Copyright	(c) Michal Konecny
License	BSD3
Maintainer	[email protected]
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

AERN2.MP.Precision

Description

Precision type and its operations. Precision expresses a limit on the size of an approximation, roughly corresponding to the number of significant bits for a floating-point number and its generalisations to other types.

Documentation

data Precision Source #

Instances

Instances details

Arbitrary Precision Source #

Instance details

Defined in AERN2.MP.Precision

Methods

arbitrary :: Gen Precision #

shrink :: Precision -> [Precision] #

Enum Precision Source #

Instance details

Defined in AERN2.MP.Precision

Methods

succ :: Precision -> Precision #

pred :: Precision -> Precision #

toEnum :: Int -> Precision #

fromEnum :: Precision -> Int #

enumFrom :: Precision -> [Precision] #

enumFromThen :: Precision -> Precision -> [Precision] #

enumFromTo :: Precision -> Precision -> [Precision] #

enumFromThenTo :: Precision -> Precision -> Precision -> [Precision] #

Num Precision Source #

Instance details

Defined in AERN2.MP.Precision

Methods

(+) :: Precision -> Precision -> Precision #

(-) :: Precision -> Precision -> Precision #

(*) :: Precision -> Precision -> Precision #

negate :: Precision -> Precision #

abs :: Precision -> Precision #

signum :: Precision -> Precision #

fromInteger :: Integer -> Precision #

Integral Precision Source #

Instance details

Defined in AERN2.MP.Precision

Methods

quot :: Precision -> Precision -> Precision #

rem :: Precision -> Precision -> Precision #

div :: Precision -> Precision -> Precision #

mod :: Precision -> Precision -> Precision #

quotRem :: Precision -> Precision -> (Precision, Precision) #

divMod :: Precision -> Precision -> (Precision, Precision) #

toInteger :: Precision -> Integer #

Real Precision Source #

Instance details

Defined in AERN2.MP.Precision

Methods

toRational :: Precision -> Rational #

Show Precision Source #

Instance details

Defined in AERN2.MP.Precision

Methods

showsPrec :: Int -> Precision -> ShowS #

show :: Precision -> String #

showList :: [Precision] -> ShowS #

Eq Precision Source #

Instance details

Defined in AERN2.MP.Precision

Methods

(==) :: Precision -> Precision -> Bool #

(/=) :: Precision -> Precision -> Bool #

Ord Precision Source #

Instance details

Defined in AERN2.MP.Precision

Methods

compare :: Precision -> Precision -> Ordering #

(<) :: Precision -> Precision -> Bool #

(<=) :: Precision -> Precision -> Bool #

(>) :: Precision -> Precision -> Bool #

(>=) :: Precision -> Precision -> Bool #

max :: Precision -> Precision -> Precision #

min :: Precision -> Precision -> Precision #

CanAddAsymmetric Precision Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type AddType Precision Precision
Instance details Defined in AERN2.MP.Precision type AddType Precision Precision = Precision

Methods

add :: Precision -> Precision -> AddType Precision Precision #

CanAddAsymmetric Precision Integer Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type AddType Precision Integer
Instance details Defined in AERN2.MP.Precision type AddType Precision Integer = Precision

Methods

add :: Precision -> Integer -> AddType Precision Integer #

CanAddAsymmetric Integer Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type AddType Integer Precision
Instance details Defined in AERN2.MP.Precision type AddType Integer Precision = Precision

Methods

add :: Integer -> Precision -> AddType Integer Precision #

HasEqAsymmetric Precision Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type EqCompareType Precision Precision
Instance details Defined in AERN2.MP.Precision type EqCompareType Precision Precision = Bool

Methods

equalTo :: Precision -> Precision -> EqCompareType Precision Precision #

notEqualTo :: Precision -> Precision -> EqCompareType Precision Precision #

HasEqAsymmetric Precision Integer Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type EqCompareType Precision Integer
Instance details Defined in AERN2.MP.Precision type EqCompareType Precision Integer = Bool

Methods

equalTo :: Precision -> Integer -> EqCompareType Precision Integer #

notEqualTo :: Precision -> Integer -> EqCompareType Precision Integer #

HasEqAsymmetric Precision Int Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type EqCompareType Precision Int
Instance details Defined in AERN2.MP.Precision type EqCompareType Precision Int = Bool

Methods

equalTo :: Precision -> Int -> EqCompareType Precision Int #

notEqualTo :: Precision -> Int -> EqCompareType Precision Int #

HasEqAsymmetric Integer Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type EqCompareType Integer Precision
Instance details Defined in AERN2.MP.Precision type EqCompareType Integer Precision = Bool

Methods

equalTo :: Integer -> Precision -> EqCompareType Integer Precision #

notEqualTo :: Integer -> Precision -> EqCompareType Integer Precision #

HasEqAsymmetric Int Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type EqCompareType Int Precision
Instance details Defined in AERN2.MP.Precision type EqCompareType Int Precision = Bool

Methods

equalTo :: Int -> Precision -> EqCompareType Int Precision #

notEqualTo :: Int -> Precision -> EqCompareType Int Precision #

ConvertibleExactly Precision Accuracy Source #

Instance details

Defined in AERN2.MP.Accuracy

Methods

safeConvertExactly :: Precision -> ConvertResult Accuracy #

ConvertibleExactly Precision Integer Source #

Instance details

Defined in AERN2.MP.Precision

Methods

safeConvertExactly :: Precision -> ConvertResult Integer #

ConvertibleExactly Integer Precision Source #

Instance details

Defined in AERN2.MP.Precision

Methods

safeConvertExactly :: Integer -> ConvertResult Precision #

CanMinMaxAsymmetric Precision Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type MinMaxType Precision Precision
Instance details Defined in AERN2.MP.Precision type MinMaxType Precision Precision = Precision

Methods

min :: Precision -> Precision -> MinMaxType Precision Precision #

max :: Precision -> Precision -> MinMaxType Precision Precision #

CanMulAsymmetric Precision Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type MulType Precision Precision
Instance details Defined in AERN2.MP.Precision type MulType Precision Precision = Precision

Methods

mul :: Precision -> Precision -> MulType Precision Precision #

CanMulAsymmetric Precision Integer Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type MulType Precision Integer
Instance details Defined in AERN2.MP.Precision type MulType Precision Integer = Precision

Methods

mul :: Precision -> Integer -> MulType Precision Integer #

CanMulAsymmetric Integer Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type MulType Integer Precision
Instance details Defined in AERN2.MP.Precision type MulType Integer Precision = Precision

Methods

mul :: Integer -> Precision -> MulType Integer Precision #

HasOrderAsymmetric Precision Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type OrderCompareType Precision Precision
Instance details Defined in AERN2.MP.Precision type OrderCompareType Precision Precision = Bool

Methods

lessThan :: Precision -> Precision -> OrderCompareType Precision Precision #

greaterThan :: Precision -> Precision -> OrderCompareType Precision Precision #

leq :: Precision -> Precision -> OrderCompareType Precision Precision #

geq :: Precision -> Precision -> OrderCompareType Precision Precision #

HasOrderAsymmetric Precision Integer Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type OrderCompareType Precision Integer
Instance details Defined in AERN2.MP.Precision type OrderCompareType Precision Integer = Bool

Methods

lessThan :: Precision -> Integer -> OrderCompareType Precision Integer #

greaterThan :: Precision -> Integer -> OrderCompareType Precision Integer #

leq :: Precision -> Integer -> OrderCompareType Precision Integer #

geq :: Precision -> Integer -> OrderCompareType Precision Integer #

HasOrderAsymmetric Precision Int Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type OrderCompareType Precision Int
Instance details Defined in AERN2.MP.Precision type OrderCompareType Precision Int = Bool

Methods

lessThan :: Precision -> Int -> OrderCompareType Precision Int #

greaterThan :: Precision -> Int -> OrderCompareType Precision Int #

leq :: Precision -> Int -> OrderCompareType Precision Int #

geq :: Precision -> Int -> OrderCompareType Precision Int #

HasOrderAsymmetric Integer Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type OrderCompareType Integer Precision
Instance details Defined in AERN2.MP.Precision type OrderCompareType Integer Precision = Bool

Methods

lessThan :: Integer -> Precision -> OrderCompareType Integer Precision #

greaterThan :: Integer -> Precision -> OrderCompareType Integer Precision #

leq :: Integer -> Precision -> OrderCompareType Integer Precision #

geq :: Integer -> Precision -> OrderCompareType Integer Precision #

HasOrderAsymmetric Int Precision Source #

Instance details

Defined in AERN2.MP.Precision

Associated Types

type OrderCompareType Int Precision
Instance details Defined in AERN2.MP.Precision type OrderCompareType Int Precision = Bool

Methods

lessThan :: Int -> Precision -> OrderCompareType Int Precision #

greaterThan :: Int -> Precision -> OrderCompareType Int Precision #

leq :: Int -> Precision -> OrderCompareType Int Precision #

geq :: Int -> Precision -> OrderCompareType Int Precision #

type AddType Precision Precision Source #

Instance details

Defined in AERN2.MP.Precision

type AddType Precision Precision = Precision

type AddType Precision Integer Source #

Instance details

Defined in AERN2.MP.Precision

type AddType Precision Integer = Precision

type AddType Integer Precision Source #

Instance details

Defined in AERN2.MP.Precision

type AddType Integer Precision = Precision

type EqCompareType Precision Precision Source #

Instance details

Defined in AERN2.MP.Precision

type EqCompareType Precision Precision = Bool

type EqCompareType Precision Integer Source #

Instance details

Defined in AERN2.MP.Precision

type EqCompareType Precision Integer = Bool

type EqCompareType Precision Int Source #

Instance details

Defined in AERN2.MP.Precision

type EqCompareType Precision Int = Bool

type EqCompareType Integer Precision Source #

Instance details

Defined in AERN2.MP.Precision

type EqCompareType Integer Precision = Bool

type EqCompareType Int Precision Source #

Instance details

Defined in AERN2.MP.Precision

type EqCompareType Int Precision = Bool

type MinMaxType Precision Precision Source #

Instance details

Defined in AERN2.MP.Precision

type MinMaxType Precision Precision = Precision

type MulType Precision Precision Source #

Instance details

Defined in AERN2.MP.Precision

type MulType Precision Precision = Precision

type MulType Precision Integer Source #

Instance details

Defined in AERN2.MP.Precision

type MulType Precision Integer = Precision

type MulType Integer Precision Source #

Instance details

Defined in AERN2.MP.Precision

type MulType Integer Precision = Precision

type OrderCompareType Precision Precision Source #

Instance details

Defined in AERN2.MP.Precision

type OrderCompareType Precision Precision = Bool

type OrderCompareType Precision Integer Source #

Instance details

Defined in AERN2.MP.Precision

type OrderCompareType Precision Integer = Bool

type OrderCompareType Precision Int Source #

Instance details

Defined in AERN2.MP.Precision

type OrderCompareType Precision Int = Bool

type OrderCompareType Integer Precision Source #

Instance details

Defined in AERN2.MP.Precision

type OrderCompareType Integer Precision = Bool

type OrderCompareType Int Precision Source #

Instance details

Defined in AERN2.MP.Precision

type OrderCompareType Int Precision = Bool

prec :: Integer -> Precision Source #

class HasPrecision t where Source #

Methods

getPrecision :: t -> Precision Source #

Instances

Instances details

HasPrecision MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods getPrecision :: MPBall -> Precision Source #
HasPrecision Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods getPrecision :: Dyadic -> Precision Source #
HasPrecision MPFloat Source #
Instance details Defined in AERN2.MP.Float.Type Methods getPrecision :: MPFloat -> Precision Source #
HasPrecision Bool Source #
Instance details Defined in AERN2.MP.Precision Methods getPrecision :: Bool -> Precision Source #
HasPrecision t => HasPrecision (Complex t) Source #
Instance details Defined in AERN2.MP.Precision Methods getPrecision :: Complex t -> Precision Source #
HasPrecision t => HasPrecision (Maybe t) Source #
Instance details Defined in AERN2.MP.Precision Methods getPrecision :: Maybe t -> Precision Source #
HasPrecision t => HasPrecision (CollectErrors es t) Source #
Instance details Defined in AERN2.MP.Precision Methods getPrecision :: CollectErrors es t -> Precision Source #

class CanSetPrecision t where Source #

Methods

setPrecision :: Precision -> t -> t Source #

Instances

Instances details

CanSetPrecision MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods setPrecision :: Precision -> MPBall -> MPBall Source #
CanSetPrecision MPFloat Source #
Instance details Defined in AERN2.MP.Float.Type Methods setPrecision :: Precision -> MPFloat -> MPFloat Source #
CanSetPrecision Bool Source #
Instance details Defined in AERN2.MP.Precision Methods setPrecision :: Precision -> Bool -> Bool Source #
CanSetPrecision t => CanSetPrecision (Complex t) Source #
Instance details Defined in AERN2.MP.Precision Methods setPrecision :: Precision -> Complex t -> Complex t Source #
CanSetPrecision t => CanSetPrecision (Maybe t) Source #
Instance details Defined in AERN2.MP.Precision Methods setPrecision :: Precision -> Maybe t -> Maybe t Source #
CanSetPrecision t => CanSetPrecision (CollectErrors es t) Source #
Instance details Defined in AERN2.MP.Precision Methods setPrecision :: Precision -> CollectErrors es t -> CollectErrors es t Source #

lowerPrecisionIfAbove :: (HasPrecision t, CanSetPrecision t) => Precision -> t -> t Source #

raisePrecisionIfBelow :: (HasPrecision t, CanSetPrecision t) => Precision -> t -> t Source #

specCanSetPrecision :: (HasPrecision t, CanSetPrecision t, CanTestFinite t, Arbitrary t, Show t, Testable prop) => T t -> (t -> t -> prop) -> Spec Source #

defaultPrecision :: Precision Source #

maximumPrecision :: Precision Source #

standardPrecisions :: Precision -> [Precision] Source #

precisionTimes2 :: Precision -> Precision Source #

iterateUntilOK :: Precision -> (a -> Bool) -> (Precision -> a) -> [(Precision, a)] Source #

class ConvertibleWithPrecision t1 t2 where Source #

Methods

safeConvertP :: Precision -> t1 -> ConvertResult t2 Source #

Instances

Instances details

ConvertibleWithPrecision Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Dyadic -> ConvertResult MPBall Source #
ConvertibleWithPrecision Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Rational -> ConvertResult MPBall Source #
ConvertibleWithPrecision Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Integer -> ConvertResult MPBall Source #
ConvertibleWithPrecision Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Int -> ConvertResult MPBall Source #
(ConvertibleWithPrecision Rational t, CanBeErrors es) => ConvertibleWithPrecision Rational (CollectErrors es t) Source #
Instance details Defined in AERN2.MP.Precision Methods safeConvertP :: Precision -> Rational -> ConvertResult (CollectErrors es t) Source #
(ConvertibleWithPrecision Integer t, CanBeErrors es) => ConvertibleWithPrecision Integer (CollectErrors es t) Source #
Instance details Defined in AERN2.MP.Precision Methods safeConvertP :: Precision -> Integer -> ConvertResult (CollectErrors es t) Source #
(ConvertibleWithPrecision Bool t, CanBeErrors es) => ConvertibleWithPrecision Bool (CollectErrors es t) Source #
Instance details Defined in AERN2.MP.Precision Methods safeConvertP :: Precision -> Bool -> ConvertResult (CollectErrors es t) Source #
(ConvertibleWithPrecision Double t, CanBeErrors es) => ConvertibleWithPrecision Double (CollectErrors es t) Source #
Instance details Defined in AERN2.MP.Precision Methods safeConvertP :: Precision -> Double -> ConvertResult (CollectErrors es t) Source #
(ConvertibleWithPrecision Int t, CanBeErrors es) => ConvertibleWithPrecision Int (CollectErrors es t) Source #
Instance details Defined in AERN2.MP.Precision Methods safeConvertP :: Precision -> Int -> ConvertResult (CollectErrors es t) Source #
ConvertibleWithPrecision (CentreRadius Rational Rational) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> CentreRadius Rational Rational -> ConvertResult MPBall Source #
(ConvertibleWithPrecision t1 t2, KnownNat p) => ConvertibleWithPrecision (WithSample (WithCurrentPrec p t2) t1) t2 Source #
Instance details Defined in AERN2.MP.WithCurrentPrec.Type Methods safeConvertP :: Precision -> WithSample (WithCurrentPrec p t2) t1 -> ConvertResult t2 Source #

convertP :: ConvertibleWithPrecision t1 t2 => Precision -> t1 -> t2 Source #

convertPFirst :: (ConvertibleWithPrecision t1 t2, HasPrecision t2) => (t2 -> t2 -> c) -> t1 -> t2 -> c Source #

convertPSecond :: (ConvertibleWithPrecision t2 t1, HasPrecision t1) => (t1 -> t1 -> c) -> t1 -> t2 -> c Source #