Infinity.jl

Provides ∞ :: Infinite <: Real representing positive infinity and -∞ is negative infinity.

Promotion between Infinite and some T <: Real will yield either:

• T itself if it can natively represent infinity (e.g. Float64, Rational); or
• InfExtended{T} <: Real otherwise, which represents the union of T and Infinite. (See the examples.)

The following Base functions are extended for these types:

• Arithmetic: +, -, *, /
• Comparison: ==, <, ≤, hash, signbit, sign, isfinite, isinf, isapprox
• Conversion: promote, convert, float, widen, big
• Random: rand(Infinite)

Additionally there is a submodule Utils exporting infinity-related functions:

• posinf(T), neginf(T): positive or negative infinity as a T if possible, or else nothing
• hasposinf(T), hasneginf(T): true if T contains positive or negative infinity
• hasinf(T): true if T contains both positive and negative infinity (this is used to decide to promote to InfExtended or not)
• isposinf(x), isneginf(x): true if x is positive or negative infinity

Installation

In Julia, type ] then run

pkg> install https://github.com/cjdoris/Infinity.jl

Example

julia> using Infinity

julia> x = [1,2,3,∞,-1,-∞]
6-element Array{InfExtended{Int64},1}:
  1
  2
  3
  ∞
 -1
 -∞

julia> sort(x)
6-element Array{InfExtended{Int64},1}:
 -∞
 -1
  1
  2
  3
  ∞

julia> float(x)
6-element Array{Float64,1}:
   1.0
   2.0
   3.0
 Inf
  -1.0
 Inf