Add typemin, typemax, ::Type version of eps. (#108)

* Add typemin, typemax, type version of eps.

* Make eps (and dist) return an Interval.

* Address #108 (comment).

Author: tkoolen

src/IntervalArithmetic.jl

@@ -12,7 +12,7 @@ using AdjacentFloats
 import Base:
     +, -, *, /, //, fma,
     <, >, ==, !=, ⊆, ^, <=,
-    in, zero, one, abs, abs2, real, min, max,
+    in, zero, one, eps, typemin, typemax, abs, abs2, real, min, max,
     sqrt, exp, log, sin, cos, tan, inv,
     exp2, exp10, log2, log10,
     asin, acos, atan, atan2,

src/intervals/arithmetic.jl

@@ -50,12 +50,15 @@ end
 const ≺ = strictprecedes # \prec
 
 
-# zero, one
+# zero, one, typemin, typemax
 zero(a::Interval{T}) where T<:Real = Interval(zero(T))
 zero(::Type{Interval{T}}) where T<:Real = Interval(zero(T))
 one(a::Interval{T}) where T<:Real = Interval(one(T))
 one(::Type{Interval{T}}) where T<:Real = Interval(one(T))
-
+typemin(::Type{Interval{T}}) where T<:AbstractFloat = wideinterval(typemin(T))
+typemax(::Type{Interval{T}}) where T<:AbstractFloat = wideinterval(typemax(T))
+typemin(::Type{Interval{T}}) where T<:Integer = Interval(typemin(T))
+typemax(::Type{Interval{T}}) where T<:Integer = Interval(typemax(T))
 
 ## Addition and subtraction
 
@@ -252,8 +255,8 @@ end
 
 
 dist(a::Interval, b::Interval) = max(abs(a.lo-b.lo), abs(a.hi-b.hi))
-eps(a::Interval) = max(eps(a.lo), eps(a.hi))
-
+eps(a::Interval) = Interval(max(eps(a.lo), eps(a.hi)))
+eps(::Type{Interval{T}}) where T<:Real = Interval(eps(T))
 
 ## floor, ceil, trunc, sign, roundTiesToEven, roundTiesToAway
 function floor(a::Interval)

test/interval_tests/consistency.jl

@@ -25,6 +25,13 @@ c = @interval(0.25, 4.0)
         @test one(a) == big(1.0)
         @test !(a == b)
         @test a != b
+        @test eps(typeof(a)) === eps(one(typeof(a)))
+        @test typemin(typeof(a)) === Interval(-Inf, nextfloat(-Inf))
+        @test typemax(typeof(a)) === Interval(prevfloat(Inf), Inf)
+        @test typemin(a) === typemin(typeof(a))
+        @test typemax(a) === typemax(typeof(a))
+        @test typemin(Interval{Int64}) === Interval(typemin(Int64))
+        @test typemax(Interval{Int64}) === Interval(typemax(Int64))
 
         @test a == Interval(a.lo, a.hi)
         @test @interval(1, Inf) == Interval(1.0, Inf)