Data.Connection.Ratio

Rational

ratw08 :: Cast k Rational (Extended Word8)

ratw16 :: Cast k Rational (Extended Word16)

ratw32 :: Cast k Rational (Extended Word32)

ratw64 :: Cast k Rational (Extended Word64)

ratwxx :: Cast k Rational (Extended Word)

ratnat :: Cast k Rational (Extended Natural)

rati08 :: Cast k Rational (Extended Int8)

rati16 :: Cast k Rational (Extended Int16)

rati32 :: Cast k Rational (Extended Int32)

rati64 :: Cast k Rational (Extended Int64)

ratixx :: Cast k Rational (Extended Int)

ratint :: Cast k Rational (Extended Integer)

ratrat :: Cast k (Rational, Rational) Rational

reduce :: Integral a => Ratio a -> Ratio a

A total version of reduce.

shiftr :: Num a => a -> Ratio a -> Ratio a

Shift by n 'units of least precision' where the ULP is determined by the denominator

This is an analog of shift32 for rationals.

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.

Constructors

!a :% !a

Instances

Preorder Rational

Defined in Data.Order

Methods

(<~) :: Rational -> Rational -> Bool

(>~) :: Rational -> Rational -> Bool

(?~) :: Rational -> Rational -> Bool

(~~) :: Rational -> Rational -> Bool

(/~) :: Rational -> Rational -> Bool

plt :: Rational -> Rational -> Bool

pgt :: Rational -> Rational -> Bool

similar :: Rational -> Rational -> Bool

pmax :: Rational -> Rational -> Maybe Rational

pmin :: Rational -> Rational -> Maybe Rational

pcompare :: Rational -> Rational -> Maybe Ordering

Connection k Rational Double

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational Double

Connection k Rational Float

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational Float

HasResolution res => Connection k Rational (Extended (Fixed res))

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended (Fixed res))

Connection k Rational (Extended SystemTime)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended SystemTime)

Connection k Rational (Extended Integer)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Integer)

Connection k Rational (Extended Int)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Int)

Connection k Rational (Extended Int64)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Int64)

Connection k Rational (Extended Int32)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Int32)

Connection k Rational (Extended Int16)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Int16)

Connection k Rational (Extended Int8)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Int8)

Connection k Rational (Extended Natural)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Natural)

Connection k Rational (Extended Word)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Word)

Connection k Rational (Extended Word64)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Word64)

Connection k Rational (Extended Word32)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Word32)

Connection k Rational (Extended Word16)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Word16)

Connection k Rational (Extended Word8)

Defined in Data.Connection.Class

Methods

cast :: Cast k Rational (Extended Word8)

Integral a => Enum (Ratio a)

Since: base-2.0.1

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]

Eq a => Eq (Ratio a)

Since: base-2.1

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

Defined in GHC.Real

Methods

(/) :: Ratio a -> Ratio a -> Ratio a

recip :: Ratio a -> Ratio a

fromRational :: Rational -> Ratio a

Integral a => Num (Ratio a)

Since: base-2.0.1

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 => Ord (Ratio a)

Since: base-2.0.1

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

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

Defined in GHC.Real

Methods

toRational :: Ratio a -> Rational

Integral a => RealFrac (Ratio a)

Since: base-2.0.1

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

Defined in GHC.Real

Methods

showsPrec :: Int -> Ratio a -> ShowS

show :: Ratio a -> String

showList :: [Ratio a] -> ShowS