Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
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

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] #
Eq Precision Source #
Instance details Defined in AERN2.MP.Precision Methods (==) :: Precision -> Precision -> Bool # (/=) :: Precision -> Precision -> Bool #
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 #
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 #
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 #
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 #
Arbitrary Precision Source #
Instance details Defined in AERN2.MP.Precision Methods arbitrary :: Gen Precision # shrink :: Precision -> [Precision] #
CanMulAsymmetric Integer Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type MulType Integer Precision # Methods mul :: Integer -> Precision -> MulType Integer Precision #
CanMulAsymmetric Precision Integer Source #
Instance details Defined in AERN2.MP.Precision Associated Types type MulType Precision Integer # Methods mul :: Precision -> Integer -> MulType Precision Integer #
CanMulAsymmetric Precision Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type MulType Precision Precision # Methods mul :: Precision -> Precision -> MulType Precision Precision #
CanAddAsymmetric Integer Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type AddType Integer Precision # Methods add :: Integer -> Precision -> AddType Integer Precision #
CanAddAsymmetric Precision Integer Source #
Instance details Defined in AERN2.MP.Precision Associated Types type AddType Precision Integer # Methods add :: Precision -> Integer -> AddType Precision Integer #
CanAddAsymmetric Precision Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type AddType Precision Precision # Methods add :: Precision -> Precision -> AddType Precision Precision #
CanMinMaxAsymmetric Precision Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type MinMaxType Precision Precision # Methods min :: Precision -> Precision -> MinMaxType Precision Precision # max :: Precision -> Precision -> MinMaxType Precision Precision #
HasEqAsymmetric Int Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type EqCompareType Int Precision # Methods equalTo :: Int -> Precision -> EqCompareType Int Precision # notEqualTo :: Int -> Precision -> EqCompareType Int Precision #
HasEqAsymmetric Integer Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type EqCompareType Integer Precision # Methods equalTo :: Integer -> Precision -> EqCompareType Integer Precision # notEqualTo :: Integer -> Precision -> EqCompareType Integer Precision #
HasEqAsymmetric Precision Int Source #
Instance details Defined in AERN2.MP.Precision Associated Types type EqCompareType Precision Int # Methods equalTo :: Precision -> Int -> EqCompareType Precision Int # notEqualTo :: Precision -> Int -> EqCompareType Precision Int #
HasEqAsymmetric Precision Integer Source #
Instance details Defined in AERN2.MP.Precision Associated Types type EqCompareType Precision Integer # Methods equalTo :: Precision -> Integer -> EqCompareType Precision Integer # notEqualTo :: Precision -> Integer -> EqCompareType Precision Integer #
HasEqAsymmetric Precision Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type EqCompareType Precision Precision # Methods equalTo :: Precision -> Precision -> EqCompareType Precision Precision # notEqualTo :: Precision -> Precision -> EqCompareType Precision Precision #
HasOrderAsymmetric Int Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type OrderCompareType Int Precision # 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 #
HasOrderAsymmetric Integer Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type OrderCompareType Integer Precision # 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 Precision Int Source #
Instance details Defined in AERN2.MP.Precision Associated Types type OrderCompareType Precision Int # 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 Precision Integer Source #
Instance details Defined in AERN2.MP.Precision Associated Types type OrderCompareType Precision Integer # 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 Precision Source #
Instance details Defined in AERN2.MP.Precision Associated Types type OrderCompareType Precision Precision # 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 #
ConvertibleExactly Integer Precision Source #
Instance details Defined in AERN2.MP.Precision Methods safeConvertExactly :: Integer -> ConvertResult Precision #
ConvertibleExactly Precision Integer Source #
Instance details Defined in AERN2.MP.Precision Methods safeConvertExactly :: Precision -> ConvertResult Integer #
ConvertibleExactly Precision Accuracy Source #
Instance details Defined in AERN2.MP.Accuracy Methods safeConvertExactly :: Precision -> ConvertResult Accuracy #
type MulType Integer Precision Source #
Instance details Defined in AERN2.MP.Precision type MulType Integer Precision = Precision
type MulType Precision Integer Source #
Instance details Defined in AERN2.MP.Precision type MulType Precision Integer = Precision
type MulType Precision Precision Source #
Instance details Defined in AERN2.MP.Precision type MulType Precision Precision = Precision
type AddType Integer Precision Source #
Instance details Defined in AERN2.MP.Precision type AddType Integer Precision = Precision
type AddType Precision Integer Source #
Instance details Defined in AERN2.MP.Precision type AddType Precision Integer = Precision
type AddType Precision Precision Source #
Instance details Defined in AERN2.MP.Precision type AddType Precision Precision = Precision
type MinMaxType Precision Precision Source #
Instance details Defined in AERN2.MP.Precision type MinMaxType Precision Precision = Precision
type EqCompareType Int Precision Source #
Instance details Defined in AERN2.MP.Precision type EqCompareType Int Precision = Bool
type EqCompareType Integer Precision Source #
Instance details Defined in AERN2.MP.Precision type EqCompareType Integer Precision = Bool
type EqCompareType Precision Int Source #
Instance details Defined in AERN2.MP.Precision type EqCompareType Precision Int = Bool
type EqCompareType Precision Integer Source #
Instance details Defined in AERN2.MP.Precision type EqCompareType Precision Integer = Bool
type EqCompareType Precision Precision Source #
Instance details Defined in AERN2.MP.Precision type EqCompareType Precision Precision = Bool
type OrderCompareType Int Precision Source #
Instance details Defined in AERN2.MP.Precision type OrderCompareType Int Precision = Bool
type OrderCompareType Integer Precision Source #
Instance details Defined in AERN2.MP.Precision type OrderCompareType Integer Precision = Bool
type OrderCompareType Precision Int Source #
Instance details Defined in AERN2.MP.Precision type OrderCompareType Precision Int = Bool
type OrderCompareType Precision Integer Source #
Instance details Defined in AERN2.MP.Precision type OrderCompareType Precision Integer = Bool
type OrderCompareType Precision Precision Source #
Instance details Defined in AERN2.MP.Precision type OrderCompareType Precision Precision = Bool

prec :: Integer -> Precision Source #

class HasPrecision t where Source #

Methods

getPrecision :: t -> Precision Source #

Instances

Instances details

HasPrecision Bool Source #
Instance details Defined in AERN2.MP.Precision Methods getPrecision :: Bool -> Precision Source #
HasPrecision MPFloat Source #
Instance details Defined in AERN2.MP.Float.Type Methods getPrecision :: MPFloat -> Precision Source #
HasPrecision Dyadic Source #
Instance details Defined in AERN2.MP.Dyadic Methods getPrecision :: Dyadic -> Precision Source #
HasPrecision MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods getPrecision :: MPBall -> Precision Source #
HasPrecision t => HasPrecision (Maybe t) Source #
Instance details Defined in AERN2.MP.Precision Methods getPrecision :: Maybe t -> Precision Source #
HasPrecision t => HasPrecision (Complex t) Source #
Instance details Defined in AERN2.MP.Precision Methods getPrecision :: Complex 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 Bool Source #
Instance details Defined in AERN2.MP.Precision Methods setPrecision :: Precision -> Bool -> Bool Source #
CanSetPrecision MPFloat Source #
Instance details Defined in AERN2.MP.Float.Type Methods setPrecision :: Precision -> MPFloat -> MPFloat Source #
CanSetPrecision MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Methods setPrecision :: Precision -> MPBall -> MPBall 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 (Complex t) Source #
Instance details Defined in AERN2.MP.Precision Methods setPrecision :: Precision -> Complex t -> Complex 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 Int MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Int -> ConvertResult MPBall Source #
ConvertibleWithPrecision Integer MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Integer -> ConvertResult MPBall Source #
ConvertibleWithPrecision Rational MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Rational -> ConvertResult MPBall Source #
ConvertibleWithPrecision Dyadic MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> Dyadic -> ConvertResult MPBall 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 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 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 (Rational, Rational) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Conversions Methods safeConvertP :: Precision -> (Rational, Rational) -> ConvertResult MPBall 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 #