Numeric.MixedTypes.Round

Rounded division + modulus

class CanDivIMod t1 t2 where

Minimal complete definition

divIMod

Associated Types

type DivIType t1 t2

type ModType t1 t2

type ModType t1 t2 = t1

Methods

divIMod :: t1 -> t2 -> (DivIType t1 t2, ModType t1 t2)

mod :: t1 -> t2 -> ModType t1 t2

divI :: t1 -> t2 -> DivIType t1 t2

Instances

CanDivIMod Double Double

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Double Double

type ModType Double Double

Methods

divIMod :: Double -> Double -> (DivIType Double Double, ModType Double Double)

mod :: Double -> Double -> ModType Double Double

divI :: Double -> Double -> DivIType Double Double

CanDivIMod Double Integer

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Double Integer

type ModType Double Integer

Methods

divIMod :: Double -> Integer -> (DivIType Double Integer, ModType Double Integer)

mod :: Double -> Integer -> ModType Double Integer

divI :: Double -> Integer -> DivIType Double Integer

CanDivIMod Int Int

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Int Int

type ModType Int Int

Methods

divIMod :: Int -> Int -> (DivIType Int Int, ModType Int Int)

mod :: Int -> Int -> ModType Int Int

divI :: Int -> Int -> DivIType Int Int

CanDivIMod Int Integer

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Int Integer

type ModType Int Integer

Methods

divIMod :: Int -> Integer -> (DivIType Int Integer, ModType Int Integer)

mod :: Int -> Integer -> ModType Int Integer

divI :: Int -> Integer -> DivIType Int Integer

CanDivIMod Int Rational

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Int Rational

type ModType Int Rational

Methods

divIMod :: Int -> Rational -> (DivIType Int Rational, ModType Int Rational)

mod :: Int -> Rational -> ModType Int Rational

divI :: Int -> Rational -> DivIType Int Rational

CanDivIMod Integer Int

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Integer Int

type ModType Integer Int

Methods

divIMod :: Integer -> Int -> (DivIType Integer Int, ModType Integer Int)

mod :: Integer -> Int -> ModType Integer Int

divI :: Integer -> Int -> DivIType Integer Int

CanDivIMod Integer Integer

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Integer Integer

type ModType Integer Integer

Methods

divIMod :: Integer -> Integer -> (DivIType Integer Integer, ModType Integer Integer)

mod :: Integer -> Integer -> ModType Integer Integer

divI :: Integer -> Integer -> DivIType Integer Integer

CanDivIMod Integer Rational

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Integer Rational

type ModType Integer Rational

Methods

divIMod :: Integer -> Rational -> (DivIType Integer Rational, ModType Integer Rational)

mod :: Integer -> Rational -> ModType Integer Rational

divI :: Integer -> Rational -> DivIType Integer Rational

CanDivIMod Rational Int

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Rational Int

type ModType Rational Int

Methods

divIMod :: Rational -> Int -> (DivIType Rational Int, ModType Rational Int)

mod :: Rational -> Int -> ModType Rational Int

divI :: Rational -> Int -> DivIType Rational Int

CanDivIMod Rational Integer

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Rational Integer

type ModType Rational Integer

Methods

divIMod :: Rational -> Integer -> (DivIType Rational Integer, ModType Rational Integer)

mod :: Rational -> Integer -> ModType Rational Integer

divI :: Rational -> Integer -> DivIType Rational Integer

CanDivIMod Rational Rational

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Rational Rational

type ModType Rational Rational

Methods

divIMod :: Rational -> Rational -> (DivIType Rational Rational, ModType Rational Rational)

mod :: Rational -> Rational -> ModType Rational Rational

divI :: Rational -> Rational -> DivIType Rational Rational

(CanDivIMod Double t2, CanTestPosNeg t2) => CanDivIMod Double (CN t2)

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Double (CN t2)

type ModType Double (CN t2)

Methods

divIMod :: Double -> CN t2 -> (DivIType Double (CN t2), ModType Double (CN t2))

mod :: Double -> CN t2 -> ModType Double (CN t2)

divI :: Double -> CN t2 -> DivIType Double (CN t2)

(CanDivIMod Int t2, CanTestPosNeg t2) => CanDivIMod Int (CN t2)

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Int (CN t2)

type ModType Int (CN t2)

Methods

divIMod :: Int -> CN t2 -> (DivIType Int (CN t2), ModType Int (CN t2))

mod :: Int -> CN t2 -> ModType Int (CN t2)

divI :: Int -> CN t2 -> DivIType Int (CN t2)

(CanDivIMod Integer t2, CanTestPosNeg t2) => CanDivIMod Integer (CN t2)

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Integer (CN t2)

type ModType Integer (CN t2)

Methods

divIMod :: Integer -> CN t2 -> (DivIType Integer (CN t2), ModType Integer (CN t2))

mod :: Integer -> CN t2 -> ModType Integer (CN t2)

divI :: Integer -> CN t2 -> DivIType Integer (CN t2)

(CanDivIMod Rational t2, CanTestPosNeg t2) => CanDivIMod Rational (CN t2)

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType Rational (CN t2)

type ModType Rational (CN t2)

Methods

divIMod :: Rational -> CN t2 -> (DivIType Rational (CN t2), ModType Rational (CN t2))

mod :: Rational -> CN t2 -> ModType Rational (CN t2)

divI :: Rational -> CN t2 -> DivIType Rational (CN t2)

CanDivIMod t1 Integer => CanDivIMod (CN t1) Integer

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType (CN t1) Integer

type ModType (CN t1) Integer

Methods

divIMod :: CN t1 -> Integer -> (DivIType (CN t1) Integer, ModType (CN t1) Integer)

mod :: CN t1 -> Integer -> ModType (CN t1) Integer

divI :: CN t1 -> Integer -> DivIType (CN t1) Integer

CanDivIMod t1 Int => CanDivIMod (CN t1) Int

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType (CN t1) Int

type ModType (CN t1) Int

Methods

divIMod :: CN t1 -> Int -> (DivIType (CN t1) Int, ModType (CN t1) Int)

mod :: CN t1 -> Int -> ModType (CN t1) Int

divI :: CN t1 -> Int -> DivIType (CN t1) Int

CanDivIMod t1 Rational => CanDivIMod (CN t1) Rational

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType (CN t1) Rational

type ModType (CN t1) Rational

Methods

divIMod :: CN t1 -> Rational -> (DivIType (CN t1) Rational, ModType (CN t1) Rational)

mod :: CN t1 -> Rational -> ModType (CN t1) Rational

divI :: CN t1 -> Rational -> DivIType (CN t1) Rational

CanDivIMod t1 Double => CanDivIMod (CN t1) Double

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType (CN t1) Double

type ModType (CN t1) Double

Methods

divIMod :: CN t1 -> Double -> (DivIType (CN t1) Double, ModType (CN t1) Double)

mod :: CN t1 -> Double -> ModType (CN t1) Double

divI :: CN t1 -> Double -> DivIType (CN t1) Double

(CanDivIMod t1 t2, CanTestPosNeg t2) => CanDivIMod (CN t1) (CN t2)

Defined in Numeric.MixedTypes.Round

Associated Types

type DivIType (CN t1) (CN t2)

type ModType (CN t1) (CN t2)

Methods

divIMod :: CN t1 -> CN t2 -> (DivIType (CN t1) (CN t2), ModType (CN t1) (CN t2))

mod :: CN t1 -> CN t2 -> ModType (CN t1) (CN t2)

divI :: CN t1 -> CN t2 -> DivIType (CN t1) (CN t2)

type CanDivIModIntegerSameType t = (CanDivIMod t t, DivIType t t ~ Integer, ModType t t ~ t)

type CanDivIModIntegerSameTypeCN t = (CanDivIMod t t, DivIType t t ~ CN Integer, ModType t t ~ t)

Rounding

class CanRound t where

A replacement for Prelude's RealFrac operations, such as round in which the result type is fixed to Integer.

If RealFrac t and CanTestPosNeg t, then one can use the default implementation to mirror Prelude's round, etc.

In other cases, it is sufficient to define properFraction.

Minimal complete definition

Nothing

Associated Types

type RoundType t

type RoundType t = Integer

Methods

properFraction :: t -> (RoundType t, t)

default properFraction :: (RealFrac t, RoundType t ~ Integer) => t -> (RoundType t, t)

truncate :: t -> RoundType t

round :: t -> RoundType t

default round :: (HasOrderCertainly t Rational, RoundType t ~ Integer) => t -> RoundType t

ceiling :: t -> RoundType t

default ceiling :: (CanTestPosNeg t, RoundType t ~ Integer) => t -> RoundType t

floor :: t -> RoundType t

default floor :: (CanTestPosNeg t, RoundType t ~ Integer) => t -> RoundType t

Instances

CanRound Double

Defined in Numeric.MixedTypes.Round

Associated Types

type RoundType Double

Methods

properFraction :: Double -> (RoundType Double, Double)

truncate :: Double -> RoundType Double

round :: Double -> RoundType Double

ceiling :: Double -> RoundType Double

floor :: Double -> RoundType Double

CanRound Rational

Defined in Numeric.MixedTypes.Round

Associated Types

type RoundType Rational

Methods

properFraction :: Rational -> (RoundType Rational, Rational)

truncate :: Rational -> RoundType Rational

round :: Rational -> RoundType Rational

ceiling :: Rational -> RoundType Rational

floor :: Rational -> RoundType Rational

class HasIntegerBounds t where

Minimal complete definition

Nothing

Methods

integerBounds :: t -> (Integer, Integer)

default integerBounds :: (CanRound t, RoundType t ~ Integer) => t -> (Integer, Integer)

Instances

HasIntegerBounds Double

Defined in Numeric.MixedTypes.Round

Methods

integerBounds :: Double -> (Integer, Integer)

HasIntegerBounds Int

Defined in Numeric.MixedTypes.Round

Methods

integerBounds :: Int -> (Integer, Integer)

HasIntegerBounds Integer

Defined in Numeric.MixedTypes.Round

Methods

integerBounds :: Integer -> (Integer, Integer)

HasIntegerBounds Rational

Defined in Numeric.MixedTypes.Round

Methods

integerBounds :: Rational -> (Integer, Integer)

Tests

specCanDivIMod :: _ => T t -> Spec

HSpec properties that each implementation of CanRound should satisfy.

specCanRound :: _ => T t -> Spec

HSpec properties that each implementation of CanRound should satisfy.

specHasIntegerBounds :: _ => T t -> Spec

HSpec properties that each implementation of CanRound should satisfy.