Modify interval power in minimal way to improve precision of a^b for …

…rational b
JuliaIntervals · Apr 13, 2016 · 8d15dee · 8d15dee
1 parent 42bd337
commit 8d15dee
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Showing 2 changed files with 4 additions and 5 deletions.
diff --git a/src/intervals/functions.jl b/src/intervals/functions.jl
@@ -93,7 +93,7 @@ function ^(a::Interval{BigFloat}, x::AbstractFloat)
     a = a ∩ domain
     (isempty(x) || isempty(a)) && return emptyinterval(a)
 
-    xx = @interval(x)
+    xx = convert(Interval{BigFloat}, x)
 
     lo = @round(T, a.lo^xx.lo, a.lo^xx.lo)
     lo1 = @round(T, a.lo^xx.hi, a.lo^xx.hi)
@@ -129,10 +129,9 @@ function ^{S<:Integer}(a::Interval{BigFloat}, r::Rational{S})
     a = a ∩ domain
     (isempty(r) || isempty(a)) && return emptyinterval(a)
 
-    r = r.num / r.den
-    a = a^r
+    y = convert(Interval{BigFloat}, r)
 
-    convert(Interval{T}, a)
+    a^y
 end
 
 # Interval power of an interval:

diff --git a/test/interval_tests/numeric.jl b/test/interval_tests/numeric.jl
@@ -76,7 +76,7 @@ facts("Power tests") do
     @fact @interval(1,27)^@interval(1/3) --> roughly(Interval(1., 3.))
     @fact @interval(1,27)^(1/3) --> roughly(Interval(1., 3.))
     @fact Interval(1., 3.) ⊆ @interval(1,27)^(1//3) --> true
-    @fact @interval(0.1,0.7)^(1//3) --> Interval(0.4641588833612778, 0.8879040017426008)
+    @fact @interval(0.1,0.7)^(1//3) --> Interval(0.46415888336127786, 0.8879040017426008)
     @fact @interval(0.1,0.7)^(1/3)  --> roughly(Interval(0.46415888336127786, 0.8879040017426008))
 
 end