Numeric.Rounded.Hardware

Documentation

newtype Rounded (r :: RoundingMode) a

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

Unbox a => Vector Vector (Rounded r a)

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)

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)

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)

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)

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

(Rounding r, Num a, RoundedRing a) => Num (Rounded r a)

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)

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)

Defined in Numeric.Rounded.Hardware.Internal.Class

Methods

toRational :: Rounded r a -> Rational

(Rounding r, RealFrac a, RoundedFractional a) => RealFrac (Rounded r a)

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)

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)

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

rnf :: Rounded r a -> ()

Eq a => Eq (Rounded r a)

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)

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)

Defined in Numeric.Rounded.Hardware.Internal.Rounding

newtype MVector s (Rounded r a)

Defined in Numeric.Rounded.Hardware.Internal.Rounding

newtype MVector s (Rounded r a) = MV_Rounded (MVector s a)

type Rep (Rounded r a)

Defined in Numeric.Rounded.Hardware.Internal.Rounding

type Rep (Rounded r a) = D1 ('MetaData "Rounded" "Numeric.Rounded.Hardware.Internal.Rounding" "rounded-hw-0.4.0-3WAAI20vt2HBtLAkTAeX6n" 'True) (C1 ('MetaCons "Rounded" 'PrefixI 'True) (S1 ('MetaSel ('Just "getRounded") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Vector (Rounded r a)

Defined in Numeric.Rounded.Hardware.Internal.Rounding

newtype Vector (Rounded r a) = V_Rounded (Vector a)

data RoundingMode

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

Bounded RoundingMode

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

minBound :: RoundingMode

maxBound :: RoundingMode

Enum RoundingMode

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

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

Read RoundingMode

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

readsPrec :: Int -> ReadS RoundingMode

readList :: ReadS [RoundingMode]

readPrec :: ReadPrec RoundingMode

readListPrec :: ReadPrec [RoundingMode]

Show RoundingMode

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

showsPrec :: Int -> RoundingMode -> ShowS

show :: RoundingMode -> String

showList :: [RoundingMode] -> ShowS

NFData RoundingMode

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

rnf :: RoundingMode -> ()

Eq RoundingMode

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

(==) :: RoundingMode -> RoundingMode -> Bool

(/=) :: RoundingMode -> RoundingMode -> Bool

Ord RoundingMode

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

Defined in Numeric.Rounded.Hardware.Internal.Rounding

type Rep RoundingMode = D1 ('MetaData "RoundingMode" "Numeric.Rounded.Hardware.Internal.Rounding" "rounded-hw-0.4.0-3WAAI20vt2HBtLAkTAeX6n" '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)

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

See rounding.

Minimal complete definition

roundingT

Instances

Rounding 'ToNearest

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

roundingT :: Tagged 'ToNearest RoundingMode

Rounding 'TowardInf

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

roundingT :: Tagged 'TowardInf RoundingMode

Rounding 'TowardNegInf

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

roundingT :: Tagged 'TowardNegInf RoundingMode

Rounding 'TowardZero

Defined in Numeric.Rounded.Hardware.Internal.Rounding

Methods

roundingT :: Tagged 'TowardZero RoundingMode

class Ord a => RoundedRing a

Rounding-controlled version of Num.

Minimal complete definition

roundedAdd, roundedSub, roundedMul, roundedFusedMultiplyAdd, backendNameT

Instances

RoundedRing CDouble

Defined in Numeric.Rounded.Hardware.Backend.C

Methods

roundedAdd :: RoundingMode -> CDouble -> CDouble -> CDouble

roundedSub :: RoundingMode -> CDouble -> CDouble -> CDouble

roundedMul :: RoundingMode -> CDouble -> CDouble -> CDouble

roundedFusedMultiplyAdd :: RoundingMode -> CDouble -> CDouble -> CDouble -> CDouble

roundedFromInteger :: RoundingMode -> Integer -> CDouble

intervalAdd :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

intervalSub :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

intervalMul :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

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)

intervalFromInteger :: Integer -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

backendNameT :: Tagged CDouble String

RoundedRing CFloat

Defined in Numeric.Rounded.Hardware.Backend.C

Methods

roundedAdd :: RoundingMode -> CFloat -> CFloat -> CFloat

roundedSub :: RoundingMode -> CFloat -> CFloat -> CFloat

roundedMul :: RoundingMode -> CFloat -> CFloat -> CFloat

roundedFusedMultiplyAdd :: RoundingMode -> CFloat -> CFloat -> CFloat -> CFloat

roundedFromInteger :: RoundingMode -> Integer -> CFloat

intervalAdd :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat)

intervalSub :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat)

intervalMul :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat)

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)

intervalFromInteger :: Integer -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat)

backendNameT :: Tagged CFloat String

RoundedRing CDouble

Defined in Numeric.Rounded.Hardware.Backend.FastFFI

Methods

roundedAdd :: RoundingMode -> CDouble -> CDouble -> CDouble

roundedSub :: RoundingMode -> CDouble -> CDouble -> CDouble

roundedMul :: RoundingMode -> CDouble -> CDouble -> CDouble

roundedFusedMultiplyAdd :: RoundingMode -> CDouble -> CDouble -> CDouble -> CDouble

roundedFromInteger :: RoundingMode -> Integer -> CDouble

intervalAdd :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

intervalSub :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

intervalMul :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

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)

intervalFromInteger :: Integer -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

backendNameT :: Tagged CDouble String

RoundedRing Integer

Defined in Numeric.Rounded.Hardware.Internal.Class

Methods

roundedAdd :: RoundingMode -> Integer -> Integer -> Integer

roundedSub :: RoundingMode -> Integer -> Integer -> Integer

roundedMul :: RoundingMode -> Integer -> Integer -> Integer

roundedFusedMultiplyAdd :: RoundingMode -> Integer -> Integer -> Integer -> Integer

roundedFromInteger :: RoundingMode -> Integer -> Integer

intervalAdd :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer)

intervalSub :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer)

intervalMul :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer)

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)

intervalFromInteger :: Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer)

backendNameT :: Tagged Integer String

RoundedRing Double

Defined in Numeric.Rounded.Hardware.Backend.Default

Methods

roundedAdd :: RoundingMode -> Double -> Double -> Double

roundedSub :: RoundingMode -> Double -> Double -> Double

roundedMul :: RoundingMode -> Double -> Double -> Double

roundedFusedMultiplyAdd :: RoundingMode -> Double -> Double -> Double -> Double

roundedFromInteger :: RoundingMode -> Integer -> Double

intervalAdd :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double)

intervalSub :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double)

intervalMul :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double)

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)

intervalFromInteger :: Integer -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double)

backendNameT :: Tagged Double String

RoundedRing Float

Defined in Numeric.Rounded.Hardware.Backend.Default

Methods

roundedAdd :: RoundingMode -> Float -> Float -> Float

roundedSub :: RoundingMode -> Float -> Float -> Float

roundedMul :: RoundingMode -> Float -> Float -> Float

roundedFusedMultiplyAdd :: RoundingMode -> Float -> Float -> Float -> Float

roundedFromInteger :: RoundingMode -> Integer -> Float

intervalAdd :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float)

intervalSub :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float)

intervalMul :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float)

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)

intervalFromInteger :: Integer -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float)

backendNameT :: Tagged Float String

Integral a => RoundedRing (Ratio a)

Defined in Numeric.Rounded.Hardware.Internal.Class

Methods

roundedAdd :: RoundingMode -> Ratio a -> Ratio a -> Ratio a

roundedSub :: RoundingMode -> Ratio a -> Ratio a -> Ratio a

roundedMul :: RoundingMode -> Ratio a -> Ratio a -> Ratio a

roundedFusedMultiplyAdd :: RoundingMode -> Ratio a -> Ratio a -> Ratio a -> Ratio a

roundedFromInteger :: RoundingMode -> Integer -> Ratio a

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))

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))

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))

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))

intervalFromInteger :: Integer -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a))

backendNameT :: Tagged (Ratio a) String

(RealFloat a, Num a, RealFloatConstants a) => RoundedRing (ViaRational a)

Defined in Numeric.Rounded.Hardware.Backend.ViaRational

Methods

roundedAdd :: RoundingMode -> ViaRational a -> ViaRational a -> ViaRational a

roundedSub :: RoundingMode -> ViaRational a -> ViaRational a -> ViaRational a

roundedMul :: RoundingMode -> ViaRational a -> ViaRational a -> ViaRational a

roundedFusedMultiplyAdd :: RoundingMode -> ViaRational a -> ViaRational a -> ViaRational a -> ViaRational a

roundedFromInteger :: RoundingMode -> Integer -> ViaRational a

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))

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))

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))

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))

intervalFromInteger :: Integer -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a))

backendNameT :: Tagged (ViaRational a) String

class RoundedRing a => RoundedFractional a

Rounding-controlled version of Fractional.

Minimal complete definition

roundedDiv

Instances

RoundedFractional CDouble

Defined in Numeric.Rounded.Hardware.Backend.C

Methods

roundedDiv :: RoundingMode -> CDouble -> CDouble -> CDouble

roundedRecip :: RoundingMode -> CDouble -> CDouble

roundedFromRational :: RoundingMode -> Rational -> CDouble

roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> CDouble

intervalDiv :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

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)

intervalRecip :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

intervalFromRational :: Rational -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

RoundedFractional CFloat

Defined in Numeric.Rounded.Hardware.Backend.C

Methods

roundedDiv :: RoundingMode -> CFloat -> CFloat -> CFloat

roundedRecip :: RoundingMode -> CFloat -> CFloat

roundedFromRational :: RoundingMode -> Rational -> CFloat

roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> CFloat

intervalDiv :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat)

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)

intervalRecip :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat)

intervalFromRational :: Rational -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat)

RoundedFractional CDouble

Defined in Numeric.Rounded.Hardware.Backend.FastFFI

Methods

roundedDiv :: RoundingMode -> CDouble -> CDouble -> CDouble

roundedRecip :: RoundingMode -> CDouble -> CDouble

roundedFromRational :: RoundingMode -> Rational -> CDouble

roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> CDouble

intervalDiv :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

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)

intervalRecip :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

intervalFromRational :: Rational -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

RoundedFractional Integer

Defined in Numeric.Rounded.Hardware.Internal.Class

Methods

roundedDiv :: RoundingMode -> Integer -> Integer -> Integer

roundedRecip :: RoundingMode -> Integer -> Integer

roundedFromRational :: RoundingMode -> Rational -> Integer

roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> Integer

intervalDiv :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer)

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)

intervalRecip :: Rounded 'TowardNegInf Integer -> Rounded 'TowardInf Integer -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer)

intervalFromRational :: Rational -> (Rounded 'TowardNegInf Integer, Rounded 'TowardInf Integer)

RoundedFractional Double

Defined in Numeric.Rounded.Hardware.Backend.Default

Methods

roundedDiv :: RoundingMode -> Double -> Double -> Double

roundedRecip :: RoundingMode -> Double -> Double

roundedFromRational :: RoundingMode -> Rational -> Double

roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> Double

intervalDiv :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double)

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)

intervalRecip :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double)

intervalFromRational :: Rational -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double)

RoundedFractional Float

Defined in Numeric.Rounded.Hardware.Backend.Default

Methods

roundedDiv :: RoundingMode -> Float -> Float -> Float

roundedRecip :: RoundingMode -> Float -> Float

roundedFromRational :: RoundingMode -> Rational -> Float

roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> Float

intervalDiv :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float)

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)

intervalRecip :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float)

intervalFromRational :: Rational -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float)

Integral a => RoundedFractional (Ratio a)

Defined in Numeric.Rounded.Hardware.Internal.Class

Methods

roundedDiv :: RoundingMode -> Ratio a -> Ratio a -> Ratio a

roundedRecip :: RoundingMode -> Ratio a -> Ratio a

roundedFromRational :: RoundingMode -> Rational -> Ratio a

roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> Ratio a

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))

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))

intervalRecip :: Rounded 'TowardNegInf (Ratio a) -> Rounded 'TowardInf (Ratio a) -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a))

intervalFromRational :: Rational -> (Rounded 'TowardNegInf (Ratio a), Rounded 'TowardInf (Ratio a))

(RealFloat a, Num a, RealFloatConstants a) => RoundedFractional (ViaRational a)

Defined in Numeric.Rounded.Hardware.Backend.ViaRational

Methods

roundedDiv :: RoundingMode -> ViaRational a -> ViaRational a -> ViaRational a

roundedRecip :: RoundingMode -> ViaRational a -> ViaRational a

roundedFromRational :: RoundingMode -> Rational -> ViaRational a

roundedFromRealFloat :: RealFloat b => RoundingMode -> b -> ViaRational a

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))

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))

intervalRecip :: Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a))

intervalFromRational :: Rational -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a))

class RoundedRing a => RoundedSqrt a

Rounding-controlled version of sqrt.

Minimal complete definition

roundedSqrt

Instances

RoundedSqrt CDouble

Defined in Numeric.Rounded.Hardware.Backend.C

Methods

roundedSqrt :: RoundingMode -> CDouble -> CDouble

intervalSqrt :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

RoundedSqrt CFloat

Defined in Numeric.Rounded.Hardware.Backend.C

Methods

roundedSqrt :: RoundingMode -> CFloat -> CFloat

intervalSqrt :: Rounded 'TowardNegInf CFloat -> Rounded 'TowardInf CFloat -> (Rounded 'TowardNegInf CFloat, Rounded 'TowardInf CFloat)

RoundedSqrt CDouble

Defined in Numeric.Rounded.Hardware.Backend.FastFFI

Methods

roundedSqrt :: RoundingMode -> CDouble -> CDouble

intervalSqrt :: Rounded 'TowardNegInf CDouble -> Rounded 'TowardInf CDouble -> (Rounded 'TowardNegInf CDouble, Rounded 'TowardInf CDouble)

RoundedSqrt Double

Defined in Numeric.Rounded.Hardware.Backend.Default

Methods

roundedSqrt :: RoundingMode -> Double -> Double

intervalSqrt :: Rounded 'TowardNegInf Double -> Rounded 'TowardInf Double -> (Rounded 'TowardNegInf Double, Rounded 'TowardInf Double)

RoundedSqrt Float

Defined in Numeric.Rounded.Hardware.Backend.Default

Methods

roundedSqrt :: RoundingMode -> Float -> Float

intervalSqrt :: Rounded 'TowardNegInf Float -> Rounded 'TowardInf Float -> (Rounded 'TowardNegInf Float, Rounded 'TowardInf Float)

(RealFloat a, RealFloatConstants a) => RoundedSqrt (ViaRational a)

Defined in Numeric.Rounded.Hardware.Backend.ViaRational

Methods

roundedSqrt :: RoundingMode -> ViaRational a -> ViaRational a

intervalSqrt :: Rounded 'TowardNegInf (ViaRational a) -> Rounded 'TowardInf (ViaRational a) -> (Rounded 'TowardNegInf (ViaRational a), Rounded 'TowardInf (ViaRational a))