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

AERN2.MP.UseMPFR.Dyadic

Contents

Dyadic numbers and their basic operations
Dyadic constructors
tests

Description

Arbitrary precision floating-point numbers with exact ring operations.

Currently, we use hmpfr when compiling with ghc 7.10 and higher and haskell-mpfr when compiling with ghc 7.8.

Synopsis

Dyadic numbers and their basic operations

data Dyadic #

Exact dyadic type based on MPFloat.

Instances

Eq Dyadic #
Methods (==) :: Dyadic -> Dyadic -> Bool # (/=) :: Dyadic -> Dyadic -> Bool #
Num Dyadic #
Methods (+) :: Dyadic -> Dyadic -> Dyadic # (-) :: Dyadic -> Dyadic -> Dyadic # (*) :: Dyadic -> Dyadic -> Dyadic # negate :: Dyadic -> Dyadic # abs :: Dyadic -> Dyadic # signum :: Dyadic -> Dyadic # fromInteger :: Integer -> Dyadic #
Ord Dyadic #
Methods compare :: Dyadic -> Dyadic -> Ordering # (<) :: Dyadic -> Dyadic -> Bool # (<=) :: Dyadic -> Dyadic -> Bool # (>) :: Dyadic -> Dyadic -> Bool # (>=) :: Dyadic -> Dyadic -> Bool # max :: Dyadic -> Dyadic -> Dyadic # min :: Dyadic -> Dyadic -> Dyadic #
Read Dyadic #
Methods readsPrec :: Int -> ReadS Dyadic # readList :: ReadS [Dyadic] # readPrec :: ReadPrec Dyadic # readListPrec :: ReadPrec [Dyadic] #
Real Dyadic #
Methods toRational :: Dyadic -> Rational #
Show Dyadic #
Methods showsPrec :: Int -> Dyadic -> ShowS # show :: Dyadic -> String # showList :: [Dyadic] -> ShowS #
Arbitrary Dyadic #
Methods arbitrary :: Gen Dyadic # shrink :: Dyadic -> [Dyadic] #
Ring Dyadic #

OrderedRing Dyadic #

OrderedCertainlyRing Dyadic #

CanRound Dyadic #
Methods properFraction :: Dyadic -> (Integer, Dyadic) # truncate :: Dyadic -> Integer # round :: Dyadic -> Integer # ceiling :: Dyadic -> Integer # floor :: Dyadic -> Integer #
HasIntegerBounds Dyadic #
Methods integerBounds :: Dyadic -> (Integer, Integer) #
CanAbs Dyadic #
Associated Types type AbsType Dyadic :: * # Methods abs :: Dyadic -> AbsType Dyadic #
CanTestInteger Dyadic #
Methods certainlyNotInteger :: Dyadic -> Bool # certainlyInteger :: Dyadic -> Bool # certainlyIntegerGetIt :: Dyadic -> Maybe Integer #
CanTestZero Dyadic #
Methods isCertainlyZero :: Dyadic -> Bool # isCertainlyNonZero :: Dyadic -> Bool #
CanTestPosNeg Dyadic #
Methods isCertainlyPositive :: Dyadic -> Bool # isCertainlyNonNegative :: Dyadic -> Bool # isCertainlyNegative :: Dyadic -> Bool # isCertainlyNonPositive :: Dyadic -> Bool #
CanNeg Dyadic #
Associated Types type NegType Dyadic :: * # Methods negate :: Dyadic -> NegType Dyadic #
HasPrecision Dyadic #
Methods getPrecision :: Dyadic -> Precision #
HasNorm Dyadic #
Methods getNormLog :: Dyadic -> NormLog #
HasAccuracy Dyadic #
Methods getAccuracy :: Dyadic -> Accuracy #
Convertible Dyadic Double #
Methods safeConvert :: Dyadic -> ConvertResult Double #
CanDiv Int Dyadic #
Associated Types type DivTypeNoCN Int Dyadic :: * # type DivType Int Dyadic :: * # Methods divideNoCN :: Int -> Dyadic -> DivTypeNoCN Int Dyadic # divide :: Int -> Dyadic -> DivType Int Dyadic #
CanDiv Integer Dyadic #
Associated Types type DivTypeNoCN Integer Dyadic :: * # type DivType Integer Dyadic :: * # Methods divideNoCN :: Integer -> Dyadic -> DivTypeNoCN Integer Dyadic # divide :: Integer -> Dyadic -> DivType Integer Dyadic #
CanDiv Rational Dyadic #
Associated Types type DivTypeNoCN Rational Dyadic :: * # type DivType Rational Dyadic :: * # Methods divideNoCN :: Rational -> Dyadic -> DivTypeNoCN Rational Dyadic # divide :: Rational -> Dyadic -> DivType Rational Dyadic #
CanDiv Dyadic Int #
Associated Types type DivTypeNoCN Dyadic Int :: * # type DivType Dyadic Int :: * # Methods divideNoCN :: Dyadic -> Int -> DivTypeNoCN Dyadic Int # divide :: Dyadic -> Int -> DivType Dyadic Int #
CanDiv Dyadic Integer #
Associated Types type DivTypeNoCN Dyadic Integer :: * # type DivType Dyadic Integer :: * # Methods divideNoCN :: Dyadic -> Integer -> DivTypeNoCN Dyadic Integer # divide :: Dyadic -> Integer -> DivType Dyadic Integer #
CanDiv Dyadic Rational #
Associated Types type DivTypeNoCN Dyadic Rational :: * # type DivType Dyadic Rational :: * # Methods divideNoCN :: Dyadic -> Rational -> DivTypeNoCN Dyadic Rational # divide :: Dyadic -> Rational -> DivType Dyadic Rational #
CanMulAsymmetric Int Dyadic #
Associated Types type MulType Int Dyadic :: * # Methods mul :: Int -> Dyadic -> MulType Int Dyadic #
CanMulAsymmetric Integer Dyadic #
Associated Types type MulType Integer Dyadic :: * # Methods mul :: Integer -> Dyadic -> MulType Integer Dyadic #
CanMulAsymmetric Rational Dyadic #
Associated Types type MulType Rational Dyadic :: * # Methods mul :: Rational -> Dyadic -> MulType Rational Dyadic #
CanMulAsymmetric Dyadic Int #
Associated Types type MulType Dyadic Int :: * # Methods mul :: Dyadic -> Int -> MulType Dyadic Int #
CanMulAsymmetric Dyadic Integer #
Associated Types type MulType Dyadic Integer :: * # Methods mul :: Dyadic -> Integer -> MulType Dyadic Integer #
CanMulAsymmetric Dyadic Rational #
Associated Types type MulType Dyadic Rational :: * # Methods mul :: Dyadic -> Rational -> MulType Dyadic Rational #
CanMulAsymmetric Dyadic Dyadic #
Associated Types type MulType Dyadic Dyadic :: * # Methods mul :: Dyadic -> Dyadic -> MulType Dyadic Dyadic #
CanPow Dyadic Int #
Associated Types type PowTypeNoCN Dyadic Int :: * # type PowType Dyadic Int :: * # Methods powNoCN :: Dyadic -> Int -> PowTypeNoCN Dyadic Int # pow :: Dyadic -> Int -> PowType Dyadic Int #
CanPow Dyadic Integer #
Associated Types type PowTypeNoCN Dyadic Integer :: * # type PowType Dyadic Integer :: * # Methods powNoCN :: Dyadic -> Integer -> PowTypeNoCN Dyadic Integer # pow :: Dyadic -> Integer -> PowType Dyadic Integer #
CanAddAsymmetric Int Dyadic #
Associated Types type AddType Int Dyadic :: * # Methods add :: Int -> Dyadic -> AddType Int Dyadic #
CanAddAsymmetric Integer Dyadic #
Associated Types type AddType Integer Dyadic :: * # Methods add :: Integer -> Dyadic -> AddType Integer Dyadic #
CanAddAsymmetric Rational Dyadic #
Associated Types type AddType Rational Dyadic :: * # Methods add :: Rational -> Dyadic -> AddType Rational Dyadic #
CanAddAsymmetric Dyadic Int #
Associated Types type AddType Dyadic Int :: * # Methods add :: Dyadic -> Int -> AddType Dyadic Int #
CanAddAsymmetric Dyadic Integer #
Associated Types type AddType Dyadic Integer :: * # Methods add :: Dyadic -> Integer -> AddType Dyadic Integer #
CanAddAsymmetric Dyadic Rational #
Associated Types type AddType Dyadic Rational :: * # Methods add :: Dyadic -> Rational -> AddType Dyadic Rational #
CanAddAsymmetric Dyadic Dyadic #
Associated Types type AddType Dyadic Dyadic :: * # Methods add :: Dyadic -> Dyadic -> AddType Dyadic Dyadic #
CanSub Int Dyadic #
Associated Types type SubType Int Dyadic :: * # Methods sub :: Int -> Dyadic -> SubType Int Dyadic #
CanSub Integer Dyadic #
Associated Types type SubType Integer Dyadic :: * # Methods sub :: Integer -> Dyadic -> SubType Integer Dyadic #
CanSub Rational Dyadic #
Associated Types type SubType Rational Dyadic :: * # Methods sub :: Rational -> Dyadic -> SubType Rational Dyadic #
CanSub Dyadic Int #
Associated Types type SubType Dyadic Int :: * # Methods sub :: Dyadic -> Int -> SubType Dyadic Int #
CanSub Dyadic Integer #
Associated Types type SubType Dyadic Integer :: * # Methods sub :: Dyadic -> Integer -> SubType Dyadic Integer #
CanSub Dyadic Rational #
Associated Types type SubType Dyadic Rational :: * # Methods sub :: Dyadic -> Rational -> SubType Dyadic Rational #
CanSub Dyadic Dyadic #
Associated Types type SubType Dyadic Dyadic :: * # Methods sub :: Dyadic -> Dyadic -> SubType Dyadic Dyadic #
CanMinMaxAsymmetric Int Dyadic #
Associated Types type MinMaxType Int Dyadic :: * # Methods min :: Int -> Dyadic -> MinMaxType Int Dyadic # max :: Int -> Dyadic -> MinMaxType Int Dyadic #
CanMinMaxAsymmetric Integer Dyadic #
Associated Types type MinMaxType Integer Dyadic :: * # Methods min :: Integer -> Dyadic -> MinMaxType Integer Dyadic # max :: Integer -> Dyadic -> MinMaxType Integer Dyadic #
CanMinMaxAsymmetric Rational Dyadic #
Associated Types type MinMaxType Rational Dyadic :: * # Methods min :: Rational -> Dyadic -> MinMaxType Rational Dyadic # max :: Rational -> Dyadic -> MinMaxType Rational Dyadic #
CanMinMaxAsymmetric Dyadic Int #
Associated Types type MinMaxType Dyadic Int :: * # Methods min :: Dyadic -> Int -> MinMaxType Dyadic Int # max :: Dyadic -> Int -> MinMaxType Dyadic Int #
CanMinMaxAsymmetric Dyadic Integer #
Associated Types type MinMaxType Dyadic Integer :: * # Methods min :: Dyadic -> Integer -> MinMaxType Dyadic Integer # max :: Dyadic -> Integer -> MinMaxType Dyadic Integer #
CanMinMaxAsymmetric Dyadic Rational #
Associated Types type MinMaxType Dyadic Rational :: * # Methods min :: Dyadic -> Rational -> MinMaxType Dyadic Rational # max :: Dyadic -> Rational -> MinMaxType Dyadic Rational #
CanMinMaxAsymmetric Dyadic Dyadic #
Associated Types type MinMaxType Dyadic Dyadic :: * # Methods min :: Dyadic -> Dyadic -> MinMaxType Dyadic Dyadic # max :: Dyadic -> Dyadic -> MinMaxType Dyadic Dyadic #
HasEqAsymmetric Int Dyadic #
Associated Types type EqCompareType Int Dyadic :: * # Methods equalTo :: Int -> Dyadic -> EqCompareType Int Dyadic # notEqualTo :: Int -> Dyadic -> EqCompareType Int Dyadic #
HasEqAsymmetric Integer Dyadic #
Associated Types type EqCompareType Integer Dyadic :: * # Methods equalTo :: Integer -> Dyadic -> EqCompareType Integer Dyadic # notEqualTo :: Integer -> Dyadic -> EqCompareType Integer Dyadic #
HasEqAsymmetric Rational Dyadic #
Associated Types type EqCompareType Rational Dyadic :: * # Methods equalTo :: Rational -> Dyadic -> EqCompareType Rational Dyadic # notEqualTo :: Rational -> Dyadic -> EqCompareType Rational Dyadic #
HasEqAsymmetric Dyadic Int #
Associated Types type EqCompareType Dyadic Int :: * # Methods equalTo :: Dyadic -> Int -> EqCompareType Dyadic Int # notEqualTo :: Dyadic -> Int -> EqCompareType Dyadic Int #
HasEqAsymmetric Dyadic Integer #
Associated Types type EqCompareType Dyadic Integer :: * # Methods equalTo :: Dyadic -> Integer -> EqCompareType Dyadic Integer # notEqualTo :: Dyadic -> Integer -> EqCompareType Dyadic Integer #
HasEqAsymmetric Dyadic Rational #
Associated Types type EqCompareType Dyadic Rational :: * # Methods equalTo :: Dyadic -> Rational -> EqCompareType Dyadic Rational # notEqualTo :: Dyadic -> Rational -> EqCompareType Dyadic Rational #
HasEqAsymmetric Dyadic Dyadic #
Associated Types type EqCompareType Dyadic Dyadic :: * # Methods equalTo :: Dyadic -> Dyadic -> EqCompareType Dyadic Dyadic # notEqualTo :: Dyadic -> Dyadic -> EqCompareType Dyadic Dyadic #
HasOrderAsymmetric Int Dyadic #
Associated Types type OrderCompareType Int Dyadic :: * # Methods lessThan :: Int -> Dyadic -> OrderCompareType Int Dyadic # greaterThan :: Int -> Dyadic -> OrderCompareType Int Dyadic # leq :: Int -> Dyadic -> OrderCompareType Int Dyadic # geq :: Int -> Dyadic -> OrderCompareType Int Dyadic #
HasOrderAsymmetric Integer Dyadic #
Associated Types type OrderCompareType Integer Dyadic :: * # Methods lessThan :: Integer -> Dyadic -> OrderCompareType Integer Dyadic # greaterThan :: Integer -> Dyadic -> OrderCompareType Integer Dyadic # leq :: Integer -> Dyadic -> OrderCompareType Integer Dyadic # geq :: Integer -> Dyadic -> OrderCompareType Integer Dyadic #
HasOrderAsymmetric Rational Dyadic #
Associated Types type OrderCompareType Rational Dyadic :: * # Methods lessThan :: Rational -> Dyadic -> OrderCompareType Rational Dyadic # greaterThan :: Rational -> Dyadic -> OrderCompareType Rational Dyadic # leq :: Rational -> Dyadic -> OrderCompareType Rational Dyadic # geq :: Rational -> Dyadic -> OrderCompareType Rational Dyadic #
HasOrderAsymmetric Dyadic Int #
Associated Types type OrderCompareType Dyadic Int :: * # Methods lessThan :: Dyadic -> Int -> OrderCompareType Dyadic Int # greaterThan :: Dyadic -> Int -> OrderCompareType Dyadic Int # leq :: Dyadic -> Int -> OrderCompareType Dyadic Int # geq :: Dyadic -> Int -> OrderCompareType Dyadic Int #
HasOrderAsymmetric Dyadic Integer #
Associated Types type OrderCompareType Dyadic Integer :: * # Methods lessThan :: Dyadic -> Integer -> OrderCompareType Dyadic Integer # greaterThan :: Dyadic -> Integer -> OrderCompareType Dyadic Integer # leq :: Dyadic -> Integer -> OrderCompareType Dyadic Integer # geq :: Dyadic -> Integer -> OrderCompareType Dyadic Integer #
HasOrderAsymmetric Dyadic Rational #
Associated Types type OrderCompareType Dyadic Rational :: * # Methods lessThan :: Dyadic -> Rational -> OrderCompareType Dyadic Rational # greaterThan :: Dyadic -> Rational -> OrderCompareType Dyadic Rational # leq :: Dyadic -> Rational -> OrderCompareType Dyadic Rational # geq :: Dyadic -> Rational -> OrderCompareType Dyadic Rational #
HasOrderAsymmetric Dyadic Dyadic #
Associated Types type OrderCompareType Dyadic Dyadic :: * # Methods lessThan :: Dyadic -> Dyadic -> OrderCompareType Dyadic Dyadic # greaterThan :: Dyadic -> Dyadic -> OrderCompareType Dyadic Dyadic # leq :: Dyadic -> Dyadic -> OrderCompareType Dyadic Dyadic # geq :: Dyadic -> Dyadic -> OrderCompareType Dyadic Dyadic #
ConvertibleExactly Int Dyadic #
Methods safeConvertExactly :: Int -> ConvertResult Dyadic #
ConvertibleExactly Integer Dyadic #
Methods safeConvertExactly :: Integer -> ConvertResult Dyadic #
ConvertibleExactly Rational Dyadic #
Methods safeConvertExactly :: Rational -> ConvertResult Dyadic #
ConvertibleExactly MPFloat Dyadic #
Methods safeConvertExactly :: MPFloat -> ConvertResult Dyadic #
ConvertibleExactly Dyadic Rational #
Methods safeConvertExactly :: Dyadic -> ConvertResult Rational #
ConvertibleExactly Dyadic MPFloat #
Methods safeConvertExactly :: Dyadic -> ConvertResult MPFloat #
ConvertibleExactly Dyadic Dyadic #
Methods safeConvertExactly :: Dyadic -> ConvertResult Dyadic #
ConvertibleExactly ErrorBound Dyadic #
Methods safeConvertExactly :: ErrorBound -> ConvertResult Dyadic #
SuitableForCE es => CanEnsureCE es Dyadic #
Associated Types type EnsureCE es Dyadic :: * # type EnsureNoCE es Dyadic :: * # Methods ensureCE :: Maybe es -> Dyadic -> EnsureCE es Dyadic # deEnsureCE :: Maybe es -> EnsureCE es Dyadic -> Either es Dyadic # ensureNoCE :: Maybe es -> Dyadic -> (Maybe (EnsureNoCE es Dyadic), es) # noValueECE :: Maybe Dyadic -> es -> EnsureCE es Dyadic # prependErrorsECE :: Maybe Dyadic -> es -> EnsureCE es Dyadic -> EnsureCE es Dyadic #
CanTestContains MPBall Dyadic #
Methods contains :: MPBall -> Dyadic -> Bool #
(CanDiv Dyadic b, CanEnsureCE es b, CanEnsureCE es (DivType Dyadic b), CanEnsureCE es (DivTypeNoCN Dyadic b), SuitableForCE es) => CanDiv Dyadic (CollectErrors es b) #
Associated Types type DivTypeNoCN Dyadic (CollectErrors es b) :: * # type DivType Dyadic (CollectErrors es b) :: * # Methods divideNoCN :: Dyadic -> CollectErrors es b -> DivTypeNoCN Dyadic (CollectErrors es b) # divide :: Dyadic -> CollectErrors es b -> DivType Dyadic (CollectErrors es b) #
(CanMulAsymmetric Dyadic b, CanEnsureCE es b, CanEnsureCE es (MulType Dyadic b), SuitableForCE es) => CanMulAsymmetric Dyadic (CollectErrors es b) #
Associated Types type MulType Dyadic (CollectErrors es b) :: * # Methods mul :: Dyadic -> CollectErrors es b -> MulType Dyadic (CollectErrors es b) #
(CanPow Dyadic b, CanEnsureCE es b, CanEnsureCE es (PowTypeNoCN Dyadic b), CanEnsureCE es (PowType Dyadic b), SuitableForCE es) => CanPow Dyadic (CollectErrors es b) #
Associated Types type PowTypeNoCN Dyadic (CollectErrors es b) :: * # type PowType Dyadic (CollectErrors es b) :: * # Methods powNoCN :: Dyadic -> CollectErrors es b -> PowTypeNoCN Dyadic (CollectErrors es b) # pow :: Dyadic -> CollectErrors es b -> PowType Dyadic (CollectErrors es b) #
(CanAddAsymmetric Dyadic b, CanEnsureCE es b, CanEnsureCE es (AddType Dyadic b), SuitableForCE es) => CanAddAsymmetric Dyadic (CollectErrors es b) #
Associated Types type AddType Dyadic (CollectErrors es b) :: * # Methods add :: Dyadic -> CollectErrors es b -> AddType Dyadic (CollectErrors es b) #
(CanSub Dyadic b, CanEnsureCE es b, CanEnsureCE es (SubType Dyadic b), SuitableForCE es) => CanSub Dyadic (CollectErrors es b) #
Associated Types type SubType Dyadic (CollectErrors es b) :: * # Methods sub :: Dyadic -> CollectErrors es b -> SubType Dyadic (CollectErrors es b) #
(CanMinMaxAsymmetric Dyadic b, CanEnsureCE es b, CanEnsureCE es (MinMaxType Dyadic b), SuitableForCE es) => CanMinMaxAsymmetric Dyadic (CollectErrors es b) #
Associated Types type MinMaxType Dyadic (CollectErrors es b) :: * # Methods min :: Dyadic -> CollectErrors es b -> MinMaxType Dyadic (CollectErrors es b) # max :: Dyadic -> CollectErrors es b -> MinMaxType Dyadic (CollectErrors es b) #
(HasEqAsymmetric Dyadic b, CanEnsureCE es b, CanEnsureCE es (EqCompareType Dyadic b), IsBool (EnsureCE es (EqCompareType Dyadic b)), SuitableForCE es) => HasEqAsymmetric Dyadic (CollectErrors es b) #
Associated Types type EqCompareType Dyadic (CollectErrors es b) :: * # Methods equalTo :: Dyadic -> CollectErrors es b -> EqCompareType Dyadic (CollectErrors es b) # notEqualTo :: Dyadic -> CollectErrors es b -> EqCompareType Dyadic (CollectErrors es b) #
(HasOrderAsymmetric Dyadic b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType Dyadic b), IsBool (EnsureCE es (OrderCompareType Dyadic b)), SuitableForCE es) => HasOrderAsymmetric Dyadic (CollectErrors es b) #
Associated Types type OrderCompareType Dyadic (CollectErrors es b) :: * # Methods lessThan :: Dyadic -> CollectErrors es b -> OrderCompareType Dyadic (CollectErrors es b) # greaterThan :: Dyadic -> CollectErrors es b -> OrderCompareType Dyadic (CollectErrors es b) # leq :: Dyadic -> CollectErrors es b -> OrderCompareType Dyadic (CollectErrors es b) # geq :: Dyadic -> CollectErrors es b -> OrderCompareType Dyadic (CollectErrors es b) #
(ConvertibleExactly Dyadic t, Monoid es) => ConvertibleExactly Dyadic (CollectErrors es t) #
Methods safeConvertExactly :: Dyadic -> ConvertResult (CollectErrors es t) #
Ring (CN Dyadic) #

OrderedRing (CN Dyadic) #

OrderedCertainlyRing (CN Dyadic) #

(CanDiv a Dyadic, CanEnsureCE es a, CanEnsureCE es (DivType a Dyadic), CanEnsureCE es (DivTypeNoCN a Dyadic), SuitableForCE es) => CanDiv (CollectErrors es a) Dyadic #
Associated Types type DivTypeNoCN (CollectErrors es a) Dyadic :: * # type DivType (CollectErrors es a) Dyadic :: * # Methods divideNoCN :: CollectErrors es a -> Dyadic -> DivTypeNoCN (CollectErrors es a) Dyadic # divide :: CollectErrors es a -> Dyadic -> DivType (CollectErrors es a) Dyadic #
(CanMulAsymmetric a Dyadic, CanEnsureCE es a, CanEnsureCE es (MulType a Dyadic), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) Dyadic #
Associated Types type MulType (CollectErrors es a) Dyadic :: * # Methods mul :: CollectErrors es a -> Dyadic -> MulType (CollectErrors es a) Dyadic #
(CanPow a Dyadic, CanEnsureCE es a, CanEnsureCE es (PowType a Dyadic), CanEnsureCE es (PowTypeNoCN a Dyadic), SuitableForCE es) => CanPow (CollectErrors es a) Dyadic #
Associated Types type PowTypeNoCN (CollectErrors es a) Dyadic :: * # type PowType (CollectErrors es a) Dyadic :: * # Methods powNoCN :: CollectErrors es a -> Dyadic -> PowTypeNoCN (CollectErrors es a) Dyadic # pow :: CollectErrors es a -> Dyadic -> PowType (CollectErrors es a) Dyadic #
(CanAddAsymmetric a Dyadic, CanEnsureCE es a, CanEnsureCE es (AddType a Dyadic), SuitableForCE es) => CanAddAsymmetric (CollectErrors es a) Dyadic #
Associated Types type AddType (CollectErrors es a) Dyadic :: * # Methods add :: CollectErrors es a -> Dyadic -> AddType (CollectErrors es a) Dyadic #
(CanSub a Dyadic, CanEnsureCE es a, CanEnsureCE es (SubType a Dyadic), SuitableForCE es) => CanSub (CollectErrors es a) Dyadic #
Associated Types type SubType (CollectErrors es a) Dyadic :: * # Methods sub :: CollectErrors es a -> Dyadic -> SubType (CollectErrors es a) Dyadic #
(CanMinMaxAsymmetric a Dyadic, CanEnsureCE es a, CanEnsureCE es (MinMaxType a Dyadic), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) Dyadic #
Associated Types type MinMaxType (CollectErrors es a) Dyadic :: * # Methods min :: CollectErrors es a -> Dyadic -> MinMaxType (CollectErrors es a) Dyadic # max :: CollectErrors es a -> Dyadic -> MinMaxType (CollectErrors es a) Dyadic #
(HasEqAsymmetric a Dyadic, CanEnsureCE es a, CanEnsureCE es (EqCompareType a Dyadic), IsBool (EnsureCE es (EqCompareType a Dyadic)), SuitableForCE es) => HasEqAsymmetric (CollectErrors es a) Dyadic #
Associated Types type EqCompareType (CollectErrors es a) Dyadic :: * # Methods equalTo :: CollectErrors es a -> Dyadic -> EqCompareType (CollectErrors es a) Dyadic # notEqualTo :: CollectErrors es a -> Dyadic -> EqCompareType (CollectErrors es a) Dyadic #
(HasOrderAsymmetric a Dyadic, CanEnsureCE es a, CanEnsureCE es (OrderCompareType a Dyadic), IsBool (EnsureCE es (OrderCompareType a Dyadic)), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) Dyadic #
Associated Types type OrderCompareType (CollectErrors es a) Dyadic :: * # Methods lessThan :: CollectErrors es a -> Dyadic -> OrderCompareType (CollectErrors es a) Dyadic # greaterThan :: CollectErrors es a -> Dyadic -> OrderCompareType (CollectErrors es a) Dyadic # leq :: CollectErrors es a -> Dyadic -> OrderCompareType (CollectErrors es a) Dyadic # geq :: CollectErrors es a -> Dyadic -> OrderCompareType (CollectErrors es a) Dyadic #
type AbsType Dyadic #
type AbsType Dyadic = Dyadic
type NegType Dyadic #
type NegType Dyadic = Dyadic
type DivType Int Dyadic #
type DivType Int Dyadic = EnsureCN (DivTypeNoCN Int Dyadic)
type DivType Integer Dyadic #
type DivType Integer Dyadic = EnsureCN (DivTypeNoCN Integer Dyadic)
type DivType Rational Dyadic #
type DivType Rational Dyadic = EnsureCN (DivTypeNoCN Rational Dyadic)
type DivType Dyadic Int #
type DivType Dyadic Int = EnsureCN (DivTypeNoCN Dyadic Int)
type DivType Dyadic Integer #
type DivType Dyadic Integer = EnsureCN (DivTypeNoCN Dyadic Integer)
type DivType Dyadic Rational #
type DivType Dyadic Rational = EnsureCN (DivTypeNoCN Dyadic Rational)
type DivType Dyadic Dyadic #
type DivType Dyadic Dyadic = EnsureCN (DivTypeNoCN Dyadic Dyadic)
type DivType Dyadic MPBall #
type DivType Dyadic MPBall = CN MPBall
type DivType MPBall Dyadic #
type DivType MPBall Dyadic = CN MPBall
type DivTypeNoCN Int Dyadic #
type DivTypeNoCN Int Dyadic = Rational
type DivTypeNoCN Integer Dyadic #
type DivTypeNoCN Integer Dyadic = Rational
type DivTypeNoCN Rational Dyadic #
type DivTypeNoCN Rational Dyadic = Rational
type DivTypeNoCN Dyadic Int #
type DivTypeNoCN Dyadic Int = Rational
type DivTypeNoCN Dyadic Integer #
type DivTypeNoCN Dyadic Integer = Rational
type DivTypeNoCN Dyadic Rational #
type DivTypeNoCN Dyadic Rational = Rational
type DivTypeNoCN Dyadic Dyadic #
type DivTypeNoCN Dyadic Dyadic = MPBall
type DivTypeNoCN Dyadic MPBall #
type DivTypeNoCN Dyadic MPBall = MPBall
type DivTypeNoCN MPBall Dyadic #
type DivTypeNoCN MPBall Dyadic = MPBall
type MulType Int Dyadic #
type MulType Int Dyadic = Dyadic
type MulType Integer Dyadic #
type MulType Integer Dyadic = Dyadic
type MulType Rational Dyadic #
type MulType Rational Dyadic = Rational
type MulType Dyadic Int #
type MulType Dyadic Int = Dyadic
type MulType Dyadic Integer #
type MulType Dyadic Integer = Dyadic
type MulType Dyadic Rational #
type MulType Dyadic Rational = Rational
type MulType Dyadic Dyadic #
type MulType Dyadic Dyadic = Dyadic
type MulType Dyadic MPBall #
type MulType Dyadic MPBall = MPBall
type MulType MPBall Dyadic #
type MulType MPBall Dyadic = MPBall
type PowType Dyadic Int #
type PowType Dyadic Int = EnsureCN (PowTypeNoCN Dyadic Int)
type PowType Dyadic Integer #
type PowType Dyadic Integer = EnsureCN (PowTypeNoCN Dyadic Integer)
type PowType MPBall Dyadic #
type PowType MPBall Dyadic = EnsureCN (PowTypeNoCN MPBall Dyadic)
type PowTypeNoCN Dyadic Int #
type PowTypeNoCN Dyadic Int = Dyadic
type PowTypeNoCN Dyadic Integer #
type PowTypeNoCN Dyadic Integer = Dyadic
type PowTypeNoCN MPBall Dyadic #
type PowTypeNoCN MPBall Dyadic = MPBall
type AddType Int Dyadic #
type AddType Int Dyadic = Dyadic
type AddType Integer Dyadic #
type AddType Integer Dyadic = Dyadic
type AddType Rational Dyadic #
type AddType Rational Dyadic = Rational
type AddType Dyadic Int #
type AddType Dyadic Int = Dyadic
type AddType Dyadic Integer #
type AddType Dyadic Integer = Dyadic
type AddType Dyadic Rational #
type AddType Dyadic Rational = Rational
type AddType Dyadic Dyadic #
type AddType Dyadic Dyadic = Dyadic
type AddType Dyadic MPBall #
type AddType Dyadic MPBall = MPBall
type AddType MPBall Dyadic #
type AddType MPBall Dyadic = MPBall
type SubType Int Dyadic #
type SubType Int Dyadic = Dyadic
type SubType Integer Dyadic #
type SubType Integer Dyadic = Dyadic
type SubType Rational Dyadic #
type SubType Rational Dyadic = Rational
type SubType Dyadic Int #
type SubType Dyadic Int = Dyadic
type SubType Dyadic Integer #
type SubType Dyadic Integer = Dyadic
type SubType Dyadic Rational #
type SubType Dyadic Rational = Rational
type SubType Dyadic Dyadic #
type SubType Dyadic Dyadic = AddType Dyadic (NegType Dyadic)
type SubType Dyadic MPBall #
type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)
type SubType MPBall Dyadic #
type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)
type MinMaxType Int Dyadic #
type MinMaxType Int Dyadic = Dyadic
type MinMaxType Integer Dyadic #
type MinMaxType Integer Dyadic = Dyadic
type MinMaxType Rational Dyadic #
type MinMaxType Rational Dyadic = Rational
type MinMaxType Dyadic Int #
type MinMaxType Dyadic Int = Dyadic
type MinMaxType Dyadic Integer #
type MinMaxType Dyadic Integer = Dyadic
type MinMaxType Dyadic Rational #
type MinMaxType Dyadic Rational = Rational
type MinMaxType Dyadic Dyadic #
type MinMaxType Dyadic Dyadic = Dyadic
type MinMaxType Dyadic MPBall #
type MinMaxType Dyadic MPBall = MPBall
type MinMaxType MPBall Dyadic #
type MinMaxType MPBall Dyadic = MPBall
type EqCompareType Int Dyadic #
type EqCompareType Int Dyadic = Bool
type EqCompareType Integer Dyadic #
type EqCompareType Integer Dyadic = Bool
type EqCompareType Rational Dyadic #
type EqCompareType Rational Dyadic = Bool
type EqCompareType Dyadic Int #
type EqCompareType Dyadic Int = Bool
type EqCompareType Dyadic Integer #
type EqCompareType Dyadic Integer = Bool
type EqCompareType Dyadic Rational #
type EqCompareType Dyadic Rational = Bool
type EqCompareType Dyadic Dyadic #
type EqCompareType Dyadic Dyadic = Bool
type EqCompareType Dyadic MPBall #
type EqCompareType Dyadic MPBall = Maybe Bool
type EqCompareType MPBall Dyadic #
type EqCompareType MPBall Dyadic = Maybe Bool
type OrderCompareType Int Dyadic #
type OrderCompareType Int Dyadic = Bool
type OrderCompareType Integer Dyadic #
type OrderCompareType Integer Dyadic = Bool
type OrderCompareType Rational Dyadic #
type OrderCompareType Rational Dyadic = Bool
type OrderCompareType Dyadic Int #
type OrderCompareType Dyadic Int = Bool
type OrderCompareType Dyadic Integer #
type OrderCompareType Dyadic Integer = Bool
type OrderCompareType Dyadic Rational #
type OrderCompareType Dyadic Rational = Bool
type OrderCompareType Dyadic Dyadic #
type OrderCompareType Dyadic Dyadic = Bool
type OrderCompareType Dyadic MPBall #
type OrderCompareType Dyadic MPBall = Maybe Bool
type OrderCompareType MPBall Dyadic #
type OrderCompareType MPBall Dyadic = Maybe Bool
type EnsureNoCE es Dyadic #
type EnsureNoCE es Dyadic = Dyadic
type EnsureCE es Dyadic #
type EnsureCE es Dyadic = CollectErrors es Dyadic
type DivType Dyadic (CollectErrors es b) #
type DivType Dyadic (CollectErrors es b) = EnsureCE es (DivType Dyadic b)
type DivTypeNoCN Dyadic (CollectErrors es b) #
type DivTypeNoCN Dyadic (CollectErrors es b) = EnsureCE es (DivTypeNoCN Dyadic b)
type MulType Dyadic (CollectErrors es b) #
type MulType Dyadic (CollectErrors es b) = EnsureCE es (MulType Dyadic b)
type PowType Dyadic (CollectErrors es b) #
type PowType Dyadic (CollectErrors es b) = EnsureCE es (PowType Dyadic b)
type PowTypeNoCN Dyadic (CollectErrors es b) #
type PowTypeNoCN Dyadic (CollectErrors es b) = EnsureCE es (PowTypeNoCN Dyadic b)
type AddType Dyadic (CollectErrors es b) #
type AddType Dyadic (CollectErrors es b) = EnsureCE es (AddType Dyadic b)
type SubType Dyadic (CollectErrors es b) #
type SubType Dyadic (CollectErrors es b) = EnsureCE es (SubType Dyadic b)
type MinMaxType Dyadic (CollectErrors es b) #
type MinMaxType Dyadic (CollectErrors es b) = EnsureCE es (MinMaxType Dyadic b)
type EqCompareType Dyadic (CollectErrors es b) #
type EqCompareType Dyadic (CollectErrors es b) = EnsureCE es (EqCompareType Dyadic b)
type OrderCompareType Dyadic (CollectErrors es b) #
type OrderCompareType Dyadic (CollectErrors es b) = EnsureCE es (OrderCompareType Dyadic b)
type DivType (CollectErrors es a) Dyadic #
type DivType (CollectErrors es a) Dyadic = EnsureCE es (DivType a Dyadic)
type DivTypeNoCN (CollectErrors es a) Dyadic #
type DivTypeNoCN (CollectErrors es a) Dyadic = EnsureCE es (DivTypeNoCN a Dyadic)
type MulType (CollectErrors es a) Dyadic #
type MulType (CollectErrors es a) Dyadic = EnsureCE es (MulType a Dyadic)
type PowType (CollectErrors es a) Dyadic #
type PowType (CollectErrors es a) Dyadic = EnsureCE es (PowType a Dyadic)
type PowTypeNoCN (CollectErrors es a) Dyadic #
type PowTypeNoCN (CollectErrors es a) Dyadic = EnsureCE es (PowTypeNoCN a Dyadic)
type AddType (CollectErrors es a) Dyadic #
type AddType (CollectErrors es a) Dyadic = EnsureCE es (AddType a Dyadic)
type SubType (CollectErrors es a) Dyadic #
type SubType (CollectErrors es a) Dyadic = EnsureCE es (SubType a Dyadic)
type MinMaxType (CollectErrors es a) Dyadic #
type MinMaxType (CollectErrors es a) Dyadic = EnsureCE es (MinMaxType a Dyadic)
type EqCompareType (CollectErrors es a) Dyadic #
type EqCompareType (CollectErrors es a) Dyadic = EnsureCE es (EqCompareType a Dyadic)
type OrderCompareType (CollectErrors es a) Dyadic #
type OrderCompareType (CollectErrors es a) Dyadic = EnsureCE es (OrderCompareType a Dyadic)

type HasDyadics t = ConvertibleExactly Dyadic t #

Dyadic constructors

type CanBeDyadic t = ConvertibleExactly t Dyadic #

dyadic :: CanBeDyadic t => t -> Dyadic #

tests

specDyadic :: Spec #

tDyadic :: T Dyadic #

A runtime representative of type Dyadic. Used for specialising polymorphic tests to concrete types.