Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

AERN2.MP.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

data Dyadic
type HasDyadics t = ConvertibleExactly Dyadic t
type CanBeDyadic t = ConvertibleExactly t Dyadic
dyadic :: CanBeDyadic t => t -> Dyadic
specDyadic :: Spec
tDyadic :: T Dyadic

Dyadic numbers and their basic operations

data Dyadic Source #

Exact dyadic type based on MPFloat.

Instances

Instances details

Eq Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods (==) :: Dyadic -> Dyadic -> Bool # (/=) :: Dyadic -> Dyadic -> Bool #
Num Dyadic Source #
Instance details Defined in AERN2.MP.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 Source #
Instance details Defined in AERN2.MP.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 Source #
Instance details Defined in AERN2.MP.Dyadic Methods readsPrec :: Int -> ReadS Dyadic # readList :: ReadS [Dyadic] # readPrec :: ReadPrec Dyadic # readListPrec :: ReadPrec [Dyadic] #
Real Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods toRational :: Dyadic -> Rational #
Show Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods showsPrec :: Int -> Dyadic -> ShowS # show :: Dyadic -> String # showList :: [Dyadic] -> ShowS #
Arbitrary Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods arbitrary :: Gen Dyadic # shrink :: Dyadic -> [Dyadic] #
CanRound Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type RoundType Dyadic # Methods properFraction :: Dyadic -> (RoundType Dyadic, Dyadic) # truncate :: Dyadic -> RoundType Dyadic # round :: Dyadic -> RoundType Dyadic # ceiling :: Dyadic -> RoundType Dyadic # floor :: Dyadic -> RoundType Dyadic #
HasIntegerBounds Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods integerBounds :: Dyadic -> (Integer, Integer) #
Ring Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic
OrderedRing Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic
OrderedCertainlyRing Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic
CanAbs Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type AbsType Dyadic # Methods abs :: Dyadic -> AbsType Dyadic #
CanTestFinite Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods isInfinite :: Dyadic -> Bool # isFinite :: Dyadic -> Bool #
CanTestInteger Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods certainlyNotInteger :: Dyadic -> Bool # certainlyInteger :: Dyadic -> Bool # certainlyIntegerGetIt :: Dyadic -> Maybe Integer #
CanTestZero Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods isCertainlyZero :: Dyadic -> Bool # isCertainlyNonZero :: Dyadic -> Bool #
CanTestPosNeg Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods isCertainlyPositive :: Dyadic -> Bool # isCertainlyNonNegative :: Dyadic -> Bool # isCertainlyNegative :: Dyadic -> Bool # isCertainlyNonPositive :: Dyadic -> Bool #
CanNeg Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type NegType Dyadic # Methods negate :: Dyadic -> NegType Dyadic #
CanGiveUpIfVeryInaccurate Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods giveUpIfVeryInaccurate :: CN Dyadic -> CN Dyadic #
HasPrecision Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods getPrecision :: Dyadic -> Precision Source #
HasNorm Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods getNormLog :: Dyadic -> NormLog Source #
HasAccuracy Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods getAccuracy :: Dyadic -> Accuracy Source # getFiniteAccuracy :: Dyadic -> Accuracy Source #
CanPow Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type PowType Dyadic Int # Methods pow :: Dyadic -> Int -> PowType Dyadic Int #
CanPow Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type PowType Dyadic Integer # Methods pow :: Dyadic -> Integer -> PowType Dyadic Integer #
CanPow MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Elementary Associated Types type PowType MPBall Dyadic # Methods pow :: MPBall -> Dyadic -> PowType MPBall Dyadic #
CanDiv Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type DivType Int Dyadic # Methods divide :: Int -> Dyadic -> DivType Int Dyadic #
CanDiv Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type DivType Integer Dyadic # Methods divide :: Integer -> Dyadic -> DivType Integer Dyadic #
CanDiv Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type DivType Rational Dyadic # Methods divide :: Rational -> Dyadic -> DivType Rational Dyadic #
CanDiv Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type DivType Dyadic Int # Methods divide :: Dyadic -> Int -> DivType Dyadic Int #
CanDiv Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type DivType Dyadic Integer # Methods divide :: Dyadic -> Integer -> DivType Dyadic Integer #
CanDiv Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type DivType Dyadic Rational # Methods divide :: Dyadic -> Rational -> DivType Dyadic Rational #
CanDiv Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType Dyadic Dyadic # Methods divide :: Dyadic -> Dyadic -> DivType Dyadic Dyadic #
CanDiv Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType Dyadic MPBall # Methods divide :: Dyadic -> MPBall -> DivType Dyadic MPBall #
CanDiv MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type DivType MPBall Dyadic # Methods divide :: MPBall -> Dyadic -> DivType MPBall Dyadic #
CanMulAsymmetric Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MulType Int Dyadic # Methods mul :: Int -> Dyadic -> MulType Int Dyadic #
CanMulAsymmetric Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MulType Integer Dyadic # Methods mul :: Integer -> Dyadic -> MulType Integer Dyadic #
CanMulAsymmetric Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MulType Rational Dyadic # Methods mul :: Rational -> Dyadic -> MulType Rational Dyadic #
CanMulAsymmetric Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MulType Dyadic Int # Methods mul :: Dyadic -> Int -> MulType Dyadic Int #
CanMulAsymmetric Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MulType Dyadic Integer # Methods mul :: Dyadic -> Integer -> MulType Dyadic Integer #
CanMulAsymmetric Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MulType Dyadic Rational # Methods mul :: Dyadic -> Rational -> MulType Dyadic Rational #
CanMulAsymmetric Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MulType Dyadic Dyadic # Methods mul :: Dyadic -> Dyadic -> MulType Dyadic Dyadic #
CanMulAsymmetric Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType Dyadic MPBall # Methods mul :: Dyadic -> MPBall -> MulType Dyadic MPBall #
CanMulAsymmetric MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type MulType MPBall Dyadic # Methods mul :: MPBall -> Dyadic -> MulType MPBall Dyadic #
CanAddAsymmetric Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type AddType Int Dyadic # Methods add :: Int -> Dyadic -> AddType Int Dyadic #
CanAddAsymmetric Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type AddType Integer Dyadic # Methods add :: Integer -> Dyadic -> AddType Integer Dyadic #
CanAddAsymmetric Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type AddType Rational Dyadic # Methods add :: Rational -> Dyadic -> AddType Rational Dyadic #
CanAddAsymmetric Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type AddType Dyadic Int # Methods add :: Dyadic -> Int -> AddType Dyadic Int #
CanAddAsymmetric Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type AddType Dyadic Integer # Methods add :: Dyadic -> Integer -> AddType Dyadic Integer #
CanAddAsymmetric Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type AddType Dyadic Rational # Methods add :: Dyadic -> Rational -> AddType Dyadic Rational #
CanAddAsymmetric Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type AddType Dyadic Dyadic # Methods add :: Dyadic -> Dyadic -> AddType Dyadic Dyadic #
CanAddAsymmetric Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType Dyadic MPBall # Methods add :: Dyadic -> MPBall -> AddType Dyadic MPBall #
CanAddAsymmetric MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type AddType MPBall Dyadic # Methods add :: MPBall -> Dyadic -> AddType MPBall Dyadic #
CanSub Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type SubType Int Dyadic # Methods sub :: Int -> Dyadic -> SubType Int Dyadic #
CanSub Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type SubType Integer Dyadic # Methods sub :: Integer -> Dyadic -> SubType Integer Dyadic #
CanSub Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type SubType Rational Dyadic # Methods sub :: Rational -> Dyadic -> SubType Rational Dyadic #
CanSub Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type SubType Dyadic Int # Methods sub :: Dyadic -> Int -> SubType Dyadic Int #
CanSub Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type SubType Dyadic Integer # Methods sub :: Dyadic -> Integer -> SubType Dyadic Integer #
CanSub Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type SubType Dyadic Rational # Methods sub :: Dyadic -> Rational -> SubType Dyadic Rational #
CanSub Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type SubType Dyadic Dyadic # Methods sub :: Dyadic -> Dyadic -> SubType Dyadic Dyadic #
CanSub Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType Dyadic MPBall # Methods sub :: Dyadic -> MPBall -> SubType Dyadic MPBall #
CanSub MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field Associated Types type SubType MPBall Dyadic # Methods sub :: MPBall -> Dyadic -> SubType MPBall Dyadic #
CanMinMaxAsymmetric Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MinMaxType Int Dyadic # Methods min :: Int -> Dyadic -> MinMaxType Int Dyadic # max :: Int -> Dyadic -> MinMaxType Int Dyadic #
CanMinMaxAsymmetric Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MinMaxType Integer Dyadic # Methods min :: Integer -> Dyadic -> MinMaxType Integer Dyadic # max :: Integer -> Dyadic -> MinMaxType Integer Dyadic #
CanMinMaxAsymmetric Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MinMaxType Rational Dyadic # Methods min :: Rational -> Dyadic -> MinMaxType Rational Dyadic # max :: Rational -> Dyadic -> MinMaxType Rational Dyadic #
CanMinMaxAsymmetric Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MinMaxType Dyadic Int # Methods min :: Dyadic -> Int -> MinMaxType Dyadic Int # max :: Dyadic -> Int -> MinMaxType Dyadic Int #
CanMinMaxAsymmetric Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MinMaxType Dyadic Integer # Methods min :: Dyadic -> Integer -> MinMaxType Dyadic Integer # max :: Dyadic -> Integer -> MinMaxType Dyadic Integer #
CanMinMaxAsymmetric Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MinMaxType Dyadic Rational # Methods min :: Dyadic -> Rational -> MinMaxType Dyadic Rational # max :: Dyadic -> Rational -> MinMaxType Dyadic Rational #
CanMinMaxAsymmetric Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MinMaxType Dyadic Dyadic # Methods min :: Dyadic -> Dyadic -> MinMaxType Dyadic Dyadic # max :: Dyadic -> Dyadic -> MinMaxType Dyadic Dyadic #
CanMinMaxAsymmetric Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType Dyadic MPBall # Methods min :: Dyadic -> MPBall -> MinMaxType Dyadic MPBall # max :: Dyadic -> MPBall -> MinMaxType Dyadic MPBall #
CanMinMaxAsymmetric MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type MinMaxType MPBall Dyadic # Methods min :: MPBall -> Dyadic -> MinMaxType MPBall Dyadic # max :: MPBall -> Dyadic -> MinMaxType MPBall Dyadic #
HasEqAsymmetric Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type EqCompareType Int Dyadic # Methods equalTo :: Int -> Dyadic -> EqCompareType Int Dyadic # notEqualTo :: Int -> Dyadic -> EqCompareType Int Dyadic #
HasEqAsymmetric Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type EqCompareType Integer Dyadic # Methods equalTo :: Integer -> Dyadic -> EqCompareType Integer Dyadic # notEqualTo :: Integer -> Dyadic -> EqCompareType Integer Dyadic #
HasEqAsymmetric Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type EqCompareType Rational Dyadic # Methods equalTo :: Rational -> Dyadic -> EqCompareType Rational Dyadic # notEqualTo :: Rational -> Dyadic -> EqCompareType Rational Dyadic #
HasEqAsymmetric Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type EqCompareType Dyadic Int # Methods equalTo :: Dyadic -> Int -> EqCompareType Dyadic Int # notEqualTo :: Dyadic -> Int -> EqCompareType Dyadic Int #
HasEqAsymmetric Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type EqCompareType Dyadic Integer # Methods equalTo :: Dyadic -> Integer -> EqCompareType Dyadic Integer # notEqualTo :: Dyadic -> Integer -> EqCompareType Dyadic Integer #
HasEqAsymmetric Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type EqCompareType Dyadic Rational # Methods equalTo :: Dyadic -> Rational -> EqCompareType Dyadic Rational # notEqualTo :: Dyadic -> Rational -> EqCompareType Dyadic Rational #
HasEqAsymmetric Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type EqCompareType Dyadic Dyadic # Methods equalTo :: Dyadic -> Dyadic -> EqCompareType Dyadic Dyadic # notEqualTo :: Dyadic -> Dyadic -> EqCompareType Dyadic Dyadic #
HasEqAsymmetric Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType Dyadic MPBall # Methods equalTo :: Dyadic -> MPBall -> EqCompareType Dyadic MPBall # notEqualTo :: Dyadic -> MPBall -> EqCompareType Dyadic MPBall #
HasEqAsymmetric MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type EqCompareType MPBall Dyadic # Methods equalTo :: MPBall -> Dyadic -> EqCompareType MPBall Dyadic # notEqualTo :: MPBall -> Dyadic -> EqCompareType MPBall Dyadic #
HasOrderAsymmetric Int Dyadic Source #
Instance details Defined in AERN2.MP.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 Source #
Instance details Defined in AERN2.MP.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 Source #
Instance details Defined in AERN2.MP.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 Source #
Instance details Defined in AERN2.MP.Dyadic 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 Source #
Instance details Defined in AERN2.MP.Dyadic 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 Source #
Instance details Defined in AERN2.MP.Dyadic 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 Source #
Instance details Defined in AERN2.MP.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 #
HasOrderAsymmetric Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType Dyadic MPBall # Methods lessThan :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall # greaterThan :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall # leq :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall # geq :: Dyadic -> MPBall -> OrderCompareType Dyadic MPBall #
HasOrderAsymmetric MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type OrderCompareType MPBall Dyadic # Methods lessThan :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic # greaterThan :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic # leq :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic # geq :: MPBall -> Dyadic -> OrderCompareType MPBall Dyadic #
ConvertibleExactly Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods safeConvertExactly :: Int -> ConvertResult Dyadic #
ConvertibleExactly Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods safeConvertExactly :: Integer -> ConvertResult Dyadic #
ConvertibleExactly Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods safeConvertExactly :: Rational -> ConvertResult Dyadic #
ConvertibleExactly MPFloat Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods safeConvertExactly :: MPFloat -> ConvertResult Dyadic #
ConvertibleExactly Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic Methods safeConvertExactly :: Dyadic -> ConvertResult Rational #
ConvertibleExactly Dyadic MPFloat Source #
Instance details Defined in AERN2.MP.Dyadic Methods safeConvertExactly :: Dyadic -> ConvertResult MPFloat #
ConvertibleExactly Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods safeConvertExactly :: Dyadic -> ConvertResult Dyadic #
ConvertibleExactly Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertExactly :: Dyadic -> ConvertResult MPBall #
ConvertibleExactly ErrorBound Dyadic Source #
Instance details Defined in AERN2.MP.ErrorBound Methods safeConvertExactly :: ErrorBound -> ConvertResult Dyadic #
Convertible Dyadic Double Source #
Instance details Defined in AERN2.MP.Dyadic Methods safeConvert :: Dyadic -> ConvertResult Double #
ConvertibleWithPrecision Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Dyadic -> ConvertResult MPBall Source #
CanTestContains MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Type Methods contains :: MPBall -> Dyadic -> Bool Source #
CanBeErrorBound t => CanPlusMinus Dyadic t Source #
Instance details Defined in AERN2.MP.Ball.Conversions Associated Types type PlusMinusType Dyadic t Source # Methods plusMinus :: Dyadic -> t -> PlusMinusType Dyadic t Source #
(CanPow Dyadic b, CanBeErrors es) => CanPow Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type PowType Dyadic (CollectErrors es b) # Methods pow :: Dyadic -> CollectErrors es b -> PowType Dyadic (CollectErrors es b) #
(CanDiv Dyadic b, CanBeErrors es) => CanDiv Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type DivType Dyadic (CollectErrors es b) # Methods divide :: Dyadic -> CollectErrors es b -> DivType Dyadic (CollectErrors es b) #
(CanMulAsymmetric Dyadic b, CanBeErrors es) => CanMulAsymmetric Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MulType Dyadic (CollectErrors es b) # Methods mul :: Dyadic -> CollectErrors es b -> MulType Dyadic (CollectErrors es b) #
(CanAddAsymmetric Dyadic b, CanBeErrors es) => CanAddAsymmetric Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type AddType Dyadic (CollectErrors es b) # Methods add :: Dyadic -> CollectErrors es b -> AddType Dyadic (CollectErrors es b) #
(CanSub Dyadic b, CanBeErrors es) => CanSub Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type SubType Dyadic (CollectErrors es b) # Methods sub :: Dyadic -> CollectErrors es b -> SubType Dyadic (CollectErrors es b) #
(CanMinMaxAsymmetric Dyadic b, CanBeErrors es) => CanMinMaxAsymmetric Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic 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, IsBool (CollectErrors es (EqCompareType Dyadic b)), CanBeErrors es) => HasEqAsymmetric Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic 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, IsBool (CollectErrors es (OrderCompareType Dyadic b)), CanBeErrors es) => HasOrderAsymmetric Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic 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) Source #
Instance details Defined in AERN2.MP.Dyadic Methods safeConvertExactly :: Dyadic -> ConvertResult (CollectErrors es t) #
Ring (CN Dyadic) Source #
Instance details Defined in AERN2.MP.Dyadic
OrderedRing (CN Dyadic) Source #
Instance details Defined in AERN2.MP.Dyadic
OrderedCertainlyRing (CN Dyadic) Source #
Instance details Defined in AERN2.MP.Dyadic
(CanPow a Dyadic, CanBeErrors es) => CanPow (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type PowType (CollectErrors es a) Dyadic # Methods pow :: CollectErrors es a -> Dyadic -> PowType (CollectErrors es a) Dyadic #
(CanDiv a Dyadic, CanBeErrors es) => CanDiv (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type DivType (CollectErrors es a) Dyadic # Methods divide :: CollectErrors es a -> Dyadic -> DivType (CollectErrors es a) Dyadic #
(CanMulAsymmetric a Dyadic, CanBeErrors es) => CanMulAsymmetric (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type MulType (CollectErrors es a) Dyadic # Methods mul :: CollectErrors es a -> Dyadic -> MulType (CollectErrors es a) Dyadic #
(CanAddAsymmetric a Dyadic, CanBeErrors es) => CanAddAsymmetric (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type AddType (CollectErrors es a) Dyadic # Methods add :: CollectErrors es a -> Dyadic -> AddType (CollectErrors es a) Dyadic #
(CanSub a Dyadic, CanBeErrors es) => CanSub (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Associated Types type SubType (CollectErrors es a) Dyadic # Methods sub :: CollectErrors es a -> Dyadic -> SubType (CollectErrors es a) Dyadic #
(CanMinMaxAsymmetric a Dyadic, CanBeErrors es) => CanMinMaxAsymmetric (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.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, IsBool (CollectErrors es (EqCompareType a Dyadic)), CanBeErrors es) => HasEqAsymmetric (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.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, IsBool (CollectErrors es (OrderCompareType a Dyadic)), CanBeErrors es) => HasOrderAsymmetric (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.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 RoundType Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type RoundType Dyadic = RoundType MPFloat
type AbsType Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type AbsType Dyadic = Dyadic
type NegType Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type NegType Dyadic = Dyadic
type PowType Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic type PowType Dyadic Int = Dyadic
type PowType Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic type PowType Dyadic Integer = Dyadic
type PowType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Elementary type PowType MPBall Dyadic = MPBall
type DivType Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type DivType Int Dyadic = Rational
type DivType Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type DivType Integer Dyadic = Rational
type DivType Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type DivType Rational Dyadic = Rational
type DivType Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic type DivType Dyadic Int = Rational
type DivType Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic type DivType Dyadic Integer = Rational
type DivType Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic type DivType Dyadic Rational = Rational
type DivType Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType Dyadic Dyadic = MPBall
type DivType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType Dyadic MPBall = MPBall
type DivType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Dyadic = MPBall
type MulType Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type MulType Int Dyadic = Dyadic
type MulType Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type MulType Integer Dyadic = Dyadic
type MulType Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type MulType Rational Dyadic = Rational
type MulType Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic type MulType Dyadic Int = Dyadic
type MulType Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic type MulType Dyadic Integer = Dyadic
type MulType Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic type MulType Dyadic Rational = Rational
type MulType Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type MulType Dyadic Dyadic = Dyadic
type MulType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType Dyadic MPBall = MPBall
type MulType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Dyadic = MPBall
type AddType Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type AddType Int Dyadic = Dyadic
type AddType Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type AddType Integer Dyadic = Dyadic
type AddType Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type AddType Rational Dyadic = Rational
type AddType Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic type AddType Dyadic Int = Dyadic
type AddType Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic type AddType Dyadic Integer = Dyadic
type AddType Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic type AddType Dyadic Rational = Rational
type AddType Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type AddType Dyadic Dyadic = Dyadic
type AddType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType Dyadic MPBall = MPBall
type AddType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Dyadic = MPBall
type SubType Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type SubType Int Dyadic = Dyadic
type SubType Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type SubType Integer Dyadic = Dyadic
type SubType Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type SubType Rational Dyadic = Rational
type SubType Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic type SubType Dyadic Int = Dyadic
type SubType Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic type SubType Dyadic Integer = Dyadic
type SubType Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic type SubType Dyadic Rational = Rational
type SubType Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type SubType Dyadic Dyadic = AddType Dyadic (NegType Dyadic)
type SubType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)
type SubType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)
type MinMaxType Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type MinMaxType Int Dyadic = Dyadic
type MinMaxType Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type MinMaxType Integer Dyadic = Dyadic
type MinMaxType Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type MinMaxType Rational Dyadic = Rational
type MinMaxType Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic type MinMaxType Dyadic Int = Dyadic
type MinMaxType Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic type MinMaxType Dyadic Integer = Dyadic
type MinMaxType Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic type MinMaxType Dyadic Rational = Rational
type MinMaxType Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type MinMaxType Dyadic Dyadic = Dyadic
type MinMaxType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType Dyadic MPBall = MPBall
type MinMaxType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type MinMaxType MPBall Dyadic = MPBall
type EqCompareType Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type EqCompareType Int Dyadic = Bool
type EqCompareType Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type EqCompareType Integer Dyadic = Bool
type EqCompareType Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type EqCompareType Rational Dyadic = Bool
type EqCompareType Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic type EqCompareType Dyadic Int = Bool
type EqCompareType Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic type EqCompareType Dyadic Integer = Bool
type EqCompareType Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic type EqCompareType Dyadic Rational = Bool
type EqCompareType Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type EqCompareType Dyadic Dyadic = Bool
type EqCompareType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType Dyadic MPBall = Kleenean
type EqCompareType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type EqCompareType MPBall Dyadic = Kleenean
type OrderCompareType Int Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type OrderCompareType Int Dyadic = Bool
type OrderCompareType Integer Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type OrderCompareType Integer Dyadic = Bool
type OrderCompareType Rational Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type OrderCompareType Rational Dyadic = Bool
type OrderCompareType Dyadic Int Source #
Instance details Defined in AERN2.MP.Dyadic type OrderCompareType Dyadic Int = Bool
type OrderCompareType Dyadic Integer Source #
Instance details Defined in AERN2.MP.Dyadic type OrderCompareType Dyadic Integer = Bool
type OrderCompareType Dyadic Rational Source #
Instance details Defined in AERN2.MP.Dyadic type OrderCompareType Dyadic Rational = Bool
type OrderCompareType Dyadic Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type OrderCompareType Dyadic Dyadic = Bool
type OrderCompareType Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType Dyadic MPBall = Kleenean
type OrderCompareType MPBall Dyadic Source #
Instance details Defined in AERN2.MP.Ball.Comparisons type OrderCompareType MPBall Dyadic = Kleenean
type PlusMinusType Dyadic t Source #
Instance details Defined in AERN2.MP.Ball.Conversions type PlusMinusType Dyadic t = MPBall
type PowType Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic type PowType Dyadic (CollectErrors es b) = CollectErrors es (PowType Dyadic b)
type DivType Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic type DivType Dyadic (CollectErrors es b) = CollectErrors es (DivType Dyadic b)
type MulType Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic type MulType Dyadic (CollectErrors es b) = CollectErrors es (MulType Dyadic b)
type AddType Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic type AddType Dyadic (CollectErrors es b) = CollectErrors es (AddType Dyadic b)
type SubType Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic type SubType Dyadic (CollectErrors es b) = CollectErrors es (SubType Dyadic b)
type MinMaxType Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic type MinMaxType Dyadic (CollectErrors es b) = CollectErrors es (MinMaxType Dyadic b)
type EqCompareType Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic type EqCompareType Dyadic (CollectErrors es b) = CollectErrors es (EqCompareType Dyadic b)
type OrderCompareType Dyadic (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Dyadic type OrderCompareType Dyadic (CollectErrors es b) = CollectErrors es (OrderCompareType Dyadic b)
type PowType (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type PowType (CollectErrors es a) Dyadic = CollectErrors es (PowType a Dyadic)
type DivType (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type DivType (CollectErrors es a) Dyadic = CollectErrors es (DivType a Dyadic)
type MulType (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type MulType (CollectErrors es a) Dyadic = CollectErrors es (MulType a Dyadic)
type AddType (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type AddType (CollectErrors es a) Dyadic = CollectErrors es (AddType a Dyadic)
type SubType (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type SubType (CollectErrors es a) Dyadic = CollectErrors es (SubType a Dyadic)
type MinMaxType (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type MinMaxType (CollectErrors es a) Dyadic = CollectErrors es (MinMaxType a Dyadic)
type EqCompareType (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type EqCompareType (CollectErrors es a) Dyadic = CollectErrors es (EqCompareType a Dyadic)
type OrderCompareType (CollectErrors es a) Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic type OrderCompareType (CollectErrors es a) Dyadic = CollectErrors es (OrderCompareType a Dyadic)

type HasDyadics t = ConvertibleExactly Dyadic t Source #

Dyadic constructors

type CanBeDyadic t = ConvertibleExactly t Dyadic Source #

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

tests

specDyadic :: Spec Source #

tDyadic :: T Dyadic Source #

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