Copyright	[2019..2020] The Accelerate Team
License	BSD3
Maintainer	Trevor L. McDonell <trevor.mcdonell@gmail.com>
Stability	experimental
Portability	non-portable (GHC extensions)
Safe Haskell	None
Language	Haskell2010

Data.Array.Accelerate.Data.Ratio

Contents

Orphan instances

Description

Standard functions on rational numbers

Since: 1.3.0.0

Synopsis

data Ratio a
(%) :: Integral a => Exp a -> Exp a -> Exp (Ratio a)
pattern (:%) :: Elt a => Exp a -> Exp a -> Exp (Ratio a)
numerator :: Exp (Ratio a) -> Elt a => Exp a
denominator :: Exp (Ratio a) -> Elt a => Exp a

Documentation

data Ratio a #

Rational numbers, with numerator and denominator of some Integral type.

Note that Ratio's instances inherit the deficiencies from the type parameter's. For example, Ratio Natural's Num instance has similar problems to Natural's.

Instances

Instances details

NFData1 Ratio	Available on `base >=4.9` Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Ratio a -> () #
Pretty Rational
Instance details Defined in Text.PrettyPrint.Annotated.WL Methods pretty :: Rational -> Doc b # prettyList :: [Rational] -> Doc b #
Integral a => Lift (Ratio a :: Type)
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Ratio a -> Q Exp # liftTyped :: Ratio a -> Q (TExp (Ratio a)) #
(FromIntegral a b, Integral b) => FromIntegral a (Ratio b) Source #
Instance details Defined in Data.Array.Accelerate.Data.Ratio Methods fromIntegral :: Exp a -> Exp (Ratio b) Source #
Integral a => Enum (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods succ :: Ratio a -> Ratio a # pred :: Ratio a -> Ratio a # toEnum :: Int -> Ratio a # fromEnum :: Ratio a -> Int # enumFrom :: Ratio a -> [Ratio a] # enumFromThen :: Ratio a -> Ratio a -> [Ratio a] # enumFromTo :: Ratio a -> Ratio a -> [Ratio a] # enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] #
Integral a => Enum (Exp (Ratio a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Ratio Methods succ :: Exp (Ratio a) -> Exp (Ratio a) # pred :: Exp (Ratio a) -> Exp (Ratio a) # toEnum :: Int -> Exp (Ratio a) # fromEnum :: Exp (Ratio a) -> Int # enumFrom :: Exp (Ratio a) -> [Exp (Ratio a)] # enumFromThen :: Exp (Ratio a) -> Exp (Ratio a) -> [Exp (Ratio a)] # enumFromTo :: Exp (Ratio a) -> Exp (Ratio a) -> [Exp (Ratio a)] # enumFromThenTo :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) -> [Exp (Ratio a)] #
Eq a => Eq (Ratio a)	Since: base-2.1
Instance details Defined in GHC.Real Methods (==) :: Ratio a -> Ratio a -> Bool # (/=) :: Ratio a -> Ratio a -> Bool #
Integral a => Fractional (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods (/) :: Ratio a -> Ratio a -> Ratio a # recip :: Ratio a -> Ratio a # fromRational :: Rational -> Ratio a #
Integral a => Fractional (Exp (Ratio a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Ratio Methods (/) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) # recip :: Exp (Ratio a) -> Exp (Ratio a) # fromRational :: Rational -> Exp (Ratio a) #
Integral a => Num (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods (+) :: Ratio a -> Ratio a -> Ratio a # (-) :: Ratio a -> Ratio a -> Ratio a # (*) :: Ratio a -> Ratio a -> Ratio a # negate :: Ratio a -> Ratio a # abs :: Ratio a -> Ratio a # signum :: Ratio a -> Ratio a # fromInteger :: Integer -> Ratio a #
Integral a => Num (Exp (Ratio a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Ratio Methods (+) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) # (-) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) # (*) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) # negate :: Exp (Ratio a) -> Exp (Ratio a) # abs :: Exp (Ratio a) -> Exp (Ratio a) # signum :: Exp (Ratio a) -> Exp (Ratio a) # fromInteger :: Integer -> Exp (Ratio a) #
Integral a => Ord (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods compare :: Ratio a -> Ratio a -> Ordering # (<) :: Ratio a -> Ratio a -> Bool # (<=) :: Ratio a -> Ratio a -> Bool # (>) :: Ratio a -> Ratio a -> Bool # (>=) :: Ratio a -> Ratio a -> Bool # max :: Ratio a -> Ratio a -> Ratio a # min :: Ratio a -> Ratio a -> Ratio a #
(Integral a, Read a) => Read (Ratio a)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Ratio a) # readList :: ReadS [Ratio a] # readPrec :: ReadPrec (Ratio a) # readListPrec :: ReadPrec [Ratio a] #
Integral a => Real (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Ratio a -> Rational #
Integral a => RealFrac (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods properFraction :: Integral b => Ratio a -> (b, Ratio a) # truncate :: Integral b => Ratio a -> b # round :: Integral b => Ratio a -> b # ceiling :: Integral b => Ratio a -> b # floor :: Integral b => Ratio a -> b #
Show a => Show (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods showsPrec :: Int -> Ratio a -> ShowS # show :: Ratio a -> String # showList :: [Ratio a] -> ShowS #
Generic (Ratio a) Source #
Instance details Defined in Data.Array.Accelerate.Orphans Associated Types type Rep (Ratio a) :: Type -> Type # Methods from :: Ratio a -> Rep (Ratio a) x # to :: Rep (Ratio a) x -> Ratio a #
(Storable a, Integral a) => Storable (Ratio a)	Since: base-4.8.0.0
Instance details Defined in Foreign.Storable Methods sizeOf :: Ratio a -> Int # alignment :: Ratio a -> Int # peekElemOff :: Ptr (Ratio a) -> Int -> IO (Ratio a) # pokeElemOff :: Ptr (Ratio a) -> Int -> Ratio a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Ratio a) # pokeByteOff :: Ptr b -> Int -> Ratio a -> IO () # peek :: Ptr (Ratio a) -> IO (Ratio a) # poke :: Ptr (Ratio a) -> Ratio a -> IO () #
NFData a => NFData (Ratio a)
Instance details Defined in Control.DeepSeq Methods rnf :: Ratio a -> () #
Hashable a => Hashable (Ratio a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Ratio a -> Int # hash :: Ratio a -> Int #
(Integral a, FromIntegral a Int64) => RealFrac (Ratio a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Ratio Methods properFraction :: (Integral b, FromIntegral Int64 b) => Exp (Ratio a) -> (Exp b, Exp (Ratio a)) Source # truncate :: (Integral b, FromIntegral Int64 b) => Exp (Ratio a) -> Exp b Source # round :: (Integral b, FromIntegral Int64 b) => Exp (Ratio a) -> Exp b Source # ceiling :: (Integral b, FromIntegral Int64 b) => Exp (Ratio a) -> Exp b Source # floor :: (Integral b, FromIntegral Int64 b) => Exp (Ratio a) -> Exp b Source #
Elt a => Elt (Ratio a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Ratio Associated Types type EltR (Ratio a) Methods eltR :: TypeR (EltR (Ratio a)) tagsR :: [TagR (EltR (Ratio a))] fromElt :: Ratio a -> EltR (Ratio a) toElt :: EltR (Ratio a) -> Ratio a
Integral a => Eq (Ratio a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Ratio Methods (==) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source # (/=) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source #
Integral a => Ord (Ratio a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Ratio Methods (<) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source # (>) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source # (<=) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source # (>=) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source # min :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) Source # max :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) Source # compare :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Ordering Source #
(Integral a, ToFloating a b) => ToFloating (Ratio a) b Source #
Instance details Defined in Data.Array.Accelerate.Data.Ratio Methods toFloating :: Exp (Ratio a) -> Exp b Source #
type Rep (Ratio a) Source #
Instance details Defined in Data.Array.Accelerate.Orphans type Rep (Ratio a) = D1 ('MetaData "Ratio" "GHC.Real" "base" 'False) (C1 ('MetaCons ":%" ('InfixI 'LeftAssociative 9) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))

(%) :: Integral a => Exp a -> Exp a -> Exp (Ratio a) infixl 7 Source #

Form the ratio of two integral numbers

pattern (:%) :: Elt a => Exp a -> Exp a -> Exp (Ratio a) Source #

numerator :: Exp (Ratio a) -> Elt a => Exp a Source #

denominator :: Exp (Ratio a) -> Elt a => Exp a Source #

Orphan instances

(FromIntegral a b, Integral b) => FromIntegral a (Ratio b) Source #
Instance details Methods fromIntegral :: Exp a -> Exp (Ratio b) Source #
Integral a => Enum (Exp (Ratio a)) Source #
Instance details Methods succ :: Exp (Ratio a) -> Exp (Ratio a) # pred :: Exp (Ratio a) -> Exp (Ratio a) # toEnum :: Int -> Exp (Ratio a) # fromEnum :: Exp (Ratio a) -> Int # enumFrom :: Exp (Ratio a) -> [Exp (Ratio a)] # enumFromThen :: Exp (Ratio a) -> Exp (Ratio a) -> [Exp (Ratio a)] # enumFromTo :: Exp (Ratio a) -> Exp (Ratio a) -> [Exp (Ratio a)] # enumFromThenTo :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) -> [Exp (Ratio a)] #
Integral a => Fractional (Exp (Ratio a)) Source #
Instance details Methods (/) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) # recip :: Exp (Ratio a) -> Exp (Ratio a) # fromRational :: Rational -> Exp (Ratio a) #
Integral a => Num (Exp (Ratio a)) Source #
Instance details Methods (+) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) # (-) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) # (*) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) # negate :: Exp (Ratio a) -> Exp (Ratio a) # abs :: Exp (Ratio a) -> Exp (Ratio a) # signum :: Exp (Ratio a) -> Exp (Ratio a) # fromInteger :: Integer -> Exp (Ratio a) #
(Integral a, FromIntegral a Int64) => RealFrac (Ratio a) Source #
Instance details Methods properFraction :: (Integral b, FromIntegral Int64 b) => Exp (Ratio a) -> (Exp b, Exp (Ratio a)) Source # truncate :: (Integral b, FromIntegral Int64 b) => Exp (Ratio a) -> Exp b Source # round :: (Integral b, FromIntegral Int64 b) => Exp (Ratio a) -> Exp b Source # ceiling :: (Integral b, FromIntegral Int64 b) => Exp (Ratio a) -> Exp b Source # floor :: (Integral b, FromIntegral Int64 b) => Exp (Ratio a) -> Exp b Source #
Elt a => Elt (Ratio a) Source #
Instance details Associated Types type EltR (Ratio a) Methods eltR :: TypeR (EltR (Ratio a)) tagsR :: [TagR (EltR (Ratio a))] fromElt :: Ratio a -> EltR (Ratio a) toElt :: EltR (Ratio a) -> Ratio a
Integral a => Eq (Ratio a) Source #
Instance details Methods (==) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source # (/=) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source #
Integral a => Ord (Ratio a) Source #
Instance details Methods (<) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source # (>) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source # (<=) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source # (>=) :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Bool Source # min :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) Source # max :: Exp (Ratio a) -> Exp (Ratio a) -> Exp (Ratio a) Source # compare :: Exp (Ratio a) -> Exp (Ratio a) -> Exp Ordering Source #
(Integral a, ToFloating a b) => ToFloating (Ratio a) b Source #
Instance details Methods toFloating :: Exp (Ratio a) -> Exp b Source #