Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

Numeric.MixedTypes.Field

Contents

Field
Division
- Tests

Description

Synopsis

type CanAddSubMulDivCNBy t s = (CanAddSubMulBy t s, CanAddSubMulBy (EnsureCN t) s, CanDivCNBy t s)
class (Ring t, CanDivCNSameType t, CanRecipCNSameType t, CanAddSubMulDivCNBy t Rational, CanAddSubMulDivCNBy t Integer, CanAddSubMulDivCNBy t Int) => Field t
class (Field t, OrderedRing t, HasOrder t Rational, HasOrder (EnsureCN t) Rational) => OrderedField t
class (Field t, OrderedCertainlyRing t, HasOrderCertainly t Rational, HasOrderCertainly (EnsureCN t) Rational) => OrderedCertainlyField t
class CanDiv t1 t2 where
- type DivTypeNoCN t1 t2
- type DivType t1 t2
- divideNoCN :: t1 -> t2 -> DivTypeNoCN t1 t2
- divide :: t1 -> t2 -> DivType t1 t2
type CanDivBy t1 t2 = (CanDiv t1 t2, DivType t1 t2 ~ t1, DivTypeNoCN t1 t2 ~ t1)
type CanDivCNBy t1 t2 = (CanDiv t1 t2, DivType t1 t2 ~ EnsureCN t1, DivTypeNoCN t1 t2 ~ t1, CanEnsureCN t1, CanDiv (EnsureCN t1) t2, DivType (EnsureCN t1) t2 ~ EnsureCN t1, DivTypeNoCN (EnsureCN t1) t2 ~ EnsureCN t1)
type CanDivSameType t = CanDivBy t t
type CanDivCNSameType t = (CanDivCNBy t t, CanDiv (EnsureCN t) (EnsureCN t), DivType (EnsureCN t) (EnsureCN t) ~ EnsureCN t, DivTypeNoCN (EnsureCN t) (EnsureCN t) ~ EnsureCN t)
type CanRecip t = CanDiv Integer t
type CanRecipSameType t = (CanDiv Integer t, DivType Integer t ~ t, DivTypeNoCN Integer t ~ t)
type CanRecipCNSameType t = (CanDiv Integer t, DivType Integer t ~ EnsureCN t, DivTypeNoCN Integer t ~ t, CanEnsureCN t, CanDiv Integer (EnsureCN t), DivType Integer (EnsureCN t) ~ EnsureCN t, DivTypeNoCN Integer (EnsureCN t) ~ EnsureCN t)
(/) :: CanDiv t1 t2 => t1 -> t2 -> DivType t1 t2
(/!) :: CanDiv t1 t2 => t1 -> t2 -> DivTypeNoCN t1 t2
recip :: CanRecip t => t -> DivType Integer t
powUsingMulRecip :: (CanBeInteger e, CanRecipCNSameType t, CanMulSameType t, CanEnsureCN t) => t -> t -> e -> EnsureCN t
specCanDiv :: (Show t1, Show t2, Show (DivType Integer (DivType Integer t1)), Show (DivType t1 t2), Show (DivType t1 t1), Show (MulType t1 (DivType t1 t2)), Arbitrary t1, Arbitrary t2, ConvertibleExactly Integer t1, ConvertibleExactly Integer t2, CanTestCertainly (EqCompareType (DivType Integer (DivType Integer t1)) t1), CanTestCertainly (EqCompareType (DivType t1 t2) t1), CanTestCertainly (EqCompareType (DivType t1 t1) t1), CanTestCertainly (EqCompareType (DivType t1 t2) (MulType t1 (DivType t1 t2))), HasEqAsymmetric (DivType Integer (DivType Integer t1)) t1, HasEqAsymmetric (DivType t1 t2) t1, HasEqAsymmetric (DivType t1 t2) (MulType t1 (DivType t1 t2)), HasEqAsymmetric (DivType t1 t1) t1, CanTestZero t1, CanTestZero t2, CanTestZero (DivType Integer t1), CanMulAsymmetric t1 (DivType t1 t2), CanDiv t1 t1, CanDiv t1 t2, CanDiv Integer t1, CanDiv Integer (DivType Integer t1)) => T t1 -> T t2 -> Spec
specCanDivNotMixed :: (Show t, Show (DivType Integer (DivType Integer t)), Show (DivType t t), Show (MulType t (DivType t t)), Arbitrary t, ConvertibleExactly Integer t, CanTestCertainly (EqCompareType (DivType Integer (DivType Integer t)) t), CanTestCertainly (EqCompareType (DivType t t) t), CanTestCertainly (EqCompareType (DivType t t) (MulType t (DivType t t))), HasEqAsymmetric (DivType Integer (DivType Integer t)) t, HasEqAsymmetric (DivType t t) t, HasEqAsymmetric (DivType t t) (MulType t (DivType t t)), CanTestZero t, CanTestZero (DivType Integer t), CanMulAsymmetric t (DivType t t), CanDiv t t, CanDiv Integer t, CanDiv Integer (DivType Integer t)) => T t -> Spec

Field

type CanAddSubMulDivCNBy t s = (CanAddSubMulBy t s, CanAddSubMulBy (EnsureCN t) s, CanDivCNBy t s) Source #

class (Ring t, CanDivCNSameType t, CanRecipCNSameType t, CanAddSubMulDivCNBy t Rational, CanAddSubMulDivCNBy t Integer, CanAddSubMulDivCNBy t Int) => Field t Source #

Instances

Field Rational Source #
Instance details Defined in Numeric.MixedTypes.Field
Field (CN Rational) Source #
Instance details Defined in Numeric.MixedTypes.Field

class (Field t, OrderedRing t, HasOrder t Rational, HasOrder (EnsureCN t) Rational) => OrderedField t Source #

Instances

OrderedField Rational Source #
Instance details Defined in Numeric.MixedTypes.Field
OrderedField (CN Rational) Source #
Instance details Defined in Numeric.MixedTypes.Field

class (Field t, OrderedCertainlyRing t, HasOrderCertainly t Rational, HasOrderCertainly (EnsureCN t) Rational) => OrderedCertainlyField t Source #

Instances

OrderedCertainlyField Rational Source #
Instance details Defined in Numeric.MixedTypes.Field
OrderedCertainlyField (CN Rational) Source #
Instance details Defined in Numeric.MixedTypes.Field

Division

class CanDiv t1 t2 where Source #

A replacement for Prelude's binary /. If t1 = t2 and Fractional t1, then one can use the default implementation to mirror Prelude's /.

Minimal complete definition

divideNoCN

Associated Types

type DivTypeNoCN t1 t2 Source #

type DivType t1 t2 Source #

Methods

divideNoCN :: t1 -> t2 -> DivTypeNoCN t1 t2 Source #

divide :: t1 -> t2 -> DivType t1 t2 Source #

divide :: (CanTestZero t2, CanEnsureCN (DivTypeNoCN t1 t2), DivType t1 t2 ~ EnsureCN (DivTypeNoCN t1 t2)) => t1 -> t2 -> DivType t1 t2 Source #

Instances

CanDiv Double Double Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Double Double :: Type Source # type DivType Double Double :: Type Source # Methods divideNoCN :: Double -> Double -> DivTypeNoCN Double Double Source # divide :: Double -> Double -> DivType Double Double Source #
CanDiv Double Int Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Double Int :: Type Source # type DivType Double Int :: Type Source # Methods divideNoCN :: Double -> Int -> DivTypeNoCN Double Int Source # divide :: Double -> Int -> DivType Double Int Source #
CanDiv Double Integer Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Double Integer :: Type Source # type DivType Double Integer :: Type Source # Methods divideNoCN :: Double -> Integer -> DivTypeNoCN Double Integer Source # divide :: Double -> Integer -> DivType Double Integer Source #
CanDiv Double Rational Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Double Rational :: Type Source # type DivType Double Rational :: Type Source # Methods divideNoCN :: Double -> Rational -> DivTypeNoCN Double Rational Source # divide :: Double -> Rational -> DivType Double Rational Source #
CanDiv Int Double Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Int Double :: Type Source # type DivType Int Double :: Type Source # Methods divideNoCN :: Int -> Double -> DivTypeNoCN Int Double Source # divide :: Int -> Double -> DivType Int Double Source #
CanDiv Int Int Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Int Int :: Type Source # type DivType Int Int :: Type Source # Methods divideNoCN :: Int -> Int -> DivTypeNoCN Int Int Source # divide :: Int -> Int -> DivType Int Int Source #
CanDiv Int Integer Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Int Integer :: Type Source # type DivType Int Integer :: Type Source # Methods divideNoCN :: Int -> Integer -> DivTypeNoCN Int Integer Source # divide :: Int -> Integer -> DivType Int Integer Source #
CanDiv Int Rational Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Int Rational :: Type Source # type DivType Int Rational :: Type Source # Methods divideNoCN :: Int -> Rational -> DivTypeNoCN Int Rational Source # divide :: Int -> Rational -> DivType Int Rational Source #
CanDiv Integer Double Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Integer Double :: Type Source # type DivType Integer Double :: Type Source # Methods divideNoCN :: Integer -> Double -> DivTypeNoCN Integer Double Source # divide :: Integer -> Double -> DivType Integer Double Source #
CanDiv Integer Int Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Integer Int :: Type Source # type DivType Integer Int :: Type Source # Methods divideNoCN :: Integer -> Int -> DivTypeNoCN Integer Int Source # divide :: Integer -> Int -> DivType Integer Int Source #
CanDiv Integer Integer Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Integer Integer :: Type Source # type DivType Integer Integer :: Type Source # Methods divideNoCN :: Integer -> Integer -> DivTypeNoCN Integer Integer Source # divide :: Integer -> Integer -> DivType Integer Integer Source #
CanDiv Integer Rational Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Integer Rational :: Type Source # type DivType Integer Rational :: Type Source # Methods divideNoCN :: Integer -> Rational -> DivTypeNoCN Integer Rational Source # divide :: Integer -> Rational -> DivType Integer Rational Source #
CanDiv Rational Double Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Rational Double :: Type Source # type DivType Rational Double :: Type Source # Methods divideNoCN :: Rational -> Double -> DivTypeNoCN Rational Double Source # divide :: Rational -> Double -> DivType Rational Double Source #
CanDiv Rational Int Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Rational Int :: Type Source # type DivType Rational Int :: Type Source # Methods divideNoCN :: Rational -> Int -> DivTypeNoCN Rational Int Source # divide :: Rational -> Int -> DivType Rational Int Source #
CanDiv Rational Integer Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Rational Integer :: Type Source # type DivType Rational Integer :: Type Source # Methods divideNoCN :: Rational -> Integer -> DivTypeNoCN Rational Integer Source # divide :: Rational -> Integer -> DivType Rational Integer Source #
CanDiv Rational Rational Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Rational Rational :: Type Source # type DivType Rational Rational :: Type Source # Methods divideNoCN :: Rational -> Rational -> DivTypeNoCN Rational Rational Source # divide :: Rational -> Rational -> DivType Rational Rational Source #
(CanMulAsymmetric Double b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Double b) (MulType b b)) => CanDiv Double (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type DivTypeNoCN Double (Complex b) :: Type Source # type DivType Double (Complex b) :: Type Source # Methods divideNoCN :: Double -> Complex b -> DivTypeNoCN Double (Complex b) Source # divide :: Double -> Complex b -> DivType Double (Complex b) Source #
(CanMulAsymmetric Int b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Int b) (MulType b b)) => CanDiv Int (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type DivTypeNoCN Int (Complex b) :: Type Source # type DivType Int (Complex b) :: Type Source # Methods divideNoCN :: Int -> Complex b -> DivTypeNoCN Int (Complex b) Source # divide :: Int -> Complex b -> DivType Int (Complex b) Source #
(CanMulAsymmetric Integer b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Integer b) (MulType b b)) => CanDiv Integer (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type DivTypeNoCN Integer (Complex b) :: Type Source # type DivType Integer (Complex b) :: Type Source # Methods divideNoCN :: Integer -> Complex b -> DivTypeNoCN Integer (Complex b) Source # divide :: Integer -> Complex b -> DivType Integer (Complex b) Source #
(CanMulAsymmetric Rational b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Rational b) (MulType b b)) => CanDiv Rational (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type DivTypeNoCN Rational (Complex b) :: Type Source # type DivType Rational (Complex b) :: Type Source # Methods divideNoCN :: Rational -> Complex b -> DivTypeNoCN Rational (Complex b) Source # divide :: Rational -> Complex b -> DivType Rational (Complex b) Source #
(CanDiv Double b, CanEnsureCE es b, CanEnsureCE es (DivType Double b), CanEnsureCE es (DivTypeNoCN Double b), SuitableForCE es) => CanDiv Double (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Double (CollectErrors es b) :: Type Source # type DivType Double (CollectErrors es b) :: Type Source # Methods divideNoCN :: Double -> CollectErrors es b -> DivTypeNoCN Double (CollectErrors es b) Source # divide :: Double -> CollectErrors es b -> DivType Double (CollectErrors es b) Source #
(CanDiv Int b, CanEnsureCE es b, CanEnsureCE es (DivType Int b), CanEnsureCE es (DivTypeNoCN Int b), SuitableForCE es) => CanDiv Int (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Int (CollectErrors es b) :: Type Source # type DivType Int (CollectErrors es b) :: Type Source # Methods divideNoCN :: Int -> CollectErrors es b -> DivTypeNoCN Int (CollectErrors es b) Source # divide :: Int -> CollectErrors es b -> DivType Int (CollectErrors es b) Source #
(CanDiv Integer b, CanEnsureCE es b, CanEnsureCE es (DivType Integer b), CanEnsureCE es (DivTypeNoCN Integer b), SuitableForCE es) => CanDiv Integer (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Integer (CollectErrors es b) :: Type Source # type DivType Integer (CollectErrors es b) :: Type Source # Methods divideNoCN :: Integer -> CollectErrors es b -> DivTypeNoCN Integer (CollectErrors es b) Source # divide :: Integer -> CollectErrors es b -> DivType Integer (CollectErrors es b) Source #
(CanDiv Rational b, CanEnsureCE es b, CanEnsureCE es (DivType Rational b), CanEnsureCE es (DivTypeNoCN Rational b), SuitableForCE es) => CanDiv Rational (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN Rational (CollectErrors es b) :: Type Source # type DivType Rational (CollectErrors es b) :: Type Source # Methods divideNoCN :: Rational -> CollectErrors es b -> DivTypeNoCN Rational (CollectErrors es b) Source # divide :: Rational -> CollectErrors es b -> DivType Rational (CollectErrors es b) Source #
CanDiv a Integer => CanDiv (Complex a) Integer Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type DivTypeNoCN (Complex a) Integer :: Type Source # type DivType (Complex a) Integer :: Type Source # Methods divideNoCN :: Complex a -> Integer -> DivTypeNoCN (Complex a) Integer Source # divide :: Complex a -> Integer -> DivType (Complex a) Integer Source #
CanDiv a Int => CanDiv (Complex a) Int Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type DivTypeNoCN (Complex a) Int :: Type Source # type DivType (Complex a) Int :: Type Source # Methods divideNoCN :: Complex a -> Int -> DivTypeNoCN (Complex a) Int Source # divide :: Complex a -> Int -> DivType (Complex a) Int Source #
CanDiv a Rational => CanDiv (Complex a) Rational Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type DivTypeNoCN (Complex a) Rational :: Type Source # type DivType (Complex a) Rational :: Type Source # Methods divideNoCN :: Complex a -> Rational -> DivTypeNoCN (Complex a) Rational Source # divide :: Complex a -> Rational -> DivType (Complex a) Rational Source #
CanDiv a Double => CanDiv (Complex a) Double Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type DivTypeNoCN (Complex a) Double :: Type Source # type DivType (Complex a) Double :: Type Source # Methods divideNoCN :: Complex a -> Double -> DivTypeNoCN (Complex a) Double Source # divide :: Complex a -> Double -> DivType (Complex a) Double Source #
CanDiv a b => CanDiv [a] [b] Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN [a] [b] :: Type Source # type DivType [a] [b] :: Type Source # Methods divideNoCN :: [a] -> [b] -> DivTypeNoCN [a] [b] Source # divide :: [a] -> [b] -> DivType [a] [b] Source #
CanDiv a b => CanDiv (Maybe a) (Maybe b) Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN (Maybe a) (Maybe b) :: Type Source # type DivType (Maybe a) (Maybe b) :: Type Source # Methods divideNoCN :: Maybe a -> Maybe b -> DivTypeNoCN (Maybe a) (Maybe b) Source # divide :: Maybe a -> Maybe b -> DivType (Maybe a) (Maybe b) Source #
(CanMulAsymmetric a b, CanAddSameType (MulType a b), CanSubSameType (MulType a b), CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType a b) (MulType b b)) => CanDiv (Complex a) (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type DivTypeNoCN (Complex a) (Complex b) :: Type Source # type DivType (Complex a) (Complex b) :: Type Source # Methods divideNoCN :: Complex a -> Complex b -> DivTypeNoCN (Complex a) (Complex b) Source # divide :: Complex a -> Complex b -> DivType (Complex a) (Complex b) Source #
(CanDiv a Integer, CanEnsureCE es a, CanEnsureCE es (DivType a Integer), CanEnsureCE es (DivTypeNoCN a Integer), SuitableForCE es) => CanDiv (CollectErrors es a) Integer Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN (CollectErrors es a) Integer :: Type Source # type DivType (CollectErrors es a) Integer :: Type Source # Methods divideNoCN :: CollectErrors es a -> Integer -> DivTypeNoCN (CollectErrors es a) Integer Source # divide :: CollectErrors es a -> Integer -> DivType (CollectErrors es a) Integer Source #
(CanDiv a Int, CanEnsureCE es a, CanEnsureCE es (DivType a Int), CanEnsureCE es (DivTypeNoCN a Int), SuitableForCE es) => CanDiv (CollectErrors es a) Int Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN (CollectErrors es a) Int :: Type Source # type DivType (CollectErrors es a) Int :: Type Source # Methods divideNoCN :: CollectErrors es a -> Int -> DivTypeNoCN (CollectErrors es a) Int Source # divide :: CollectErrors es a -> Int -> DivType (CollectErrors es a) Int Source #
(CanDiv a Rational, CanEnsureCE es a, CanEnsureCE es (DivType a Rational), CanEnsureCE es (DivTypeNoCN a Rational), SuitableForCE es) => CanDiv (CollectErrors es a) Rational Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN (CollectErrors es a) Rational :: Type Source # type DivType (CollectErrors es a) Rational :: Type Source # Methods divideNoCN :: CollectErrors es a -> Rational -> DivTypeNoCN (CollectErrors es a) Rational Source # divide :: CollectErrors es a -> Rational -> DivType (CollectErrors es a) Rational Source #
(CanDiv a Double, CanEnsureCE es a, CanEnsureCE es (DivType a Double), CanEnsureCE es (DivTypeNoCN a Double), SuitableForCE es) => CanDiv (CollectErrors es a) Double Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN (CollectErrors es a) Double :: Type Source # type DivType (CollectErrors es a) Double :: Type Source # Methods divideNoCN :: CollectErrors es a -> Double -> DivTypeNoCN (CollectErrors es a) Double Source # divide :: CollectErrors es a -> Double -> DivType (CollectErrors es a) Double Source #
(CanDiv a b, CanEnsureCE es a, CanEnsureCE es b, CanEnsureCE es (DivType a b), CanEnsureCE es (DivTypeNoCN a b), SuitableForCE es) => CanDiv (CollectErrors es a) (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.Field Associated Types type DivTypeNoCN (CollectErrors es a) (CollectErrors es b) :: Type Source # type DivType (CollectErrors es a) (CollectErrors es b) :: Type Source # Methods divideNoCN :: CollectErrors es a -> CollectErrors es b -> DivTypeNoCN (CollectErrors es a) (CollectErrors es b) Source # divide :: CollectErrors es a -> CollectErrors es b -> DivType (CollectErrors es a) (CollectErrors es b) Source #

type CanDivBy t1 t2 = (CanDiv t1 t2, DivType t1 t2 ~ t1, DivTypeNoCN t1 t2 ~ t1) Source #

type CanDivCNBy t1 t2 = (CanDiv t1 t2, DivType t1 t2 ~ EnsureCN t1, DivTypeNoCN t1 t2 ~ t1, CanEnsureCN t1, CanDiv (EnsureCN t1) t2, DivType (EnsureCN t1) t2 ~ EnsureCN t1, DivTypeNoCN (EnsureCN t1) t2 ~ EnsureCN t1) Source #

type CanDivSameType t = CanDivBy t t Source #

type CanDivCNSameType t = (CanDivCNBy t t, CanDiv (EnsureCN t) (EnsureCN t), DivType (EnsureCN t) (EnsureCN t) ~ EnsureCN t, DivTypeNoCN (EnsureCN t) (EnsureCN t) ~ EnsureCN t) Source #

type CanRecip t = CanDiv Integer t Source #

type CanRecipSameType t = (CanDiv Integer t, DivType Integer t ~ t, DivTypeNoCN Integer t ~ t) Source #

type CanRecipCNSameType t = (CanDiv Integer t, DivType Integer t ~ EnsureCN t, DivTypeNoCN Integer t ~ t, CanEnsureCN t, CanDiv Integer (EnsureCN t), DivType Integer (EnsureCN t) ~ EnsureCN t, DivTypeNoCN Integer (EnsureCN t) ~ EnsureCN t) Source #

(/) :: CanDiv t1 t2 => t1 -> t2 -> DivType t1 t2 infixl 7 Source #

(/!) :: CanDiv t1 t2 => t1 -> t2 -> DivTypeNoCN t1 t2 infixl 7 Source #

recip :: CanRecip t => t -> DivType Integer t Source #

powUsingMulRecip :: (CanBeInteger e, CanRecipCNSameType t, CanMulSameType t, CanEnsureCN t) => t -> t -> e -> EnsureCN t Source #

Tests

specCanDiv :: (Show t1, Show t2, Show (DivType Integer (DivType Integer t1)), Show (DivType t1 t2), Show (DivType t1 t1), Show (MulType t1 (DivType t1 t2)), Arbitrary t1, Arbitrary t2, ConvertibleExactly Integer t1, ConvertibleExactly Integer t2, CanTestCertainly (EqCompareType (DivType Integer (DivType Integer t1)) t1), CanTestCertainly (EqCompareType (DivType t1 t2) t1), CanTestCertainly (EqCompareType (DivType t1 t1) t1), CanTestCertainly (EqCompareType (DivType t1 t2) (MulType t1 (DivType t1 t2))), HasEqAsymmetric (DivType Integer (DivType Integer t1)) t1, HasEqAsymmetric (DivType t1 t2) t1, HasEqAsymmetric (DivType t1 t2) (MulType t1 (DivType t1 t2)), HasEqAsymmetric (DivType t1 t1) t1, CanTestZero t1, CanTestZero t2, CanTestZero (DivType Integer t1), CanMulAsymmetric t1 (DivType t1 t2), CanDiv t1 t1, CanDiv t1 t2, CanDiv Integer t1, CanDiv Integer (DivType Integer t1)) => T t1 -> T t2 -> Spec Source #

HSpec properties that each implementation of CanDiv should satisfy.

specCanDivNotMixed :: (Show t, Show (DivType Integer (DivType Integer t)), Show (DivType t t), Show (MulType t (DivType t t)), Arbitrary t, ConvertibleExactly Integer t, CanTestCertainly (EqCompareType (DivType Integer (DivType Integer t)) t), CanTestCertainly (EqCompareType (DivType t t) t), CanTestCertainly (EqCompareType (DivType t t) (MulType t (DivType t t))), HasEqAsymmetric (DivType Integer (DivType Integer t)) t, HasEqAsymmetric (DivType t t) t, HasEqAsymmetric (DivType t t) (MulType t (DivType t t)), CanTestZero t, CanTestZero (DivType Integer t), CanMulAsymmetric t (DivType t t), CanDiv t t, CanDiv Integer t, CanDiv Integer (DivType Integer t)) => T t -> Spec Source #

HSpec properties that each implementation of CanDiv should satisfy.