Data.ExtendedReal · extended-reals-0.2.7.0

datadata Extended r

Extended r is an extension of r with positive/negative infinity (±∞).

Constructors

NegInf
negative infinity (-∞)
Finite !r
finite value
PosInf
positive infinity (+∞)

Instances16Functor, Foldable, Traversable, Lift, Bounded, Eq, …

Functor ExtendedDefined in extended-reals-0.2.7.0 · Data.ExtendedReal
Foldable ExtendedDefined in extended-reals-0.2.7.0 · Data.ExtendedReal
Traversable ExtendedDefined in extended-reals-0.2.7.0 · Data.ExtendedReal
Lift r => Lift (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
Bounded (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
Eq r => Eq (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
(Fractional r, Ord r) => Fractional (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
Note that Extended r is not a field, nor a ring.
Data r => Data (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
(Num r, Ord r) => Num (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
Note that Extended r is not a field, nor a ring.
PosInf + NegInf is left undefined as usual, but we define 0 * PosInf = 0 * NegInf = 0 by following the convention of probability or measure theory.
Ord r => Ord (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
Read r => Read (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
Show r => Show (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
Generic (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
NFData r => NFData (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
Hashable r => Hashable (Extended r)Defined in extended-reals-0.2.7.0 · Data.ExtendedReal
type Rep (Extended r) = D1 ('MetaData "Extended" "Data.ExtendedReal" "extended-reals-0.2.7.0-CarTkajRhlGEck6IalUYb7" 'False) (C1 ('MetaCons "NegInf" 'PrefixI 'False) U1 :+: (C1 ('MetaCons "Finite" 'PrefixI 'False) (S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 r)) :+: C1 ('MetaCons "PosInf" 'PrefixI 'False) U1))Defined in extended-reals-0.2.7.0 · Data.ExtendedReal

valueinf :: Extended r

Infinity (∞)

valueisFinite :: Extended r -> Bool

isFinite x = not (isInfinite x).

valueisInfinite :: Extended r -> Bool

isInfinite x returns True iff x is PosInf or NegInf.

valuefromRealFloat :: RealFloat r => r -> Extended r

Helper to convert Double and Float to Extended, taking care of infinite values automatically.

Example3 expressions

>>> fromRealFloat (1 / 0)PosInf>>> fromRealFloat (-1 / 0)NegInf>>> fromRealFloat (0 / 0)*** Exception: fromRealFloat: argument should not be NaN

Beware that an ordinal infinity might not be equal to an arithmetic infinity. PosInf / NegInf stand for infinite elements with regards to ordering, so:

Example2 expressions

>>> fromRealFloat (Down (1 / 0))NegInf>>> fromRealFloat (Down (-1 / 0))PosInf

valuetoRealFloat :: RealFloat r => Extended r -> r

Helper to convert Extended to Double or Float, taking care of infinite values automatically.

Example4 expressions

>>> toRealFloat PosInf :: DoubleInfinity>>> toRealFloat NegInf :: Double-Infinity>>> toRealFloat PosInf :: Down DoubleDown (-Infinity)>>> toRealFloat NegInf :: Down DoubleDown Infinity