaRational a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.ViaRational Methods roundedAdd :: RoundingMode -> ViaRational a -> ViaRational a -> ViaRational a Source # roundedSub :: RoundingMode -> ViaRational a -> ViaRational a -> ViaRational a Source # roundedMul :: RoundingMode -> ViaRational a -> ViaRational a -> ViaRational a Source # roundedFusedMultiplyAdd :: RoundingMode -> ViaRational a -> ViaRational a -> ViaRational a -> ViaRational a Source # roundedFromInteger :: RoundingMode -> Integer -> ViaRational a Source # intervalAdd :: Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a)) Source # intervalSub :: Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a)) Source # intervalMul :: Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a)) Source # intervalMulAdd :: Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a)) Source # intervalFromInteger :: Integer -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a)) Source # backendNameT :: Tagged (ViaRational a) String Source #

class RoundedRing a => RoundedFractional a Source #

Rounding-controlled version of Fractional.

Minimal complete definition

roundedDiv

Instances

Instances details

RoundedFractional Double Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.Default Methods roundedDiv :: RoundingMode -> Double -> Double -> Double Source # roundedRecip :: RoundingMode -> Double -> Double Source # roundedFromRational :: RoundingMode -> Rational -> Double Source # roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> Double Source # intervalDiv :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double) Source # intervalDivAdd :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double) Source # intervalRecip :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double) Source # intervalFromRational :: Rational -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double) Source #
RoundedFractional Float Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.Default Methods roundedDiv :: RoundingMode -> Float -> Float -> Float Source # roundedRecip :: RoundingMode -> Float -> Float Source # roundedFromRational :: RoundingMode -> Rational -> Float Source # roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> Float Source # intervalDiv :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float) Source # intervalDivAdd :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float) Source # intervalRecip :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float) Source # intervalFromRational :: Rational -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float) Source #
RoundedFractional Integer Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Class Methods roundedDiv :: RoundingMode -> Integer -> Integer -> Integer Source # roundedRecip :: RoundingMode -> Integer -> Integer Source # roundedFromRational :: RoundingMode -> Rational -> Integer Source # roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> Integer Source # intervalDiv :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer) Source # intervalDivAdd :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer) Source # intervalRecip :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer) Source # intervalFromRational :: Rational -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer) Source #
RoundedFractional LongDouble Source #	Only available on x86/x86_64 systems. Note that `LongDouble` may not work correctly on Win64.
Instance details Defined in Numeric.Rounded.Hardware.Backend.X87LongDouble Methods roundedDiv :: RoundingMode -> LongDouble -> LongDouble -> LongDouble Source # roundedRecip :: RoundingMode -> LongDouble -> LongDouble Source # roundedFromRational :: RoundingMode -> Rational -> LongDouble Source # roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> LongDouble Source # intervalDiv :: Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> (Rounded 'TowardNegInf LongDouble, Rounded 'TowardInf LongDouble) Source # intervalDivAdd :: Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> (Rounded 'TowardNegInf LongDouble, Rounded 'TowardInf LongDouble) Source # intervalRecip :: Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> (Rounded 'TowardNegInf LongDouble, Rounded 'TowardInf LongDouble) Source # intervalFromRational :: Rational -> (Rounded 'TowardNegInf LongDouble, Rounded 'TowardInf LongDouble) Source #
RoundedFractional CDouble Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.C Methods roundedDiv :: RoundingMode -> CDouble -> CDouble -> CDouble Source # roundedRecip :: RoundingMode -> CDouble -> CDouble Source # roundedFromRational :: RoundingMode -> Rational -> CDouble Source # roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> CDouble Source # intervalDiv :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalDivAdd :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalRecip :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalFromRational :: Rational -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source #
RoundedFractional CFloat Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.C Methods roundedDiv :: RoundingMode -> CFloat -> CFloat -> CFloat Source # roundedRecip :: RoundingMode -> CFloat -> CFloat Source # roundedFromRational :: RoundingMode -> Rational -> CFloat Source # roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> CFloat Source # intervalDiv :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat) Source # intervalDivAdd :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat) Source # intervalRecip :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat) Source # intervalFromRational :: Rational -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat) Source #
RoundedFractional CDouble Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.FastFFI Methods roundedDiv :: RoundingMode -> CDouble -> CDouble -> CDouble Source # roundedRecip :: RoundingMode -> CDouble -> CDouble Source # roundedFromRational :: RoundingMode -> Rational -> CDouble Source # roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> CDouble Source # intervalDiv :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalDivAdd :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalRecip :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source # intervalFromRational :: Rational -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source #
Integral a => RoundedFractional (Ratio a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Class Methods roundedDiv :: RoundingMode -> Ratio a -> Ratio a -> Ratio a Source # roundedRecip :: RoundingMode -> Ratio a -> Ratio a Source # roundedFromRational :: RoundingMode -> Rational -> Ratio a Source # roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> Ratio a Source # intervalDiv :: Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a)) Source # intervalDivAdd :: Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a)) Source # intervalRecip :: Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a)) Source # intervalFromRational :: Rational -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a)) Source #
(RealFloat a, Num a, RealFloatConstants a) => RoundedFractional (ViaRational a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.ViaRational Methods roundedDiv :: RoundingMode -> ViaRational a -> ViaRational a -> ViaRational a Source # roundedRecip :: RoundingMode -> ViaRational a -> ViaRational a Source # roundedFromRational :: RoundingMode -> Rational -> ViaRational a Source # roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> ViaRational a Source # intervalDiv :: Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a)) Source # intervalDivAdd :: Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a)) Source # intervalRecip :: Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a)) Source # intervalFromRational :: Rational -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a)) Source #

class RoundedRing a => RoundedSqrt a Source #

Rounding-controlled version of sqrt.

Minimal complete definition

roundedSqrt

Instances

Instances details

RoundedSqrt Double Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.Default Methods roundedSqrt :: RoundingMode -> Double -> Double Source # intervalSqrt :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double) Source #
RoundedSqrt Float Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.Default Methods roundedSqrt :: RoundingMode -> Float -> Float Source # intervalSqrt :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float) Source #
RoundedSqrt LongDouble Source #	Only available on x86/x86_64 systems. Note that `LongDouble` may not work correctly on Win64.
Instance details Defined in Numeric.Rounded.Hardware.Backend.X87LongDouble Methods roundedSqrt :: RoundingMode -> LongDouble -> LongDouble Source # intervalSqrt :: Rounded 'TowardNegInf LongDouble -> Rounded 'TowardInf LongDouble -> (Rounded 'TowardNegInf LongDouble, Rounded 'TowardInf LongDouble) Source #
RoundedSqrt CDouble Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.C Methods roundedSqrt :: RoundingMode -> CDouble -> CDouble Source # intervalSqrt :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source #
RoundedSqrt CFloat Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.C Methods roundedSqrt :: RoundingMode -> CFloat -> CFloat Source # intervalSqrt :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat) Source #
RoundedSqrt CDouble Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.FastFFI Methods roundedSqrt :: RoundingMode -> CDouble -> CDouble Source # intervalSqrt :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble) Source #
(RealFloat a, RealFloatConstants a) => RoundedSqrt (ViaRational a) Source #
Instance details Defined in Numeric.Rounded.Hardware.Backend.ViaRational Methods roundedSqrt :: RoundingMode -> ViaRational a -> ViaRational a Source # intervalSqrt :: Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a)) Source #