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
• InfExtendedReal{T} <: Real otherwise, which represents positive/negative infinity, or a finite value of type T. (See the examples.)

The following Base functions are extended for these types:

• Arithmetic: typemin, typemax, +, -, *, /
• 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 InfExtendedReal or not)
• isposinf(x), isneginf(x): true if x is positive or negative infinity

Promotion between Infinite and some T <: Dates.TimeType will yield:

• InfExtendedTime{T} <: Dates.TimeType, which represents positive/negative infinity, or a finite value of type T. (See the examples.)

The following Base functions are extended for these types:

• Arithmetic: typemin, typemax, T+Period, T-Period
• Comparison: ==. <, ≤, hash, isfinite, isinf
• Conversion: promote, convert

In Julia, type ] then run

pkg> add Infinity

julia> using Infinity

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

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

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

julia> using Dates

julia> x = [Date(2012, 1, 1), Date(2013, 1, 1), Date(2013, 1, 2), ∞, Date(1987, 1, 1), -∞]
6-element Array{InfExtendedTime{Date},1}:
 InfExtendedTime{Date}(2012-01-01)
 InfExtendedTime{Date}(2013-01-01)
 InfExtendedTime{Date}(2013-01-02)
 InfExtendedTime{Date}(∞)
 InfExtendedTime{Date}(1987-01-01)
 InfExtendedTime{Date}(-∞)

julia> sort(x)
6-element Array{InfExtendedTime{Date},1}:
 InfExtendedTime{Date}(-∞)
 InfExtendedTime{Date}(1987-01-01)
 InfExtendedTime{Date}(2012-01-01)
 InfExtendedTime{Date}(2013-01-01)
 InfExtendedTime{Date}(2013-01-02)
 InfExtendedTime{Date}(∞)

julia> Day(1) + x
6-element Array{InfExtendedTime{Date},1}:
 InfExtendedTime{Date}(2012-01-02)
 InfExtendedTime{Date}(2013-01-02)
 InfExtendedTime{Date}(2013-01-03)
 InfExtendedTime{Date}(∞)
 InfExtendedTime{Date}(1987-01-02)
 InfExtendedTime{Date}(-∞)