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 :: Mutable Vector s (Rounded r a) -> ST s (Vector (Rounded r a))

basicUnsafeThaw :: Vector (Rounded r a) -> ST s (Mutable Vector s (Rounded r a))

basicLength :: Vector (Rounded r a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Rounded r a) -> Vector (Rounded r a)

basicUnsafeIndexM :: Vector (Rounded r a) -> Int -> Box (Rounded r a)

basicUnsafeCopy :: Mutable Vector s (Rounded r a) -> Vector (Rounded r a) -> ST s ()

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 :: Int -> ST s (MVector s (Rounded r a))

basicInitialize :: MVector s (Rounded r a) -> ST s ()

basicUnsafeReplicate :: Int -> Rounded r a -> ST s (MVector s (Rounded r a))

basicUnsafeRead :: MVector s (Rounded r a) -> Int -> ST s (Rounded r a)

basicUnsafeWrite :: MVector s (Rounded r a) -> Int -> Rounded r a -> ST s ()

basicClear :: MVector s (Rounded r a) -> ST s ()

basicSet :: MVector s (Rounded r a) -> Rounded r a -> ST s ()

basicUnsafeCopy :: MVector s (Rounded r a) -> MVector s (Rounded r a) -> ST s ()

basicUnsafeMove :: MVector s (Rounded r a) -> MVector s (Rounded r a) -> ST s ()

basicUnsafeGrow :: MVector s (Rounded r a) -> Int -> ST s (MVector s (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 #

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 () #

Generic (Rounded r a) Source #

Instance details

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Associated Types

type Rep (Rounded r a)
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding type Rep (Rounded r a) = D1 ('MetaData "Rounded" "Numeric.Rounded.Hardware.Internal.Rounding" "rounded-hw-0.4.0.2-8N1qAeGOePG57F1jKA4niW" 'True) (C1 ('MetaCons "Rounded" 'PrefixI 'True) (S1 ('MetaSel ('Just "getRounded") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Rounded r a -> Rep (Rounded r a) x #

to :: Rep (Rounded r a) x -> 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 #

(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, 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 #

(Rounding r, 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 #

NFData a => NFData (Rounded r a) Source #

Instance details

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

rnf :: 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 #

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 #

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-0.4.0.2-8N1qAeGOePG57F1jKA4niW" '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] #

Generic RoundingMode Source #

Instance details

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Associated Types

type Rep RoundingMode

Instance details

Defined in Numeric.Rounded.Hardware.Internal.Rounding

type Rep RoundingMode = D1 ('MetaData "RoundingMode" "Numeric.Rounded.Hardware.Internal.Rounding" "rounded-hw-0.4.0.2-8N1qAeGOePG57F1jKA4niW" '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)))

Methods

from :: RoundingMode -> Rep RoundingMode x #

to :: Rep RoundingMode x -> 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 #

NFData RoundingMode Source #

Instance details

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

rnf :: 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 #

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-0.4.0.2-8N1qAeGOePG57F1jKA4niW" '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 'TowardInf Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods roundingT :: Tagged 'TowardInf RoundingMode
Rounding 'TowardNegInf Source #
Instance details Defined in Numeric.Rounded.Hardware.Internal.Rounding Methods roundingT :: Tagged 'TowardNegInf 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 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 #
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 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 #
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 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 #
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 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 #
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 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 #
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 #
(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 #