AERN2.MP.Dyadic

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.

Dyadic numbers and their basic operations

data Dyadic

Exact dyadic type based on MPFloat.

Instances

Eq Dyadic

Defined in AERN2.MP.Dyadic

Methods

(==) :: Dyadic -> Dyadic -> Bool

(/=) :: Dyadic -> Dyadic -> Bool

Num Dyadic

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

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

Defined in AERN2.MP.Dyadic

Methods

readsPrec :: Int -> ReadS Dyadic

readList :: ReadS [Dyadic]

readPrec :: ReadPrec Dyadic

readListPrec :: ReadPrec [Dyadic]

Real Dyadic

Defined in AERN2.MP.Dyadic

Methods

toRational :: Dyadic -> Rational

Show Dyadic

Defined in AERN2.MP.Dyadic

Methods

showsPrec :: Int -> Dyadic -> ShowS

show :: Dyadic -> String

showList :: [Dyadic] -> ShowS

Arbitrary Dyadic

Defined in AERN2.MP.Dyadic

Methods

arbitrary :: Gen Dyadic

shrink :: Dyadic -> [Dyadic]

CanRound Dyadic

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

Defined in AERN2.MP.Dyadic

Methods

integerBounds :: Dyadic -> (Integer, Integer)

Ring Dyadic

Defined in AERN2.MP.Dyadic

OrderedRing Dyadic

Defined in AERN2.MP.Dyadic

OrderedCertainlyRing Dyadic

Defined in AERN2.MP.Dyadic

CanAbs Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type AbsType Dyadic

Methods

abs :: Dyadic -> AbsType Dyadic

CanTestFinite Dyadic

Defined in AERN2.MP.Dyadic

Methods

isInfinite :: Dyadic -> Bool

isFinite :: Dyadic -> Bool

CanTestInteger Dyadic

Defined in AERN2.MP.Dyadic

Methods

certainlyNotInteger :: Dyadic -> Bool

certainlyInteger :: Dyadic -> Bool

certainlyIntegerGetIt :: Dyadic -> Maybe Integer

CanTestZero Dyadic

Defined in AERN2.MP.Dyadic

Methods

isCertainlyZero :: Dyadic -> Bool

isCertainlyNonZero :: Dyadic -> Bool

CanTestPosNeg Dyadic

Defined in AERN2.MP.Dyadic

Methods

isCertainlyPositive :: Dyadic -> Bool

isCertainlyNonNegative :: Dyadic -> Bool

isCertainlyNegative :: Dyadic -> Bool

isCertainlyNonPositive :: Dyadic -> Bool

CanNeg Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type NegType Dyadic

Methods

negate :: Dyadic -> NegType Dyadic

CanGiveUpIfVeryInaccurate Dyadic

Defined in AERN2.MP.Dyadic

Methods

giveUpIfVeryInaccurate :: CN Dyadic -> CN Dyadic

HasPrecision Dyadic

Defined in AERN2.MP.Dyadic

Methods

getPrecision :: Dyadic -> Precision

HasNorm Dyadic

Defined in AERN2.MP.Dyadic

Methods

getNormLog :: Dyadic -> NormLog

HasAccuracy Dyadic

Defined in AERN2.MP.Dyadic

Methods

getAccuracy :: Dyadic -> Accuracy

getFiniteAccuracy :: Dyadic -> Accuracy

CanPow Dyadic Int

Defined in AERN2.MP.Dyadic

Associated Types

type PowType Dyadic Int

Methods

pow :: Dyadic -> Int -> PowType Dyadic Int

CanPow Dyadic Integer

Defined in AERN2.MP.Dyadic

Associated Types

type PowType Dyadic Integer

Methods

pow :: Dyadic -> Integer -> PowType Dyadic Integer

CanPow MPBall Dyadic

Defined in AERN2.MP.Ball.Elementary

Associated Types

type PowType MPBall Dyadic

Methods

pow :: MPBall -> Dyadic -> PowType MPBall Dyadic

CanDiv Int Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type DivType Int Dyadic

Methods

divide :: Int -> Dyadic -> DivType Int Dyadic

CanDiv Integer Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type DivType Integer Dyadic

Methods

divide :: Integer -> Dyadic -> DivType Integer Dyadic

CanDiv Rational Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type DivType Rational Dyadic

Methods

divide :: Rational -> Dyadic -> DivType Rational Dyadic

CanDiv Dyadic Int

Defined in AERN2.MP.Dyadic

Associated Types

type DivType Dyadic Int

Methods

divide :: Dyadic -> Int -> DivType Dyadic Int

CanDiv Dyadic Integer

Defined in AERN2.MP.Dyadic

Associated Types

type DivType Dyadic Integer

Methods

divide :: Dyadic -> Integer -> DivType Dyadic Integer

CanDiv Dyadic Rational

Defined in AERN2.MP.Dyadic

Associated Types

type DivType Dyadic Rational

Methods

divide :: Dyadic -> Rational -> DivType Dyadic Rational

CanDiv Dyadic Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Dyadic Dyadic

Methods

divide :: Dyadic -> Dyadic -> DivType Dyadic Dyadic

CanDiv Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType Dyadic MPBall

Methods

divide :: Dyadic -> MPBall -> DivType Dyadic MPBall

CanDiv MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type DivType MPBall Dyadic

Methods

divide :: MPBall -> Dyadic -> DivType MPBall Dyadic

CanMulAsymmetric Int Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type MulType Int Dyadic

Methods

mul :: Int -> Dyadic -> MulType Int Dyadic

CanMulAsymmetric Integer Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type MulType Integer Dyadic

Methods

mul :: Integer -> Dyadic -> MulType Integer Dyadic

CanMulAsymmetric Rational Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type MulType Rational Dyadic

Methods

mul :: Rational -> Dyadic -> MulType Rational Dyadic

CanMulAsymmetric Dyadic Int

Defined in AERN2.MP.Dyadic

Associated Types

type MulType Dyadic Int

Methods

mul :: Dyadic -> Int -> MulType Dyadic Int

CanMulAsymmetric Dyadic Integer

Defined in AERN2.MP.Dyadic

Associated Types

type MulType Dyadic Integer

Methods

mul :: Dyadic -> Integer -> MulType Dyadic Integer

CanMulAsymmetric Dyadic Rational

Defined in AERN2.MP.Dyadic

Associated Types

type MulType Dyadic Rational

Methods

mul :: Dyadic -> Rational -> MulType Dyadic Rational

CanMulAsymmetric Dyadic Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type MulType Dyadic Dyadic

Methods

mul :: Dyadic -> Dyadic -> MulType Dyadic Dyadic

CanMulAsymmetric Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType Dyadic MPBall

Methods

mul :: Dyadic -> MPBall -> MulType Dyadic MPBall

CanMulAsymmetric MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type MulType MPBall Dyadic

Methods

mul :: MPBall -> Dyadic -> MulType MPBall Dyadic

CanAddAsymmetric Int Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type AddType Int Dyadic

Methods

add :: Int -> Dyadic -> AddType Int Dyadic

CanAddAsymmetric Integer Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type AddType Integer Dyadic

Methods

add :: Integer -> Dyadic -> AddType Integer Dyadic

CanAddAsymmetric Rational Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type AddType Rational Dyadic

Methods

add :: Rational -> Dyadic -> AddType Rational Dyadic

CanAddAsymmetric Dyadic Int

Defined in AERN2.MP.Dyadic

Associated Types

type AddType Dyadic Int

Methods

add :: Dyadic -> Int -> AddType Dyadic Int

CanAddAsymmetric Dyadic Integer

Defined in AERN2.MP.Dyadic

Associated Types

type AddType Dyadic Integer

Methods

add :: Dyadic -> Integer -> AddType Dyadic Integer

CanAddAsymmetric Dyadic Rational

Defined in AERN2.MP.Dyadic

Associated Types

type AddType Dyadic Rational

Methods

add :: Dyadic -> Rational -> AddType Dyadic Rational

CanAddAsymmetric Dyadic Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type AddType Dyadic Dyadic

Methods

add :: Dyadic -> Dyadic -> AddType Dyadic Dyadic

CanAddAsymmetric Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType Dyadic MPBall

Methods

add :: Dyadic -> MPBall -> AddType Dyadic MPBall

CanAddAsymmetric MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type AddType MPBall Dyadic

Methods

add :: MPBall -> Dyadic -> AddType MPBall Dyadic

CanSub Int Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type SubType Int Dyadic

Methods

sub :: Int -> Dyadic -> SubType Int Dyadic

CanSub Integer Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type SubType Integer Dyadic

Methods

sub :: Integer -> Dyadic -> SubType Integer Dyadic

CanSub Rational Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type SubType Rational Dyadic

Methods

sub :: Rational -> Dyadic -> SubType Rational Dyadic

CanSub Dyadic Int

Defined in AERN2.MP.Dyadic

Associated Types

type SubType Dyadic Int

Methods

sub :: Dyadic -> Int -> SubType Dyadic Int

CanSub Dyadic Integer

Defined in AERN2.MP.Dyadic

Associated Types

type SubType Dyadic Integer

Methods

sub :: Dyadic -> Integer -> SubType Dyadic Integer

CanSub Dyadic Rational

Defined in AERN2.MP.Dyadic

Associated Types

type SubType Dyadic Rational

Methods

sub :: Dyadic -> Rational -> SubType Dyadic Rational

CanSub Dyadic Dyadic

Defined in AERN2.MP.Dyadic

Associated Types

type SubType Dyadic Dyadic

Methods

sub :: Dyadic -> Dyadic -> SubType Dyadic Dyadic

CanSub Dyadic MPBall

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType Dyadic MPBall

Methods

sub :: Dyadic -> MPBall -> SubType Dyadic MPBall

CanSub MPBall Dyadic

Defined in AERN2.MP.Ball.Field

Associated Types

type SubType MPBall Dyadic

Methods

sub :: MPBall -> Dyadic -> SubType MPBall Dyadic

CanMinMaxAsymmetric Int Dyadic

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Defined in AERN2.MP.Dyadic

Methods

safeConvertExactly :: Int -> ConvertResult Dyadic

ConvertibleExactly Integer Dyadic

Defined in AERN2.MP.Dyadic

Methods

safeConvertExactly :: Integer -> ConvertResult Dyadic

ConvertibleExactly Rational Dyadic

Defined in AERN2.MP.Dyadic

Methods

safeConvertExactly :: Rational -> ConvertResult Dyadic

ConvertibleExactly MPFloat Dyadic

Defined in AERN2.MP.Dyadic

Methods

safeConvertExactly :: MPFloat -> ConvertResult Dyadic

ConvertibleExactly Dyadic Rational

Defined in AERN2.MP.Dyadic

Methods

safeConvertExactly :: Dyadic -> ConvertResult Rational

ConvertibleExactly Dyadic MPFloat

Defined in AERN2.MP.Dyadic

Methods

safeConvertExactly :: Dyadic -> ConvertResult MPFloat

ConvertibleExactly Dyadic Dyadic

Defined in AERN2.MP.Dyadic

Methods

safeConvertExactly :: Dyadic -> ConvertResult Dyadic

ConvertibleExactly Dyadic MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertExactly :: Dyadic -> ConvertResult MPBall

ConvertibleExactly ErrorBound Dyadic

Defined in AERN2.MP.ErrorBound

Methods

safeConvertExactly :: ErrorBound -> ConvertResult Dyadic

Convertible Dyadic Double

Defined in AERN2.MP.Dyadic

Methods

safeConvert :: Dyadic -> ConvertResult Double

ConvertibleWithPrecision Dyadic MPBall

Defined in AERN2.MP.Ball.Conversions

Methods

safeConvertP :: Precision -> Dyadic -> ConvertResult MPBall

CanTestContains MPBall Dyadic

Defined in AERN2.MP.Ball.Type

Methods

contains :: MPBall -> Dyadic -> Bool

CanBeErrorBound t => CanPlusMinus Dyadic t

Defined in AERN2.MP.Ball.Conversions

Associated Types

type PlusMinusType Dyadic t

Methods

plusMinus :: Dyadic -> t -> PlusMinusType Dyadic t

(CanPow Dyadic b, CanBeErrors es) => CanPow Dyadic (CollectErrors es b)

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)

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)

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)

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)

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)

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)

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)

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)

Defined in AERN2.MP.Dyadic

Methods

safeConvertExactly :: Dyadic -> ConvertResult (CollectErrors es t)

Ring (CN Dyadic)

Defined in AERN2.MP.Dyadic

OrderedRing (CN Dyadic)

Defined in AERN2.MP.Dyadic

OrderedCertainlyRing (CN Dyadic)

Defined in AERN2.MP.Dyadic

(CanPow a Dyadic, CanBeErrors es) => CanPow (CollectErrors es a) Dyadic

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

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

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

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

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

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

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

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

Defined in AERN2.MP.Dyadic

type RoundType Dyadic = RoundType MPFloat

type AbsType Dyadic

Defined in AERN2.MP.Dyadic

type AbsType Dyadic = Dyadic

type NegType Dyadic

Defined in AERN2.MP.Dyadic

type NegType Dyadic = Dyadic

type PowType Dyadic Int

Defined in AERN2.MP.Dyadic

type PowType Dyadic Int = Dyadic

type PowType Dyadic Integer

Defined in AERN2.MP.Dyadic

type PowType Dyadic Integer = Dyadic

type PowType MPBall Dyadic

Defined in AERN2.MP.Ball.Elementary

type PowType MPBall Dyadic = MPBall

type DivType Int Dyadic

Defined in AERN2.MP.Dyadic

type DivType Int Dyadic = Rational

type DivType Integer Dyadic

Defined in AERN2.MP.Dyadic

type DivType Integer Dyadic = Rational

type DivType Rational Dyadic

Defined in AERN2.MP.Dyadic

type DivType Rational Dyadic = Rational

type DivType Dyadic Int

Defined in AERN2.MP.Dyadic

type DivType Dyadic Int = Rational

type DivType Dyadic Integer

Defined in AERN2.MP.Dyadic

type DivType Dyadic Integer = Rational

type DivType Dyadic Rational

Defined in AERN2.MP.Dyadic

type DivType Dyadic Rational = Rational

type DivType Dyadic Dyadic

Defined in AERN2.MP.Ball.Field

type DivType Dyadic Dyadic = MPBall

type DivType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type DivType Dyadic MPBall = MPBall

type DivType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type DivType MPBall Dyadic = MPBall

type MulType Int Dyadic

Defined in AERN2.MP.Dyadic

type MulType Int Dyadic = Dyadic

type MulType Integer Dyadic

Defined in AERN2.MP.Dyadic

type MulType Integer Dyadic = Dyadic

type MulType Rational Dyadic

Defined in AERN2.MP.Dyadic

type MulType Rational Dyadic = Rational

type MulType Dyadic Int

Defined in AERN2.MP.Dyadic

type MulType Dyadic Int = Dyadic

type MulType Dyadic Integer

Defined in AERN2.MP.Dyadic

type MulType Dyadic Integer = Dyadic

type MulType Dyadic Rational

Defined in AERN2.MP.Dyadic

type MulType Dyadic Rational = Rational

type MulType Dyadic Dyadic

Defined in AERN2.MP.Dyadic

type MulType Dyadic Dyadic = Dyadic

type MulType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type MulType Dyadic MPBall = MPBall

type MulType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type MulType MPBall Dyadic = MPBall

type AddType Int Dyadic

Defined in AERN2.MP.Dyadic

type AddType Int Dyadic = Dyadic

type AddType Integer Dyadic

Defined in AERN2.MP.Dyadic

type AddType Integer Dyadic = Dyadic

type AddType Rational Dyadic

Defined in AERN2.MP.Dyadic

type AddType Rational Dyadic = Rational

type AddType Dyadic Int

Defined in AERN2.MP.Dyadic

type AddType Dyadic Int = Dyadic

type AddType Dyadic Integer

Defined in AERN2.MP.Dyadic

type AddType Dyadic Integer = Dyadic

type AddType Dyadic Rational

Defined in AERN2.MP.Dyadic

type AddType Dyadic Rational = Rational

type AddType Dyadic Dyadic

Defined in AERN2.MP.Dyadic

type AddType Dyadic Dyadic = Dyadic

type AddType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type AddType Dyadic MPBall = MPBall

type AddType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type AddType MPBall Dyadic = MPBall

type SubType Int Dyadic

Defined in AERN2.MP.Dyadic

type SubType Int Dyadic = Dyadic

type SubType Integer Dyadic

Defined in AERN2.MP.Dyadic

type SubType Integer Dyadic = Dyadic

type SubType Rational Dyadic

Defined in AERN2.MP.Dyadic

type SubType Rational Dyadic = Rational

type SubType Dyadic Int

Defined in AERN2.MP.Dyadic

type SubType Dyadic Int = Dyadic

type SubType Dyadic Integer

Defined in AERN2.MP.Dyadic

type SubType Dyadic Integer = Dyadic

type SubType Dyadic Rational

Defined in AERN2.MP.Dyadic

type SubType Dyadic Rational = Rational

type SubType Dyadic Dyadic

Defined in AERN2.MP.Dyadic

type SubType Dyadic Dyadic = AddType Dyadic (NegType Dyadic)

type SubType Dyadic MPBall

Defined in AERN2.MP.Ball.Field

type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)

type SubType MPBall Dyadic

Defined in AERN2.MP.Ball.Field

type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)

type MinMaxType Int Dyadic

Defined in AERN2.MP.Dyadic

type MinMaxType Int Dyadic = Dyadic

type MinMaxType Integer Dyadic

Defined in AERN2.MP.Dyadic

type MinMaxType Integer Dyadic = Dyadic

type MinMaxType Rational Dyadic

Defined in AERN2.MP.Dyadic

type MinMaxType Rational Dyadic = Rational

type MinMaxType Dyadic Int

Defined in AERN2.MP.Dyadic

type MinMaxType Dyadic Int = Dyadic

type MinMaxType Dyadic Integer

Defined in AERN2.MP.Dyadic

type MinMaxType Dyadic Integer = Dyadic

type MinMaxType Dyadic Rational

Defined in AERN2.MP.Dyadic

type MinMaxType Dyadic Rational = Rational

type MinMaxType Dyadic Dyadic

Defined in AERN2.MP.Dyadic

type MinMaxType Dyadic Dyadic = Dyadic

type MinMaxType Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType Dyadic MPBall = MPBall

type MinMaxType MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

type MinMaxType MPBall Dyadic = MPBall

type EqCompareType Int Dyadic

Defined in AERN2.MP.Dyadic

type EqCompareType Int Dyadic = Bool

type EqCompareType Integer Dyadic

Defined in AERN2.MP.Dyadic

type EqCompareType Integer Dyadic = Bool

type EqCompareType Rational Dyadic

Defined in AERN2.MP.Dyadic

type EqCompareType Rational Dyadic = Bool

type EqCompareType Dyadic Int

Defined in AERN2.MP.Dyadic

type EqCompareType Dyadic Int = Bool

type EqCompareType Dyadic Integer

Defined in AERN2.MP.Dyadic

type EqCompareType Dyadic Integer = Bool

type EqCompareType Dyadic Rational

Defined in AERN2.MP.Dyadic

type EqCompareType Dyadic Rational = Bool

type EqCompareType Dyadic Dyadic

Defined in AERN2.MP.Dyadic

type EqCompareType Dyadic Dyadic = Bool

type EqCompareType Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType Dyadic MPBall = Kleenean

type EqCompareType MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

type EqCompareType MPBall Dyadic = Kleenean

type OrderCompareType Int Dyadic

Defined in AERN2.MP.Dyadic

type OrderCompareType Int Dyadic = Bool

type OrderCompareType Integer Dyadic

Defined in AERN2.MP.Dyadic

type OrderCompareType Integer Dyadic = Bool

type OrderCompareType Rational Dyadic

Defined in AERN2.MP.Dyadic

type OrderCompareType Rational Dyadic = Bool

type OrderCompareType Dyadic Int

Defined in AERN2.MP.Dyadic

type OrderCompareType Dyadic Int = Bool

type OrderCompareType Dyadic Integer

Defined in AERN2.MP.Dyadic

type OrderCompareType Dyadic Integer = Bool

type OrderCompareType Dyadic Rational

Defined in AERN2.MP.Dyadic

type OrderCompareType Dyadic Rational = Bool

type OrderCompareType Dyadic Dyadic

Defined in AERN2.MP.Dyadic

type OrderCompareType Dyadic Dyadic = Bool

type OrderCompareType Dyadic MPBall

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType Dyadic MPBall = Kleenean

type OrderCompareType MPBall Dyadic

Defined in AERN2.MP.Ball.Comparisons

type OrderCompareType MPBall Dyadic = Kleenean

type PlusMinusType Dyadic t

Defined in AERN2.MP.Ball.Conversions

type PlusMinusType Dyadic t = MPBall

type PowType Dyadic (CollectErrors es b)

Defined in AERN2.MP.Dyadic

type PowType Dyadic (CollectErrors es b) = CollectErrors es (PowType Dyadic b)

type DivType Dyadic (CollectErrors es b)

Defined in AERN2.MP.Dyadic

type DivType Dyadic (CollectErrors es b) = CollectErrors es (DivType Dyadic b)

type MulType Dyadic (CollectErrors es b)

Defined in AERN2.MP.Dyadic

type MulType Dyadic (CollectErrors es b) = CollectErrors es (MulType Dyadic b)

type AddType Dyadic (CollectErrors es b)

Defined in AERN2.MP.Dyadic

type AddType Dyadic (CollectErrors es b) = CollectErrors es (AddType Dyadic b)

type SubType Dyadic (CollectErrors es b)

Defined in AERN2.MP.Dyadic

type SubType Dyadic (CollectErrors es b) = CollectErrors es (SubType Dyadic b)

type MinMaxType Dyadic (CollectErrors es b)

Defined in AERN2.MP.Dyadic

type MinMaxType Dyadic (CollectErrors es b) = CollectErrors es (MinMaxType Dyadic b)

type EqCompareType Dyadic (CollectErrors es b)

Defined in AERN2.MP.Dyadic

type EqCompareType Dyadic (CollectErrors es b) = CollectErrors es (EqCompareType Dyadic b)

type OrderCompareType Dyadic (CollectErrors es b)

Defined in AERN2.MP.Dyadic

type OrderCompareType Dyadic (CollectErrors es b) = CollectErrors es (OrderCompareType Dyadic b)

type PowType (CollectErrors es a) Dyadic

Defined in AERN2.MP.Dyadic

type PowType (CollectErrors es a) Dyadic = CollectErrors es (PowType a Dyadic)

type DivType (CollectErrors es a) Dyadic

Defined in AERN2.MP.Dyadic

type DivType (CollectErrors es a) Dyadic = CollectErrors es (DivType a Dyadic)

type MulType (CollectErrors es a) Dyadic

Defined in AERN2.MP.Dyadic

type MulType (CollectErrors es a) Dyadic = CollectErrors es (MulType a Dyadic)

type AddType (CollectErrors es a) Dyadic

Defined in AERN2.MP.Dyadic

type AddType (CollectErrors es a) Dyadic = CollectErrors es (AddType a Dyadic)

type SubType (CollectErrors es a) Dyadic

Defined in AERN2.MP.Dyadic

type SubType (CollectErrors es a) Dyadic = CollectErrors es (SubType a Dyadic)

type MinMaxType (CollectErrors es a) Dyadic

Defined in AERN2.MP.Dyadic

type MinMaxType (CollectErrors es a) Dyadic = CollectErrors es (MinMaxType a Dyadic)

type EqCompareType (CollectErrors es a) Dyadic

Defined in AERN2.MP.Dyadic

type EqCompareType (CollectErrors es a) Dyadic = CollectErrors es (EqCompareType a Dyadic)

type OrderCompareType (CollectErrors es a) Dyadic

Defined in AERN2.MP.Dyadic

type OrderCompareType (CollectErrors es a) Dyadic = CollectErrors 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.