Fix computation of range length in certain cases (fix 0.5/#20373)

This is the 0.5 edition: with this change a, b, n are always hit
exactly by a:s:a+n*s construction tests. There are two parts to
the fix: 1) check that the lifted rational endpoint is exact even
*after* we've reduced terms of the fractions; 2) apply the same
fix that I've proposed for the length in the non-lifted case.

base/range.jl

@@ -169,13 +169,16 @@ function colon{T<:AbstractFloat}(start::T, step::T, stop::T)
                 a *= div(e,b)
                 c *= div(e,d)
                 eT = convert(T,e)
-                if (a+n*c)/eT == stop
+                if a/eT == start && (a+n*c)/eT == stop
                     return FloatRange{T}(a, c, n+1, eT)
                 end
             end
         end
     end
-    FloatRange{T}(start, step, floor(r)+1, one(step))
+    len = max(0, floor(r) + 1)
+    stop′ = start + len*step
+    len += (start < stop′ <= stop) + (start > stop′ >= stop)
+    FloatRange{T}(start, step, len, one(step))
 end
 
 colon{T<:AbstractFloat}(a::T, b::T) = colon(a, one(a), b)

test/ranges.jl

@@ -326,6 +326,25 @@ for T = (Float32, Float64,),# BigFloat),
     @test [r[n:-2:1];] == [r;][n:-2:1]
 end
 
+# issue #20373 (unliftable ranges with exact end points)
+@test [3*0.05:0.05:0.2;]    == [linspace(3*0.05,0.2,2);]   == [3*0.05,0.2]
+@test [0.2:-0.05:3*0.05;]   == [linspace(0.2,3*0.05,2);]   == [0.2,3*0.05]
+@test [-3*0.05:-0.05:-0.2;] == [linspace(-3*0.05,-0.2,2);] == [-3*0.05,-0.2]
+@test [-0.2:0.05:-3*0.05;]  == [linspace(-0.2,-3*0.05,2);] == [-0.2,-3*0.05]
+
+for T = (Float32, Float64,), i = 1:2^15, n = 1:5
+    start, step = randn(T), randn(T)
+    stop = start + (n-1)*step
+    r = start:step:stop
+    @test n == length(r)
+    @test start == first(r)
+    @test stop  == last(r)
+    l = linspace(start,stop,n)
+    @test n == length(l)
+    @test_skip start == first(l)
+    @test_skip stop  == last(l)
+end
+
 # linspace & ranges with very small endpoints
 for T = (Float32, Float64)
     z = zero(T)