Fractal.RUFF.Types.Ratio

Rational numbers with ruff-specific operations.

Documentation

class Q r where

Rational numbers with ruff-specific operations.

Minimal complete definition

(%), numerator, denominator

Associated Types

type Z r

Methods

(%) :: Z r -> Z r -> r infixl 7

smart constuctor

numerator :: r -> Z r

extract numerator

denominator :: r -> Z r

extract denominator

(%!) :: Z r -> Z r -> r infixl 7

unsafe constructor

zero :: Integral (Z r) => r

0

half :: Integral (Z r) => r

1/2

one :: Integral (Z r) => r

1

fromQ :: Integral (Z r) => r -> Rational

convert to Prelude.Rational

toQ :: Integral (Z r) => Rational -> r

convert from Prelude.Rational

wrap :: Integral (Z r) => r -> r

wrap into [0,1)

doubleWrap :: Integral (Z r) => r -> r

doubling map to [0,1)

double :: Integral (Z r) => r -> r

doubling map from [0,1) to [0,1)

doubleOdd :: Integral (Z r) => r -> r

doubling map from [0,1) to [0,1) for odd denominator

preimages :: Integral (Z r) => r -> (r, r)

doubling map preimages from [0,1) to [0,1)x[0,1)

Instances

Integral a => Q (Ratio a)

Associated Types

type Z (Ratio a) :: *

Methods

(%) :: Z (Ratio a) -> Z (Ratio a) -> Ratio a

numerator :: Ratio a -> Z (Ratio a)

denominator :: Ratio a -> Z (Ratio a)

(%!) :: Z (Ratio a) -> Z (Ratio a) -> Ratio a

zero :: Ratio a

half :: Ratio a

one :: Ratio a

fromQ :: Ratio a -> Rational

toQ :: Rational -> Ratio a

wrap :: Ratio a -> Ratio a

doubleWrap :: Ratio a -> Ratio a

double :: Ratio a -> Ratio a

doubleOdd :: Ratio a -> Ratio a

preimages :: Ratio a -> (Ratio a, Ratio a)

Integral a => Q (Ratio a)

Associated Types

type Z (Ratio a) :: *

Methods

(%) :: Z (Ratio a) -> Z (Ratio a) -> Ratio a

numerator :: Ratio a -> Z (Ratio a)

denominator :: Ratio a -> Z (Ratio a)

(%!) :: Z (Ratio a) -> Z (Ratio a) -> Ratio a

zero :: Ratio a

half :: Ratio a

one :: Ratio a

fromQ :: Ratio a -> Rational

toQ :: Rational -> Ratio a

wrap :: Ratio a -> Ratio a

doubleWrap :: Ratio a -> Ratio a

double :: Ratio a -> Ratio a

doubleOdd :: Ratio a -> Ratio a

preimages :: Ratio a -> (Ratio a, Ratio a)

data Ratio a

Ratio data structure

Constructors

!a :% !a

Instances

Eq a => Eq (Ratio a)

Methods

(==) :: Ratio a -> Ratio a -> Bool

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

Data a => Data (Ratio a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ratio a -> c (Ratio a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ratio a)

toConstr :: Ratio a -> Constr

dataTypeOf :: Ratio a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Ratio a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ratio a))

gmapT :: (forall b. Data b => b -> b) -> Ratio a -> Ratio a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ratio a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ratio a -> r

gmapQ :: (forall d. Data d => d -> u) -> Ratio a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Ratio a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a)

Integral a => Ord (Ratio a)

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)

Methods

readsPrec :: Int -> ReadS (Ratio a)

readList :: ReadS [Ratio a]

readPrec :: ReadPrec (Ratio a)

readListPrec :: ReadPrec [Ratio a]

(Integral a, Show a) => Show (Ratio a)

Methods

showsPrec :: Int -> Ratio a -> ShowS

show :: Ratio a -> String

showList :: [Ratio a] -> ShowS

Integral a => Q (Ratio a)

Associated Types

type Z (Ratio a) :: *

Methods

(%) :: Z (Ratio a) -> Z (Ratio a) -> Ratio a

numerator :: Ratio a -> Z (Ratio a)

denominator :: Ratio a -> Z (Ratio a)

(%!) :: Z (Ratio a) -> Z (Ratio a) -> Ratio a

zero :: Ratio a

half :: Ratio a

one :: Ratio a

fromQ :: Ratio a -> Rational

toQ :: Rational -> Ratio a

wrap :: Ratio a -> Ratio a

doubleWrap :: Ratio a -> Ratio a

double :: Ratio a -> Ratio a

doubleOdd :: Ratio a -> Ratio a

preimages :: Ratio a -> (Ratio a, Ratio a)

type Z (Ratio a)

type Z (Ratio a) = a

type Rational = Ratio Integer

Rational type