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{-|
Module : Numeric.InfInt
Copyright : (c) UU, 2019
License : MIT
Maintainer : Tom Smeding
Stability : experimental
Portability : POSIX, macOS, Windows
-}
module Numeric.InfInt where
-- | The integers with ±∞ added. This is not a full ring ('∞ + -∞' is
-- undefined, for instance), but it works well enough.
data InfInt = MInfinity | Finite Int | Infinity
deriving (Show, Eq, Ord)
instance Num InfInt where
Infinity + MInfinity = undefined
Infinity + _ = Infinity
MInfinity + Infinity = undefined
MInfinity + _ = MInfinity
Finite n + Finite m = Finite (n + m)
Finite _ + Infinity = Infinity
Finite _ + MInfinity = MInfinity
Finite n * Finite m = Finite (n * m)
Finite 0 * _ = undefined
Finite n * Infinity = if n < 0 then MInfinity else Infinity
Finite n * MInfinity = if n < 0 then Infinity else MInfinity
Infinity * Finite m = Finite m * Infinity
Infinity * Infinity = Infinity
Infinity * MInfinity = MInfinity
MInfinity * Finite m = Finite m * MInfinity
MInfinity * Infinity = MInfinity
MInfinity * MInfinity = Infinity
abs (Finite n) = Finite (abs n)
abs _ = Infinity
signum (Finite n) = Finite (signum n)
signum MInfinity = (-1)
signum Infinity = 1
fromInteger n = Finite (fromInteger n)
negate (Finite n) = Finite (-n)
negate Infinity = MInfinity
negate MInfinity = Infinity
-- | If the number is finite, return the finite component.
toFinite :: InfInt -> Maybe Int
toFinite (Finite n) = Just n
toFinite Infinity = Nothing
toFinite MInfinity = Nothing
-- | @isFinite = isJust . toFinite@
isFinite :: InfInt -> Bool
isFinite (Finite _) = True
isFinite _ = False
|
