Copyright	(c) Masahiro Sakai 2014
License	BSD-style
Maintainer	masahiro.sakai@gmail.com
Stability	provisional
Portability	non-portable (DeriveDataTypeable)
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.ExtendedReal

Description

Extension of real numbers with positive/negative infinities (±∞). It is useful for describing various limiting behaviors in mathematics.

Remarks:

∞ - ∞ is left undefined as usual, but we define 0 × ∞ = 0 × -∞ = 0 by following the convention of probability or measure theory.

References:

Wikipedia contributors, "Extended real number line," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Extended_real_number_line (accessed September 1, 2014).

Synopsis

Documentation

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

Constructors

Instances

Functor Extended
Bounded (Extended r)
Eq r => Eq (Extended r)
(Fractional r, Ord r) => Fractional (Extended r)	Note that `Extended r` is not a field, nor a ring.
Data r => Data (Extended r)
(Num r, Ord r) => Num (Extended r)	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)
Read r => Read (Extended r)
Show r => Show (Extended r)
NFData r => NFData (Extended r)
Hashable r => Hashable (Extended r)
Typeable (* -> *) Extended

isFinite x = not (isInfinite x).

isInfinite x returns True iff x is PosInf or NegInf.