-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Directed rounding for built-in floating types -- -- Please see the README on GitHub at -- https://github.com/minoki/haskell-floating-point/tree/master/rounded-hw#readme @package rounded-hw @version 0.2.0 module Numeric.Rounded.Hardware.Backend.ViaRational newtype ViaRational a ViaRational :: a -> ViaRational a instance Foreign.Storable.Storable a => Foreign.Storable.Storable (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance GHC.Num.Num a => GHC.Num.Num (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance GHC.Generics.Generic (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance GHC.Show.Show a => GHC.Show.Show (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance GHC.Classes.Ord a => GHC.Classes.Ord (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance GHC.Classes.Eq a => GHC.Classes.Eq (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance Control.DeepSeq.NFData a => Control.DeepSeq.NFData (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance (GHC.Float.RealFloat a, GHC.Num.Num a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a) => Numeric.Rounded.Hardware.Internal.Class.RoundedRing (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance (GHC.Float.RealFloat a, GHC.Num.Num a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a) => Numeric.Rounded.Hardware.Internal.Class.RoundedFractional (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance (GHC.Float.RealFloat a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a) => Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance (GHC.Float.RealFloat a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a, Foreign.Storable.Storable a) => Numeric.Rounded.Hardware.Internal.Class.RoundedRing_Vector Data.Vector.Storable.Vector (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance (GHC.Float.RealFloat a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a, Foreign.Storable.Storable a) => Numeric.Rounded.Hardware.Internal.Class.RoundedFractional_Vector Data.Vector.Storable.Vector (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance (GHC.Float.RealFloat a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a, Foreign.Storable.Storable a) => Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt_Vector Data.Vector.Storable.Vector (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance (GHC.Float.RealFloat a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a, Data.Vector.Unboxed.Base.Unbox a) => Numeric.Rounded.Hardware.Internal.Class.RoundedRing_Vector Data.Vector.Unboxed.Base.Vector (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance (GHC.Float.RealFloat a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a, Data.Vector.Unboxed.Base.Unbox a) => Numeric.Rounded.Hardware.Internal.Class.RoundedFractional_Vector Data.Vector.Unboxed.Base.Vector (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance (GHC.Float.RealFloat a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a, Data.Vector.Unboxed.Base.Unbox a) => Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt_Vector Data.Vector.Unboxed.Base.Vector (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance Data.Vector.Unboxed.Base.Unbox a => Data.Vector.Generic.Mutable.Base.MVector Data.Vector.Unboxed.Base.MVector (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance Data.Vector.Unboxed.Base.Unbox a => Data.Vector.Generic.Base.Vector Data.Vector.Unboxed.Base.Vector (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) instance Data.Vector.Unboxed.Base.Unbox a => Data.Vector.Unboxed.Base.Unbox (Numeric.Rounded.Hardware.Backend.ViaRational.ViaRational a) -- | The types in this module implements rounding-mode-controlled -- operations in C. -- -- There are several ways to control rounding mode in C, and an -- appropriate technology will be selected at compile time. This library -- implements the following options: -- -- -- -- You should not need to import this module directly. -- -- This module is not available if the package flag pure-hs is -- set. module Numeric.Rounded.Hardware.Backend.C -- | A wrapper providing particular instances for RoundedRing, -- RoundedFractional and RoundedSqrt. -- -- This type is different from CFloat from -- Foreign.C.Types. newtype CFloat CFloat :: Float -> CFloat -- | A wrapper providing particular instances for RoundedRing, -- RoundedFractional and RoundedSqrt. -- -- This type is different from CDouble from -- Foreign.C.Types. newtype CDouble CDouble :: Double -> CDouble data family MVector s a data family Vector a roundedFloatFromInt64 :: RoundingMode -> Int64 -> Float roundedFloatFromWord64 :: RoundingMode -> Word64 -> Float roundedDoubleFromInt64 :: RoundingMode -> Int64 -> Double roundedDoubleFromWord64 :: RoundingMode -> Word64 -> Double instance Foreign.Storable.Storable Numeric.Rounded.Hardware.Backend.C.CFloat instance GHC.Num.Num Numeric.Rounded.Hardware.Backend.C.CFloat instance GHC.Generics.Generic Numeric.Rounded.Hardware.Backend.C.CFloat instance GHC.Show.Show Numeric.Rounded.Hardware.Backend.C.CFloat instance GHC.Classes.Ord Numeric.Rounded.Hardware.Backend.C.CFloat instance GHC.Classes.Eq Numeric.Rounded.Hardware.Backend.C.CFloat instance Foreign.Storable.Storable Numeric.Rounded.Hardware.Backend.C.CDouble instance GHC.Num.Num Numeric.Rounded.Hardware.Backend.C.CDouble instance GHC.Generics.Generic Numeric.Rounded.Hardware.Backend.C.CDouble instance GHC.Show.Show Numeric.Rounded.Hardware.Backend.C.CDouble instance GHC.Classes.Ord Numeric.Rounded.Hardware.Backend.C.CDouble instance GHC.Classes.Eq Numeric.Rounded.Hardware.Backend.C.CDouble instance Control.DeepSeq.NFData Numeric.Rounded.Hardware.Backend.C.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedRing Numeric.Rounded.Hardware.Backend.C.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedFractional Numeric.Rounded.Hardware.Backend.C.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt Numeric.Rounded.Hardware.Backend.C.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedRing_Vector Data.Vector.Storable.Vector Numeric.Rounded.Hardware.Backend.C.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedFractional_Vector Data.Vector.Storable.Vector Numeric.Rounded.Hardware.Backend.C.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt_Vector Data.Vector.Storable.Vector Numeric.Rounded.Hardware.Backend.C.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedRing_Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.C.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedFractional_Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.C.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt_Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.C.CDouble instance Data.Vector.Generic.Mutable.Base.MVector Data.Vector.Unboxed.Base.MVector Numeric.Rounded.Hardware.Backend.C.CDouble instance Data.Vector.Generic.Base.Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.C.CDouble instance Data.Vector.Unboxed.Base.Unbox Numeric.Rounded.Hardware.Backend.C.CDouble instance Control.DeepSeq.NFData Numeric.Rounded.Hardware.Backend.C.CFloat instance Numeric.Rounded.Hardware.Internal.Class.RoundedRing Numeric.Rounded.Hardware.Backend.C.CFloat instance Numeric.Rounded.Hardware.Internal.Class.RoundedFractional Numeric.Rounded.Hardware.Backend.C.CFloat instance Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt Numeric.Rounded.Hardware.Backend.C.CFloat instance Numeric.Rounded.Hardware.Internal.Class.RoundedRing_Vector Data.Vector.Storable.Vector Numeric.Rounded.Hardware.Backend.C.CFloat instance Numeric.Rounded.Hardware.Internal.Class.RoundedFractional_Vector Data.Vector.Storable.Vector Numeric.Rounded.Hardware.Backend.C.CFloat instance Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt_Vector Data.Vector.Storable.Vector Numeric.Rounded.Hardware.Backend.C.CFloat instance Numeric.Rounded.Hardware.Internal.Class.RoundedRing_Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.C.CFloat instance Numeric.Rounded.Hardware.Internal.Class.RoundedFractional_Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.C.CFloat instance Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt_Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.C.CFloat instance Data.Vector.Generic.Mutable.Base.MVector Data.Vector.Unboxed.Base.MVector Numeric.Rounded.Hardware.Backend.C.CFloat instance Data.Vector.Generic.Base.Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.C.CFloat instance Data.Vector.Unboxed.Base.Unbox Numeric.Rounded.Hardware.Backend.C.CFloat -- | The types in this module implements interval addition and subtraction -- in assembly. -- -- Currently, the only platform supported is x86_64. -- -- One of the following technology will be used to control rounding mode: -- -- -- -- You should not need to import this module directly. -- -- This module may not be available depending on the platform or package -- flags. module Numeric.Rounded.Hardware.Backend.FastFFI newtype CDouble CDouble :: Double -> CDouble fastIntervalAdd :: Double -> Double -> Double -> Double -> (Double, Double) fastIntervalSub :: Double -> Double -> Double -> Double -> (Double, Double) fastIntervalRecip :: Double -> Double -> (Double, Double) data family MVector s a data family Vector a instance Foreign.Storable.Storable Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance GHC.Num.Num Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance GHC.Generics.Generic Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance GHC.Show.Show Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance GHC.Classes.Ord Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance GHC.Classes.Eq Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedRing_Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedFractional_Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt_Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Control.DeepSeq.NFData Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedRing Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedFractional Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedRing_Vector Data.Vector.Storable.Vector Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedFractional_Vector Data.Vector.Storable.Vector Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt_Vector Data.Vector.Storable.Vector Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Data.Vector.Generic.Mutable.Base.MVector Data.Vector.Unboxed.Base.MVector Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Data.Vector.Generic.Base.Vector Data.Vector.Unboxed.Base.Vector Numeric.Rounded.Hardware.Backend.FastFFI.CDouble instance Data.Vector.Unboxed.Base.Unbox Numeric.Rounded.Hardware.Backend.FastFFI.CDouble module Numeric.Rounded.Hardware.Internal -- | 
--   >>> binaryFloatToDecimalDigitsRn ToNearest 3 (0.125 :: Double)
--   ([1,2,5],0)
--   
--   >>> binaryFloatToDecimalDigitsRn ToNearest 3 (12.5 :: Double)
--   ([1,2,5],2)
--
binaryFloatToDecimalDigitsRn :: forall a. RealFloat a => RoundingMode -> Int -> a -> ([Int], Int) -- | 
--   >>> binaryFloatToFixedDecimalDigitsRn ToNearest 3 (0.125 :: Double)
--   [1,2,5]
--   
--   >>> binaryFloatToFixedDecimalDigitsRn ToNearest 3 (12.5 :: Double)
--   [1,2,5,0,0]
--
binaryFloatToFixedDecimalDigitsRn :: forall a. RealFloat a => RoundingMode -> Int -> a -> [Int] -- | 
--   >>> binaryFloatToDecimalDigits (0.125 :: Double)
--   ([1,2,5],0)
--   
--   >>> binaryFloatToDecimalDigits (12.5 :: Double)
--   ([1,2,5],2)
--
binaryFloatToDecimalDigits :: RealFloat a => a -> ([Int], Int) -- | 
--   >>> showEFloatRn ToNearest (Just 0) (0 :: Double) ""
--   "0e0"
--   
--   >>> showEFloatRn ToNearest Nothing (0 :: Double) ""
--   "0.0e0"
--   
--   >>> showEFloatRn ToNearest Nothing (0.5 :: Double) ""
--   "5.0e-1"
--
showEFloatRn :: RealFloat a => RoundingMode -> Maybe Int -> a -> ShowS -- | 
--   >>> showFFloatRn ToNearest (Just 0) (0 :: Double) ""
--   "0"
--   
--   >>> showFFloatRn ToNearest Nothing (0 :: Double) ""
--   "0.0"
--   
--   >>> showFFloatRn ToNearest Nothing (-0 :: Double) ""
--   "-0.0"
--   
--   >>> showFFloatRn ToNearest Nothing (-0.5 :: Double) ""
--   "-0.5"
--
showFFloatRn :: RealFloat a => RoundingMode -> Maybe Int -> a -> ShowS showGFloatRn :: RealFloat a => RoundingMode -> Maybe Int -> a -> ShowS -- | The type for IEEE754 rounding-direction attributes. data RoundingMode -- | Round to the nearest value (IEEE754 roundTiesToEven) ToNearest :: RoundingMode -- | Round downward (IEEE754 roundTowardNegative) TowardNegInf :: RoundingMode -- | Round upward (IEEE754 roundTowardPositive) TowardInf :: RoundingMode -- | Round toward zero (IEEE754 roundTowardZero) TowardZero :: RoundingMode -- | Returns the opposite rounding direction. -- -- TowardNegInf and TowardInf are swapped. oppositeRoundingMode :: RoundingMode -> RoundingMode -- | This class allows you to recover the runtime value from a type-level -- rounding mode. -- -- See rounding. class Rounding (r :: RoundingMode) -- | Recovers the value from type-level rounding mode. rounding :: Rounding r => proxy r -> RoundingMode -- | Lifts a rounding mode to type-level. reifyRounding :: RoundingMode -> (forall s. Rounding s => Proxy s -> a) -> 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. newtype Rounded (r :: RoundingMode) a Rounded :: a -> Rounded (r :: RoundingMode) a [getRounded] :: Rounded (r :: RoundingMode) a -> a data family MVector s a data family Vector a -- | Returns the smallest value that is larger than the argument. -- -- IEEE 754 nextUp operation. -- -- 
--   >>> nextUp 1 == (0x1.000002p0 :: Float)
--   True
--   
--   >>> nextUp 1 == (0x1.0000_0000_0000_1p0 :: Double)
--   True
--   
--   >>> nextUp (1/0) == (1/0 :: Double)
--   True
--   
--   >>> nextUp (-1/0) == (- maxFinite :: Double)
--   True
--   
--   >>> nextUp 0 == (0x1p-1074 :: Double)
--   True
--   
--   >>> nextUp (-0) == (0x1p-1074 :: Double)
--   True
--   
--   >>> nextUp (-0x1p-1074) :: Double -- returns negative zero
--   -0.0
--
nextUp :: RealFloat a => a -> a -- | Returns the largest value that is smaller than the argument. -- -- IEEE 754 nextDown operation. -- -- 
--   >>> nextDown 1 == (0x1.ffff_ffff_ffff_fp-1 :: Double)
--   True
--   
--   >>> nextDown 1 == (0x1.fffffep-1 :: Float)
--   True
--   
--   >>> nextDown (1/0) == (maxFinite :: Double)
--   True
--   
--   >>> nextDown (-1/0) == (-1/0 :: Double)
--   True
--   
--   >>> nextDown 0 == (-0x1p-1074 :: Double)
--   True
--   
--   >>> nextDown (-0) == (-0x1p-1074 :: Double)
--   True
--   
--   >>> nextDown 0x1p-1074 -- returns positive zero
--   0.0
--   
--   >>> nextDown 0x1p-1022 == (0x0.ffff_ffff_ffff_fp-1022 :: Double)
--   True
--
nextDown :: RealFloat a => a -> a -- | Returns the value whose magnitude is smaller than that of the -- argument, and is closest to the argument. -- -- This operation is not in IEEE, but may be useful to some. -- -- 
--   >>> nextTowardZero 1 == (0x1.ffff_ffff_ffff_fp-1 :: Double)
--   True
--   
--   >>> nextTowardZero 1 == (0x1.fffffep-1 :: Float)
--   True
--   
--   >>> nextTowardZero (1/0) == (maxFinite :: Double)
--   True
--   
--   >>> nextTowardZero (-1/0) == (-maxFinite :: Double)
--   True
--   
--   >>> nextTowardZero 0 :: Double -- returns positive zero
--   0.0
--   
--   >>> nextTowardZero (-0 :: Double) -- returns negative zero
--   -0.0
--   
--   >>> nextTowardZero 0x1p-1074 :: Double
--   0.0
--
nextTowardZero :: RealFloat a => a -> a distanceUlp :: RealFloat a => a -> a -> Maybe Integer -- | fusedMultiplyAdd a b c computes a * b + c as -- a single, ternary operation. Rounding is done only once. -- -- May make use of hardware FMA instructions if the target architecture -- has it; set fma3 package flag on x86 systems. -- -- IEEE 754 fusedMultiplyAdd operation. -- -- 
--   \(a :: Double) (b :: Double) (c :: Double) -> fusedMultiplyAdd a b c == fromRational (toRational a * toRational b + toRational c)
--
fusedMultiplyAdd :: RealFloat a => a -> a -> a -> a roundedFromInteger_default :: RealFloat a => RoundingMode -> Integer -> a roundedFromRational_default :: RealFloat a => RoundingMode -> Rational -> a intervalFromInteger_default :: RealFloat a => Integer -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalFromIntegral :: (Integral i, RealFloat a) => i -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalFromRational_default :: RealFloat a => Rational -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) class RealFloatConstants a -- | <math> positiveInfinity :: RealFloatConstants a => a -- | <math> negativeInfinity :: RealFloatConstants a => a maxFinite :: RealFloatConstants a => a minPositive :: RealFloatConstants a => a -- | The correctly-rounded value of <math> pi_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> pi_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> three_pi_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> three_pi_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> five_pi_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> five_pi_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> log2_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> log2_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> exp1_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> exp1_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> exp1_2_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> exp1_2_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> expm1_2_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> expm1_2_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> sqrt2_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> sqrt2_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> sqrt2m1_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> sqrt2m1_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> sqrt1_2_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> sqrt1_2_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> three_minus_2sqrt2_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> three_minus_2sqrt2_up :: RealFloatConstants a => Rounded 'TowardInf a -- | The correctly-rounded value of <math> two_minus_sqrt2_down :: RealFloatConstants a => Rounded 'TowardNegInf a -- | The correctly-rounded value of <math> two_minus_sqrt2_up :: RealFloatConstants a => Rounded 'TowardInf a -- | Lifted version of RoundedSqrt class (RoundedSqrt a, RoundedRing_Vector vector a) => RoundedSqrt_Vector vector a -- | Equivalent to map . roundedSqrt map_roundedSqrt :: RoundedSqrt_Vector vector a => RoundingMode -> vector a -> vector a -- | Equivalent to map . roundedSqrt map_roundedSqrt :: (RoundedSqrt_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -- | Lifted version of RoundedFractional class (RoundedFractional a, RoundedRing_Vector vector a) => RoundedFractional_Vector vector a -- | Equivalent to zipWith . roundedDiv zipWith_roundedDiv :: RoundedFractional_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedDiv zipWith_roundedDiv :: (RoundedFractional_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -> vector a -- | Lifted version of RoundedRing class RoundedRing a => RoundedRing_Vector vector a -- | Equivalent to \r -> foldl (roundedAdd r) 0 roundedSum :: RoundedRing_Vector vector a => RoundingMode -> vector a -> a -- | Equivalent to zipWith . roundedAdd zipWith_roundedAdd :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedSub zipWith_roundedSub :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedMul zipWith_roundedMul :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith3 . roundedFusedMultiplyAdd zipWith3_roundedFusedMultiplyAdd :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -> vector a -- | Equivalent to \r -> foldl (roundedAdd r) 0 roundedSum :: (RoundedRing_Vector vector a, Vector vector a, Num a) => RoundingMode -> vector a -> a -- | Equivalent to zipWith . roundedAdd zipWith_roundedAdd :: (RoundedRing_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedSub zipWith_roundedSub :: (RoundedRing_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedMul zipWith_roundedMul :: (RoundedRing_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith3 . roundedFusedMultiplyAdd zipWith3_roundedFusedMultiplyAdd :: (RoundedRing_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -> vector a -> vector a -- | Rounding-controlled version of sqrt. class RoundedRing a => RoundedSqrt a roundedSqrt :: RoundedSqrt a => RoundingMode -> a -> a intervalSqrt :: RoundedSqrt a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) -- | Rounding-controlled version of Fractional. class RoundedRing a => RoundedFractional a roundedDiv :: RoundedFractional a => RoundingMode -> a -> a -> a roundedRecip :: RoundedFractional a => RoundingMode -> a -> a roundedRecip :: (RoundedFractional a, Num a) => RoundingMode -> a -> a roundedFromRational :: RoundedFractional a => RoundingMode -> Rational -> a roundedFromRational :: (RoundedFractional a, RealFloat a) => RoundingMode -> Rational -> a roundedFromRealFloat :: (RoundedFractional a, RealFloat b) => RoundingMode -> b -> a roundedFromRealFloat :: (RoundedFractional a, Fractional a, RealFloat b) => RoundingMode -> b -> a intervalDiv :: RoundedFractional a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalDivAdd :: RoundedFractional a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalRecip :: RoundedFractional a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalFromRational :: RoundedFractional a => Rational -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) -- | Rounding-controlled version of Num. class Ord a => RoundedRing a roundedAdd :: RoundedRing a => RoundingMode -> a -> a -> a roundedSub :: RoundedRing a => RoundingMode -> a -> a -> a roundedMul :: RoundedRing a => RoundingMode -> a -> a -> a roundedFusedMultiplyAdd :: RoundedRing a => RoundingMode -> a -> a -> a -> a roundedFromInteger :: RoundedRing a => RoundingMode -> Integer -> a roundedFromInteger :: (RoundedRing a, RealFloat a) => RoundingMode -> Integer -> a -- | 
--   \x_lo x_hi y_lo y_hi -> intervalAdd (Rounded x_lo) (Rounded x_hi) (Rounded y_lo) (Rounded y_hi) == (Rounded (roundedAdd TowardNegInf x_lo y_lo), Rounded (roundedAdd TowardInf x_hi y_hi))
--
intervalAdd :: RoundedRing a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) -- | 
--   \x_lo x_hi y_lo y_hi -> intervalSub (Rounded x_lo) (Rounded x_hi) (Rounded y_lo) (Rounded y_hi) == (Rounded (roundedSub TowardNegInf x_lo y_hi), Rounded (roundedSub TowardInf x_hi y_lo))
--
intervalSub :: RoundedRing a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalMul :: RoundedRing a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalMulAdd :: RoundedRing a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalFromInteger :: RoundedRing a => Integer -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) backendNameT :: RoundedRing a => Tagged a String -- | Returns the name of backend as a string. -- -- Example: -- -- 
--   >>> :m + Data.Proxy
--   >>> backendName (Proxy :: Proxy Double)
--   "FastFFI+SSE2"
--
backendName :: RoundedRing a => proxy a -> String -- | The type for IEEE754 rounding-direction attributes. data RoundingMode -- | Round to the nearest value (IEEE754 roundTiesToEven) ToNearest :: RoundingMode -- | Round downward (IEEE754 roundTowardNegative) TowardNegInf :: RoundingMode -- | Round upward (IEEE754 roundTowardPositive) TowardInf :: RoundingMode -- | Round toward zero (IEEE754 roundTowardZero) TowardZero :: RoundingMode -- | Returns the opposite rounding direction. -- -- TowardNegInf and TowardInf are swapped. oppositeRoundingMode :: RoundingMode -> RoundingMode -- | This class allows you to recover the runtime value from a type-level -- rounding mode. -- -- See rounding. class Rounding (r :: RoundingMode) -- | Recovers the value from type-level rounding mode. rounding :: Rounding r => proxy r -> RoundingMode -- | Lifts a rounding mode to type-level. reifyRounding :: RoundingMode -> (forall s. Rounding s => Proxy s -> a) -> 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. newtype Rounded (r :: RoundingMode) a Rounded :: a -> Rounded (r :: RoundingMode) a [getRounded] :: Rounded (r :: RoundingMode) a -> a data family MVector s a data family Vector a module Numeric.Rounded.Hardware.Class -- | Rounding-controlled version of Num. class Ord a => RoundedRing a roundedAdd :: RoundedRing a => RoundingMode -> a -> a -> a roundedSub :: RoundedRing a => RoundingMode -> a -> a -> a roundedMul :: RoundedRing a => RoundingMode -> a -> a -> a roundedFusedMultiplyAdd :: RoundedRing a => RoundingMode -> a -> a -> a -> a roundedFromInteger :: RoundedRing a => RoundingMode -> Integer -> a roundedFromInteger :: (RoundedRing a, RealFloat a) => RoundingMode -> Integer -> a -- | 
--   \x_lo x_hi y_lo y_hi -> intervalAdd (Rounded x_lo) (Rounded x_hi) (Rounded y_lo) (Rounded y_hi) == (Rounded (roundedAdd TowardNegInf x_lo y_lo), Rounded (roundedAdd TowardInf x_hi y_hi))
--
intervalAdd :: RoundedRing a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) -- | 
--   \x_lo x_hi y_lo y_hi -> intervalSub (Rounded x_lo) (Rounded x_hi) (Rounded y_lo) (Rounded y_hi) == (Rounded (roundedSub TowardNegInf x_lo y_hi), Rounded (roundedSub TowardInf x_hi y_lo))
--
intervalSub :: RoundedRing a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalMul :: RoundedRing a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalMulAdd :: RoundedRing a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalFromInteger :: RoundedRing a => Integer -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) backendNameT :: RoundedRing a => Tagged a String -- | Rounding-controlled version of Fractional. class RoundedRing a => RoundedFractional a roundedDiv :: RoundedFractional a => RoundingMode -> a -> a -> a roundedRecip :: RoundedFractional a => RoundingMode -> a -> a roundedRecip :: (RoundedFractional a, Num a) => RoundingMode -> a -> a roundedFromRational :: RoundedFractional a => RoundingMode -> Rational -> a roundedFromRational :: (RoundedFractional a, RealFloat a) => RoundingMode -> Rational -> a roundedFromRealFloat :: (RoundedFractional a, RealFloat b) => RoundingMode -> b -> a roundedFromRealFloat :: (RoundedFractional a, Fractional a, RealFloat b) => RoundingMode -> b -> a intervalDiv :: RoundedFractional a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalDivAdd :: RoundedFractional a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalRecip :: RoundedFractional a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) intervalFromRational :: RoundedFractional a => Rational -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) -- | Rounding-controlled version of sqrt. class RoundedRing a => RoundedSqrt a roundedSqrt :: RoundedSqrt a => RoundingMode -> a -> a intervalSqrt :: RoundedSqrt a => Rounded 'TowardNegInf a -> Rounded 'TowardInf a -> (Rounded 'TowardNegInf a, Rounded 'TowardInf a) -- | Lifted version of RoundedRing class RoundedRing a => RoundedRing_Vector vector a -- | Equivalent to \r -> foldl (roundedAdd r) 0 roundedSum :: RoundedRing_Vector vector a => RoundingMode -> vector a -> a -- | Equivalent to zipWith . roundedAdd zipWith_roundedAdd :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedSub zipWith_roundedSub :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedMul zipWith_roundedMul :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith3 . roundedFusedMultiplyAdd zipWith3_roundedFusedMultiplyAdd :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -> vector a -- | Equivalent to \r -> foldl (roundedAdd r) 0 roundedSum :: (RoundedRing_Vector vector a, Vector vector a, Num a) => RoundingMode -> vector a -> a -- | Equivalent to zipWith . roundedAdd zipWith_roundedAdd :: (RoundedRing_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedSub zipWith_roundedSub :: (RoundedRing_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedMul zipWith_roundedMul :: (RoundedRing_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith3 . roundedFusedMultiplyAdd zipWith3_roundedFusedMultiplyAdd :: (RoundedRing_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -> vector a -> vector a -- | Lifted version of RoundedFractional class (RoundedFractional a, RoundedRing_Vector vector a) => RoundedFractional_Vector vector a -- | Equivalent to zipWith . roundedDiv zipWith_roundedDiv :: RoundedFractional_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedDiv zipWith_roundedDiv :: (RoundedFractional_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -> vector a -- | Lifted version of RoundedSqrt class (RoundedSqrt a, RoundedRing_Vector vector a) => RoundedSqrt_Vector vector a -- | Equivalent to map . roundedSqrt map_roundedSqrt :: RoundedSqrt_Vector vector a => RoundingMode -> vector a -> vector a -- | Equivalent to map . roundedSqrt map_roundedSqrt :: (RoundedSqrt_Vector vector a, Vector vector a) => RoundingMode -> vector a -> vector a -- | Although popular CPUs allow program to control the rounding direction -- of floating-point operations, such feature is not directly accessible -- to Haskell. -- -- Several options are available to control the rounding direction, -- including -- -- -- -- This library implements the first and third options, in -- Numeric.Rounded.Hardware.Backend.ViaRational and -- Numeric.Rounded.Hardware.Backend.C/Numeric.Rounded.Hardware.Backend.FastFFI -- respectively. -- -- The default implementation for Float and Double depends -- on the platform and package flags. To help the programmer identify -- which implementation is used, this module provides a function to -- obtain the name of implementation. -- -- To disable use of FFI, enable the package flag pure-hs. module Numeric.Rounded.Hardware.Backend -- | Returns the name of backend as a string. -- -- Example: -- -- 
--   >>> :m + Data.Proxy
--   >>> backendName (Proxy :: Proxy Double)
--   "FastFFI+SSE2"
--
backendName :: RoundedRing a => proxy a -> String module Numeric.Rounded.Hardware -- | 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. newtype Rounded (r :: RoundingMode) a Rounded :: a -> Rounded (r :: RoundingMode) a [getRounded] :: Rounded (r :: RoundingMode) a -> a -- | The type for IEEE754 rounding-direction attributes. data RoundingMode -- | Round to the nearest value (IEEE754 roundTiesToEven) ToNearest :: RoundingMode -- | Round downward (IEEE754 roundTowardNegative) TowardNegInf :: RoundingMode -- | Round upward (IEEE754 roundTowardPositive) TowardInf :: RoundingMode -- | Round toward zero (IEEE754 roundTowardZero) TowardZero :: RoundingMode -- | This class allows you to recover the runtime value from a type-level -- rounding mode. -- -- See rounding. class Rounding (r :: RoundingMode) -- | Rounding-controlled version of Num. class Ord a => RoundedRing a -- | Rounding-controlled version of Fractional. class RoundedRing a => RoundedFractional a -- | Rounding-controlled version of sqrt. class RoundedRing a => RoundedSqrt a module Numeric.Rounded.Hardware.Interval.Class class IsInterval i where { type family EndPoint i; } withEndPoints :: IsInterval i => (Rounded 'TowardNegInf (EndPoint i) -> Rounded 'TowardInf (EndPoint i) -> i) -> i -> i singleton :: IsInterval i => EndPoint i -> i makeInterval :: IsInterval i => Rounded 'TowardNegInf (EndPoint i) -> Rounded 'TowardInf (EndPoint i) -> i width :: IsInterval i => i -> Rounded 'TowardInf (EndPoint i) hull :: IsInterval i => i -> i -> i intersection :: IsInterval i => i -> i -> i maybeIntersection :: IsInterval i => i -> i -> Maybe i equalAsSet :: IsInterval i => i -> i -> Bool -- | a is a subset of b subset :: IsInterval i => i -> i -> Bool weaklyLess :: IsInterval i => i -> i -> Bool precedes :: IsInterval i => i -> i -> Bool interior :: IsInterval i => i -> i -> Bool strictLess :: IsInterval i => i -> i -> Bool strictPrecedes :: IsInterval i => i -> i -> Bool disjoint :: IsInterval i => i -> i -> Bool infix 4 `disjoint` infix 4 `strictPrecedes` infix 4 `strictLess` infix 4 `interior` infix 4 `precedes` infix 4 `weaklyLess` infix 4 `subset` infix 4 `equalAsSet` module Numeric.Rounded.Hardware.Interval.NonEmpty data Interval a I :: !Rounded 'TowardNegInf a -> !Rounded 'TowardInf a -> Interval a increasing :: (forall r. Rounding r => Rounded r a -> Rounded r a) -> Interval a -> Interval a maxI :: Ord a => Interval a -> Interval a -> Interval a minI :: Ord a => Interval a -> Interval a -> Interval a powInt :: (Ord a, Num a, RoundedRing a) => Interval a -> Int -> Interval a null :: Interval a -> Bool inf :: Interval a -> Rounded 'TowardNegInf a sup :: Interval a -> Rounded 'TowardInf a width :: (Num a, RoundedRing a) => Interval a -> Rounded 'TowardInf a hull :: RoundedRing a => Interval a -> Interval a -> Interval a instance GHC.Generics.Generic (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) instance GHC.Show.Show a => GHC.Show.Show (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) instance Control.DeepSeq.NFData a => Control.DeepSeq.NFData (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) instance (GHC.Num.Num a, Numeric.Rounded.Hardware.Internal.Class.RoundedRing a) => GHC.Num.Num (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) instance (GHC.Num.Num a, Numeric.Rounded.Hardware.Internal.Class.RoundedFractional a) => GHC.Real.Fractional (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) instance (GHC.Num.Num a, Numeric.Rounded.Hardware.Internal.Class.RoundedFractional a, Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt a, GHC.Classes.Eq a, GHC.Float.RealFloat a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a) => GHC.Float.Floating (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) instance (GHC.Float.RealFloat a, Numeric.Rounded.Hardware.Internal.Class.RoundedRing a) => Numeric.Rounded.Hardware.Interval.Class.IsInterval (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) instance (Data.Vector.Unboxed.Base.Unbox a, GHC.Classes.Ord a, GHC.Real.Fractional a) => Data.Vector.Generic.Mutable.Base.MVector Data.Vector.Unboxed.Base.MVector (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) instance (Data.Vector.Unboxed.Base.Unbox a, GHC.Classes.Ord a, GHC.Real.Fractional a) => Data.Vector.Generic.Base.Vector Data.Vector.Unboxed.Base.Vector (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) instance (Data.Vector.Unboxed.Base.Unbox a, GHC.Classes.Ord a, GHC.Real.Fractional a) => Data.Vector.Unboxed.Base.Unbox (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) instance (Data.Primitive.Types.Prim a, GHC.Classes.Ord a, GHC.Real.Fractional a) => Data.Array.Base.MArray (Data.Array.Base.STUArray s) (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) (GHC.ST.ST s) instance (Data.Primitive.Types.Prim a, GHC.Classes.Ord a, GHC.Real.Fractional a) => Data.Array.Base.IArray Data.Array.Base.UArray (Numeric.Rounded.Hardware.Interval.NonEmpty.Interval a) module Numeric.Rounded.Hardware.Interval data Interval a I :: !Rounded 'TowardNegInf a -> !Rounded 'TowardInf a -> Interval a Empty :: Interval a increasing :: (forall r. Rounding r => Rounded r a -> Rounded r a) -> Interval a -> Interval a maxI :: Ord a => Interval a -> Interval a -> Interval a minI :: Ord a => Interval a -> Interval a -> Interval a powInt :: (Ord a, Num a, RoundedRing a) => Interval a -> Int -> Interval a null :: Interval a -> Bool inf :: Interval a -> Rounded 'TowardNegInf a sup :: Interval a -> Rounded 'TowardInf a width :: (Num a, RoundedRing a) => Interval a -> Rounded 'TowardInf a widthUlp :: RealFloat a => Interval a -> Maybe Integer hull :: RoundedRing a => Interval a -> Interval a -> Interval a intersection :: RoundedRing a => Interval a -> Interval a -> Interval a instance GHC.Generics.Generic (Numeric.Rounded.Hardware.Interval.Interval a) instance GHC.Show.Show a => GHC.Show.Show (Numeric.Rounded.Hardware.Interval.Interval a) instance Control.DeepSeq.NFData a => Control.DeepSeq.NFData (Numeric.Rounded.Hardware.Interval.Interval a) instance (GHC.Num.Num a, Numeric.Rounded.Hardware.Internal.Class.RoundedRing a) => GHC.Num.Num (Numeric.Rounded.Hardware.Interval.Interval a) instance (GHC.Num.Num a, Numeric.Rounded.Hardware.Internal.Class.RoundedFractional a) => GHC.Real.Fractional (Numeric.Rounded.Hardware.Interval.Interval a) instance (GHC.Num.Num a, Numeric.Rounded.Hardware.Internal.Class.RoundedFractional a, Numeric.Rounded.Hardware.Internal.Class.RoundedSqrt a, GHC.Classes.Eq a, GHC.Float.RealFloat a, Numeric.Rounded.Hardware.Internal.Constants.RealFloatConstants a) => GHC.Float.Floating (Numeric.Rounded.Hardware.Interval.Interval a) instance (GHC.Num.Num a, Numeric.Rounded.Hardware.Internal.Class.RoundedRing a, GHC.Float.RealFloat a) => Numeric.Rounded.Hardware.Interval.Class.IsInterval (Numeric.Rounded.Hardware.Interval.Interval a) instance (Data.Vector.Unboxed.Base.Unbox a, GHC.Classes.Ord a, GHC.Real.Fractional a) => Data.Vector.Generic.Mutable.Base.MVector Data.Vector.Unboxed.Base.MVector (Numeric.Rounded.Hardware.Interval.Interval a) instance (Data.Vector.Unboxed.Base.Unbox a, GHC.Classes.Ord a, GHC.Real.Fractional a) => Data.Vector.Generic.Base.Vector Data.Vector.Unboxed.Base.Vector (Numeric.Rounded.Hardware.Interval.Interval a) instance (Data.Vector.Unboxed.Base.Unbox a, GHC.Classes.Ord a, GHC.Real.Fractional a) => Data.Vector.Unboxed.Base.Unbox (Numeric.Rounded.Hardware.Interval.Interval a) instance (Data.Primitive.Types.Prim a, GHC.Classes.Ord a, GHC.Real.Fractional a) => Data.Array.Base.MArray (Data.Array.Base.STUArray s) (Numeric.Rounded.Hardware.Interval.Interval a) (GHC.ST.ST s) instance (Data.Primitive.Types.Prim a, GHC.Classes.Ord a, GHC.Real.Fractional a) => Data.Array.Base.IArray Data.Array.Base.UArray (Numeric.Rounded.Hardware.Interval.Interval a) module Numeric.Rounded.Hardware.Rounding -- | The type for IEEE754 rounding-direction attributes. data RoundingMode -- | Round to the nearest value (IEEE754 roundTiesToEven) ToNearest :: RoundingMode -- | Round downward (IEEE754 roundTowardNegative) TowardNegInf :: RoundingMode -- | Round upward (IEEE754 roundTowardPositive) TowardInf :: RoundingMode -- | Round toward zero (IEEE754 roundTowardZero) TowardZero :: RoundingMode -- | Returns the opposite rounding direction. -- -- TowardNegInf and TowardInf are swapped. oppositeRoundingMode :: RoundingMode -> RoundingMode -- | This class allows you to recover the runtime value from a type-level -- rounding mode. -- -- See rounding. class Rounding (r :: RoundingMode) -- | Recovers the value from type-level rounding mode. rounding :: Rounding r => proxy r -> RoundingMode -- | Lifts a rounding mode to type-level. reifyRounding :: RoundingMode -> (forall s. Rounding s => Proxy s -> a) -> a module Numeric.Rounded.Hardware.Vector.Storable coercion :: Coercion (Vector a) (Vector (Rounded r a)) fromVectorOfRounded :: Vector (Rounded r a) -> Vector a toVectorOfRounded :: Vector a -> Vector (Rounded r a) coercionM :: Coercion (MVector s a) (MVector s (Rounded r a)) fromMVectorOfRounded :: MVector s (Rounded r a) -> MVector s a toMVectorOfRounded :: MVector s a -> MVector s (Rounded r a) -- | Equivalent to \r -> foldl (roundedAdd r) 0 roundedSum :: RoundedRing_Vector vector a => RoundingMode -> vector a -> a -- | Equivalent to zipWith . roundedAdd zipWith_roundedAdd :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedSub zipWith_roundedSub :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedMul zipWith_roundedMul :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith3 . roundedFusedMultiplyAdd zipWith3_roundedFusedMultiplyAdd :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedDiv zipWith_roundedDiv :: RoundedFractional_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to map . roundedSqrt map_roundedSqrt :: RoundedSqrt_Vector vector a => RoundingMode -> vector a -> vector a -- | Equivalent to sum sum :: forall r a. (Rounding r, Storable a, RoundedRing_Vector Vector a) => Vector (Rounded r a) -> Rounded r a -- | Equivalent to zipWith (+) zipWith_add :: forall r a. (Rounding r, Storable a, RoundedRing_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -- | Equivalent to zipWith (-) zipWith_sub :: forall r a. (Rounding r, Storable a, RoundedRing_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -- | Equivalent to zipWith (*) zipWith_mul :: forall r a. (Rounding r, Storable a, RoundedRing_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -- | Equivalent to zipWith3 fusedMultiplyAdd zipWith3_fusedMultiplyAdd :: forall r a. (Rounding r, Storable a, RoundedRing_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -- | Equivalent to zipWith (/) zipWith_div :: forall r a. (Rounding r, Storable a, RoundedFractional_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -- | Equivalent to map sqrt map_sqrt :: forall r a. (Rounding r, Storable a, RoundedSqrt_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) module Numeric.Rounded.Hardware.Vector.Unboxed -- | Equivalent to \r -> foldl (roundedAdd r) 0 roundedSum :: RoundedRing_Vector vector a => RoundingMode -> vector a -> a -- | Equivalent to zipWith . roundedAdd zipWith_roundedAdd :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedSub zipWith_roundedSub :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedMul zipWith_roundedMul :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to zipWith3 . roundedFusedMultiplyAdd zipWith3_roundedFusedMultiplyAdd :: RoundedRing_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -> vector a -- | Equivalent to zipWith . roundedDiv zipWith_roundedDiv :: RoundedFractional_Vector vector a => RoundingMode -> vector a -> vector a -> vector a -- | Equivalent to map . roundedSqrt map_roundedSqrt :: RoundedSqrt_Vector vector a => RoundingMode -> vector a -> vector a -- | Equivalent to sum sum :: forall r a. (Rounding r, Unbox a, RoundedRing_Vector Vector a) => Vector (Rounded r a) -> Rounded r a -- | Equivalent to zipWith (+) zipWith_add :: forall r a. (Rounding r, Unbox a, RoundedRing_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -- | Equivalent to zipWith (-) zipWith_sub :: forall r a. (Rounding r, Unbox a, RoundedRing_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -- | Equivalent to zipWith (*) zipWith_mul :: forall r a. (Rounding r, Unbox a, RoundedRing_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -- | Equivalent to zipWith3 fusedMultiplyAdd zipWith3_fusedMultiplyAdd :: forall r a. (Rounding r, Unbox a, RoundedRing_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -- | Equivalent to zipWith (/) zipWith_div :: forall r a. (Rounding r, Unbox a, RoundedFractional_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a) -> Vector (Rounded r a) -- | Equivalent to map sqrt map_sqrt :: forall r a. (Rounding r, Unbox a, RoundedSqrt_Vector Vector a) => Vector (Rounded r a) -> Vector (Rounded r a)